The study of elementary particles 1774694301, 9781774694305

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The Study of Elementary Particles

THE STUDY OF ELEMENTARY PARTICLES

S.N. Shukla

ARCLER

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The Study of Elementary Particles S.N. Shukla

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e-book Edition 2023 ISBN: 978-1-77469-695-8 (e-book)

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ABOUT THE AUTHOR

SachchidaNand Shukla, is presently working as Professor, Department of Physics & Electronics, Dr. RamManohar Lohia Avadh University, Ayodhya, UP, India. He did his Masters in Physics (Electronics) in 1988 and Ph.D. in 1992 from the same university. Dr. Shukla holds 27 years experience of teaching M.Sc. (Physics) and M.Sc. (Electronics) students and 3 years experience of teaching B.Tech., MCA and B.Sc. (Electronics) students. He has published 85 research papers in peer-reviewed/ indexed journals of International/National repute & conference proceedings and 02 books. In his supervision 14 research scholars have been awarded Ph.D. degree. In addition to it he is the recipient of Best Scientist National Award (2018) of IRDP Group of Journals, Chennai and Maatee Ratan Samman (2017). He has also been selected as Fellow of IACSIT (International Association of Computer Science and Information Technology, Singapore) and Associate Fellow of IAPS (International Academy of Physical Sciences) in 2018. In view of Dr. Shukla’s academic achievements his employer institution, Dr. RamManohar Lohia Avadh University, has conferred upon him the ‘Certificate of Appreciation’ in 2018. Besides having a wide exposure to various key positions of University administration like Pro Vice Chancellor, Registrar, Director College Development Council (CDC), Coordinator UGC and RUSA, Head of Physics Department etc, Dr. Shukla has membership of 08 academic bodies of international repute. To name a few are ISCA (The Indian Science Congress Association, Kolkata, India), IETE (The Institution of Electronics and Telecommunication Engineers, New Delhi, India), NASI (The National Academy of Sciences, India, Allahabad, India), IAPS (International Academy of Physical Sciences, Allahabad, India) and SCIEI (Science and Engineering Institute, Hong Kong, SAR of China).

In addition, he is also gracing the Editorial Boards of 04 international journals IJAREEIE (International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering), APM (Applied Physics & Mathematics), JUSPS (Journal of Ultra Scientist of Physical Sciences) and IRJ (International Researcher’s Journal) and the board of reviewer of IRJECE (International Journal of Electronics & Communication Engineering).

TABLE OF CONTENTS

List of Figures ......................................................................................................xiii List of Abbreviations ........................................................................................... xix Abstract .............................................................................................................. xxi Preface........................................................................ ................................. ....xxiii Chapter 1

Basic Constituents of Matter ..................................................................... 1 1.1. Atoms ................................................................................................. 3 1.2. Structure of Atoms .............................................................................. 4 1.3. Properties of Atoms ............................................................................. 9 1.4. Particles ............................................................................................ 12 1.5. Conceptual Properties of Particles ..................................................... 14 1.6. Molecule .......................................................................................... 16 1.7. Nuclei/Nucleus................................................................................. 23

Chapter 2

Classification of Elementary Particles ...................................................... 31 2.1. Classification According to Spin........................................................ 35 2.2. Fermion ............................................................................................ 36 2.3. Quarks.............................................................................................. 40 2.4. Lepton .............................................................................................. 43 2.5. Boson ............................................................................................... 44 2.6. Elementary Bosons............................................................................ 45 2.7. Higgs Boson ..................................................................................... 45 2.8. Photon .............................................................................................. 47 2.9. Gluon ............................................................................................... 49 2.10. W and Z Bosons ............................................................................. 49 2.11. Composite Bosons .......................................................................... 51 2.12. Classification According to Mass..................................................... 51 2.13. Classification According to Charge ................................................. 57

Chapter 3

Standard Model of Particle Physics ......................................................... 61 3.1. Introduction ...................................................................................... 62 3.2. The Smallest Building Blocks ............................................................ 63 3.3. Expanding the Scope of Particles ....................................................... 64 3.4. Matter Particles ................................................................................. 67 3.5. Standard Model (SM) Mathematical Concepts................................... 71 3.6. The SM Higgs and Flavor .................................................................. 74 3.7. Positronium ...................................................................................... 79

Chapter 4

Theories Beyond the Standard Model of Elementary Particles ................ 83 4.1. Introduction ...................................................................................... 84 4.2. Grand Unified Theory ....................................................................... 87 4.3. Supersymmetry ................................................................................. 89 4.4. String Theory..................................................................................... 91 4.5. Preon Theory .................................................................................... 93 4.6. Technicolor ....................................................................................... 95 4.7. History of Elementary Particles .......................................................... 97 4.8. The Classical ERA ............................................................................. 99 4.9. History of the Photon Particle.......................................................... 100 4.10. History of the Mesons ................................................................... 101 4.11. The History of Antiparticles ........................................................... 102 4.12. The Evolution of Neutrinos ............................................................ 103 4.13. History of Strange Particles............................................................ 104 4.14. The Eightfold Method .................................................................... 105 4.15. History of Quark Model ................................................................ 107 4.16. The November Revolution ............................................................ 109 4.17. Intermediate Vector Bosons ........................................................... 110

Chapter 5

Particle Interaction in Elementary Particles .......................................... 113 5.1. Fundamental Interaction ................................................................. 118 5.2. Strong Nuclear Force ...................................................................... 119 5.3. The Electromagnetic Force (EMF) .................................................... 123 5.4. The Weak Nuclear Force ................................................................. 129 5.5. Gravitational Force ......................................................................... 133 5.6. Hadron Interactions ........................................................................ 136 5.7. Mesonic Interactions....................................................................... 139 viii

Chapter 6

Particle Collision in Elementary Particles .............................................. 141 6.1. Examples of Mechanisms Put in Place to Test Particle Collision in Elementary Particles................................................... 144 6.2. Working.......................................................................................... 147 6.3. Experiments Sites Inside the Hadron ............................................... 157 6.4. Discoveries From Colliding Particles ............................................... 165 6.5. Calculations of the Dynamics of Collision ...................................... 168

Chapter 7

New Discoveries in Particles ................................................................. 171 7.1. Parity Violation in Weak Interactions ............................................... 174 7.2. Cp Violation.................................................................................... 176 7.3. Implications of the Discovery of CP Violation ................................. 180 7.4. Neutrino Masses ............................................................................. 181 7.5. Heavy Quack Symmetry ................................................................. 185 7.6. Effective Field Theory (EFT) ............................................................. 187 7.7. Feynman’s Paradox ......................................................................... 188 7.8. Hadrons.......................................................................................... 190

Chapter 8

Applications of Elementary Particles ..................................................... 193 8.1. Introduction .................................................................................... 194 8.2. Applications of Elementary Particles................................................ 194 8.3. Use of Elementary Particles in the Sakata Model ............................. 195 8.4. Application of Elementary Particles in Measurement Problems ........ 197 8.5. Application of Elementary Particles in Muon Precession Frequency 198 8.6. Antineutrino Energy Spectrum......................................................... 199 8.7. Application of Elementary Particles in More Discoveries of Physics . 200 8.8. Application of Elementary Particles in Nanoparticle Tracking .......... 201 8.9. The Photo-Sensor Panel Technology ................................................ 202 8.10. Application of Elementary Particles to the Problem of Compositeness ............................................................................. 204 8.11. Application of Elementary Particles in the Control of Airborne Infectious Disease.......................................................... 205 8.12. Application of Elementary Particles in Organic Chemistry ............. 206 8.13. Application of Elementary Particles in Controlling Covid-19 in Ventilation Systems................................................................... 208 8.14. Application of Elementary Particles in Quadratic Time .................. 209

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8.15. Application of Elementary Particles in Transferable Dynamic Molecular Charge ......................................................... 211 8.16. Application of Elementary Particles in Neutron Imaging Experiments ................................................................................. 212 8.17. Application of Elementary Particles in Quark-Gluon Plasma ......... 213 8.18. Application of Elementary Particles in Tomographic Imaging of Laser-Plasma Structures ............................................................ 214 8.19. Application of Elementary Particles in Multistage Geminate Reactions ..................................................................................... 215 8.20. Application of Elementary Particles in Modern Circulating Accelerators ................................................................................. 215 Chapter 9

Conservation Laws and Symmetry of Elementary Particles ................... 219 9.1. Conservation of Mass and Energy ................................................... 222 9.2. Conservation of Energy ................................................................... 223 9.3. Mass–Energy Equivalence ............................................................... 224 9.4. Mass Conservation .......................................................................... 225 9.5. Conservation of Linear Momentum ................................................. 229 9.6. Angular Momentum Conservation .................................................. 231 9.7. General Considerations .................................................................. 233 9.8. Charge Conservation ...................................................................... 236 9.9. Symmetries in Elementary Particle Physics ...................................... 236 9.10. Symmetries ................................................................................... 237 9.11. Symmetries and Particle Physics.................................................... 238 9.12. Local or Gauge Symmetries .......................................................... 241 9.13. The Standard Model (SM) .............................................................. 243 9.14. Spontaneous Symmetry Breaking (SSB) ......................................... 245

Chapter 10 Future of Elementary Particles ..............................................................249 10.1. Ghost-Hunting Machines .............................................................. 250 10.2. Further Exploration of the Sky ....................................................... 252 10.3. Upgrades in the LHC .................................................................... 254 10.4. Different Thinking ......................................................................... 256 10.5. New Observations ........................................................................ 257

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10.6. The Muon’s Moment ..................................................................... 258 10.7. Going Bigger ................................................................................ 259 Bibliography .......................................................................................... 263 Index ..................................................................................................... 269

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LIST OF FIGURES Figure 1.1. There are four basic constituents of matter Figure 1.2. Atoms are found in various forms of matter Figure 1.3. Subatomic particles make up a particle Figure 1.4. The nucleus is made of protons and neutrons Figure 1.5. An electron cloud Figure 1.6. The composition of the nucleus determines properties of atoms Figure 1.7. There are different shapes and sizes of atoms Figure 1.8. Particles are formed through combination of subatomic particles Figure 1.9. Molecules are formed through the combination of atoms Figure 1.10. Covalent bonds are formed through sharing of valence electrons Figure 1.11. Ionic bonds are formed through complete transfer of valence electrons Figure 1.12. There are different kinds of molecular geometries Figure 1.13. The nuclei are at the center of the atom Figure 1.14. Oval shaped nuclei Figure 2.1. The particle content of the standard model of physics Figure 2.2. In quantum physics, wave-particle duality states that any particle or quantum phenomenon can be characterized as either a particle or a wave. This behavior has been demonstrated not only for elementary particles, but also for composite particles such as atoms and molecules Figure 2.3. The strong nuclear force holds protons together in the nucleus of an atom. Neutrons are non-charged subatomic particles (they are neutral). Neutrons, like protons, are bonded into the nucleus of an atom by the strong nuclear force Figure 2.4. Fermions are a type of elementary particle. They are extremely little and light. Because atoms are built up of fermions can be regarded of as the building blocks of matter. In honor of the eminent physicist Enrico Fermi, Paul Dirac termed them fermions Figure 2.5. The spin–statistics theorem in quantum mechanics ties a particle’s intrinsic spin (angular momentum not attributable to orbital motion) to the particle statistics it obeys. All particles that travel in three dimensions have either integer spin or halfinteger spin in units of the decreased Planck constant

Figure 2.6. Any member of a class of primary subatomic particles that interact via the strong force and are thought to be essential elements of matter quarks unite with one another via the strong force to form protons and neutrons, much how the latter particles combine in varying amounts to form atomic nuclei Figure 2.7. Leptons can only carry one unit of electric charge or they can be neutral. Electrons, muons, and taus are the charged leptons. Each of them has a negative charge as well as a different mass. Electrons, the lightest leptons, have a mass that is only one-tenth of that of a proton. Muons are heavier than electrons, weighing more than 200 times as much. Taus, on the other hand, are around 3,700 times more massive than electrons. Leptons are involved in several processes such as beta decay Figure 2.8. Higgs boson, also called Higgs particle that is the carrier particle, or boson, of the Higgs field, a field that permeates space and endows all elementary subatomic particles with mass through its interactions with them Figure 2.9. Movement of a photon as electromagnetic radiation Figure 2.10. A W boson is created and disappears during the beta-minus decay process. Down quarks decay producing W bosons and up quarks. After then, the W boson decays into an electron and an electron antineutrino Figure 2.11. An artist’s representation depicting gravitons as mediating particles in the force of gravitation Figure 2.12. Zooming in on gluons’ contribution to proton spin Figure 2.13. Alpha (α) radioactivity Figure 2.14. Positron (positive electron). Cloud chamber photograph by C. D. Anderson of the first positron ever identified. A 6 mm lead plate separates the chamber. The deflection and direction of the particle’s ion trail indicate that the particle is a positron Figure 3.1. All particles are categorized into fermions and bosons Figure 3.2. Detailed imaging of a particle structure Figure 3.3. The Muon is a light particle with negligible magnetic influence Figure 3.4. Comparison of broken and unbroken particle symmetry Figure 3.5. Subatomic particle disintegration contravenes the standard model of physics Figure 3.6. The CPT theorem is determined by charge, parity, and time Figure 4.1. A list of elementary particles Figure 4.2. The electromagnetic force in elementary particles Figure 4.3. The grand unified theory Figure 4.4. Illustration of supersymmetry theory Figure 4.5. An illustration of the string theory Figure 4.6. A preon square which is part of the preon theory

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Figure 4.7. An illustration of the technicolor theory Figure 4.8. An illustration of a brief history of elementary particles Figure 4.9. An image of a photon Figure 4.10. An image of a meson particle Figure 4.11. An image of an antiparticle Figure 4.12. A neutrino as seen on the telescope Figure 4.13. An image listing some strange particles Figure 4.14. An image showing the Eightfold method Figure 4.15. Illustration of the quark model Figure 4.16. Illustration of the intermediate vector boson Figure 5.1. A diagrammatic illustration on particle interaction in elementary particles via the sub-=atomic components Figure 5.2. The difference between fermions and bosons can be illustrated by the elementary table regarding leptons and quarks Figure 5.3. The QCD framework for Production and reaction processes Figure 5.4. The strong nuclear force in action Figure 5.5. Elements required for a nucleus reaction Figure 5.6. Quantum electrodynamics; the theory used to explain the strong nuclear force Figure 5.7. An illustration of how the electromagnetic force helped build and form matter Figure 5.8. Electromagnetism – a branch of physics necessary for the electromagnetic force Figure 5.9. James Clerk Maxwell; one of the first brains behind the electromagnetic force Figure 5.10. An amazing caption on how this force has enable humanity to power the world Figure 5.11. An illustration of the working of the weak nuclear force Figure 5.12. A diagrammatic representation of radioactive beta decay Figure 5.13. Gravitational force as discovered by Isaac Newton acts on the same way as in elementary particles Figure 5.14. A sample hadron-hadron interaction Figure 5.15. Mesonic corrections of three-quark (baryon) currents where the quarks interact while the meson is in flight. The dashed line denotes an external photon or other operator

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Figure 6.1. An illustration of particle collision as illustrated by quantum computing Figure 6.2. Illustration of a particle detector; in most cases, this is where the collision may be observed Figure 6.3. A section of the LHC Figure 6.4. A disassembled section of the LHC Figure 6.5. An aerial scientific view of the LHC with its experimental sections Figure 6.6. LHC injector complex Figure 6.7. Here, particles are injected, accelerated, and collided Figure 6.8. A section of the Linac 2 Figure 6.9. The new and most recent Linac 4 Figure 6.10. Diagrammatic representation of the main ring including its components Figure 6.11. Cross-sectional view of the LHC main dipole Figure 6.12. The ALICE experiment Figure 6.13. The ATLAS experiment subsystems Figure 6.14. The compact muon solenoid (CMS) Figure 6.15. Schematic view of the LHCb Figure 6.16. Top quark Figure 7.1. The large hadron collider where particles discoveries are made while they break the known laws of physics Figure 7.2. Subatomic particle disintegration: The basis of particle discovery Figure 7.3. Sketches of conceptually parity violation in beta decay Figure 7.4. The BrookHaven National Laboratory; where the discovery was made Figure 7.5. CP violation – the different types Figure 7.6. CP violation discovery at 3 σ fraction Figure 7.7. Discovery of CP violation in charm particles Figure 7.8. The significance with which CP violation can be discovered as a function Figure 7.9. A graphical view of neutrino mass Figure 7.10. Neutrino mass eigenstate flavor composition and mass pattern in the two cases of normal (left) and inverted (right) hierarchies Figure 7.11. Symmetry and asymmetry which led to the formation of the universe Figure 7.12. An illustration of effective field theory Figure 7.13. An insightful quote by Richard Feyman Figure 8.1. An illustration of the Parton picture

xvi

Figure 8.2. An illustration of the Sakata model Figure 8.3. An illustration of the nuclear scale used in solving measurement problems Figure 8.4. Graphs on muon precession frequency Figure 8.5. A graph on antineutrino energy spectra Figure 8.6. An illustration of the nanoparticle tracking analysis Figure 8.7. An illustration of some photo-sensor panel technologies Figure 8.8. An illustration of both elementary particles and composite particles Figure 8.9. An illustration of the transmission of airborne infectious disease Figure 8.10. An illustration of subatomic particles and their respective masses Figure 8.11. The COVID-19 ventilation system explaining how it operates Figure 8.12. A graph on time complexity simplification Figure 8.13. An illustration of molecular dynamic simulation Figure 8.14. An illustration of the neutron imaging method Figure 8.15. A quark-gluon plasma Figure 8.16. An illustration of modern circulating accelerator Figure 9.1. Mass near the M87* black hole are converted into very energetic astrophysical jet, stretching 5,000 light years Figure 9.2. The world line: A diagrammatic representation of spacetime Figure 9.3. The interactions of hadrons. (a) Bubble chamber photograph; (b) sketch that represents the photograph Figure 9.4. In the 19th century, several novel discoveries were made as a result of Antoine Lavoisier’s discovery of the law of conservation of mass. Antoine Lavoisier’s discoveries spawned Joseph Proust’s law of definite proportions and John Dalton’s atomic hypothesis. Lavoisier’s quantitative tests demonstrated that burning used oxygen rather than phlogiston, as previously supposed Figure 9.5. Methane combustion reaction where 4 hydrogen atoms, 4 oxygen atoms, and 1 carbon atom are present before and after the process. The overall mass after the reaction is the same as it was before it Figure 9.6. A pool break-off shot Figure 9.7. This gyroscope remains upright while spinning due to the conservation of its angular momentum Figure 9.8. Velocity of the particle m with respect to the origin O can be resolved into components parallel to (v∥) and perpendicular to (v⊥) the radius vector r. The angular momentum of m is proportional to the perpendicular component v⊥ of the velocity, or equivalently, to the perpendicular distance r⊥ from the origin Figure 9.9. A figure skater in a spin uses conservation of angular momentum – decreasing her moment of inertia by drawing in her arms and legs increases her rotational speed xvii

Figure 9.10. Collision of two incoming electrons, 1 and 2, into two outgoing electrons 3 and 4 Figure 9.11. Pattern of particles that allowed prediction of the Ω-particle. Particles in the same row have similar masses: Particles with the same electric charge (shown by superscripts) also lie on straight lines Figure 9.12. Collision of two electrons resulting from exchange of a photon Figure 9.13. Electromagnetic vertex of an electron: The electron emits a photon with a probability, in emissions per second, proportional to the electron’s charge Figure 9.14. Quark triplets and the gluon vertex Figure 9.15. Forces and symmetry Figure 10.1. The future of elementary particles involves several discoveries being made Figure 10.2. There is limited information on neutrino particles Figure 10.3. Fermilab has actively been involved in several experiments on new particles Figure 10.4. Scientists are working to establish the source of dark matter Figure 10.5. Dark matter-hunting telescopes have been used in most research facilities Figure 10.6. The Large Hardon Collider has provided much knowledge in particle physics Figure 10.7. Various detectors have been used to detect the presence of particles in the atmosphere Figure 10.8. Further research is expected to give more information on muons Figure 10.9. Some projects have not been achieved due to lack of funds Figure 10.10. Research may require improvement of techniques used

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LIST OF ABBREVIATIONS

BNL

Brookhaven National Laboratory

CERN

European Organization for Nuclear Research

CMS

compact muon solenoid

CSC

cathode strip chambers

DT

drift tubes

ECAL

electromagnetic calorimeters

EFT

effective field theory

EMF

electromagnetic force

FDs

frequency doublers

GUTs

grand unified theories

ITR

transition region detector

LEBT

low energy beam transport

LHC

large hadron collider

MEBT

medium energy beam transport

MeV

mega-electron volts

PS

proton synchrotron

PSB

proton synchrotron booster

QCD

quantum chromodynamics

QED

quantum electrodynamics

QFD

quantum flavordynamics

QGP

quark–gluon plasma

RF

radio-frequency

RFQs

radio frequency quadrupoles

RHIC

relativistic heavy ion collider

RPC

resistive plate chambers

SI

system of units

SM

standard model

SPS

super proton synchrotron

SSB

spontaneous symmetry breaking

TOE

theory of everything

TOF

time-of-flight

TPC

time projection chamber

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ABSTRACT From the inception of particle physics during the 1930s up to the recent 21st century drives, the inventive concepts and technologies of molecular physics have infiltrated the mainstream society to change how we live. There is a long and developing list of viable applications with regards to particle physics. Today, every significant medical center globally uses accelerators generating x-rays, neutrons, protons, and heavy ions for diagnosis and cure of illnesses. It is believed that there are more than 7,000 actives medical linacs across the planet that have treated around 30 million patients. Likewise, biomedical researchers use molecular physics advances to unravel the design of proteins, data that is critical to understanding biological cycles and treating illness. A better comprehension of protein design allows for the improvement of viable medications, for example, Kaletra, among the globe’s most-prescribed medication to combat AIDS. The future for particle physics is bright and still more is yet to be discovered.

PREFACE Particle physics (otherwise called high energy physics) is a subsection of physics that examines the concept of particles that comprise matter and radiation. While the word particle can allude to different kinds of small objects (for example, protons, gas, and even dust particles), particle physics typically explores the unchangeably slightest fundamental particles and the basic connections important to clarify their process. In modern science, these elementary particles are excitations of the quantum that additionally oversee their connections. The modern prevailing hypothesis explaining these key particles and fields, alongside their elements, is known as the standard model (SM). Consequently, contemporary particle physics examines the Standard Model and its different potential additions, for example to the most current “known” molecule, the Higgs boson, including the most renowned force field called gravity. Contemporary particle physics research is centered on subatomic particles, such as nuclear constituents, protons, electrons, and neutrons, which are created by radioactive and dispersing processes; these particles include photons, muons, and neutrinos, including a wide scope of fascinating particles. Particle elements are likewise dependent on quantum mechanics; they show wave-molecule duality, showing molecule-like conduct under specific test conditions and wave-like conduct in others. In scientific terms, they are depicted by quantum style vectors in a Hilbert arena, which is additionally treated in quantum field hypothesis. After the particle physicist’s convention, the word elementary particles are relevant to those particles which are, as indicated by modern understanding, assumed to be unbreakable and not made out of other particles. Every particle and their relations can be depicted predominantly by a quantum field hypothesis called the Standard Model. The Standard Model, as of now, has 61 elementary particles. Those elementary particles can consolidate to form composite particles, representing the many different types of particles that have been found since the 1960s. The Standard Model has been found to concur with practically every one of the experimental tests performed to date. In any case, most molecule physicists accept that it is a fragmented depiction of nature and that a more basic hypothesis anticipates disclosure. As of late, estimations of neutrino mass have provided the primary trial deviations from the Standard Model, since neutrinos are massless in the standard model. In science, analysts utilize the super strong X-beam light emissions synchrotron light sources to make the most splendid lights on the planet. These brilliant sources offer instruments to such applications as protein structure investigation, drug research, materials science, and reclamation of artwork. Also, every major health institution uses particle physics to deliver, protons, neutrons x-rays and weighty particles for the analysis and treatment of infection. It is estimated there are 7,000 hospitals globally that actively use the technology for technology.

On a basic level, all physics can be gotten from the research on fundamental particles. Practically speaking, regardless of whether “particle physics” is interpreted as meaning as it were “high-energy iota smashers,” different technologies have emerged during these initial investigations that later found extensive uses in society. Particle accelerators are utilized to deliver medical isotopes for examination and treatment (for instance, isotopes applied in PET imaging), or utilized directly in outdoor beam radiotherapy.

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CHAPTER

1

BASIC CONSTITUENTS OF MATTER

CONTENTS 1.1. Atoms ................................................................................................. 3 1.2. Structure of Atoms .............................................................................. 4 1.3. Properties of Atoms ............................................................................. 9 1.4. Particles ............................................................................................ 12 1.5. Conceptual Properties of Particles ..................................................... 14 1.6. Molecule .......................................................................................... 16 1.7. Nuclei/Nucleus................................................................................. 23

2

The Study of Elementary Particles

In classical physics and chemistry, matter is defined as any substance that occupies space and has mass. There are various objects that we interact with that can be touched that are composed of atoms. These objects are composed of subatomic particles interacting with each other. Scientifically, matter is composed of particles or a combination of particles and atoms. Both the particles and atoms act as if they have volume or rest mass. Matter does not include massless particles such as waves of light, energy phenomena or photons (Zimmermann, 2018). Matter is known to exist in various phases also known as states. Some of the everyday phases include gases, liquids, and solids. In the case of water, it exists in their forms. Water exists in soils state as ice, in liquid state as fluid water and in gaseous state as water vapor. Other than the three main states, there are other developed states of matter which include quark-gluon plasma, fermionic condensates, Bose-Einstein condensates, and plasma (Figure 1.1).

Figure 1.1. There are four basic constituents of matter. Source: https://study.com/academy/lesson/constituents-of-matter-definitionsalculations.html.

An atom is at visualized as a nucleus of neutrons and protons. There is as surrounding cloud of orbiting electrons. These electrons take up the space in the electron. The quantum nature of atoms governs subatomic particles and their properties. For this reason, they may not act as other everyday particles

Basic Constituents of Matter

3

may appear to act. They may act as waves as they do not have well-defined positions or sizes. In particle physics, the standard model (SM) stipulates that matter is not a fundamental concept. This is attributed to the fact that elementary constituents of atoms are quantum entities (Woithe et al., 2017). This means that they do not have inherent volume or size. Fermions are point particles are forced to keep a distance from other particles in some conditions. This is as a result of the exclusion principle and other fundamental interactions. Fermions are also known as leptons or quarks. This contributes to the property of matter as it occupies space. There are four main basic constituents of matter namely atoms, molecules, nuclei, and particles.

1.1. ATOMS Atoms are the smallest unit of matter. They form chemical elements. Ionized or neutral atoms are found in plasma, gas, liquid, and solids. Atoms may have a diameter of 100 picometers. This means that they are very small in size. There small size is due to quantum effects. Atoms are composed of electrons and a nucleus. The electrons are normally bounded to the nucleus. The nucleus has a number of protons and neutrons with an exception of hydrogen as it does not have any neutrons. The nucleus carries a large percentage of the mass of an atom. Electron have a negative charge, protons a positive charge while neutrons do no bear any charge (Wood and Heyde, 2016). An atom is said to be electrically neutral when the number of electrons and protons are equal. In the case where there are fewer or more electrons than protons, then the atom will be positively or negatively charged. Atoms bearing charges are called ions. Electromagnetic forces (EMFs) enable the electros of an atom to be attracted to protons in the atomic nucleus. The nuclear force, on the other hand, allows both neutrons and protons be attracted to each other in the nucleus. The nuclear force is known to be stronger than the electromagnetic. Nuclear force also repels positively charged protons from each other. There are special cases where nuclear force is weaker than EMF. In such a case, different elements are produced as the nucleus is split. Splitting of the nucleus is a form of nuclear decay. The atomic number is the number of protons in the nucleus. The atomic number is used in defining the chemical element in which an element belongs. Copper is an element with atomic number 29. It therefore has 29 protons. The isotope of an element is defined by the number of neutrons. Chemical bonds enable atoms to be attached to one another forming chemical compounds. Atoms possess the

4

The Study of Elementary Particles

ability to dissociate and associate. This ability influences physical changes noted in atoms studied in chemistry (Figure 1.2).

Figure 1.2. Atoms are found in various forms of matter. Source: https://energywavetheory.com/atoms/.

1.2. STRUCTURE OF ATOMS 1.2.1. Subatomic Particles In physics, the word atom is used to refer to a particle that cannot be split into smaller pieces. Particles are made up if different subatomic particles. Neutrons, protons, and electrons are the constituent particles of an atom. Of all the constituent particles, electrons are the least massive and they have a negative electrical charge. The size of electrons is measured using specific instruments. Although electrons are very light, they recorded a positive rest mass when measured (Wallace, 2011). This led to the discovery of the neutrino mass. Normally, the opposite electric charges enable electrons to be bound to a positively charged nucleus. There are attraction forces that jeep them bounded. When the atomic number is greater or less than the number of electrons then the atom becomes positively or negatively charged and the atom is called an ion (Figure 1.3).

Basic Constituents of Matter

5

Figure 1.3. Subatomic particles make up a particle. Source: https://www.shutterstock.com/search/subatomic+particles.

A proto has a mass that is about 1,836 times that of an electron. It has a positive charge. The term atomic number is used to refer to the number of protons in an atom. A special case of atoms is the hydrogen atom. It is referred to a proton as it had a distinct particle. Neutrons are very different from protons and neutrons in that it does not have an electrical charge. They also have a free mass. Its mass is about 1,839 times that of an electron. Of the three constituent particles, neutrons are the heaviest. The mass of neutrons can be reduced through nuclear binding energy. Nucleons are the term used to refer to protons and neutrons. Nucleons have comparable dimensions; however, the surface of the particles is not sharply defined. In physics, the SM stipulates those electrons are elementary particles having no internal structure while the neutrons and protons are composite particles having elementary particles collectively known as quarks. Atoms have two kinds of quarks having a fractional electrical charge. Protons have three types of quarks. Two quarks are up while one quark is at the bottom. This is opposite in neutrons as they have two down quarks and one up quark (Viaux et al., 2013). A strong force or strong interaction holds quarks together. This process is mediated by gluons. The nuclear force holds neutrons and protons in the nucleus. Nuclear force is defined as a residuum if the strong force having different range-properties. The gluon belongs

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to the gauge bosons family. Gluons are elementary particles that mediate physical forces.

1.2.2. Nucleus An atom contains both protons and neutrons bounded in the nucleus hence the name atomic nucleus. Protons and neutrons are collectively known as nucleons. The radius of a nucleus is measured in femtometers. The radius of the nucleus is smaller than the radius of the atom. A residual strong force enables the nucleons to be bound together by short-ranged potential. The residual strong force is stronger than electrostatic force when there are relatively small distances between nucleons. When atoms have the same atomic number then they are said to be of the same element. In an element, there may be a variation in the number of neutrons (Volovik, 2015). This determines the isotope of the element. The nuclide is determined by the number of neutrons and protons. The stability of the nucleus is determined by the number of neutrons relative to protons. This leads to some isotopes undergoing radioactive decay (Figure 1.4).

Figure 1.4. The nucleus is made of protons and neutrons. Source: https://www.britannica.com/science/atom.

Fermions is a term used to refer to neutrons, electrons, and protons. The principle of Pauli exclusion is obeyed by fermions. The principle prohibits identical fermions form filling the same quantum state at the same time.

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This means that each proton in a nucleus should occupy a different quantum state from other protons. The same case applies to neutrons in the nucleus and electrons in the electron cloud. When a nucleus has different number of protons than neutrons then it can drop to a lower energy level. The drop in state is caused by radioactive decay. The decay causes a decline in the number of neutrons and protons such that they almost balance. This causes atoms to attain stability as matching number of neutrons and protons increases stability. An increase in the atomic number there is a needed increase in the proportion of neutrons that causes a mutual repulsion in protons (Van Noorden, 2012). This enables the nucleus to maintain its stability. There are cases where there are modifications that can be made to the number of neutrons and protons. This modification requires high energies to deal with the issue of strong force. The joining of multiple atomic particles to form heavier nuclides. This process is known as nuclear fusion. Nuclear fusion occurs when two energetic nuclei collide. The opposite of nuclear fusion is nuclear fission. This process results in the nucleus of an atom splitting into smaller nuclei. Nuclear fission is a form of radioactive decay. Modification of the nucleus of an atom can be done by bombarding it with high energy photons or subatomic particles. The modification causes a change in the number of protons in the nucleus. This in turn causes the atom to become a different chemical element. When a comparison is made, the mass of an atom is less than the mass of individual particles after separation. The difference is caused by the emission of energy. Energy is calculated using Albert Einstein’s massenergy equivalence formula which involves the multiplication of mass and the square of the speed of light. The energy is a deficit known as the binding energy of the new nucleus. This energy is non-recoverable. This energy enabled fused particles to remain together. An exothermic process involves the fusion between two nuclei resulting in the creation of a larger nuclei with lower atomic numbers. Exothermic process causes the release of high amounts of energy that exceed the binding energy (Ünel and Sekmen, 2018). This kind of reaction is noted in stars and the process is self-sustaining. A decline in binding energy per nucleon was noted in heavier nuclei. Endothermic process involves a fusion process which results in the production on nuclei with atomic numbers higher than 26 while the atomic masses are higher than 60.

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1.2.3. Electron Cloud An EMF causes electrons in an atom to be attracted to protons in the nucleus. This force is involved in binding of electrons in an electrostatic potential well that surrounds the smaller nucleus. The presence of this force means that an external energy source is needed to enable an electron to escape. The attractive force is stronger when electrons are close to the nucleus. This means that a lot of energy will be required for electrons that are near the center of the potential. Electrons are known to exhibit two properties namely wave and particle properties. There is a region inside the potential well known as the electron cloud. In the electron cloud, a particle forms a three-dimensional standing wave (Tluczykont et al., 2012). A standing wave is one that does not move relative to the nucleus. This kind of behavior in electrons is called atomic orbitals. Atomic orbital is a mathematical function used in characterizing the ability of an electron to appear at a particular position when measured. There are quantized or discrete sets of orbitals that exist around the nucleus. The orbitals possess different characteristics. There are cases where the orbitals have one or more rings or node structure. There is also a difference in orbitals depending on the orientation, shape, and size (Figure 1.5).

Figure 1.5. An electron cloud. Source: https://www.quora.com/What-does-an-electron-cloud-look-like.

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The energy level of the electron influences the atomic orbital. When an electron absorbs a photon, it changes it state to a higher energy level. The photon in this case has sufficient energy. This energy boosts the electron into a new quantum state. An electron can also move from a higher energy level to a lower energy state. This process is a spontaneous emission. In the process, excess energy is emitted through the radiation of excess energy as a photon. Atomic spectral lines influence the difference in the energies of electrons in the quantum states (Shlomi et al., 2020). The difference is energies also influence the characteristic energy values. The electron binding energy is the amount of energy required to add or remove and electron. The electron binding energy is less than the binding energy of nucleons. Electrically neutral atoms are those that have equal number of protons and neutrons while ions are atoms with a deficit of an excess of electrons. For electrons that are far from the nucleus, they can easily be transferred to another atom of shared with other atoms. This mechanism enables atoms to become compounds that are covalent and ionic network crystals.

1.3. PROPERTIES OF ATOMS 1.3.1. Nuclear Properties Two atoms are said to be of the same chemical element when they have identical number of protons in their nucleus. If the two atoms have the same number of protons but different numbers of neutrons then they become different isotopes of the same elements. Hydrogen atom s are known to admit one proton but its isotopes have no neutrons, one neutron, two neutrons or more. A set of atomic numbers are formed by known elements for a single-proton element hydrogen. Isotopes of elements with atomic numbers higher than 82 exhibit radioactive properties (Seshavatharam and Lakshminarayana, 2013). However, the radioactivity of bismuth is known to be practically negligible. There about 339 nuclides known to be naturally occurring. Of the 339 nuclides, about 252 do not exhibit decay properties. These group of nuclides are referred to as stable isotopes. Theoretically, there about 90 nuclides known to be stable isotopes while the other 162 have not been observed to decay. These isotopes are formally recognized as stable (Figure 1.6).

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Figure 1.6. The composition of the nucleus determines properties of atoms. Source: https://www.nuclear-power.com/nuclear-power/reactor-physics/atomic-nuclear-physics/atom-properties-of-atoms/.

1.3.2. Mass Protons and neutrons in the nucleus contribute to a large percentage of the atom’s mass. The total number of nucleons also known as particles is called the mass number of the atom. The mass number of an atom is a positive integer and does not have any dimensions as it expresses a count. Carbon 12 is an isotope of carbon with 12 nucleons brought about by six neutrons and six protons. The mass number has been used to identify it. Daltons is the term used to express the actual mass of an atom at rest. Daltons are also called the unified atomic mass unit. Daltons defines a twelfth of the mass of a free neutral atom of carbon 12. Scientifically, it is said that a given atom has an atomic mass is approximately equal to its mass number multiplied by the atomic mass unit. The generated value may not exactly be an integer in exception of carbon 12. Lead is the heaviest stable atom. Lead has a mass of 207.9766521 Da.

1.3.3. Size and Shape The atomic radius of an atom is used to define the dimensions of an atom as they do not have a well-defined outer boundary. The atomic radius is the measure of the distance in which an electron cloud extends from the nucleus. The atomic radius makes an atom to exhibit a spherical shape. Atoms in free space or vacuum obey the atomic a radius and are spherical in shape. When

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atoms forma chemical bond, the distances between the two nuclei may be used to derive the atomic radii. The location of an atom on the atomic chart, the quantum mechanical property called spin and the number of neighboring atoms causes the variation in the radius of an atom (Radovic et al., 2018). Down a column in the Periodic Table, there is a notable increase in the size of an atom and a decrease in atomic size when the Periodic Table is observed from left to right. In the Periodic Table, the smallest atom is helium while the largest is Caesium with atomic radius of 32 and 225 respectively. There is a deviation in the shape of an atom from the spherical symmetry when it is subjected to external forces. The extent of deformation is dependent on the orbital type of the outer shell electron and field magnitude. This was demonstrated in group-theoretical considerations. Crystals are known to have aspheric deviations. At low-symmetry lattice sites, large crystalelectrical field. Chalcogen ions and sulfur ions in pyrite-type compounds have been noted to have significant ellipsoidal deformations (Figure 1.7).

Figure 1.7. There are different shapes and sizes of atoms. Source: https://chem.libretexts.org/Courses/Mount_Royal_University/ Chem_1201/Unit_2._Periodic_Properties_of_the_Elements/2.08%3A_Sizes_ of_Atoms_and_Ions.

1.3.4. Energy Levels In an atom, there are electrons that have a potential energy that is negative relative to the distance from the nucleus goes to infinity. The potential energy is dependent on the position of the electron as it reaches the minimum inside of the nucleus. The potential energy is therefore inversely proportional to the distance. The quantum-mechanical model stipulates that when an electron is bound, it can occupy a set of states that are centered on the nucleus. The state occupied by the electron corresponds to a particular energy level. This is explained in the time-independent Schrodinger equation (Pitkänen, 2011). The amount of energy required to unbind an electron from an atom is used

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to measure the energy level of an electron. The energy level is measured in units of electron-volts. The ground state is the lowest energy state of a bound electron. Under certain conditions, an electron is able to transition to a higher state which is an excited state. An increase in the distance to the nucleus causes an increase in the electron’s energy. The interaction between electrons affects energy dependence. This means that it is not affected by electrostatic potential of the nucleus.

1.3.5. States The physical conditions influence the quantities of atoms found in different states of matter. Some of the physical conditions include pressure and temperature. When these conditions are varied, the state of that material may transition between plasmas, gases, liquids, and solids. Though a material exists in a given state, it may have different allotropes. Solid carbon is an example of such a material with different allotropes. Carbon can exist as diamond or graphite. There are gaseous allotropes which include ozone and dioxygen. Atoms can form Bose-Einstein condensate when they are placed in temperatures close to absolute zero. At absolute zero mechanical effects are observed at the atomic scale. These mechanical effects become apparent to the macroscopic scale. When a collection of atoms is at absolute zero temperature it is super-cooled. In this state, they behave like a single super atom. This enables one to conduct fundamental checks of their quantum mechanical behavior.

1.4. PARTICLES According to physical sciences, particles are defined as small localized objects that have been ascribed various chemical or physical properties. Some of these properties include mass, density, or volume. Particles may vary in quantity or size. There are subatomic particles which include the electron, microscopic particles such as molecules and atoms, macroscopic particles such as powders and granular materials (Amsler et al., 2008). Particles have been used in several experiments to create scientific models of large objects. Particles used in creating these models are chosen depending of their density. The term particle is generally used in various though its definition is refined according to the scientific field. The term particulate is used to refer to any object made up of particles (Figure 1.8).

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Figure 1.8. Particles are formed through combination of subatomic particles. Source: https://www.livescience.com/65427-fundamental-elementary-particles. html.

Fundamental particle or elementary particle is a term used in particle physics to refer to a subatomic particle that is not composed of other particles. Some of the particles assumed to be elementary include antimatter particles, fundamental bosons, matter particles and fundament fermions. Examples of fundamental fermions include leptons, antileptons, quarks, and antiquarks. Higgs boson and gauge bosons are fundamental bosons and are force particles involved in the mediation of interactions between fermions. A composite particle is on that has two or more elementary particles. Naturally, matter contains atoms. The atoms were once presumed to be elementary particles. The Greek term atomos was used to mean that it is unable to cut. There were several controversies in 1905 with some scientists suggesting that matter is composed of energy while others regarded molecules as mathematical illusion. In early 1930s, subatomic constituents of atoms were first discovered. These subatomic constituents include a particle of electromagnetic radiation, photons, protons, and electrons. During this time the conception of particles was being altered under the advent of quantum mechanics. During this time, it was observed that one particle could span a field in a similar manner to a wave. This is a paradox has an eluding satisfactory explanation (Abdelrahman and Sohaly, 2018).

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Neutrons and protons through the quantum theory were found to contain quarks. These quarks include the down quarks and the up quarks. This led to them being considered as elementary particles. In a molecule, an electron is able to exercise three degrees of freedom including orbital, spin, and charge. A free electron is one that does on orbit an atomic nucleus. This kind of electron does not have an orbital motion. It is regarded as an elementary particle as it is un-split-able. A practical outlook led to the discarding if ultimate constituent of substance. This led to the embodying of particle physics in the SM. There are theories beyond the SM as well as several elaborations led to the doubling of the number of elementary particles through the hypothesis that each known particle is able to associate with a shadow partner which is very massive. About all super partners have not been discovered. Elementary boson involved in the mediation of gravitation; the graviton is still hypothetical. Some hypothesis stipulates that space time is quantized. In the hypotheses there may be atoms of time and space.

1.5. CONCEPTUAL PROPERTIES OF PARTICLES Modeling nature makes use of the concept of particles. The modeling nature is mostly used when treatment of a phenomena is complex or uses difficult computation. Conceptual properties of particles are used to simplify assumptions on processes involved. A good illustration of the use of particles is demonstrated Mark Zemansky and Francis Sears were able to calculate the landing location and the speed of a baseball when thrown in air. In the analysis, the baseball was stripped of its properties (Pashkin and Leitenstorfer, 2014). The stripping process involved the idealizing of the baseball as a rigid smooth sphere. Other factors such as friction, buoyancy, and rotation were neglected causing the reduction of problem to ballistics of a classical point particle. Statistical physics is the realm that deal with the treatment of large numbers of particles.

1.5.1. Size There are three main classes of sizes of particles. When a particle is larger than molecules and atoms it is referred to as a macroscopic particle. Macroscopic particles are usually abstracted as point-like particles though they have structures, shapes, and volume among others. There are different kinds of macroscopic particles that include sand, dust, and powder, prices of debris in a car accident or objects in the galaxy. There are also microscopic particles.

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They are particles whose sizes ranges from atoms to molecules. Colloidal particles, nanoparticles, and carbon dioxide are examples of microscopic particles. Most of these particles are studied in molecular physics, atomic physics, and chemistry (Olive et al., 2014). When particles are smaller than atoms, they are called subatomic particles. Subatomic particles are therefore the smallest kind of particles. Subatomic particles include constituents of atoms such as electrons, neutrons or protons and other types of particles that can be produced by cosmic rays or particle accelerators. Subatomic oar is studied in particle physics. Quantum mechanics has been used in the study of subatomic particles and microscopic particles as these particles have really small sizes. Both subatomic and microscopic particles exhibit a phenomena demonstrated in particle in a box model. This constitutes the wave-particle duality. This takes into consideration whether a particle is identical or distinct.

1.5.2. Composition Composition can be used in classifying particles. When particles have composition, it is referred to as composite particles. Composite particles are particles that are made of other particles. This is well illustrated by carbon-14 atom which is made of six electrons, eight neutrons and six protons. Fundamental particles also known as elementary particles. They refer to particles that are not made of other particles. There are very few numbers of fundamental particles known in existence which include gluons, quarks, and leptons. There are possibilities that some of the particles may turn up to be composite particles and may seem to be elementary for a given moment. Elementary particles are considered to be truly punctual while composite particles are considered to be point-like.

1.5.3. State Particle decay has been noted to occur in composite particles and elementary particles. Stable particles do not experience particle decay. They include electrons or helium-4 nucleus. Stable particles may have an infinite lifetime or significantly large enough to hinder some attempts to observe this kinds of decay (McKenzie, 2014). When particles are observed to exhibit hindrances to decay are called to be observationally stable. Generally, particles decay involves particles moving from a high-energy state to a lower-energy state through the emission of a kind of radiation. This may involve the emission of photons.

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1.5.4. N-Body Simulation N-body simulations are also called N-particle simulations are simulations of dynamic system of particles. These simulations are influenced by some conditions which include gravity. Though it is mostly studied in computational physics under computational fluid dynamics, it is also common in cosmology. The number of particles considered is N. When there are higher N, the simulations become computationally intensive. When the system has large numbers of particles will be approximated to small number of particles and there are various methods used to optimize the simulation of algorithms.

1.5.5. Distribution of Particles An essential component of a colloid is colloidal particles. When a substance is dispersed microscopically throughout another substance, it is called a colloid. A colloidal system can be gaseous, liquid, or solid in nature. A colloidal system can also be dispersed or continuous in nature. For dispersedphase particles, their diameter is between 5 and 200 nanometers. When a particle has a diameter smaller than the range then it will form a solution rather than a colloid (Macklin et al., 2014). Colloidal systems are also called colloidal suspensions or colloidal solutions. Colloidal systems are usually subject of colloid and interface science. An aerosol is formed when both liquid and solid particles are suspended in a gas. Some suspended solid may be held in liquids. There are cases where particles are suspended as atmospheric particulate matter. This may include air pollution. Space debris or marine debris many be very large particles. Macroscopic particles that may be a conglomeration of discrete solids are at times described as granular materials.

1.6. MOLECULE A molecule is defined as an electrically neutral group of atoms held together by a chemical bond. In most cases, molecules, and ions are distinguished through the presence of electric charges. Molecules do not possess any electrical charge. In a different context such as that of biochemistry, organic chemistry and quantum physics, the distinction of dropped. The term is used to refer to polyatomic ions. The term molecule is used in the kinetic theory of gases to refer to any gaseous particle despite its composition. This places less emphasis on the requirement of a molecule to have two or more atoms. This is because the noble gases are individual atoms. When a

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molecule is composed of atoms of a single chemical element, it is called homo-nuclear. For instance, there are two atoms in an oxygen molecule. If the chemical compound I had made up of more than one element then it is said to be heteronuclear. A good example is water. It is made up of oxygen and hydrogen atoms (Figure 1.9) (Lyons, 2012).

Figure 1.9. Molecules are formed through the combination of atoms. Source: https://www.britannica.com/science/molecule.

Non-covalent interactions connect complexes and atoms. These interactions include ionic bonds and hydrogen bonds. This kind of connections are not considered to be single molecules. It is common for molecules to be considered to be a component of matter. Molecules make up most of the atmosphere and oceans. A large percentage of organic substances are molecules. Molecules are substances of life. They include vitamins, fats, carbohydrates, sugars, nucleic acids, amino acids, and proteins. Nutrient minerals are not molecules but they are generally ionic compounds. There are some ionic compounds made of molecules but a majority of the solid substances on the earth are completely or partly made of crystals or ionic compounds that do not contain molecules. They include all minerals that constitute the substance of the core of the earth, the molten interior, bedrock, boulders, rocks, pebbles, clay, sand, and earth. Though all these substances have chemic bonds, their molecules are not identifiable.

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Solid metals do not have molecules as there is a theme of repeated unit-cellular structure that holds for metal that are condensed phases made through metallic bonding. Solids exist in vitreous disordered states in solids. In this case atoms are held together by chemical bonds in the absence of any definable molecule or a regularity of repeating unit-cellular-structure characterizing metals, covalent crystals, and salts.

1.6.1. Bonding Covalent bonding is among the various was molecules are held together. There are some non-metallic elements existing as molecules in the environment either as a homo-nuclear molecules or compounds. These elements do not exist as free atoms. There are those who consider a metallic crystal as a single giant molecule held together through metallic bonding. There are those who are keen to outline the fact that metals have behavioral tendencies different from molecules (Long et al., 2021).

1.6.2. Covalent A covalent bond is formed when atom shares electrons. For instance, when hydrogen atoms share two electrons. The pair of electrons shared in covalent bonds are known as the lone pairs, bonding pairs, or shared pairs. Covalent bonding is when there is a stable balance of repulsive and attractive forces between atoms through the sharing of electrons (Figure 1.10).

Figure 1.10. Covalent bonds are formed through sharing of valence electrons. Source: https://biologydictionary.net/covalent-bond/.

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1.6.3. Ionic Sodium fluoride is formed when fluorine and sodium undergo a redox reaction. In this kind of reaction, the sodium loses the outer electron enabling it to gain a stable electron configuration. The lost electron finds its way to the fluorine atom exothermically. An ionic bond is a kind of bond formed when there is an electrostatic attraction found between oppositely charged ions. Ionic bonding is the main form of interaction that occurs between ionic compounds. An ion is an atom that has lost one or more electrons and are therefore termed as cations. Ions could also be atoms that have gained one or more electrons and are therefore called anions (Liu et al., 2017). Electrovalence is the term used to refer to the transfer of electrons and it is very different from covalence. An anion is a non-metal atom while a cation is a metal atom. Ions can be complex in nature. Ionic bonding may create solids at normal pressures and temperatures and in the absence of separate identifiable molecule. If these materials were to undergo sublimation and vaporization then separate molecules could be produced and electrons are fully transferred enough for the bonds to be regarded ionic and not covalent (Figure 1.11).

Figure 1.11. Ionic bonds are formed through complete transfer of valence electrons. Source: https://www.thoughtco.com/examples-of-ionic-bonds-and-compounds-603982.

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1.6.4. Molecular Size There are a number of molecules whose sizes are too small such that they cannot be seen by the naked eye. Molecules having several polymers may record macroscopic sizes. This includes biopolymers such as DNA. Molecules are often at times used as a building block for organic synthesis. Such molecules have dimensions of fee angstroms with about a billionth of a meter. Single molecules when placed under light cannot be observed. There are cases where small molecules or the outlines of individual atoms are traced when an atomic force microscope is used. Super-molecules and macromolecules are among the largest molecules. Diatomic hydrogen is the smallest molecule with a bond length of 0.74 Å. Sizes displayed by molecules in a solution is called the effective molecular radius (Leader, 2016).

1.6.5. Molecular Formulas In the study of molecules, different chemical formula types were developed. When developing the chemical formula of a molecule, a line of chemical element symbols, numbers, and other symbols were used. Some of these symbols include minus signs, plus signs, brackets, dashes, and parentheses. The symbols are limited to a topographic line of symbols including superscripts and subscripts. A simple type of chemical formula is a compound’s empirical formula. It entails the simplest integer ratio of all chemical element constituting it. Water is a good illustration with a ratio of 2:1 that is two hydrogen atoms and one oxygen atom. Ethanol has three elements namely carbon, hydrogen, and oxygen, with a ratio of 2:6:1. The compound’s empirical formula does not uniquely determine the kind of molecule as there are molecules with the same ratios as noted in ethanol and dimethyl ether. Isomers are molecules having similar atoms in different arrangements. Most carbohydrates have the same ratio of 1:2:1 of carbon: hydrogen: oxygen. They therefore have the same empirical formula though the total numbers of atoms in the molecule are different (Lasserre, 2014). The exact number of atoms in a molecule is reflected by the molecular formula. For this reason, the molecular formula is used to characterize different molecules. There are cases where different isomers have the same

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atomic composition though they are different molecules. In most cases, the molecular formula is the same as the empirical formula as noted in acetylene molecule with a molecular formula of C2H2 though the simplest integer ratio of the element is CH. The chemical formula of a molecule can be used to calculate the molecular mass. Molecular mass is expresses in conventional atomic mass units which is the same as 1)12 of the mass of neutral carbon-12 atom. Stoichiometric calculations make use of formula unit when dealing with network solids.

1.6.6. Structural Formula There are molecules with a complicated 3-dimensional structure with is not atoms being bonded to four different substitutes. A molecule may not be completely specified through the use of a semi-structural chemical formula or a simple molecular formula. Structural formula is used in this case to specify the molecule. The structural formula is considered to be a graphical type of formula. The structural formula can be represented with the use of one-dimensional chemical name under the chemical nomenclature. The chemical nomenclature requires the use of several words and terms that may not be part of chemical formulas.

1.6.7. Molecular Geometry When molecules are observed, they were noted to have fixed equilibrium geometries characterized by molecules at certain angles and bond lengths. At the equilibrium geometries, molecules continuously oscillate through rotational and vibrational motions. When a substance is made up molecules with the same average geometrical structure are called pure substances (Kibble, 2015). Properties of molecules are determined by their structures and chemical formula. Reactivity of molecules is highly studied in most chemical reactions. Although isomers have the same chemical formula, they have different properties brought about by their difference in structures. Stereoisomers have different biochemical activities and at the same time have the same physio-chemical properties (Figure 1.12).

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Figure 1.12. There are different kinds of molecular geometries. Source: https://www.thoughtco.com/molecular-geometry-definition-chemistryglossary-606380.

1.6.8. Molecular Spectroscopy The manner in which molecules respond to their interactions with probing signals of known energy is known as molecular spectroscopy. It was observed that molecules have quantized energy levels. These levels can be analyzed through the detection of a molecule’s energy exchange through emission or absorbance. Spectroscopy studies a matter but it does not refer to diffraction studies of particles such as high energy X-rays, electrons or neutrons interact with a regular arrangement of molecules. Changes in the rotation of molecules are measured through microwave spectroscopy. The methods can also be used in the identification of molecules in outer space (Kohls and Mele, 2018). Vibration of molecules is measured through the use of infrared spectroscopy. Some of the vibrations in molecules include twisting motions, bending motion, and stretching motion. This method is also used in the identification of the kinds of bonds or functional groups of molecules. Absorption or emission lines are formed when there are changes in arrangement of electrons. These lines are noted near infrared light, visible light, or ultraviolet light. The environment of particular nuclei in molecules are used to measure nuclear resonance. This method is also used in characterizing the number of atoms in different positions in a molecule.

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Quantum mechanics has greatly been used in theoretical chemistry and molecular physics to study molecules. Studies have been useful in understanding chemical bonds. The hydrogen molecule -ion is considered to be the simplest molecule. It also has the simplest of all chemical bonds by having one-electron bond. The hydrogen molecule-in has one negatively charged electron and two positively charged protons. In this case, the Schrodinger equation for the system is used as it enables easy solving of problems. The lack of electron-electron repulsion makes the equation easy. The adoption of technology such as the use of fast digital computers have enabled the approximation of complicated molecules.

1.7. NUCLEI/NUCLEUS The nucleus was discovered by Ernest Rutherford in 1911. The nucleus is located at the core of atoms hence the name atomic nuclei. The atomic nuclei are composed of electrically neutral neutrons and electrically positive on protons. The protons and neutrons in the nucleus are held together by the strong force which is the strongest known fundamental force. 0.1% of the volume of an atom is the nucleus. Though it occupies a small portion, it carries a large percentage of the mass of an atom. The negatively charged electrons enshrouding the nucleus determine the chemical properties of a substance (Kahle et al., 2016). In most cases the number of protons in the nucleus will match the number of electrons. If the nuclei of an atom are unstable, it will undergo radioactive decay that will enable the atom to attain a stable state. Radioactive decay involves the emission of photons as gamma decay, emission of helium nuclei which is alpha decay of capture or emission of positrons or electrons that is beta decay. There are cases where the radioactive decay involves a combination of process. In most cases, the nuclei of an atom may be ellipsoidal or spherical in shape though it may take on other shapes. The nuclei of an atom can rotate and vibrate when struck by other particles. In some atoms, their instability will cause it to change or break apart causing a change in the relative number of neutrons or protons. Nuclear physics is the branch of physics concerned with understanding and studying the atomic nucleus, forces binding it together and its composition (Figure 1.13).

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Figure 1.13. The nuclei are at the center of the atom. Source: https://www.physicsforums.com/threads/heavy-atomic-nucleus-image.502912/.

1.7.1. Nuclear Makeup Protons and neutrons make up the nucleus of an atom. These elements are the manifestation of elementary particles known as quarks. The quarks are usually held together by a nuclear strong force in stable combinations of hard-ons. These combinations are called baryons. The nuclear strong force is found in the nucleus and it extends far from each baryon such that protons and neutrons are bound together against the repulsive electrical force found between positively charged protons. The range of the nuclear strong force is small. The force thins out and drops to zero when it is beyond the edge of the nucleus. The electrically negative charged electrons are held together in their orbits around the nucleus by a collective action of positively charged nucleus (Jaeckel and Ringwald, 2010). When the collection of negatively charged electrons orbit the nucleus, there is a display of an affinity of configurations and numbers of electrons making the orbit stable. The number of protons in

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the nucleus determines the kind of chemical element the atom represents. When an atom is neutral, it will have equal number of electrons orbiting the nucleus. Stable electronic configurations can be created through individual chemical elements. The stable configurations are created when the chemical elements combine to share their electrons. By sharing the electrons, there are stable electronic orbits about a nucleus. The entire charge of a nucleus is defined by protons. This gives the element its chemical identity. Neutrons do not bear any charge and are therefore considered to be electrically neutral. Neutrons and protons contribute the same amount in mass of protons. The phenomenon of isotopes can be explained by using neutrons. Neutrons are mostly used in the reduction of repulsion in the nucleus.

1.7.2. Composition and Shape Neutrons and protons have been identified as fermions. These kinds of fermions have different value of strong isospin quantum number whereby two neutrons and two protons may share the same space wave function. This is because they do not have identical quantum entities. Though fermions are of a given particle, they are at times vied as two different quantum state. Two fermions, a proton, and a neutron, two neutrons or two protons can exhibit bosonic behavior. This behavior is noted when the two fermions become loosely bound in pairs and have an integer spin. A unique case where a hyperon containing one or more unusual quarks or strange quarks can share a wave function. This case is called hyper nucleus. The hyperon is a third baryon. The hyper nucleus is considered to be extremely unstable. It is not found on earth. It is found in high-energy physics experiment. The neutron has a core of radius that is approximately equal to 0.3 FM and is positively charged. The neutron is surrounded by a compensating negative charge of radius. The radius of the negative charge ranges between 0.3 fm and 2 fm. An exponential decay of the positive charge distribution is noted in protons (Ishimori et al., 2010). The nuclei can take different shapes. It may be pearshaped, triaxial which is a combination of prolate and oblate deformation, discus-shape which is an oblate deformation, the prolate deformation which is rugby ball-shaped or spherical (Figure 1.14).

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Figure 1.14. Oval shaped nuclei. Source: http://thescienceexplorer.com/universe/thanks-pear-shaped-nucleuswe-likely-won-t-ever-time-travel.

1.7.3. Forces The nuclear force or residual strong force bind the nuclei together. The residual strong force is defined as a minor residuum of string interactions that binds quarks together resulting in the formation of neutrons and protons. Nuclear force is weak between protons and neutrons as it is neutralized within them. In a similar manner EMFs between neutral atoms are weaker compared to the electromagnetic force internally holding parts of the atoms together. Forces between neutral atoms include Van der Waals forces acting between two inert gas atoms while EMFs holding parts of the atom together include forces holding electrons in an inert gas atoms bound to the nucleus. At the distance of nucleon separation, the nuclear force is highly attractive. At this point, nuclear force overwhelms repulsion between protons causes by EMF. This facilitates the existence of the nuclei. The residual strong force works within a limited range as it experiences decay within distance. For this reason, stable nuclei are those whose nuclei is smaller than a given size. Lead-298 is the largest known element with a stable nucleus (Humbert-Droz et al., 2019). Lead has a total of 208 nucleons categorized by 82 protons and 126 neutrons. When the nuclei of an atom are larger than that of lead then it is unstable. Such nuclei tend to be short-lived having large numbers of nucleons. A special case is bismuth-209 which is stable to beta decay. This nucleus has the longest half-life to alpha decay of known

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isotopes. The residual strong force is able to cause an attraction between nucleon Paris. This is because the force was found to be effective over short distances which include few femtometers or two nucleon diameters. The residual strong force between neutrons and protons causes the formation deuterons. The force also works between neutrons and protons.

1.7.4. Nuclear Models Nuclear models have been used to get a better understanding of the nuclear structure. The SM of physics was widely used as it was deemed to be able to adequately describe the behavior of the nucleus and its composition. The challenge was that there was much difficulty in with regards to generating predictions from the theory for most areas under particle physics. There are two main reasons for this. The first reason is with regards to quantum chromodynamics (QCD). The QCD has been used to derive the physics within a nucleus (Heckman, 2010). There is a challenge of using this method is that utilization of mathematical and computational approaches in lowenergy systems are extremely limited. Phase transition occurring between low-hadronic matter and high-energy quark matter causes the challenge. The phase transition has rendered the perturbative techniques unusable. This has created a challenge in the construction of accurate QCD-derived model of forces between nucleons. The currently used approaches are limited to chiral effective field theory (EFT) or phenomenological models. The other challenge is that even though the nuclear force is constrained, significant amounts of computational power is needed to accurately compute properties of nuclei ab initio. There have been several developments in manybody theory have made this a possibility for relatively stable and low mass nuclei. However, further improvements are needed in both mathematical and computational power approaches are needed before highly unstable nucleus or heavy nuclei may be tackled. Experiments were initially compared to relatively crude models which as imperfect. These models were useful in completely explaining experimental data on nuclear structures. Among the various basic quantities, the nuclear radius is among those that can be predicted by using various models. For stable nuclei, their nuclear radius is approximately proportional to cube roots of mass number of the nucleus (Graña and Herráez, 2021). This value is particularly accurate when the nuclei contain several nucleons that are arranged in spherical configurations. Stable nucleus is known to have constant density and a formula is used to calculate the nuclear radius R. Packing of neutrons and protons in the

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nucleus gives approximately the same total size as packing of hard spheres of a constant size into an almost spherical bag or constant size.

1.7.5. Models of Nuclear Structure Models of nuclear structure include the liquid drop model. In the liquid drop model, early models of the nucleus visualized the nucleus as a rotating liquid drop. In the liquid drop model, the trade-off of both relatively short-range nuclear forces and long-range EMF causes a behavior that is resembles surface tension forces in liquid drops of different sizes. The formula has been found to be successful in explaining important phenomena of nuclei including that changing amounts of binding energy with changes to composition and size. The formula however does not explain the special stability known to occur when the nuclei have special magic numbers of neutrons and protons. The semi-empirical mass formula has been used in approximating the binding energy of many nuclei considered to be the sum of five types of energies (Fraser, 2011). There are pictures of nucleus as drops of incompressible liquid and have been used to account for the observed variation in the nucleus binding energy. In the liquid drop model, when an assembly of nucleons of the same size is packed together into the smallest volume then the interior of each nucleon as a certain number of other nucleons in contact with it. In this case, the volume is proportional to the nuclear energy. This is covered in the volume energy. Under surface energy, when the nucleon at the surface of a nucleus interacts with fewer other nucleons, the binding energy is less. Surface energy takes into account this information making it negative and therefore proportional to the surface area. With regards to coulomb energy, the electric repulsion present between each proton pair in a nucleus contributes towards the decrease in binding energy. There is also the asymmetry energy also called the Pauli energy. This kind of energy makes use of the Pauli exclusion principle. The coulomb energy has been very useful by eliminating the likelihood of the most stable form of nuclear matter may have the same number of protons and neutrons. This is because the presence of unequal number of protons and neutrons would mean that filling of higher levels of one type of particle while the lower energy levels are left vacant for other types. The final type of energy is pairing energy. This kind of energy is a correction term that arise from the tendency of pairs of protons and pairs of neutrons to occur. Nuclei with even number of particles is more stable than one with odd numbers.

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1.7.6. Facts of Nuclei There are more than 19 million trillion nuclei in a typical grain of sand. This value is 100 times more than the number of seconds since the creation of the universe. Of the total atomic mass, the nucleus accounts for about 99.9994% though it takes up less than one trillionth of an atom’s volume. All nuclei bear the same density such that is the moon was smashed to the same density it may fit I to a Yankee stadium (Francescon et al., 2013).

CHAPTER

2

CLASSIFICATION OF ELEMENTARY PARTICLES

CONTENTS 2.1. Classification According to Spin........................................................ 35 2.2. Fermion ............................................................................................ 36 2.3. Quarks.............................................................................................. 40 2.4. Lepton .............................................................................................. 43 2.5. Boson ............................................................................................... 44 2.6. Elementary Bosons............................................................................ 45 2.7. Higgs Boson ..................................................................................... 45 2.8. Photon .............................................................................................. 47 2.9. Gluon ............................................................................................... 49 2.10. W and Z Bosons ............................................................................. 49 2.11. Composite Bosons .......................................................................... 51 2.12. Classification According to Mass..................................................... 51 2.13. Classification According to Charge ................................................. 57

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Particle physics (sometimes referred to as high physics) is the study of the constitution of particles that make up matter and radiation. Despite the fact that the term particle can apply to a variety of very small objects (such as electrons, gas particles, or even dust), particle physics usually focuses on the indivisibly tiniest measurable particles and the basic interactions that explain their behavior. These fundamental particles, according to present understanding, are excitations of the quantum fields which regulate their interactions. The standard model (SM) is the currently prevalent theory for understanding these elementary particles and fields, as well as their behavior. As a result, contemporary particle physics focuses on the SM and its numerous extensions, such as the latest “discovered” particle, the Higgs boson, or even the earliest recognized force, gravity (Feroz et al., 2009). An elementary particle, also known as a fundamental particle, is a subatomic particle that is not made up of other smaller components. The fundamental fermions, which are “matter particles” and “antimatter particles,” and the fundamental bosons, which are “force particles” that facilitate interactions among fermions, are commonly considered to be elementary particles. A composite particle is one that contains two or more fundamental particles (Figure 2.1).

Figure 2.1. The particle content of the standard model of physics. Source: https://en.wikipedia.org/wiki/Particle_physics#/media/File:Standard_ Model_of_Elementary_Particles_Anti.svg.

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Standard matter is made up of atoms, which were once assumed to be elementary particles (atomos means “unable to be split” in Greek). However, the presence of the atom was debated until the early 20th century, when some pioneering physicists dismissed molecules as quantitative illusions and claimed that matter was essentially made up of energy. The electron and proton, as well as the photon, a unit of electromagnetic radiation, were the very first subatomic elements of the atom to be recognized in the 1930s. The new arrival of quantum physics was fundamentally redefining the understanding of particles in that era, as a single particle may appear to traverse a field as if it were a wave, a contradiction that eluded sufficient answer at the time (Farnsworth and Boyle, 2015). A subatomic particle is a unit that is smaller than an atom in physical science. Per the SM of particle physics, a subatomic particle could either be a composite particle (for instance, a proton, neutron, or meson) or an elementary particle (like an electron, photon, or muon). Such particles and their interactions are studied in particle physics and nuclear physics. Experiments demonstrated that light can act both like a flow of particles (photons) and like a wave. The idea of wave-particle dualism was coined as a result of this, to reflect the fact that quantum-scale particles operate like either of those particles and waves. One other concept is the uncertainty principle, which asserts that a few of their properties, like their concurrent position and momentum, are impossible to measure precisely. It has been demonstrated that the wave-particle duality holds true not only for photons but also for more heavy particles (Figure 2.2).

Figure 2.2. In quantum physics, wave-particle duality states that any particle or quantum phenomenon can be characterized as either a particle or a wave. This behavior has been demonstrated not only for elementary particles, but also for composite particles such as atoms and molecules. Source: https://www.livescience.com/24509-light-wave-particle-duality-experiment.html.

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In quantum field theory, particle interactions are defined as the production and elimination of quanta of matching fundamental interactions. This is a combination of particle physics and field theory (El Naschie, 2009). Among even particle physicists, there are many different definitions of what a particle is. The following are examples of expert attempts to define a particle: • A particle is a wave function that has been collapsed; • A particle is an irreducible representation of the Poincaré group; • A particle could be a vibrating string (string theory); • A particle is a measurable object in a detector. Protons and neutrons were discovered to include quarks – up quarks and down quarks – which are now regarded elementary particles, thanks to quantum theory. Inside a molecule, the electron’s three degrees of freedom (charge, spin, and orbital) can be separated into three quasiparticles through the wavefunction (holon, spinon, and orbiton). A free electron, on the other hand, appears indivisible and is still considered a fundamental particle because it is not orbiting an atomic nucleus and therefore lacks orbital motion. In the 1980s, the status of an elementary particle as a basic constituent of matter was mainly abandoned in favor of a more practical viewpoint, which was reflected in particle physics’ SM, which is known as science’s most empirically accurate hypothesis (Dubois-Violette and Todorov, 2019). Many extensions and theories outside the SM, like the popular supersymmetry, propose that every existing particle has a “shadow” partner that is significantly more substantial, albeit all such superpartners have yet to be identified. Meanwhile, the graviton, an elementary boson that mediates gravitation, remains a speculative concept. Furthermore, some hypotheses claim that spacetime is in a state of quantization, implying that “atoms” of space and time exist inside these theories (Figure 2.3).

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Figure 2.3. The strong nuclear force holds protons together in the nucleus of an atom. Neutrons are non-charged subatomic particles (they are neutral). Neutrons, like protons, are bonded into the nucleus of an atom by the strong nuclear force. Source: https://aether.lbl.gov/elements/stellar/strong/strong.html

The fundamental elements of matter and their interactions are the subject of elementary-particle physics. A vast quantity of experimental data has been gathered over the last few decades, and several patterns and systematic aspects have been noticed. The electromagnetic, weak, and strong interactions have all been designed and tested using phenomenally competent mathematical theories. These ideas, together known as the SM, are probably certainly valid descriptions of Nature, all the way down to a measurement scale of 1/1000th the size of the atomic nucleus, to first estimate (Dubbers and Schmidt, 2011). There have also been some promising but theoretical advancements in the endeavor to integrate these interactions into a single underlying paradigm, and even to integrate quantum gravity into a parameter-free “theory of everything (TOE).” Here in this chapter, we will look at these elementary or fundamental particles and the way they are classified.

2.1. CLASSIFICATION ACCORDING TO SPIN Fundamental particles, and consequently composite particles (hadrons) and atomic nuclei, have spin as an intrinsic type of angular momentum. In quantum physics, spin is a kind of angular momentum. The second kind being orbital angular momentum. The orbital angular momentum

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operator is the quantum-mechanical counterpart of the classical angular momentum of orbital revolution, and it emerges when the wavefunction of the orbital revolution has repeating pattern as the angle changes. Spin is the quantum-mechanical equivalent of light polarization for photons; spin has no classical analog for electrons. Experiments like the Stern–Gerlach experiment, in which silver atoms were shown to have two potential discrete angular momenta while having no orbital angular momentum, infer the presence of electron spin angular momentum. The presence of the electron spin can also be deduced theoretically from the spin–statistics theorem and the Pauli Exclusion Principle —and conversely, one can deduce the Pauli Exclusion Principle from the specific spin of the electron (Dubois-Violette, 2016). For certain particles, like photons, spin is expressed mathematically as a vector, whereas for others, like electrons, it is expressed as spinors and bispinors. Spinors and bispinors act similarly to vectors in that they have fixed magnitudes and change when rotated, but they have an unusual “direction.” The value of spin angular momentum is the identical for all elementary particles of a particular sort, however the direction can vary. These are expressed by assigning a spin quantum number to the particle. Spin has the same SI unit as classical angular momentum (i.e., N•m•s or J.s or kg•m2•s1). In practice, spin is computed as a dimensionless spin quantum number by dividing the spin angular momentum by the decreased Planck constant, which has the same dimensions as angular momentum. The “spin quantum number” is frequently referred to as “spin.” It is obvious through this that it is a quantum number.

2.2. FERMION A fermion is a particle in particle physics that matches Fermi–Dirac statistics and possesses half-even integer spin: spin 1/2, spin 3/2, etc. The Pauli Exclusion Principle is followed by these particles. All quarks and leptons, along with all composite particles made up of an odd number of them, including all baryons and several atoms and nuclei, are referred to as fermions. Bosons, on the other hand, follow the Bose–Einstein statistics (Alexandre, 2011). Fermi-Dirac statistics are a sort of quantum statistics that deals with the physics of a system made up of many similar particles that follow the Pauli

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Exclusion Principle. The Fermi–Dirac distribution of particles over energy levels is one of the outcomes. It is termed after Enrico Fermi and Paul Dirac, who separately developed the distribution in the 1920s. (Although Fermi came up with it first, before Dirac). Fermi–Dirac statistics is a branch of statistical mechanics that employs quantum physics ideas. Fermi–Dirac (F–D) statistics apply to identical and imperceptible fermions in thermodynamic equilibrium with half-integer spin (1/2, 3/2, etc.). The system can be represented in units of single energy levels if there is no interaction amongst particles. The F–D distribution of particles over various states, where no two particles may inhabit the same state, is the outcome, and it has a significant impact on the system’s attributes. The most typical application of F–D statistics is to electrons, which are a sort of fermion with spin 1/2. Bose–Einstein (B–E) statistics are a parallel to F–D statistics, and they apply to comparable and discernible particles with integer spin (0, 1, 2, etc.), known as bosons. Maxwell–Boltzmann (M–B) statistics are employed in classical physics to characterize identical and distinct particles. Unlike F–D statistics, many particles can inhabit the same state in B–E and M–B statistics (Figure 2.4).

Figure 2.4. Fermions are a type of elementary particle. They are extremely little and light. Because atoms are built up of fermions can be regarded of as the building blocks of matter. In honor of the eminent physicist Enrico Fermi, Paul Dirac termed them fermions. Source: http://tid.uio.no/epf/adventures-res/particleadventure_2.1/frameless/ fermibos.html.

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The Pauli Exclusion Principle is a quantum mechanical concept that asserts more than one identical fermion (sub-particles with half-integer spin) within a quantum system cannot hold the same quantum state at the same time. Wolfgang Pauli, an Austrian scientist, first proposed this principle for electrons in the 1920, and then extended it to all fermions with his spin– statistics argument (DeMille et al., 2017). It is impossible for two electrons of a poly-electron atom to have the identical values of the four quantum numbers: n, the primary quantum number; l, the azimuthal quantum number; ml, the magnetic quantum number; and ms, the spin quantum number in the case of electrons in atoms. If two electrons share the same orbital, for example, their n, l, and ml values are the same; hence, their ms must be different, and the electrons will have opposite half-integer spin projections of 1/2 and 1/2. Particles with an integer spin, or bosons, are not subject to the Pauli Exclusion Principle: any number of identical bosons can occupy the same quantum state, as with, for instance, photons produced by a laser or atoms in a Bose–Einstein condensate. A more precise statement is that the overall wave function is antisymmetric for fermions and symmetric for bosons when two identical particles are exchanged. This indicates that if the space and spin values of two identical particles are swapped, the whole wave function for fermions changes sign while the sign for bosons remains unchanged (Dolenec et al., 2017). Interchanging two fermions in the same state (for instance, the same orbital with the same spin in the same atom) has no effect, and the overall wave function remains intact. Its only way the whole wave function can simultaneously change sign and remain unchanged, as necessary for fermions, is for it to be zero throughout, which means the state cannot occur. Because the sign of bosons does not vary, this explanation is not applicable. Some fermions are primary particles, such as electrons, whereas others, such as protons, are composite particles. Particles with integer spin are bosons, while particles with half-integer spin are fermions, per the spinstatistics theorem in relativistic quantum field theory (Figure 2.5).

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Figure 2.5. The spin–statistics theorem in quantum mechanics ties a particle’s intrinsic spin (angular momentum not attributable to orbital motion) to the particle statistics it obeys. All particles that travel in three dimensions have either integer spin or half-integer spin in units of the decreased Planck constant. Source: https://alchetron.com/Spin%E2%80%93statistics-theorem.

Fermions have another unique trait in conjunction to their spin: they have preserved baryon or lepton quantum numbers. As a result, what is commonly known as the spin-statistics relationship is actually a spin statistics-quantum number relationship. As a consequence of the Pauli Exclusion Principle, only one fermion can occupy a particular quantum state at a given time. If multiple fermions have the same spatial probability distribution, then at least one property of each fermion, such as its spin, must be different. Fermions are usually associated with matter, whereas bosons are generally force carrier particles, although in the current state of particle physics the distinction between the two concepts is unclear. Weakly interacting fermions can also display bosonic behavior under extreme conditions. At low temperature fermions show superfluidity for uncharged particles and superconductivity for charged particles (Calvo et al., 2016). Composite fermions, such as protons and neutrons, are the key building blocks of everyday matter. The name fermion was coined by English theoretical physicist Paul Dirac from the surname of Italian physicist Enrico Fermi. Quarks and leptons are the two types of elementary fermions recognized by the SM. The model differentiates 24 distinct fermions in all. There are six quarks (up, down, strange, charm, bottom, and top) and six leptons (electron, electron neutrino, muon, muon neutrino, tauon, tauon neutrino).

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Fermions are classified mathematically into three categories: • Weyl fermions (massless); • Dirac fermions (heavy); and • Fermions of Majorana (each its own antiparticle). Most SM fermions are thought to be Dirac fermions, while it is unclear whether neutrinos are Dirac or Majorana fermions at this moment (or both). Dirac fermions can be thought of as two Weyl fermions together. Weyl fermions were experimentally created in Weyl semimetals in 2015.

2.3. QUARKS A quark is a fundamental ingredient of matter and a classified of elementary particle. Hadrons are composite particles made up of quarks, the most stable of which are protons and neutrons, the building blocks of atomic nuclei. Up quarks, down quarks, and electrons make up all frequently seen matter. Quarks are never discovered in isolation due to a phenomenon known as color confinement; they can only be found within hadrons, which contain baryons (like protons and neutrons) and mesons, or in quark–gluon plasmas (QGP). As a result, a lot of what we know about quarks comes from observations of hadrons (Capelle and Campo, 2013). Electric charge, mass, color charge, and spin are all fundamental features of quarks. They are the only known elementary particles whose electric charges are not integer multiples of the elementary charge, and they are the only known particles in the SM of particle physics to experience all four fundamental interactions, also known as fundamental forces (electromagnetism, gravitation, strong interaction, and weak interaction). Quarks are divided into six flavors: up, down, charm, strange, top, and bottom. The masses of up and down quarks are the smallest of all quarks. Particle decay, or the transfer from a higher mass state to a lower mass one, transforms heavier quarks into up and down quarks quickly. Up and down quarks are the most frequent and stable in the universe as a result of this, but odd, charm, bottom, and top quarks can only be generated in high-energy collisions (like in particle accelerators). There is an antiquark for every quark flavor, which varies from the quark solely in that some of its properties (like the electric charge) have same magnitude but opposite sign (Figure 2.6).

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Figure 2.6. Any member of a class of primary subatomic particles that interact via the strong force and are thought to be essential elements of matter quarks unite with one another via the strong force to form protons and neutrons, much how the latter particles combine in varying amounts to form atomic nuclei. Source: https://www.shutterstock.com/search/quark.

Physicists Murray Gell-Mann and George Zweig separately devised the quark model. Quarks were proposed as part of a hadron ordering scheme, but until deep inelastic scattering investigations at the Stanford Linear Accelerator Center, there was scant evidence for their physical existence. All six flavors have been proven in accelerator program experiments. The top quark was the last to be discovered, having been discovered in 1995 at Fermilab. The SM is a theoretical framework that encompasses all known fundamental particles. Up (u), down (d), strange (s), charm (c), bottom (b), and top (t) are the six flavors of quarks (q) in this paradigm. Antiquarks are quark antiparticles that are represented by a bar over the sign for the associated quark, for example, u for an up antiquark (Boyle and Farnsworth, 2014). Antiquarks have the same mass, mean lifespan, and spin as their respective quarks, but the electric charge and other charges have the opposite sign, as with antimatter in general. As per the spin–statistics theorem, quarks are spin-1/2 particles, meaning that they are classified as fermions. They are bound by Pauli’s exclusion principle, which stipulates that no two identical fermions can occupy the same quantum state at the same time. This differs from bosons (particles with integer spin), which can exist in any number of states. Quarks, unlike leptons, have a color charge, which causes them to interact violently. The

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production of composite particles known as hadrons is caused by the ensuing attraction between various quarks. Valence quarks are the quarks that dictate the quantum numbers of hadrons; aside from these, each hadron can have an endless number of virtual “sea” quarks, antiquarks, and gluons that have no effect on its quantum numbers. Hadrons are divided into two types: baryons, which have three valence quarks, and mesons, which have a valence quark and an antiquark. The proton and neutron, the building constituents of the atomic nucleus, are the most prevalent baryons. There are many different types of hadrons, the majority of which are distinguished by their quark composition and the qualities that these constituent quarks confer. The presence of “exotic” hadrons with additional valence quarks, such as tetraquarks and pentaquarks, has been hypothesized since the inception of the quark model, but was not discovered until the early 21st century. There are three generations of elementary fermions, each with two leptons and two quarks. Up and down quarks are in the first generation, strange, and charm quarks are in the second, and bottom and top quarks are in the third. There have been no successful discoveries a fourth generation of quarks and other elementary fermions, and there is strong indirect evidence that only three generations exist. Higher-generation particles have more mass and less stability, leading weak interactions to cause them to disintegrate into lower-generation particles (Bass, 2020). In nature, only first-generation (up and down) quarks are frequent. Heavier quarks can only be produced in high-energy collisions (such as those involving cosmic rays) and decay rapidly; yet, they are thought to have existed in the first fractions of a second following the Big Bang, when the cosmos was extraordinarily hot and dense (the quark epoch). Heavier quark studies are carried out in artificially constructed environments, like particle accelerators. Quarks are the only known elementary particles with electric charge, mass, color charge, and flavor, and they participate in all four fundamental interactions of modern physics: electromagnetism, gravity, strong interaction, and weak interaction. Other than at extremes of energy and distance scales, gravity is too weak to be significant to individual particle interactions (Planck distance or Planck energy). Gravitation, on the other hand, is not explained by the SM because no viable quantum theory of gravity exists.

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2.4. LEPTON In particle physics, a lepton is a half-integer spin (spin 12) elementary particle that does not interact strongly. Charged leptons (leptons that act almost like electrons or muons) and neutral leptons (neutrinos) are the two primary types of leptons. Charged leptons can mix with other particles to form composite particles like atoms and positronium, whereas neutrinos seldom interact with other particles and are thus almost never observed. The electron is the most well-known of all leptons. There are six flavors of leptons that are organized into three generations. The electron (e-) and the electron neutrino (ve) are the first-generation leptons; the muon (μ–) and the muon neutrino (νμ) are the second-generation leptons; and the tau (τ–) and the tau neutrino (ντ) are the third-generation leptons. Of all the charged leptons, electrons have the smallest mass (Bellotti, 2011). The heavier muons and taus will decay quickly into electrons and neutrinos as a result of particle decay, which is defined as the transition from a higher mass state to a lower mass state. As a result, electrons are the most abundant charged lepton in the universe and are stable, whereas muons and taus can only be generated in high-energy collisions (again like those observed in cosmic rays and particle accelerators). Electric charge, spin, and mass are only a few of the fundamental features of leptons. Leptons, unlike quarks, are not affected by the strong interaction, but are affected by the other three fundamental interactions: gravity, the weak interaction, and electromagnetism, which is proportional to charge and so 0 for electrically neutral neutrinos. There is a similar sort of antiparticle, known as an antilepton, for each lepton flavor. The antilepton is the same as a lepton, with an equal magnitude but an opposite sign. Neutrinos may be their own antiparticle, according to some hypotheses. Whether or if this is the case is unknown at this time. The SM is incomplete without leptons. Along with protons and neutrons, electrons are one of the constituents of atoms. Exotic atoms with muons and taus instead of electrons, as well as lepton–antilepton particles like positronium, can be created (Figure 2.7).

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Figure 2.7. Leptons can only carry one unit of electric charge or they can be neutral. Electrons, muons, and taus are the charged leptons. Each of them has a negative charge as well as a different mass. Electrons, the lightest leptons, have a mass that is only one-tenth of that of a proton. Muons are heavier than electrons, weighing more than 200 times as much. Taus, on the other hand, are around 3,700 times more massive than electrons. Leptons are involved in several processes such as beta decay. Source: https://en.wikipedia.org/wiki/Lepton.

2.5. BOSON A boson is a subatomic particle with an integer spin quantum number in particle physics (0,1,2…). Bosons are one of two fundamental subatomic particle classes; fermions, which have odd half-integer spin (1/2,3/2…), are the other. Every subatomic particle that can be seen is either a boson or a fermion. Unlike fermions, which are frequently referred to as the elements of “ordinary matter,” some bosons are subatomic particles that play a unique role in particle physics. Some elementary bosons (for instance, gluons) operate as force carriers, causing forces between other particles, whereas others (like the Higgs boson) cause mass. Bosons that are built up of smaller parts, like as mesons, are composite particles (Beringer et al., 2012). Superfluidity emerges outside of particle physics because composite bosons (Bose particles), such as low-temperature helium-4 atoms, obey Bose–Einstein statistics, and superconductivity arises because some quasiparticles, such as Cooper pairs, behave similarly.

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Paul Dirac used the term boson to honor Satyendra Nath Bose, an Indian physicist and professor of physics at the University of Calcutta and the University of Dhaka, who devised the theory describing such particles, now known as Bose–Einstein statistics, in collaboration with Albert Einstein.

2.6. ELEMENTARY BOSONS All observable elementary particles are bosons (with integer spin) or fermions (with non-integer spin) (with odd half-integer spin). The primary particles that make up ordinary matter (leptons and quarks) are fermions, but in particle physics, the elementary bosons play a unique role (Zimmermann, 2018). They can either operate as force carriers, causing forces between other particles, or they can cause the phenomena of mass. There are five elementary bosons in the SM of particle physics: • •

There is only one scalar boson (spin=0). H0 Higgs boson – the particle that, through the Higgs process, causes the occurrence of mass. Four force carriers that are vector bosons (spin=1). The gauge bosons are as follows: •

Photons (eight distinct varieties) – force carriers that mediate the strong force. • Z Neutral weak boson – the carrier of the weak force. • W± Charged weak bosons (two types) — also known as force carriers, these particles mediate the weak force. The graviton (G), a tensor boson (spin of 2), has been proposed as the force carrier for gravity, however all efforts to include gravity into the SM have been unsuccessful thus far.

2.7. HIGGS BOSON The Higgs boson, also known as the Higgs particle, is an elementary particle in particle physics that is created by the quantum excitation of the Higgs field, one of the fields in particle physics. The Higgs particle is a large scalar boson that links to (interact with) mass in the SM. It has zero spin, even or positive parity, no electric charge, and no color charge. It is also extremely unstable, rapidly decomposing into other particles (Woithe et al., 2017).

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The Higgs field is a scalar field with two electrically charged and two neutral elements that make up a complex doublet with the weak isospin SU (2) symmetry (Figure 2.8).

Figure 2.8. Higgs boson, also called Higgs particle that is the carrier particle, or boson, of the Higgs field, a field that permeates space and endows all elementary subatomic particles with mass through its interactions with them. Source: https://www.smithsonianmag.com/science-nature/how-the-higgs-boson-was-found-4723520/.

Its potential has a non-zero value throughout (even in empty space), which breaks the electroweak interaction’s weak isospin symmetry and gives some particles mass via the Higgs process. Both the field and the boson are titled after physicist Peter Higgs, who suggested the Higgs mechanism, a means for some particles to acquire mass, in 1964 alongside five other scientists in three teams. (At the time, all known fundamental particles[c] should have no mass at extremely high energies, but completely understanding how some particles acquire mass at lower energies has proven to be extremely difficult.) If these theories are

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right, a particle known as a scalar boson with specific properties should also exist. The Higgs boson was named after this particle, and it could be used to determine whether the Higgs field was the best theory (Wood and Heyde, 2016). The ATLAS and CMS experiments at the large hadron collider (LHC) at The European Organization for Nuclear Research (CERN) near Geneva, Switzerland, detected a subatomic particle with the expected qualities in 2012, after a 40-year search. The characteristics of the new particle were later proven to fit those of a Higgs boson. Peter Higgs and François Englert, physicists from the three teams, were awarded the Nobel Prize in Physics in 2013 for their model expectations. Although Higgs’ name has become synonymous with this idea, it was created separately by various researchers in the 1960s and 1970s. The Higgs boson has been dubbed the “God particle” in the popular press, despite the fact that many physicists disagree.

2.8. PHOTON The photon is an elementary particle. It is the force carrier for the electromagnetic force (EMF) and the quantum of the electromagnetic field, which includes electromagnetic radiation like light and radio waves. Because photons have no mass, they always travel at the speed of light in a vacuum, which is 299,792,458 m/s (about 186,282 mi/s). The photon falls to the boson family of particles. Photons, like other elementary particles, are best explained by quantum physics, and their behavior exhibits wave-particle duality, with qualities of both waves and particles. Albert Einstein’s work, which relied on Max Planck’s study, gave birth to the current photon notion in the first two decades of the 20th century (Wallace, 2011). Planck stated that the energy held within a material entity should be understood as constituted of an integer number of distinct, equal-sized components while attempting to describe how matter and electromagnetic radiation can be in thermal equilibrium with each other. Einstein proposed that light is made up of distinct units of energy to describe the photoelectric effect. Gilbert N. Lewis coined the name photon to describe these energy units in 1926. Many more experiments followed, confirming Einstein’s theory. Photons and other fundamental particles are presented as a natural outcome of physical laws that have a specific symmetry at every location

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in spacetime in the SM of particle physics. This symmetry determines the inherent properties of particles, like charge, mass, and spin. Lasers, Bose–Einstein condensation and quantum field theory are all examples of how the photon notion has led to significant developments in practical and theoretical physics. It has been used in photochemistry, high-resolution imaging, and molecular distance measurements. Photons have since been researched as components of quantum computers and for optical imaging and optical communication technologies such as quantum cryptography. A photon is a stable particle that has no mass and no electric charge. A photon can have three different polarization states in a vacuum. All other quantum numbers of the photon (like lepton number, baryon number, and flavor quantum numbers) are zero since the photon is the gauge boson for electromagnetism. Also, rather than the Pauli Exclusion Principle, the photon follows Bose–Einstein statistics (Viaux et al., 2013). In many natural processes, radiation in the form of photons is emitted. When a charge is accelerated, for instance, synchrotron radiation is produced. Photons of various energies, spanning from radio waves to gamma rays, are emitted during a molecular, atomic, or nuclear transition to a lower energy level. When a particle and its antiparticle are annihilated (for instance, electron–positron annihilation), photons are emitted (Figure 2.9).

Figure 2.9. Movement of a photon as electromagnetic radiation. Source: https://www.differencebetween.com/difference-between-photon-andvs-electron/.

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2.9. GLUON A gluon is a fundamental particle that serves as the exchange particle (or gauge boson) for the strong interaction between quarks. It is similar to the EMF’s photon exchange between two charged particles. Quarks are bound together by gluons to produce hadrons like protons and neutrons. In quantum chromodynamics (QCD), gluons are vector gauge bosons that facilitate strong interactions between quarks (QCD). The strong interaction’s color charge is carried by gluons. The photon, on the other hand, mediates electromagnetic interactions but has no electric charge. As a result, gluons both participate in and mediate the strong interaction, making QCD substantially more difficult to understand than quantum electrodynamics (QED) (Volovik, 2015). The gluon is a vector boson, which implies it has the same spin as the photon. Because gauge invariance demands the polarization to be transversal to the direction in which the gluon is traveling, gauge bosons without mass like the gluon have only two polarization states. Unbroken gauge invariance in quantum field theory necessitates the existence of gauge bosons with zero mass. Experiments have shown that the gluon’s rest mass is only a few meV/ c2. The intrinsic parity of the gluon is negative.

2.10. W AND Z BOSONS The W and Z bosons are vector bosons in particle physics that are collectively known as the weak bosons or, more broadly, the intermediate vector bosons. The weak interaction is mediated by these elementary particles, whose symbols are W+, W, and Z0. The W bosons are antiparticles and have either a positive or negative electric charge of one elementary charge. The Z0 boson is its own antiparticle and is electrically neutral. Each of the three particles has a spin of one. There is a magnetic moment in the W bosons, but none in the Z0. With a half-life of roughly 31,025 seconds, all three of these particles are extremely short-lived. Their experiment was crucial in the development of what is now known as the SM. The weak force is represented by the W bosons. The extra particle was given the name “Z particle” by physicist Steven Weinberg, who subsequently explained that it was the model’s final additional particle. The W and Z bosons had already been given names, and the Z bosons were given their names since they had no electric charge.

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The two W bosons have been identified as neutrino absorption and emission mediators. The W boson charge causes nuclear transmutation by inducing electron or positron emission or absorption during these processes (Figure 2.10).

Figure 2.10. A W boson is created and disappears during the beta-minus decay process. Down quarks decay producing W bosons and up quarks. After then, the W boson decays into an electron and an electron antineutrino. Source: https://www.open.edu/openlearn/science-maths-technology/particlephysics/content-section-8.1.

When neutrinos scatter elastically from matter, the Z boson facilitates the transfer of momentum, spin, and energy (a process which conserves charge). When bubble chambers are irradiated with neutrino beams, such behavior is virtually as prevalent as inelastic neutrino interactions. The absorption and emission of electrons and positrons are not affected by the Z boson (Van Noorden, 2012). When an electron appears as a new free particle with kinetic energy, it is created as a consequence of a neutrino interaction with the electron (with momentum transfer through the Z boson), because this behavior occurs more frequently when a neutrino beam is present. The neutrino merely collides with the electron (via a boson exchange) and then scatters away, passing some of the neutrino’s momentum to the electron.

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2.11. COMPOSITE BOSONS Depending on their constituents, composite particles (like hadrons, nuclei, and atoms) could be bosons or fermions. Any composite particle composed of an even number of fermions is a boson, because bosons have integral spin while fermions have odd half-integral spin: • •

All sorts of mesons are included in composite bosons; Even-mass stable nuclei like deuterium, helium-4 (the alpha particle), carbon-12, and lead-208. Bose–Einstein statistics describe the behavior of many indistinguishable bosons at large densities as quantum particles. The fact that the number of bosons that can occupy the same quantum state is unrestricted is a feature that becomes relevant in superfluidity and other uses of Bose–Einstein condensates (Ünel and Sekmen, 2018). As a result, a gas of helium-4 atoms condenses into a low-energy state and becomes a superfluid when chilled to temperatures near absolute zero and the kinetic energy of the particles becomes insignificant.

2.12. CLASSIFICATION ACCORDING TO MASS On the basis of mass, elementary particles are divided into four types: • • • •

Massless particles; Light particles; Intermediate particles; and Heavy particles.

2.12.1. Massless Particles A massless particle is an elementary particle with zero invariant mass in particle physics. The photon (carrier of electromagnetism) and the gluon (massless particle) are both gauge bosons (carrier of the strong force). Gluons, on the other hand, are never seen as free particles since they are contained within hadrons. Neutrinos were once assumed to be massless particles. Due to the fact that neutrinos change flavor as they move, at least two types of neutrinos must have mass. The discovery of neutrino oscillation earned Canadian scientist Arthur B. McDonald and Japanese scientist Takaaki Kajita a share of the 2015 Nobel Prize in Physics.

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Special relativity helps us understand the dynamics of massless particles. These particles, for instance, must always travel at the speed of light. To differentiate them from bradyons and tachyons, they are sometimes referred to as luxons. Rest mass refers to invariant mass in special relativity. All observers, regardless of reference frames, have the same rest mass (Tluczykont et al., 2012). Because they contain relativistic mass, which acts as the gravity charge, massless particles are known to undergo the same gravitational acceleration as other particles (which gives empirical verification for the equivalence principle). As a consequence, perpendicular components of force applied on massless particles essentially change their direction of movement, with gravitational lensing, the angle change in radians being GM/rc2, as indicated by general relativity. The force component parallel to the motion still has an effect on the particle, but it does so by altering the frequency instead of the speed. That is due to the fact that a massless particle’s momentum is determined solely by frequency and direction, whereas the momentum of low-speed heavy objects is determined by mass, speed, and direction. Gravitational lensing depends on spacetime curvature because massless particles move in straight lines in spacetime, called geodesics. The gluon-gluon interaction is a bit different: gluons exert forces on each other, but because their accelerations are parallel to the line connecting them (even if somewhat not at the same time), the acceleration will be zero except if the gluons move in a direction perpendicular to the line connecting them, causing velocity to be perpendicular to acceleration. Gravitons are massless tensor bosons (with a spin 2) that mediate gravitational interaction in theories that propose that gravity is quantized. They do not have any concrete experimental proof to back them up. Gravitational waves, on the other hand, can provide indirect proof of gravitons (Figure 2.11).

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Figure 2.11. An artist’s representation depicting gravitons as mediating particles in the force of gravitation. Source: https://www.scienceabc.com/pure-sciences/gravitons-definition-theory-how-much-thor-hammer-mjolnir-weight.html.

2.12.2. Light Particles Neutrinos, which were previously assumed to be massless and stable, now have minuscule masses; the lightest neutrino is the lightest fermion and is stable, as its decay would be into bosons, which could not conserve angular momentum. According to current thinking, the electron and the lightest neutrino or neutrinos are the only massive particles that are strictly stable. The electron is the lightest charged particle; its decay would result in neutral particles, which would not be able to conserve charge. Although there is no basic reason why the proton should be stable, it is stable for all practical purposes, having a half-life greater than 1,034 years (Shlomi et al., 2020).

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2.12.3. Intermediate Particles Force carriers, also known as messenger particles or intermediate particles in quantum field theory, are particles that generate forces between other particles. These particles are packages of energy (quanta) from a certain type of field. For each sort of elementary particle, there is a specific type of field. There is an electromagnetic field, for example, whose quanta are photons. The notion is notably essential in particle physics, where gauge bosons are force carrier particles that facilitate electromagnetic, weak, and strong interactions. Fields are used to describe nature in quantum field theories. Each field has a corresponding characterization as a collection of particles of a specific sort. A force between two particles can be defined as the action of one particle’s force field on the other, or as the transfer of virtual force carrier particles between them. The energy of a wave in a field is quantized (for instance, electromagnetic waves in an electromagnetic field), and the quantum excitations of the field can be understood as particles. The SM incorporates the following particles, each of which is a field excitation: • •

Gluons are powerful gauge field excitations; Photons, W bosons, and Z bosons are electroweak gauge field excitations; • Higgs bosons are excitations of one constituent of the Higgs field, which is responsible for the mass of fundamental particles (Seshavatharam and Lakshminarayana, 2013); • Furthermore, composite particles like mesons and quasiparticles can be represented as effective field excitations. Gravity is not a feature of the SM, although it is considered that gravitons, which are the excitations of gravitational waves, may exist. Because the theory is inadequate and the interactions of single gravitons could be too weak to detect, the status of this particle is currently uncertain (Figure 2.12).

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Figure 2.12. Zooming in on gluons’ contribution to proton spin. Source: https://www.energy.gov/science/np/articles/zooming-gluons-contribution-proton-spin.

There are two ways to think about what happens when one particle scatters off another, changing its direction. In the field diagram, we imagine that the field created by one particle exerted a force on the other. Instead, consider one particle producing a virtual particle that is absorbed by another. The virtual particle is responsible for transferring momentum from one particle to the next. Because these corrections may be seen as Feynman diagrams incorporating additional virtual particles, this particle perspective is particularly useful when there are a large number of intricate quantum corrections to the calculation (Radovic et al., 2018). Another virtual particle example is beta decay, in which a virtual W boson is produced by a nucleon and later decays to e and (anti)neutrino. The relevance of the perturbation theory from which it is developed limits the explanation of forces in regards to virtual particles. In some cases, like low-energy QCD and the representation of bound states, perturbation theory fails.

2.12.4. Heavy Particles Heavy charged particles are energetic particles with a mass of one atomic mass unit or higher. This group comprises alpha particles, as well as protons, deuterons, fission fragments, and other energetic heavy particles that are frequently created in accelerators. These particles have at least one electronic

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charge and interact with matter largely through the Coulomb force, which occurs between the particle’s positive charge and the negative charge on electrons in the absorber material. In this scenario, the force between the two opposite charges is attractive. When a charged particle moves around an electron in the absorber, a little fraction of its momentum is transferred to the electron (Figure 2.13).

Figure 2.13. Alpha (α) radioactivity. Source: https://physicsopenlab.org/2016/02/11/alpha-%CE%B1-radioactivity/.

As a consequence, the charged particle slows slightly, and the electron (which was virtually at rest before) picks up some of the charged particle’s kinetic energy. The charged particle is interacting with many electrons in the absorber material at the same time, and the cumulative result of all the Coulomb forces acts like a drag force on the particle. The particle slows down continually from the moment it enters the absorber until it comes to a stop. Since the charged particle is millions of times more massive than electrons it interacts with, it is deflected from a straight-line path as it approaches rest. The time it takes for a particle to halt varies between a few picoseconds (11,012 second) in solids or liquids and a few nanoseconds (1,109 second) in gases. These durations are short enough that the stopping time can be deemed instantaneous for many applications, and this assumption is used in the parts that follow that explain the reaction of radiation detectors (Pitkänen, 2011). When a charged particle moves around an electron in the absorber, a little fraction of its momentum is transferred to the electron. Several aspects of the particle-deceleration process are critical to comprehending the behavior of radiation detectors. Initially, the particle’s mean range is the average distance it travels before stopping. The mean range of a charged particle rises with increasing initial kinetic energy for a given material. At normal temperature and pressure, standard value for

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charged particles with beginning energies of a few MeV are tens to hundreds of micrometers in solids or liquids and a few centimeters in gases. The specific energy loss at a given position along the particle track is a second feature (path). This quantity is a function of particle energy and quantifies the differential energy absorbed per unit pathlength (dE/dx) in the material. In principle, as the particle slows and loses energy, the dE/dx value rises. When a result, as the particle slows down, the density with which energy is deposited in the absorber increases. Due to their limited range, charged particles have a relatively high average dE/dx value, and they are sometimes referred to as high dE/dx radiations.

2.13. CLASSIFICATION ACCORDING TO CHARGE A charged particle is a particle with an electric charge in physics. It could be an ion, including a molecule or atom, with an excess or shortage of electrons in comparison to protons. It might also be an electron, a proton, or another primary particle, all of which are thought to have the same charge (apart from antimatter). An atomic nucleus devoid of electrons, including an alpha particle, could also be a charged particle (Pashkin and Leitenstorfer, 2014). A plasma is a concentration of charged particles, atomic nuclei, and separated electrons, but it can also be a gas with a high concentration of charged particles. Positive (+) and negative (-) charges are arbitrarily labeled. There are just two ‘categories’ of charges known; there is nothing inherent in positive charges that deems them positive, and the same is true for negative charges. Elementary particles are classified into three types based on charge types: • • •

Particles that are positive; Particles that are negative; and Particles that are neutral.

2.13.1. Positive Particles A proton is a subatomic particle with the sign p or p+, a positive electric charge of +1 e elementary charge, and a slightly smaller mass than a neutron. Protons and neutrons, each with a mass of around one atomic mass unit, are referred to collectively as “nucleons” (properties of an atomic nuclei).

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Every atom has one or more protons in its nucleus; they are an essential component of the nucleus. The atomic number refers to the number of protons in the nucleus, which is the defining attribute of an element (represented by the symbol Z). Because each element has a distinct quantity of protons, each element has a distinct atomic number (Olive et al., 2014). The positron, also known as the antielectron, is the electron’s antiparticle or antimatter counterpart. It has the same electric charge as an electron, the same spin as an electron, and the same mass as an electron. Annihilation happens when a positron hits electron. When two or more photons collide at low energies, they produce two or more photons. Positron emission radioactive decay (via weak interactions) or pair creation from a suitably intense photon interacting with an atom in a substance can both produce positrons. Alpha particles, also known as alpha rays or alpha radiation, are made up of two protons and two neutrons bonded together to form a particle that resembles a helium-4 nucleus. They are often formed during the alpha decay process, although they can also be generated in other ways. The first letter of the Greek alphabet, is named after an alpha particle, or 2+ is the sign for the alpha particle. They are also sometimes expressed as He2+ or 42He2+, denoting a helium ion with a +2 charge, because they are equivalent to helium nuclei (missing its two electrons). As soon as ion gains electrons from its surroundings, the alpha particle 42He transforms into a regular (uncharged) helium atom (McKenzie, 2014). Positively charged pions and cations are examples of other positively charged substances (Figure 2.14).

Figure 2.14. Positron (positive electron). Cloud chamber photograph by C. D. Anderson of the first positron ever identified. A 6 mm lead plate separates the

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chamber. The deflection and direction of the particle’s ion trail indicate that the particle is a positron. Source: https://en.wikipedia.org/wiki/Positron#/media/File:PositronDiscovery. png.

2.13.2. Negatively Charged Particles The electron is a subatomic particle (expressed as e– or β–) with a negative one elementary charge electric charge. Electrons are the first generation of the lepton particle class and are widely regarded as elementary particles due to the lack of known components or substructure. The mass of an electron is roughly 1/1836 that of a proton. An inherent angular momentum (spin) of a half-integer value, defined in units of the decreased Planck constant, is one of the electron’s quantum mechanical properties. According to the Pauli Exclusion Principle, no two electrons may possess the same quantum state because they are fermions (Amsler et al., 2008). Electrons, like all elementary particles, have both particle and wave properties: they may collide with other particles and be diffracted like light. Because electrons have a smaller mass and thus a longer de Broglie wavelength for a given energy, their wave characteristics are easier to examine with tests than those of other particles such as neutrons and protons. The antiproton, p (pronounced p-bar), is the proton’s antiparticle. Antiprotons are stable, but they have a brief lifetime since every collision with a proton causes both particles to be obliterated in an explosion of energy. Muons, tauons, anions, and negatively charged pions are examples of negatively charged particles.

2.13.3. Particles with No Charge The neutron is a subatomic particle with the symbol n or n0 that has a neutral (neither positive or negative) charge and a slightly larger mass than a proton. Atomic nuclei are made up of protons and neutrons. Protons and neutrons are both known as nucleons because they function alike within the nucleus and each have a mass of around one atomic mass unit. Nuclear physics describes their features and interactions. A neutrino is a fermion (an elementary particle with a spin of 1/2) that interacts only with gravity and the weak interaction. The neutrino is dubbed so because it is electrically neutral and has such a minuscule rest mass (-ino) that it was formerly considered to be zero (Macklin et al., 2014).

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The neutrino’s rest mass is substantially lower than any other known elementary particles, barring massless particles. The gravitational interaction is exceedingly weak, and neutrinos do not engage in the strong interaction. As a result, neutrinos often pass-through conventional matter unobstructed and undetected. Neutral pions, the z boson, the Higgs boson, and atoms are other particles that have no charge.

CHAPTER

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STANDARD MODEL OF PARTICLE PHYSICS

CONTENTS 3.1. Introduction ...................................................................................... 62 3.2. The Smallest Building Blocks ............................................................ 63 3.3. Expanding the Scope of Particles ....................................................... 64 3.4. Matter Particles ................................................................................. 67 3.5. Standard Model (SM) Mathematical Concepts................................... 71 3.6. The SM Higgs and Flavor .................................................................. 74 3.7. Positronium ...................................................................................... 79

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3.1. INTRODUCTION The hypotheses and discoveries of multiple physicists since the 1930s have spurred increased knowledge into the basic matter structure: every matter in the universe is viewed as produced using a couple of fundamental blocks called key particles, managed by four principal powers. A comprehension of how these particles and respective forces work and are connected with one another is epitomized in the standard model (SM) of molecular physics. Founded in the mid-1970s, it has effectively clarified practically all experimental outcomes and definitively anticipated a wide assortment of peculiarities. Across time and through many trials, the SM has become laid out as an all-around tested physics concept (Figure 3.1) (Lyons, 2012).

Figure 3.1. All particles are categorized into fermions and bosons. Source: https://pediaa.com/difference-between-fermions-and-bosons/.

The SM of molecular physics defines three of the four known universal forces omitting gravity, as well as categorizing renowned elementary particles. All common matter, comprising each atom within the Periodic Table of compounds, comprises of only three kinds of matter compounds: up-down quarks, which comprise of the nucleus protons and neutrons, and electrons that encompass the core. The SM incorporates the matter atoms (quarks and leptons), the force transporting particles (bosons), plus the Higgs boson. It clarifies how particles known as quarks (comprising protons and neutrons) and leptons (electrons) constitute all known matter. The universal SM took quite some time to develop. Physicist J.J. Thomson found the electron in 1897, and researchers at the large hadron collider (LHC) identified the last part of the riddle, the Higgs boson, much later in 2012. Researchers use the SM of Particle Physics to define the universe’s building block. It clarifies how particles known as quarks (comprising of protons and neutrons) and leptons (electrons) constitute all physical matter.

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It likewise clarifies how force delivery particles, which have a place in the more extensive group of bosons, impact on quarks and leptons. The major forces that run the universe include: electromagnetism, the strong and weak force. Electromagnetism is conveyed by photons and includes the connection of electric fields and attractive fields. The strong force, which is conveyed by gluons, ties together nuclear cores to make them stable. The weak force, transferred by W and Z bosons, causes atomic responses that have run the Sun and different stars for billions of years. The other central force is gravity, which is not sufficiently clarified by the SM (Long et al., 2021). Regardless of its success at clarifying the universe, the SM has limits. For instance, the Higgs boson provides mass to quarks, charged leptons (similar to electrons), including the W and Z bosons. Notwithstanding, there is no proof yet on whether the Higgs boson additionally provides mass to neutrinos – microparticles that seldom interact with other material in the universe. Likewise, physicists comprehend that around 95% of the universe is not made of traditional matter as is known. All things considered, a large part of the universe comprises of dark matter and energy that do not match the SM. The theory explained: The SM may seem like a dull name in science, but in excess of a fourth of physics Nobel Prizes within the last century are immediate contributions to or direct aftereffects of the SM. Many remember the energy among researchers and broadcast over the Higgs boson discovery in 2012. However, that much-hyped occasion did not emerge from the blue – it covered a five-decade continuous line-up for the SM (Liu et al., 2017). All endeavors to override it to show in the research facility that it should be considerably improved – and there have been numerous throughout recent years – has fizzled. To put it plainly, the SM responds this inquiry: What is matter made of, and can it hold together?

3.2. THE SMALLEST BUILDING BLOCKS Obviously, it is not a secret that the universe is made of particles, and particles are made of atoms. Scientist Dmitri Mendeleev discovered during the 1860s how to arrange all molecules – the chemical elements – into the Periodic Table. Notwithstanding, there are 118 unique chemical components including carbon, aluminum, iron, and selenium among 114 others. Physicists prefer straightforward things. There is need to reduce things down to their pith, a couple of fundamental building blocks. Ancient people believed everything is made of only five components – earth, fire, air, water, and aether. Five is a lot less complex than the 118. It is likewise off-base.

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By 1932, researchers realized that all molecules are made of only three particles: protons, neutrons, and electrons. The neutrons and protons are tied together firmly into the core. The electrons, multiple times lighter, spin around the core at speeds moving toward that of light. Physicists Bohr, Schrodinger, Heisenberg, Planck, and companions had developed another science – quantum mechanics – to clarify this motion (Leader, 2016). Three elements are significantly less complex than five. Yet, mutually bond how? The negative electrons and positive protons are bound together by electromagnetism. Yet, the protons are completely bound together in the core and their positive charges ought to push them intensely apart. The neutral neutrons will not help. What ties these protons and neutrons together? This is what the SM of particle physics seeks to explain.

3.3. EXPANDING THE SCOPE OF PARTICLES In the interim, nature has declined from keep its scope of particles to only three. Actually four, counting the photon, the molecule of light that Einstein defined. Four roses to five when Anderson defined electrons as having positive charge – positrons – striking the Earth from space. Five became six when the pion, which Yukawa anticipated would hold the nucleus together, was found (Figure 3.2).

Figure 3.2. Detailed imaging of a particle structure. Source: https://physics.aps.org/articles/v13/196.

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Next came the Muon – multiple times heavier than the electron, yet in any case a twin. That summarizes it. Number seven. Not directly, repetitive. By the 1960s there were many “major” particles. Instead of the efficient Periodic Table, there were simply not insignificant forms of baryons (weighty particles like protons and neutrons), mesons (like Yukawa’s pions) and leptons (light particles like the electron, and the subtle neutrinos) – with no structure and no core principles (Lasserre, 2014). Into this break entered the SM. It was anything but a short-term blaze of brightness. No Archimedes jumped out yelling “aha.” Instead, there was a progression of essential bits of knowledge by a couple of key people during the 1960s that changed this entanglement into a basic hypothesis, and after five decades of test check and hypothetical elaboration more was found (Figure 3.3).

Figure 3.3. The Muon is a light particle with negligible magnetic influence. Source: https://nmi3.eu/muon-research/characteristics-of-muons.html.

Quarks. They are available in six varieties called flavors. Like frozen yogurt, with the exception of not being as delectable. Rather than vanilla, chocolate, etc., there are physics particles. In 1964, Gell-Mann, and Zweig revealed the plans: Mix and match any three quarks to get a baryon. Protons are a pair up and a down quark tied together; neutrons are a pair down and an up. Pick one quark and one antiquark to derive a meson. The pion is an up or down quark tied to an anti-up or cross-down. All the regular compounds are made of up-down quarks, electrons, and anti-quarks.

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All things considered, they are attached to each other so firmly that you never under any circumstance observe a quark or anti-quark all alone. The hypothesis of that binding, including the responsible particles called gluons are called quantum chromodynamics (QCD). It is a fundamental structure of the SM, however numerically complex, in any event, representing an inexplicable matter of basic math (Kibble, 2015). The other part of the SM is “Leptons Model.” The name of the milestone 1967 paper by Steven Weinberg which merged quantum mechanics with the imperative bits of information on how particles connect and paired the two into one hypothesis. It consolidated the distinguishable electromagnetism, merging it with what physicists named “the weak power” which causes specific radioactive decays, and clarified that they were unique parts of one force. It merged the Higgs system for providing mass to primary particles. From that point forward, the SM has anticipated the consequences of many tests, including the disclosure of a few types of quarks and of the W and Z bosons – weighty particles that are for weak connections what the photon is for electromagnetism. The likelihood that neutrinos are not massless was disregarded during the 1960s, however slipped effectively into the SM during the 1990s, about three decades late to the party. Finding the Higgs boson in 2012, since predicted by the SM and pursued by scientists, was a thrill yet not surprising. It was one more pivotal triumph for the SM over the dark matter that molecular physicists have more than once cautioned lingered over the cosmsos (Kohls and Mele, 2018). Worried that the SM did not typify their assumptions for straightforwardness, researchers stressed over its numerical self-consistency, or examining the possible need to carry the power of gravity into the crease, physicists have made various recommendations for hypotheses past the SM. These consist of exciting names such as, supersymmetry, technicolor, string theory and grand unified theories (GUTs). Unfortunately, for their defenders, past the-Standard-Model hypotheses have not yet effectively anticipated any new test peculiarity or any test inconsistency with the SM. Following 50 years, a long way from requiring a redesign, the SM genuinely deserves applaud as the Absolutely Amazing Theory of Almost Everything. However, the SM is not the response. Regardless of whether people overlook the presence of dark matter and energy, there are a few things that the SM cannot clarify. The below points do an incredible deal in clarifying particle physics:

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• •

Neutrinos have weight which are not consistent by the SM. Matter–antimatter disproportion. SM cannot clarify this. Because we exist in a universe of matter and antimatter is simply found in tests, or emerging from particles racing across the universe and hitting the globe, that is something difficult to ignore (Kahle et al., 2016). • The SM was made piecemeal from the three powers which influence atoms (electromagnetic, weak, and strong powers.) Gravity is excluded. By any stretch of the imagination. That is a major opening. • The SM incorporates a weak atomic force however doesn’t clarify it completely. It can’t clarify why there’s a right-left lopsidedness, known as the equality violation. Electrons made in the subatomic cycle called β decay are constantly ‘left-sided.’ • As of late, there are solid rumors that a fifth force might have been found. That didn’t emerge from the SM which was fabricated like a structure made of Legos. • Gravity – the force that coalesces to blend space and time together. Not little potatoes. • Dark matter and dark energy – these are not demonstrated to exist yet there is exceptionally solid proof that they do. As it were, the SM resembles a visually impaired individual’s reality. They realize there is something mind boggling past what they can “envision” yet they can’t envision what that is. That is the means by which disjointed the SM is. It doesn’t compute nearly everything since nobody has the foggiest idea how much there is yet to clarify (Jaeckel and Ringwald, 2010).

3.4. MATTER PARTICLES All matter in the universe consists of basic particles, the structural composition of matter. These particles consist of two primary forms called quarks and leptons. Every group comprises of six particles, which are connected two by two, or “generational.” The slightest and most stable elements constitute the original, denser, and less-stable atoms and comprise the second and third generations. All solid matter in the universe is produced using particles belonging in the original generation; any heavier particles rapidly rot to more steady ones. The six quarks are combined in three generations – where the “up quark” and “down quark” comprise the original, trailed by

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the “charm” and “strange,” and “top” quarks, plus “bottom (beauty) quark.” Quarks additionally come in three unique “colors” and just blend in such ways as to frame colorless items. The six leptons are comparably organized in three forms – the “electron” and “electron neutrino,” the “muon” and “muon neutrino,” and “tau” and “tau neutrino.” Both the electron, muon, and tau have an electric field and a sizeable mass, though the neutrinos are electrically neutral and have almost no mass.

3.4.1. Force and Carrier Particles The four major forces at work within the universe: the strong, weak, electromagnetic, and gravitational forces operate over various ranges and have unique strengths. Gravity is a weak yet infinite force. The electromagnetic force (EMF) likewise has limitless reach but commonly more grounded than gravity. The strong and weak forces are viable just over a short reach and effective at the range of subatomic particles. Notwithstanding its name, the weak force is a lot more impactful than gravity yet it is the most fragile of the other three. The strong force, like the name proposes, is the most profound of each of the four key forces (Ishimori et al., 2010). Three of the basic forces result from the trading of force transporter particles, which have a place with a more extensive group known as “bosons.” Matter particles transfer discrete quantities of energy by trading bosons with one another. Every fundamental force consists of its unique relating boson – the strong force is conveyed by the “gluon,” the EMF is conveyed by the “photon,” whereas the “W and Z bosons” are liable for the weak force. Though not yet discovered, the “graviton” must be the relating force conveying molecule of gravity. The SM incorporates the electromagnetic, strong, and weak forces including their transporter particles, and clarifies well the way in which these forces follow up on the matter particles in general. Be that as it may, the most recognizable force in our day-to-day existence, gravity, isn’t essential for the SM, as fitting gravity easily into this system has ended up being a troublesome test (Humbert-Droz et al., 2019). The quantum hypothesis used to depict the observable world, and the overall hypothesis of relativity used to portray the universe, are hard to squeeze into a solitary structure. Nobody has figured out how to make the two numerically viable with regards to the SM. Yet, fortunately for particle physics, with regards to the microscopic size of particles, the impact of gravity is so feeble as to be irrelevant. Only when matter is in mass, at the size of the human body or trees for instance, does the impact of gravity

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rule. Thus, the SM actually functions admirably notwithstanding its hesitant exclusion of one of the major forces. Everything seems fine; however, it isn’t the ideal opportunity for physicists to quit just yet. Despite the fact that the SM is presently the best portrayal of the subatomic world, it doesn’t clarify the total picture. The hypothesis fuses just three of four crucial forces, discarding gravity. There are additionally significant inquiries that it doesn’t respond to questions like, for example, “What is dark matter?” or “What befell the antimatter after the huge explosion?;” “For what reason are there three quarks and leptons generations with such unique mass scales?” and that’s only the tip of the iceberg. To wrap things up is a molecule known as the Higgs boson, a fundamental part of the SM. On 4/07/2012, the CMS and ATLAS tests at CERN’s LHC recounted they had each observed another molecule in the mass space around 126 GeV. This molecule is reliable with the Higgs boson; however, it will take further work to decide if it is the Higgs boson anticipated by the SM. The Higgs boson, as proposed within the SM, is the least complex form of the BroutEnglert-Higgs module. Different forms of Higgs bosons are anticipated by different theories that go past the SM (Heckman, 2010). A year later on 8th October 2013, the physics Nobel prize was shared by Peter Higgs and François Englert “for the hypothetical disclosure of an instrument that adds to how we might interpret the beginning of mass of subatomic particles, and which as of late was affirmed through the revelation of the anticipated fundamental molecule, by the CMS and ATLAS tests at CERN’s LHC.” Thus, while the SM precisely defines the peculiarities within its space, it is as yet inadequate. Maybe it is just a piece of a greater picture that incorporates new particle physics concealed somewhere down in the subatomic world or in unknown parts of the universe. New data from tests at the LHC will assist with tracking down a greater amount of these missing parts.

3.4.2. Spontaneous Symmetry Breaking (SSB) To continue further, there’s need for addressing the riddle of vector boson masses. The W± µ vector bosons prompting the successful collaboration can comprise a mass of around 80 GeV. Then again, the gauge balance forestalls a mass span for the check vectors. The measure symmetry should then be in some way broken, for the gauge vectors to gain a mass. This should be possible through the element of unconstrained uniformity breaking.

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However, vector boson masses are not by any means the only issue. The SM fermions would likewise be compelled to be massless within the sight of a definite SU (2) L×U (1) Y balance. One can verify that no measure invariant fermion mass gauge can be composed, given the quantum computation (Graña and Herráez, 2021). The broadest mass term couples pair remaining provided fermions in a mix that, as every one of the terms in the Lagrangian, should be invariant within the measure symmetry. There are three potential forms of mass terms which can be developed: ψL, ψ ∗ RψL, ψ ∗ R. It is not difficult to determine that no such mix of left or right fermions can be measure invariant. This is because of the SM gauge balance being chiral in any event, when limited to a discretionary subset of fermions (Figure 3.4).

Figure 3.4. Comparison of broken and unbroken particle symmetry. Source: https://www.science.org/doi/10.1126/science.337.6100.1289.

Spontaneous breaching of the gauge equilibrium is then required to represent the SM range of vector bosons and fermions. Below is an outline the primary aspects of spontaneous symmetry breaking (SSB) of universal and gauge balances (Higgs model). Spontaneous symmetry breaking (SSB) is fascinating and exquisite in light of the fact that no express breaking of the balance is presented. The conditions of the elements are actually symmetric; however, they concede provisions that are not. Specifically, one has SSB whenever the ground condition of the structure isn’t symmetric. Thereafter, the actual framework “suddenly” breaks the balance. With regards to QFT, SSB is defined by a) the Lagrangian being invariant within the symmetry, b) the flows related to the balance being rationed, additionally at the quantum level, c) the vacuum (ground condition) of the hypothesis being not invariant within the balance, d) the range being not invariant. Its elements include 1) it permits for a reliable breaking of measure balances, specifically a steady

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quantization of large vectors; 2) it becomes acknowledged in nature both on account of international and gauge balances (Fraser, 2011). According to the perspective of physical science at the electroweak scale, the chiral design of the SM is a riddle. At the Planck scale, nonetheless, such design is welcome since it clarifies why the SM fermions are as light as for the Planck scale: they are kept from gaining a mass term until the electroweak balance is broken, at a much lower scale. One can push this debate a stride further and contend that this is the motivation behind why the SM fermions are completely chiral: since, supposing otherwise there would be not a really obvious explanation for why they ought not to be a lot heavier. Chiral fermions may simply be the only ones making due at low energy due to their chiral structure. In old style mechanics one can consider a ball compelled to slide on the symmetric (under pivots around the focal hub) surface subject to a gravitational field pointing downwards. The conditions of the elements are symmetric. The main issue, where the ball is in line, is likewise symmetric, yet temperamental. To remain in a steady ground express, the structure ought to maintain a situation at the lower part of the surface, accordingly immediately breaking the rotational balance. In quantum mechanics, one can think about a rotationally invariant arrangement of coupled twists (a ferromagnet). The base energy state is arrived at when the twists are adjusted. To remain in the ground state, in this way, the framework should have a typical course for the twists, hence unexpectedly breaking rotational invariance. In QFT, a subjective distinction emerges, as the quantity of levels of opportunity isn’t limited any longer and a quantum superposition of ruffian vacua isn’t permitted: different ground states are not depicted inside a similar Hilbert space.

3.5. STANDARD MODEL (SM) MATHEMATICAL CONCEPTS The present discussion is about SSB in QFT. We are intrigued by the spontaneous breaking of measure invariance; however, we want to examine the spontaneous breaking of universal balances first. Consider Ω as the ground condition of our QFT. SSB emerges if the vacuum conjecture value (vev) of the fields in the hypothesis, hφi ≡ hω|φ(x)|ωi, isn’t invariant (subsequently not disappearing) under the balance (hφi is invariant if Ω is). As we would rather not break Poincaré invariance, no one but scalars can get a non-evaporating vev and hφ(x) i doesn’t rely upon the space-

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time coordinate x (Francescon et al., 2013). Considering a Lagrangian, the worth of the vev of the scalar fields can be effortlessly acquired by limiting the viable scalar potential, for example the scalar potential including the supposed one-molecule unchangeable quantum revisions. It is generally expected plausible to disregard quantum revisions and simply consider the minimization of the old-style potential, which is how we will regard the following. A direct unequivocal illustration of SSB in QFT can be acquired in the hypothesis of a complicated scalar field φ with Lagrangian L = (∂µφ) † (∂ µφ) – V (φ †φ), V (φ †φ) = µ 2φ †φ + λ 2 (φ †φ) 2 (Fraser, 2011). The Lagrangian is symmetric under a worldwide U (1) change φ(x) → e –iαφ(x). The boundary λ should be non-negative for the prospect to be limited from beneath. Considering it’s completely positive. Alternatively, the parameter µ 2 can have double signs (in spite of being composed as a square to pressure and has the element of a squared mass). The state of the possible V and the design of the ground state significantly relies upon that sign. If µ 2 < 0, the base of the potential relates to hφi = veiθ, where v 2 = |µ 2 |/λ and θ parametrizes the place of φ in the circle with scale v of savage minima. The structure has a self-assertive value of θ, accordingly immediately breaking the U (1) constancy. Without any deficiency of over-simplification, we can expect θ = 0. Taking into account the state of the potential, it is helpful to parametrize the field as φ(x) = r(x) e ig(x), where g(x) parametrizes the “level headings” along which the potential is consistent. As V doesn’t rely upon g(x), the comparing genuine level of opportunity is massless and just has subordinate relations (Feroz et al., 2009). Such massless levels of opportunity generally emerge within the sight of SSB in QFT. They are designated “Goldstone” bosons. One can likewise utilize a direct parametrization of the Goldstone boson by growing φ(x) = v+φ 0 (x) = v+ (h(x) +iG(x))/√ 2. G(x) can be considered as the linearization of vg(x). As far as h and G, the potential is V = λ 8 (h 2 + G 2) 2 + λ √ 2 vh (h 2 + G 2) + |µ 2 |h 2 + const. We can likewise confirm that G is massless, though the actual level of prospect h obtains a mass relative to the balance breaking scale v and to its self-coupling, m2 h = 2|µ 2 | = 2λv2. The two boundaries µ 2, λ in the potential V can be exchanged for v and m2 h. The example above can be summed up to the case of a conventional ceaseless global balance group G and a nonexclusive scalar field content.

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As indicated by the Goldstone hypothesis each damaged generator in G/H is related to a free massless scalar (Goldstone boson), conveying a similar quantum figure as the generators. The prototypical illustration of precipitously broken global balance in QFT is the chiral balance of QCD with two quarks. In the cutoff wherein the overall quark masses concur the QCD Lagrangian (excluding electromagnetic collaborations) for u and d is invariant under autonomous unitary changes of the left and right parts of the u and d fields, relating to the balance bunch U(2)L ×U(2)R = SU(2)L ×U(1) L ×SU(2)R ×U(1)R. Call j µa L, j µ L, j µa R, j µ R the flows related to the four gathering factors. Then, at that point, j µ V = j µ R + j µ L is the saved current related to Baryon number and j µa A = j µa R + j µa L are the saved isospin. What might be said about the “hub” flows j µ An and j µa A? The first, j µ A, ends up being broken by quantum redresses. The relating balance is strange. The subsequent current, j µa A, ends up being rationed, consequently. Thusly, it either compares to an evenness or it is unexpectedly broken. We don’t have proof for j µa A to relate to a balance. In the event that it did, particles would sort out themselves in multiplets with same twist, Baryon integer, equality, and roughly (in reality mu 6= md, electromagnetic associations exist, and the chiral consistency SU (2) L × SU(2)R is just estimated) same mass, which isn’t easily noticed. Then again, in all actuality there’s proof for the balance to be unexpectedly broken (Farnsworth and Boyle, 2015). Assuming that is the situation, we ought to notice three light (not actually massless in reality) pseudo-Goldstone bosons with zero Baryon number, conversion, negative equality, and isospin 1, as the comparative broken generators. The lightest hadrons, the pions, have without a doubt a significant number of properties. They are in this way viewed as the pseudo-Goldstone bosons emerging on the grounds of spontaneous breaking SU (2) L x SU (2) V of the estimated chiral structure of the Lagrangian light quark QCD. We have talked about up until this point the spontaneous flouting of an international symmetry. We examine the case we are all the more openly keen on, the unconstrained breach of gauge invariance. The primary element of such a peculiarity is that the measure vector related to each damaged generator enjoys a longitudinal portion and a mass. The extra longitudinal level of opportunity is given by the Goldstone boson related to the incomplete generator, which becomes “consumed” by the vector. This is exactly what is required to define the massive vector boson found in nature, the W± and the Z, in a hypothetically predictable manner. To perceive how these functions, consider the perplexing

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scalar field again and promote the global U (1) balance to a check balance. The gauge hypothesis structure gives Lgauge = – 1 4 FµνF µν + (Dµφ) † (D µφ) –V (φ †φ) +gauge fixing, Dµ = ∂µ+igAµ. Breaking U (1) suddenly can be done by measuring µ 2 < 0. The complicated field fosters a vev hφi = v, as previously. Respectively, a mass span M2 = 2g 2 v 2 is created for the vector boson, relative to the balance breaking scale and to its (gauge) adding to φ, as should be visible from (Dµφ) † (Dµφ) = (∂µφ 0) † (∂ µφ 0) + M2AµAµ/2 +. The Goldstone boson becomes consumed by the vector boson, of which it turns into the longitudinal part. This should be open to parametrizing φ(x) as far as r(x) and g(x) are concerned, and by seeing that {φ(x) = r(x)e ig(x) Aµ(x) is identical to φ(x) = r(x) Aµ(x) – 1 g ∂µg(x), as the two arrangements are connected by a measure change. We can accordingly choose a “unitary” check in which the field φ(x) is genuine, as highlighted in the above equation, which can be perceived as the longitudinal part of Aµ(x). This can be summed up to the example of a traditional nonstop international symmetry group G including a nonexclusive scalar field content. In the overall case, as referenced, the measure vector related to each damaged generator gets a mass by absorbing the comparing Goldstone boson. This goes under the name of “Higgs” instrument (El Naschie, 2009). With regards to gauge theories, different from international balances, the Goldstone bosons don’t compare to actual scalar levels of opportunity. The scalar fields precipitously breaking the gauge evenness are known as Higgs fields. The function of the vev of the scalar range is then played by the condensate of a fermion bilinear that emerges progressively as a result of fresh strong relations. This is the way chiral balance breaking in QCD is believed to emerge. While it isn’t eluded that such dynamical balance breaking system assumes a part in the breach of the electroweak balance, such a prospect is currently disfavored.

3.6. THE SM HIGGS AND FLAVOR We are currently ready to consider the SM and review its unrestrained breaking. The presence of fermion including vector boson masses is proof that the SM measure invariance ought to be suddenly broken. We recognize that solid and electromagnetic alliances are not detached as, for instance, the electric charge is moderated and the photon weightless. Thusly, the SSB of the SM must save SU (3) c×U(1)em as a whole subgroup. To instantaneously break the SM, we ought to present a scalar field, the Higgs, fostering a vev

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and indicate its quantum numbers within the SM gauge set. Such quantum numbers are directed by the need of the fermions to get a mass term, as presently seen. Consider the electron mass term, which has the structure m (eReL + h.c.). When the left element eL is confined in the lepton doublet L that connection ought to begin from a SM invariant relation including the bilinear eRL (Dubois-Violette and Todorov, 2019). Presently, such a bilinear isn’t invariant within GSM. It changes as a doublet with Y = 1/2 within SU (2) L×U (1) Y (and is obviously invariant across SU (3) c). To that end the electron mass isn’t permitted by the gauge synchrony. Notwithstanding, eRL can be essential for a measure invariant renormalizable relation, including an extra field with fitting quantum numbers. The primary possibility is the Yukawa collaboration λeRLH∗ with an intricate dual scalar field H (expectedly taken as the field form showing up in the connection), the Higgs field. H is a doublet with Y = 1/2 under SU (2) L×U (1) Y and is a SU (3) c singlet. Its dual parts contract with the two parts in L. A mass term for the electron can now be produced assuming that H gets a vev, when the value of the vev is subbed to the field in the Yukawa configuration above. It just so happens; one Higgs doublet H leads the mass of each SM fermion. Such a Lagrangian is provided by – LY = λ E ijeiRLjH ∗ + λ D ijdiRQjH ∗ + λ U ijuiRQjH + h.c., whereby all the three SM families are incorporated through the family integers I, j = 1, 2, 3. As a result of this family unit, every one of the three Yukawa connections described above is a conventional 3 × 3 compound structure. When the Higgs receives a vev, all the SM fermions enjoy a mass corresponding to their Yukawa pairs. SU (2) and SU (3) constrictions have been perceived in the above equation. The SU(2) invariant extraction of the doublet lists of Q and H in the up-quark Yukawa communication is acquired through the 2 × 2 cross-symmetric tensor ab like QH = QaabHb (12 = 1). The Lagrangian LY is the beginning of the flavor system of the SM. It is a direct result of that Lagrangian that can be derived for instance from an electron on a muon. The Lagrangian gauge, notwithstanding, doesn’t have any impact between them (Dubbers and Schmidt, 2011). As in the SSB model with a solitary complex scalar field, we take λH > 0 and µ 2 < 0 to get a steady, symmetry breaching potential. This finishes the meaning of the SM. We consider the gauge set as in the equation; indicating the fermion and scalar substance; their quantum numbers under the SM measure set; additionally determining the broadest renormalizable

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symmetric Lagrangian for the above fields (the dynamic terms of the multitude of fermions + LY + LH). The gauge hypothesis meanwhile then, permits for the determination of the complete Lagrangian. Think about the Higgs Lagrangian, along with the remainder of the SM Lagrangian. The SM of Particle Physics in the base of its true capacity, the Higgs doublet fosters a vev. Without any deficiency of over-simplification, such a vev can be composed as hHi = (0 v), with v > 0 and v 2 = |µ 2 | λH ≈ (174 GeV)2. Some other types of the Higgs vev, indeed, have up to a SU (2) L×U (1) Y check change. The scale v ≈ 174 GeV is known as the electroweak constancy breaking scale, or electroweak scale. Since the Higgs doesn’t feel solid interactions, the last option is surely whole. Allow us subsequently to focus on the electroweak group SU (2)L×U(1)Y. Its conventional generator can be composed as T = aY + baTa, with a, ba genuine. While following up on the Higgs, Ta = σa/2 and Y = 1/2. Thusly ThHi = (v/2) (b1 – ib2, a – b3) T and the solid generators, for which ThHi = 0, are those for which b1 = b2 = 0 and a = b3. There is then just one (up to standardization) electroweak generator solid by the Higgs vev, given by T3 + Y = Q. The electric charge is complete, as desired (Dubois-Violette, 2016). Note that the last option can be considered as an expectation, as the Higgs quantum numbers, deciding the whole generators, were fixed by free contemplations (getting a mass for the electron). From the 4 generators of the electroweak set just one is whole, and that implies that 3 are detached. We consequently, anticipate that 3 vector bosons should gain a mass and 3 Higgs genuine level of opportunity (the Goldstones) to be consumed by them. Out of the 4 genuine (2 complex) Higgs levels of opportunity, just one then, relates to an actual scalar, the Higgs boson. To recognize the Goldstone (and in this way the physical) levels of prospect we can utilize an overall property of the Goldstone bosons: they compare to removals from the vev along the level bearings of the potential. We can move along the level bearings of the potential by performing GSM change (which leave the likely invariant) along a subjective arrangement of broken generators. From δhHi = iGaTahHi = (v/2)(iG1 + G2, –iG3) T we see that we can compose the Higgs doublet as far as the Goldstone parts G± = (G1 ∓ iG2)/√ 2, G0 = –G3 and the actual part h as H = iG+ v + h + iG0 √ 2 are concerned. Regarding the CP change under which H → H∗, h is even and the Goldstones are odd. We can compose the Higgs potential in the unitary check where the Goldstones are taken out from the Higgs fields and consolidated in the relating vector bosons as demonstrated: V (h) = V (H)G=0 = m2 h 2 h 2 + λH √ 2 vh3 + λH 8 h 4 + const (DeMille et al., 2017).

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Whereas the electroweak scale is renowned from the estimation of the Fermi steady GF, as can be seen, the Higgs mass (or identically the Higgs coupling) is right now an obscure boundary. We have nevertheless three unique requirements on it. The first is a hypothetical imperative: to keep away from a solid coupling system, the Higgs mass must be lighter than around a TeV. Assuming the Higgs mass was heavier than that, the hypothesis would turn out to be firmly relating before the Higgs could be created. This isn’t priori rejected. Nonetheless, keeping the hypothesis perturbative permits a quantitative extrapolation to higher energies. Additionally, there are requirements from accuracy tests on conventional impacts of strong relations at a range as low as a TeV. The beginning of a perturbative system should be visible as follows. One can figure the abundancy A(WLWL → WLWL) for the dispersing of the longitudinal part of the W boson. The last option are only the Goldstone bosons initially sitting in the Higgs doublet along with the actual Higgs boson whose mass we are attempting to force. The extension in fractional waves gives A = ∑ l alAl, where al are halfway wave amplitudes. The s-wave adequacy is limited by unitarity to be |a0| ≤ 1. If the actual Higgs isn’t considered, a tree level computation, including the measure boson self-couplings, gives a0 ∼ s/(16πv2), where s is the focal point of mass squared energy. The unitarity bound would then be soaked for s ≈ (1.2 TeV)2, except if such a negative conduct is dropped by the graphs including the exchange of a Higgs mass less than 1.2 TeV. Since we recognize that unitarity isn’t disregarded, the clear infringement should be because of the weakness of the tree level estimation, motioning thus an unequivocally collaborating system where higher request perturbative rectifications are pretty much as extensive as the lower request commitments. A more grounded, second limitation can be acquired by expecting that the SM holds and is steady and perturbative up to a scale Λ (Dolenec et al., 2017). This contention utilizes the model that the Higgs coupling λH, as every one of the couplings in the Lagrangian, relies upon the energy size of the cycle in which it is involved. Under the notion that the SM holds up to the scale Λ, the value of the Higgs coupling at any scale up to Λ can be determined as a component of the rating at the electroweak scale, for example of the Higgs mass. Incidentally, an excessively huge value of the Higgs mass would bring about a precarious raise of λH with the energy, prompting a Landau-post, for example a non-perturbative system, before the scale Λ, in this way going against the underlying theories. We get this way a maximum breaking point on the Higgs mass as an element of the scale Λ. Then again, a minimum value of the Higgs mass would make λH

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negative previously Λ, consequently bringing about a disproportion. The Higgs potential would indeed turn out to be profoundly negative for upsides of the Higgs field bigger than the scale at which λH becomes negative. The electroweak scale least wanted would in this manner be, best case scenario, metastable. This prompts a lower limit on the Higgs mass as a component of the scale Λ (Figure 3.5).

Figure 3.5. Subatomic particle disintegration contravenes the standard model of physics. Source: https://scitechdaily.com/subatomic-particle-disintegration-violatesthe-standard-model-of-physics-completely-unexpected/.

Justifications exist for why SM may not be a definitive hypothesis of everything—while the SM has been tried with extraordinary achievement, particularly in its gauge section, there are a couple of experimental tests that are not represented by the SM: the presence of dark matter, the baryon deviation of the universe and, to wrap things up, gravity itself. There are equally exploratory evidences that, albeit not going against the SM, address solid clue for material science past the SM: the impossible to miss design of the SM measure quantum numbers, and neutrino masses. The SM quantum numbers can be well perceived as far as excellent bound together speculations are concerned, which additionally lead to the fruitful, exact expectation of the solid coupling inside supersymmetric models. Neutrino masses can be fused in the SM through a viable collaboration of two lepton doublets and two Higgses. In any case, the presence of a viable, non-renormalizable cooperation addresses a solid clue for new physical science emerging at

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a higher scale (Calvo et al., 2016). There are then various hypothetical riddles that don’t address an obvious sign for new particle physics, however we would be extremely glad to understand as far as physical science past the SM: the obscurity of the electroweak scale contrasted with the Planck scale, family replication, the presence of minor Yukawa couplings and the exceptional example of fermion masses and mixings. At last, the SM has various hypothetical issues. The simplicity/unitarity issue, connected with the dependability of the Higgs mass regarding radiative amendments within the sight of another high size (of which we have something like an undeniable model: the Planck scale); the comparable (according to a QFT perspective) issue of the diminutiveness of the cosmological equilibrium. The strong CP-issue.

3.7. POSITRONIUM An optimal way to determine how we might interpret discrete balances is with positronium. Positronium is an electromagnetically bound condition of e+ e– that can decay to photons: e+ e– – → 2γ, 3γ,… It is bound together very much like the Hydrogen particle, then again, actually a positron is answerable for the limiting rather than a proton. The wave function is Φ = Ψ (r, θ, φ; µ) Ξ(s) = Ψ (r, θ, φ; µ) (ψe– ⊗ ψe+) where Ψ is the wavefunction of the Hydrogen particle, yet with low mass µ = 1 me + 1 me –1 = 1 2 me. Its energy levels will be given by the Bohr recipe En = –α 2mc2 4n2 for n = 1, 2, 3,… where α = e 2 4π~c ‘ 1,137 is a dimensionless amount called the fine-structure consistent. The wave function Ψ gives data about the relative spatial connection between any two particles no matter what their construction. The item Ξ(s) = (ψe+ ⊗ ψe–) is the twist a piece of the wave function, made out of the twists of the electron and positron. Since each of these are turn 1/2, they can consolidate to give an all-out twist of 0 or 1. Utilizing the Clebsch-Gordon tables ??, where Ξ(1, 1) = ψ ↑ e– ψ ↑ e+ Ξ(1, 0) = √ 1 2 ψ ↑ e– ψ ↓ e+ + ψ ↓ e– ψ ↑ e+ Ξ(1, –1) = ψ ↓ e– ψ ↓ e+ trio S = 1 ORTHOPOSITRONIUM (6.23) Ξ(0, 0) = 1 √ 2 ψ ↑ e– ψ ↓ e+ – ψ ↓ e– ψ ↑ e+ singlet S = 0 PARAPOSITRONIUM(6.24) Now review that chargeformation switches a twirl around (which I’ll compose as twist ↑) e– out of control ↑ e +. Thus, under C: C [ξ(1, 1)] = C h ψ ↑ e– ψ ↑ e+ I = ψ ↑ e+ ψ ↑ e– = –ψ ↑ e– ψ ↑ e+ = –ξ(1, 1) (6.25). It was once imagined that they didn’t exist, however research at the Sudbury Neutrino Observatory emphatically suggest that neutrinos have mass, and that implies that both left and righthanded neutrinos and antineutrinos exist (Capelle and Campo, 2013).

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A Dual-Body decay procedure is “easier” to consider than a 3-Body one – the stage space is bigger for decay into more modest quantities of objects – so we anticipate that PARA should rot quicker than ORTHO. Additionally, the amplitude for discharge of one photon is relative to the charge e electron. This implies that the likelihood for PARA to decay will be corresponding to |e 2 | 2 ∼ α 2. Since ORTHO decays by originating 3 photons rather than 2, its rot rate is expected to be more modest than PARA’s by an element of α. Positronium decay relies upon the electron and positron obliterating one another, a condition that can happen assuming they are in a similar spot simultaneously. Thus, the rot rate should be corresponding to |ψ (0)|, for example the square of the wave function at the beginning, which is the place where the electron and positron “crash.” From nuclear physics we observe that |ψ (0)| 2 = 1 πa3 = α 6 8πr3 e where a = 2re α2 is the Bohr range of the positronium molecule, and re = e 2 4πmc2 is the old-style electron span. The real hypothetical computations are] Γ (PARA → 2γ) = 4π} cr2 e |ψ (0)| 2 = mec 2 2 α 5 = 1.252 × 10–10s–1 = 8.00 (nsec)–1 (6.30) Γ (ORTHO → 3γ) = 2 9π π 2 – 9 mec 2α 6 = 1.374 × 10–7 s–1 = 7.21 (µsec)–1 for the decay of the ground states. The 2-photon and 3-photon decays are the prevailing cycles; decays into extra photons are higher-range correction. Until lately, more exact estimations created a riddle. While the congruity among hypothesis and examination for PARA was consistently looking great, there existed an inconsistency among hypothesis and investigation for ORTHO that was unexplained for quite a long time. Tests as recent as 1990 compared by no less than 6 standard deviations from the hypothetical estimation. This drove scholars to suggest that a wide range of extraordinary speculations that were some of the time rather odd expansions of the SM. These beliefs included axions, C-odd bosons, millicharged particles, low quantities of gamma beams, and surprisingly a hypothetical mirror universe. Positrons are engaged through two gaps of an aluminum pit onto a permeable silica film. The transmitted warm positronium decays in vacuum (Bass, 2020). Nonetheless, in May 2003, R.S. Vallery and fellow associates distributed a paper defining the consequences of a more cautious review on orthopositronium. They developed orthopositronium by launching a low-energy positron bar into a unique micron-dense nanoporous silica film; orthopositronium shaped starting from the slowed positrons as they caught

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electrons. Vallery and colleagues had the option to quantify what amount of time this required by recognizing the gamma beams after Discrete Symmetries damage in a scintillator. This perspective, overcame issues experienced in past trials to quantify decay rates, which at times estimated enthusiastic positronium damage on the detector cavity dividers. In the Vallery test, just positrons that demolished their bound electrons were distinguished. They estimated a lifetime for ORTHO in concurrence with the present QED computation that varied by just around 0.014% from the hypothetical value! The moral? At some point a basic clarification – for this situation, that something was off-base with the tests – is the correct one. For PARA there is the Pφ PARA = – (–1)’ Φ PARA where the principal minus sign is because of the contrary equality of the electron and positron, and the (–1)’ emerges from the equality of the spatial wave function. Since ground charge = 0, the last state for the two transmitted photons from PARA should have negative equality. In the rest casing of PARA, the 3-momenta of the photons should be ~k and –~k. The underlying state has no rakish force (J = 0). The last state wave function |γ1γ2i can rely upon the photon momenta and polarizations, and should likewise have J = 0 by rakish force protection. Accordingly, it should be a scalar capacity of the momenta and polarizations. Besides, since photons are bosons, we should have |γ1γ2i = + |γ2γ1i. Thus |γ1γ2i = An eˆ1 · eˆ2 + B (ˆe1 × eˆ2) · ˆk where An and B are scalar elements of the force and polarizations (Bellotti, 2011). The polarization point φ relates to a turn opposite to the page. In case one radiated photon displays a X-polarization, the other consistently shows a Y-polarization, i.e., the planes of their polarizations should be opposite to one another. This might be affirmed tentatively by using the element that Compton-dissipating cross segments for spellbound photons are fundamentally more noteworthy for dispersing into the plane at right points to the E-vector of the occurrence photon, i.e., 90° to the heading of polarization. The optical model of the dispersing material is the polarizing channel. The Klein-Nishina recipe shows the dispersing cross segment σ is relative to: σ = k k0 + k0 k – 2 sin2 θ cos2 φ. The CPT theorem is illustrated in Figure 3.6.

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Figure 3.6. The CPT theorem is determined by charge, parity, and time. Source: https://www.youtube.com/watch?v=tq7I74u93hI.

Strong and electromagnetic relations are seen to independently moderate C, P, and T and current hypotheses of these relations (QCD and QED) are developed so these balances are preserved. Weak relations, in any case, disregard C and P independently (Beringer et al., 2012). Parity infraction in β-decay was first witnessed by Wu et al. and has been observed directly in atomic reactions like 16O J P = 2– –→ 12C J P = 2+ +4He Γ = (1.0 ± 0.3) × 10–10s. Weak relations likewise contravene C-invariance: no left-sided antineutrinos have ever been noticed. Lastly, Kaon decays disregard both C and P.

CHAPTER

4

THEORIES BEYOND THE STANDARD MODEL OF ELEMENTARY PARTICLES

CONTENTS 4.1. Introduction ...................................................................................... 84 4.2. Grand Unified Theory ....................................................................... 87 4.3. Supersymmetry ................................................................................. 89 4.4. String Theory..................................................................................... 91 4.5. Preon Theory .................................................................................... 93 4.6. Technicolor ....................................................................................... 95 4.7. History of Elementary Particles .......................................................... 97 4.8. The Classical ERA ............................................................................. 99 4.9. History of the Photon Particle.......................................................... 100 4.10. History of the Mesons ................................................................... 101 4.11. The History of Antiparticles ........................................................... 102 4.12. The Evolution of Neutrinos ............................................................ 103 4.13. History of Strange Particles............................................................ 104 4.14. The Eightfold Method .................................................................... 105 4.15. History of Quark Model ................................................................ 107 4.16. The November Revolution ............................................................ 109 4.17. Intermediate Vector Bosons ........................................................... 110

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4.1. INTRODUCTION Elementary particles which are the tiniest building blocks of the universe have been discovered and studied. They are regarded by researchers as zerodimensional points with no spatial dimensions, and as a result, they lack any kind of internal organization. The standard model (SM) of physics, which describes particle interactions and almost all forces, recognizes a total of 10 elementary particles in its description of the universe. Electrons are probably the most well-known of these particles (Figure 4.1).

Figure 4.1. A list of elementary particles. Source: https://www.google.com/imgres?imgurl=https%3A%2F%2Fupl oad.wikimedia.org%2Fwikipedia%2Fcommons%2F0%2F00%2FStanda rd_Model_of_Elementary_Particles.svg&imgrefurl=https%3A%2F%2Fen. wikipedia.org%2Fwiki%2FElementary_particle&tbnid=zXyoAo_ YmoFxJM&vet=12ahUKEwj-kuDJ0Oj1AhXci_0HHTZ7DaEQM ygAegUIARDaAQ.i&docid=zlWp_8SU1451sM&w=1390&h=1 330&q=elementary%20particles&ved=2ahUKEwj-kuDJ0Oj1AhXci_0HHTZ7DaEQMygAegUIARDaAQ.

Atoms are made up of protons and neutrons that are positively charged. Even though electrons are considered to be zero-dimensional point particles, a cloud of other virtual particles constantly flits in and out of existence around them, acting as though they were a component of the electron itself. As a result of the electrons having both positive and negative poles, some theories predict that this cloud of virtual particles will be slightly asymmetrical (Abdelrahman and Sohaly, 2018).

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The behavior of electrons and positrons may be different if this is the case, which may shed light on a variety of mysteries surrounding the nature of matter and antimatter. Numerous measurements have been made to determine the shape of an electron, and each measurement has revealed that it is perfectly round, leaving physicists perplexed as to how the mysteries of antimatter can be resolved. The tau and muon are the heavier cousins of the electron. When highenergy cosmic rays collide with the top of the Earth’s atmosphere, they can produce muons as well as a shower of other particles such as electrons and neutrons. Muons are produced when high-energy cosmic rays collide with the top of the Earth’s atmosphere. Taus is even more difficult to obtain because they are 3,400 times heavier than electrons, making them even more difficult to obtain. There are four types of fundamental particles in the universe: neutrinos, electrons, taus, and positrons. The quark, which is the building block of protons and neutrons, is one of the most fundamental particles in the universe. Quarks and leptons are the fundamental building blocks of matter. A long time ago, scientists believed that atoms were the tiniest objects that could exist on the planet. They were completely wrong. In the early 20th century, it was discovered that protons and neutrons were the building blocks of atomic nuclei (Boyle and Farnsworth, 2014). Only in 1964 were some theoretical models proposed to explain the inner workings of protons, neutrons, and other members of the particle zoo, and these models were found to be insufficient. Quarks, which are small particles that exist inside protons and neutrons and are found in nuclei, are available in six different flavors. A proton is made up of two up quarks and one down quark, whereas a neutron is made up of two down quarks and one up quark. When it comes to quarks, up, and down quarks are the most common types to be found. Because our universe has a lot of up and down quarks, protons, and neutrons make up most of the matter we can see. In 1977, five of the six quarks had been isolated in the laboratory: the up, down, strange, charm, and bottom quarks. But it was not until 1995 that the sixth particle, the top quark, was identified. Similarly intense was the hunt for the Higgs boson, which followed shortly after it was discovered. Because the top quark is approximately 100 trillion times heavier than the up quark, it necessitates the expenditure of substantially more energy during its production in particle accelerators.

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Electricity, gravity, strong, and weak nuclear forces, and electromagnetic fields are the four fundamental tenets of nature. There is a fundamental particle linked to each one of these. The electromagnetic force (EMF) is carried by photons, which are the most well-known particles. The strong nuclear force is caused by the interactions between the gluons and quarks that make up protons and neutrons (Alexandre, 2011). The W and Z bosons are the two fundamental particles that convey the weak force, which is responsible for mediating various nuclear events. When physicists used neutrinos, which can only feel weak forces and gravity, they proved that these bosons were real (Figure 4.2).

Figure 4.2. The electromagnetic force in elementary particles. Source: https://www.google.com/imgres?imgurl=http%3A%2F%2Fabyss.uoregon.edu%2F~js%2Fimages%2Fvirtual_photons.gif&imgrefurl=http%3A% 2F%2Fabyss.uoregon.edu%2F~js%2Fast123%2Flectures%2Flec07.html&tbnid=ONPdm5PNc2AE5M&vet=12ahUKEwj2yM6B0ej1AhXG0OAKHQFgBw 4QMygBegUIARC9AQ.i&docid=YXHTm2hDkHNL2M&w=437&h=400&q= electromagenetic%20force%20in%20elementary%20particles&ved=2ahUKE wj2yM6B0ej1AhXG0OAKHQFgBw4QMygBegUIARC9AQ.

In this universe, gravity occupies an odd position relative to other forces. According to physicists who believe this is the case, it is believed to be related to a fundamental particle known as a graviton. Finally, there is the Higgs boson, which is considered to be the monarch of elementary particles and the source of mass for all other particles in existence. The quest for the Higgs boson was a huge undertaking for scientists who were striving to complete the SM of particle physics (Zimmermann, 2018).

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Even though the Higgs particle looks to be exactly what scientists predicted, they had hoped for something even more extraordinary. The SM is widely acknowledged to be insufficient; for example, it does not adequately describe gravity. Researchers believed that the discovery of the Higgs boson would hint at other ideas that could eventually replace the SM. They haven’t come across anything yet, however.

4.2. GRAND UNIFIED THEORY One of the three-gauge interactions from the SM can be combined into a single force in the Grand Unified Theory at extremely high energies, according to the theory’s description. This type of force is referred to as “electromagnetic, weak or powerful” (GUT). Despite the fact that no united force has been observed, several GUT models think that there is such a thing as a unified force. Three interactions could be combined, which would allow researchers to travel back in time to a time when these three fundamental interactions were not yet distinct from one another (Figure 4.3).

Figure 4.3. The grand unified theory. Source: https://www.google.com/imgres?imgurl=https%3A%2F%2Fuplo ad.wikimedia.org%2Fwikipedia%2Fcommons%2Fthumb%2F2%2F24%2 FGeorgi-Glashow_charges.svg%2F200px-Georgi-Glashow_charges.svg. png&imgrefurl=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FGrand_ Unified_Theory&tbnid=-Jk5ozlPYI6Z-M&vet=12ahUKEwjAkO-t0ej1AhWWgqQKHUhpD4wQMygAegUIARDIAQ.i&docid=e7mNVHJR4ulnVM&w=200 &h=200&q=grand%20unified%20theory&ved=2ahUKEwjAkO-t0ej1AhWWgqQKHUhpD4wQMygAegUIARDIAQ.

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Numerous studies have found that at extremely high energies, electromagnetic, and weak interactions combine to form a single electroweak interaction, which is supported by experimental evidence. According to conventional wisdom, the strong and electroweak interactions are thought to combine into a single electronuclear interaction at higher energies. It is possible to demonstrate this interaction with only a single coupling constant because it has a larger gauge symmetry and a greater number of force carriers. If gravity and the electron-nuclear interaction were to work together, it would be possible to develop a theory of everything (TOE). Due to their extremely large masses, it is unlikely that particle collider tests will be able to detect any of the new particles predicted by GUT models. Because the effects of grand unification cannot be observed directly, the effects of grand unification can be observed indirectly through phenomena such as proton decay, elementary particle dipole moments, and neutrino properties (Woithe et al., 2017). Even though GUTs are supposed to make the SM easier to understand, realistic models are still difficult to construct because they require more fields and interactions, as well as possibly even more space dimensions, to make sense of fermion masses and mixing angles. When it comes to family symmetries, the conventional GUT models may not be sufficient to determine what is going on. As a result, GUT theories have not been widely adopted as a result, as well as the fact that grand unification has not been demonstrated to be effective. The fact that electrons and protons appear to cancel each other out to a very high degree is not explained by the SM of particle physics, but this property of fundamental particles is critical for the existence of the macroscopic world. It should be noted that the SM only allows for a limited number of charges in its descriptions of both weak interactions and strong interactions. However, the weak hypercharge interaction, on the other hand, can be defined by an abelian symmetry that allows for an infinite number of charged particles to interact together. Using weak and strong interactions, it is possible to combine them to form a single grand unified interaction that can be described by a single larger simple symmetry group that encompasses the SM (Wood and Heyde, 2016). This is because all known elementary particles have electric charges that are exact multiples of one-third of the charge associated with the term “elementary.” It is possible to determine the quantized nature and values of all fundamental particle charges in this manner without having to think about it. It is preferable to use grand unification because it reduces the number of different input parameters required. As a

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result of its predictions of the relative strengths of fundamental interactions that have already been observed, such as the weak mixing angle, it is also limited by observation. Although there are many parallels between the theory of great unity and Maxwell’s theory of electromagnetic induction, their physical implications, and mathematical structures are vastly different. “Great unity” and “Maxwell’s theory of electromagnetic induction” are two terms that come to mind.

4.3. SUPERSYMMETRY In a supersymmetric theory, the equations for force and matter are the same, so they work in the same way. Any theories that have this kind of phenomenon are amenable to the concept of supersymmetry in theoretical and mathematical physics. There are several different supersymmetric theories. The same holds true for fermions and bosons. Asymmetry in space and time between these two types of particles is called “supersymmetry.” There is a particle in one class that is identical to or superior to a particle in the other class. If the electron is present, a basically related particle known as a “selectron” is also expected to be present in a supersymmetric theory (Wallace, 2011). This is a reasonable assumption to make. If supersymmetry were perfectly “unbroken,” every pair of “superpartners” would have the same mass and other quantum features. In the most fundamental supersymmetry concepts, this is how it would work. In more advanced supersymmetry theories, superpartners with different masses are possible (Figure 4.4).

Figure 4.4. Illustration of supersymmetry theory. Source: https://www.google.com/imgres?imgurl=https%3A%2F%2Fcdn. arstechnica.net%2Fwp-content%2Fuploads%2F2014%2F04%2F

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SM-SUSY-diagram.jpg&imgrefurl=https%3A%2F%2Farstechnica. com%2Fscience%2F2014%2F04%2Fa-sort-of-particle-free-supersymmetry-found-in-exotic-materials%2F&tbnid= YZ7QHYYbJqkQMM&vet= 12ahUKEwicwvrb0ej1AhVI1-AKHTJUB-0QMygAeg UIARC0AQ.i&docid= Tdh9dbM0i98JRM&w=640&h=391&q=supersymmetry%20theory%20 in%20elementary%20particles&ved=2ahUKEwicwvrb0ej1AhVI1-AKHTJUB0QMygAegUIARC0AQ.

Supersymmetry can be used in physics in a variety of ways, from quantum mechanics and statistical mechanics to quantum field theory, nuclear physics, optics, and stochastic dynamics. Astronomy can also profit from it. It can also be used in fields outside of physics, such as finance. A supersymmetric extension of the SM, which has been employed in highenergy physics, is also a viable option for physics beyond the SM. The supersymmetric extensions of the SM have not been proven to be correct. Because no particles in the SM may be superpartners, adding supersymmetry to the model necessitates three times the number of particles. The more particles there are, the newer interactions are possible. The Minimal Supersymmetric SM is the simplest supersymmetric model compatible with the SM, and it may include the extra particles required to be superpartners of those in the SM if they aren’t already there (Amsler et al., 2008). The Higgs boson’s quadratic mass renormalization cancels out in fermionic top quark loop-tadpole complexes. These diagrams are used in the SM’s supersymmetric extension. One of the first concepts proposed was the Minimal Supersymmetric SM. One of them was the question of hierarchy. There are four quadrupledivergent contributions in the traditional model. This demonstrates that the Higgs mass renormalization is vast and that this is the maximum scale that the Higgs mass can reach unless an unintended cancellation occurs. At the electroweak scale, large quantum corrections known as Planck-scale corrections are received at the same time. When examining the relationship between the electroweak and Planck scales, it’s vital to make sure you know what you’re looking at. The “hierarchy problem” is an example of a common issue. If supersymmetry was closer to the electroweak scale, the hierarchy problem in the SM could be solved, as it was in the Minimal Supersymmetric SM. Because fermionic Higgs interactions, like Planck-scale interactions, cancel each other out naturally, they require fewer quantum corrections

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to work. Natural hierarchies would form between the Planck size and the electroweak scale without the need for extensive fine-tuning. Weak interactions and gravitational interactions could have dramatically different sizes if supersymmetry is restored at a very low level. It’s possible that little, unobtrusive factors are to blame. At high energy, gauge symmetry groups are thought to be unified. For this reason, the Minimal Supersymmetric SM aims for grand unification. Using the SM is correct. Electromagnetic gauge couplings don’t come together at high energies, although weak and strong electromagnetic couplings do. As a result, the SM has been proven to be true. The three gauge coupling constants in the SM are extremely sensitive to the current particle composition of the renormalization group development (Viaux et al., 2013). They do not fit together with the same amount of energy when the renormalization group is undertaken using the SM. The gauge coupling constants are projected to converge after accounting for the fact that there is no SUSY at the electroweak scale. Furthermore, sprinting in a different direction to disturb radiative electroweak symmetry is a natural technique. Weakly interacting large particles have been hypothesized as possible candidates for dark matter in some supersymmetric extensions of the SM. This holds for the Minimal Supersymmetric SM as well as its supersymmetric extensions. It has to do with R-parity if there is a supersymmetric dark matter competitor. This amount of thermal remnants has been computed in order to back up the theory that dark matter particles could have created via electroweak supersymmetry. This is the way of introducing supersymmetry into a real-world theory that is most often employed. Because the ground state does not respect symmetry, it is disrupted by chance. Some people refer to this as the “mainstream paradigm.” In their current state, MSSM particles are unable to breach supersymmetry indefinitely. This cognitive difference can be traced back to a new school of thought. The only criterion for this new field is that it constantly breaks supersymmetry and produces super particles with masses on the order of a teraelectron volt. Many models can do so, and the majority of the variations between them are minimal.

4.4. STRING THEORY When it comes to particle physics, string theory claims that one-dimensional objects known as strings are superior to point-like particles. It’s fascinating to see how string theory depicts the movement of these strands through space

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and their interactions with one another. Normal particles’ mass, charge, and other properties are determined, in large part, by how quickly they move through the universe. This is true for distances that are greater than the length of a single piece of string (Volovik, 2015). In string theory, it is just one of the many different ways that the string can move. The graviton is a quantum particle that provides information about gravity to other particles. Quantum gravity is at the heart of string theory, and it is this that is being discussed here (Figure 4.5).

Figure 4.5. An illustration of the string theory. Source: https://www.google.com/imgres?imgurl=https%3A%2F%2Fwww. researchgate.net%2Fprofile%2FIgnatios-Antoniadis%2Fpublication%2F2 27330311%2Ffigure%2Ffig1%2FAS%3A302294965997568%4014490841 44275%2FIn-string-theory-the-elementary-constituent-of-matter-is-a-miniscule-string-having.png&imgrefurl=https%3A%2F%2Fwww.researchgate. net%2Ffigure%2FIn-string-theory-the-elementary-constituent-of-matter-is-aminiscule-string-having_fig1_227330311&tbnid=6DYoV_bOR8dwaM&vet= 12ahUKEwiZhIaI0uj1AhXIVMAKHfIpCxMQMygAegUIARC7AQ.i&docid=e ALvInpaL1DDKM&w=566&h=582&q=string%20theory%20in%20elementary%20particles&ved=2ahUKEwiZhIaI0uj1AhXIVMAKHfIpCxMQMygAeg UIARC7AQ.

String theory investigates a wide range of topics and attempts to resolve a wide range of fundamental physics problems. There has been significant progress in mathematical physics as a result of the application of string theory to problems in black holes, the early universe, nuclear physics, and

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condensed matter physics, among other areas. It has also had a significant impact on pure mathematics. As a strong contender for the title of “theory of everything,” string theory holds the promise of being able to mathematically describe all of the fundamental forces and types of matter that exist in the universe. The extent to which string theory explains reality and the amount of space we have to build our model are both unknown to us. When string theory was first proposed in the late 1960s and early 1970s, it was considered a strong nuclear force theory. However, quantum chromodynamics (QCD) was chosen as the new theory. As a result of its flaws, it was discovered that string theory was a good choice for quantum gravity because the flaws that made it bad for nuclear physics in the first place were the same flaws that made it bad for quantum gravity in the first place (Van Noorden, 2012). Bosons are present in the first form of string theory, which is known as bosonic string theory. As time went on, supersymmetry, which connects bosons and fermions, turned into superstring theory. All superstring theories were thought to be limited examples of the M-theory, which is a single theory in 11 dimensions. This was thought to be true before the mid-1990s. String theory is linked to a different kind of physical theory called a quantum field theory by the anti-de Sitter theory correspondence, which was found in late 1997. When it comes to string theory, one of the problems is that it can’t be set up in every case. Particle physics theories based on string theory have been slowed down by their ability to describe a wide range of possible universes, which has slowed them down. Because of these problems, some physicists aren’t sure how important it is to keep studying string theory unification.

4.5. PREON THEORY Point particles called preons are components of quarks and leptons. They are also part of other particles called preons. In 1974, Jogesh Pati and Abdus Salam came up with the idea. Interest in preon theories has dropped off since the 1980s, as the SM of particle physics still functions well and there is no clear proof that leptons and quarks are built out of each other. They contain plus, minus, 0 and minus, zero, and anti-zero. There are six more preons in W bosons than there are in quarks, but there are only three (Figure 4.6).

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Figure 4.6. A preon square which is part of the preon theory. Source: https://www.google.com/imgres?imgurl=https%3A%2F%2Fwww. researchgate.net%2Fprofile%2FAlfons-Buchmann%2Fpublication%2F235 453553%2Ffigure%2Ffig4%2FAS%3A807094408187906%401569437710 093%2FPreon-square-The-two-fundamental-preons-T-V-and-their-antiparticles-are-placed-at.png&imgrefurl=https%3A%2F%2Fwww.researchgate. net%2Ffigure%2FPreon-square-The-two-fundamental-preons-T-V-and-theirantiparticles-are-placed-at_fig4_235453553&tbnid=Gp0SKfREXFuhqM&v et=12ahUKEwje4v2h0uj1AhUXcxoKHTv5CsUQMygvegUIARCXAg.i&doc id=nMn-NEzj_ibROM&w=565&h=532&q=preon%20theory%20in%20elementary%20particles&ved=2ahUKEwje4v2h0uj1AhUXcxoKHTv5CsUQMyg vegUIARCXAg.

The SM thinks that some things in the hadronic region are intriguing. Some of them: In this chapter, we will speak about the proton spin conundrum, the EMC effect, and how the charge distributions of nucleons function. “Preon” was developed because quarks and leptons are both spin-half fermions, hence the name was used to characterize them. Preon models that feature spin-1 bosons are nevertheless called “preons.” In the preon theories, there are fewer fundamental particles than there are in the SM, and the rules that govern how those fundamental particles combine and interact are different from one model to the next. People that study the SM employ preon models, which try to explain the SM by forecasting modest modifications to it, as well as novel particles and events that don’t fit into the SM (Ünel and Sekmen, 2018).

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There are various reasons for studying preons. When you start with a number of particles, you can break them down into a smaller set of more basic particles, many of which merely have differing charges. A good example of why preon research is significant is that electrons and positrons are practically the same except for their charge. This is what motivates preon research. It is hoped that the process used to generate the Periodic Table can be employed again. It’s not straightforward to calculate how many particles have electric and color charges, or how many experimental input parameters are needed by the SM to explain these parameters. Alternatives to the Higgs field may need supersymmetry to solve some of the flaws in the Higgs field’s theory in order to explain the electroweak symmetry breach. In theory, supersymmetry is hard to explain. A way to think about neutrino oscillations and mass: Create and test novel concepts, like the idea that there could be candidates for cold dark matter.

4.6. TECHNICOLOR Because of the Technicolor physics hypotheses, the W and Z bosons have a greater amount of mass. Early Technicolor theories were based on the theory of QCD, which is the “color” theory of the strong nuclear force (Figure 4.7).

Figure 4.7. An illustration of the technicolor theory. Source: https://www.google.com/imgres?imgurl=https%3A%2F%2Fscx2 .b-cdn.net%2Fgfx%2Fnews%2Fhires%2F2011%2Ftestingtechn.jpg&im grefurl=https%3A%2F%2Fphys.org%2Fnews%2F2011-05-technicolor-

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The Study of Elementary Particles

physics.html&tbnid=UEo9-pOIK_nUwM&vet=12ahUKEwi8zM_S0uj1AhWkReUKHacbC6wQMygCegUIARC4AQ.i&docid=b7Bw1OewVMmtHM &w=1104&h=1018&q=technicolor%20theory%20in%20elementary%20 particles&ved=2ahUKEwi8zM_S0uj1AhWkReUKHacbC6wQMygCegUIARC4AQ.

Instead of using fundamental Higgs bosons to explain the results, technicolor models were employed to cause the W and Z bosons to have various masses at different moments by introducing new gauge interactions into the equation of state. At high energies, these interactions are asymptotically free. However, at lower energies, they must be extremely strong and difficult to break up in order to be asymptotically free (and hence unobservable). By employing a dynamical technique, we can get past the difficulty of the hierarchy that the SM has (Tluczykont et al., 2012). Following the discovery of the Higgs boson at the CERN particle accelerator in 2012, the original models were thrown out the window. According to current theory, it’s still feasible for a Higgs boson to be in a mixed state. It is necessary to use extra gauge interactions to “stretch” Technicolor or composite Higgs models in order to obtain the masses of quarks and leptons, but this is not an easy feat to accomplish. Because of restrictions on neutral current and precise electroweak measurements, extending the Technicolor was a challenging task to do. The situation was made even more complicated when employing QCD. When Higgs bosons appear in technicolor or other mixed-up forms, it is not yet apparent how particle dynamics will be extended to account for them. Research into gauge theories with strong interactions other than quantum mechanics is a significant component of Technicolor’s work, and these theories have the potential to help with some of these challenges. Walking “technicolor” is a very dynamic framework that nearly always behaves in the same way because it has an infrared fixed point that is just beyond the threshold for spontaneous chiral symmetry breaking (Shlomi et al., 2020). Walking Technicolor is a very dynamic framework that almost always behaves in the same manner. Non-perturbative lattice simulations are being utilized to determine whether or not walking is possible. If that’s the case, the results are consistent with precise electroweak measurements. The way it works is as follows: a particle known as the Higgs boson, discovered in experiments at the large hadron collider (LHC), is the particle

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that causes electroweak symmetry to be broken. If the Bardeen-Hill-Lindner theory is right, the Higgs boson might be a mixture of top and anti-top quarks, according to the researchers. When solving composite Higgs models, the top quark infrared fixed point is frequently employed as a solution. At really high energies, however, it is possible that new dynamics, such as topcolor, will be required. With the use of lattice gauge theory in conjunction with highly interacting technicolor theories, it is possible to examine walking and conformal dynamics from the ground up. In 2007, Catterall, and Sannino used lattice gauge theory to investigate SU gauge theories with two types of Dirac fermions in the symmetric form of the SU gauge theory. They discovered evidence of conformity, which was later corroborated by additional studies (Seshavatharam and Lakshminarayana, 2013). Year 2010 was a particularly fruitful year for SU gauge theory with fermions in the fundamental representation. Things aren’t as straightforward as they used to be. It is possible to build nontrivial infrared fixed points if there are 12 flavors, but not if there are just eight. As long as there are only eight tastes, there are no infrared fixed spots to worry about. There has been some disagreement about the outcomes of research that has used various types of lattice approaches; therefore, there is still some discussion. These concerns are being investigated by a number of research institutions to determine how they might impair precise electroweak measurements, which are extremely significant.

4.7. HISTORY OF ELEMENTARY PARTICLES The electron was discovered by J.J. Thomson in 1897, making it the first subatomic particle to be discovered. Thomson was the one who discovered it. After Ernest Rutherford discovered the nucleus of the atom in 1911, it was discovered that it was made up of only one proton. The procedure was as follows: In 1932, the neutron was discovered, making it the first particle ever discovered. All atoms are composed of protons and neutrons, with the exception of hydrogen. Protons and neutrons reside in the nucleus of the atom, which is surrounded by electrons in an orbit around the nucleus. As a result of the Big Bang, particles that had never before been observed by ordinary atoms began to develop (Figure 4.8).

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Figure 4.8. An illustration of a brief history of elementary particles. Source: https://maxmakukov.wordpress.com/2014/12/17/history-of-elementary-particles/

P. A. M. Dirac, who developed the relativistic quantum theory in 1928 and predicted the presence of the positron, which is the electron’s antithesis, predicted the existence of the positron in 1932. The neutrino was discovered in 1930 as a result of problems with beta decay, and the existence of the neutrino, in theory, was firmly proved by 1934. It was not discovered until 1956, however. In addition, the photon, which Einstein initially considered in 1905 as part of his quantum theory of the photoelectric effect, was among the items that were included in the list of objects that were added to it (Radovic et al., 2018). Scientists have discovered the next set of particles they require to better comprehend the strong interactions, also known as the strong nuclear force, that hold nucleons together in an atomic nucleus, allowing them to better grasp these interactions. Hideki Yukawa came up with the idea that nucleons might trade mesons in 1935, and the rest is history. An interaction force between nucleons that is analogous to how photons interact with other

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charged particles, such as how they do, is created in a similar way to how photons interact with other charged particles. The following year, muons or muons were discovered. They had the appropriate amount of mass to be referred to as such, and they were referred to as such. Although this was the case, the particle’s behavior did not correspond to that of its theoretical counterpart. Yukawa predicted that the pi meson, often known as the pion, would be discovered in 1947, and he was correct. The muon and the pion were discovered in cosmic rays at the beginning of their existence. The discovery of particles released by cosmic rays has led to further investigation. Scientists were first able to observe these fundamental particles in the 1950s as a result of collisions induced by a particle accelerator. There has been a lot of discussion on the subject of fundamental particle physics concerning how particle physics and cosmology interact with one another. Quarks and leptons that are known, for example, are typically split into three groups, with each group consisting of two quarks and two leptons. Academics have speculated about the possibility of more groups of component particles (Pitkänen, 2011). According to the results of these tests at the Stanford Linear Accelerator and CERN, there are only three types of elementary particles that have been discovered so far. As a result of this discovery, the theory that there can only be four families in the cosmos is supported. The history of elementary particles can be divided into different eras, based on the different types of elementary particles which were discovered in different eras.

4.8. THE CLASSICAL ERA As part of his investigation into cathode rays produced by heated filaments, Thomson made the discovery of the electron. Magnets, he realized, have the ability to deflect cathode rays. Although the electrons held an electric charge, he was able to determine that they were negatively charged based on the structure of the electrons. In order to determine the particle’s speed and charge/mass ratio, Thomson had to pass the particle through a series of crossing electric and magnetic fields. He then made adjustments to the field strength in order to achieve a net deflection of zero. Aspects of atoms that

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are heavier and more neutral than electrons are as follows: Thomson made the assumption that the electrons were suspended in a heavy, positively charged paste because electrons do not have a great deal of electrical charge. For his part, Rutherford’s renowned scattering experiment proved that the positive charge of an atom is concentrated in a small core (nucleus) located at the center of the atom. It was Niels Bohr who first proposed the electronproton model of hydrogen in 1914, and it has been in use since then (Pashkin and Leitenstorfer, 2014). Using this model, the electron revolves around the hydrogen nucleus much like a planet orbiting the sun. Many people believed that heavier atom nuclei were made up of two or more protons surrounded by the same number of electrons as the number of protons they contained. In contrast, the next heaviest element, despite the fact that it has the ability to carry two electrons, is four times heavier than hydrogen. In 1932, Chadwick discovered the neutron, which is the proton’s twin that is completely uncharged, whereas the proton is charged. The neutron is being used to combat the problem of excess weight. Because the helium nucleus already has two protons and two neutrons, this is the method that is employed.

4.9. HISTORY OF THE PHOTON PARTICLE While thinking about statistics in 1900, Plank recognized that presuming electromagnetic radiation is quantized will allow him to find a solution to his original difficulty. This enabled him to determine the black-body spectrum of electromagnetic radiation emitted by a heated object, which was previously unknown. The manner the radiation was released, he reasoned, was the explanation for the quantization of the radiation for reasons he didn’t understand. But Planck didn’t know why the radiation was quantized. Because quantum light provides energy to electrons, Einstein utilized Planck’s idea and his formula to demonstrate in 1905 that when electromagnetic radiation strikes a metal surface, electrons will dissipate because quantum light gives them energy. The wavelength of light that is dispersed by a particle that is not moving varies as a result of Compton’s experiment. We can observe in this scattering how the photon behaves both as a particle and as a wave at the same time, which is interesting (Figure 4.9).

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Figure 4.9. An image of a photon. Source: https://www.google.com/imgres?imgurl=https%3A%2F%2Fstat ic.wikia.nocookie.net%2Fgalnet%2Fimages%2Fc%2Fca%2FFruton.png %2Frevision%2Flatest%3Fcb%3D20150324024605&imgrefurl=https%3 A%2F%2Fgalnet.fandom.com%2Fwiki%2FPhoton&tbnid=u46XeDhXtAhrM&vet=12ahUKEwj11dKu0-j1AhXNEsAKHbrOAhQQMygDegUIARDD AQ.i&docid=rbwtt927GGJE0M&w=1748&h=1181&q=photon%20elementary%20particles&ved=2ahUKEwj11dKu0-j1AhXNEsAKHbrOAhQQMygDegUIARDDAQ.

4.10. HISTORY OF THE MESONS Because protons have a positive charge, they should be attracted to one another rather than remain in the same place. For this reason, scientists are discussing what is holding nuclei together at this particular moment in time (1934). A powerful force might be at work here; it’s entirely plausible. The short range and strong amplitude of the effect are created by a magnetic field that attracts protons and neutrons in the same way that a magnetic field attracts electrons in the same way that a magnetic field attracts electrons (Olive et al., 2014). According to Yukawa, the mass of an electron is approximately 300 times greater than the mass of a human being. It is referred to as a meson because its weight is in the middle between that of an electron and that of a proton. In 1937, two different groups independently discovered a particle that appeared strikingly similar to Yukawa’s. Some of the particle’s characteristics, such as its life period and mass, did not match Yukawa’s (Figure 4.10).

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Figure 4.10. An image of a meson particle. Source: https://www.google.com/imgres?imgurl=https%3A%2F%2Fupl oad.wikimedia.org%2Fwikipedia%2Fcommons%2Fthumb%2Fc%2Fc0 %2FMeson_nonet_-_spin_0.svg%2F1200px-Meson_nonet_-_spin_0.svg. png&imgrefurl=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FMeson&tb nid=4QapXbFZI8TbxM&vet=12ahUKEwjpo8PK0-j1AhXEjKQKHcVDBOIQMygAegUIARC3AQ.i&docid=lpqlUg0H7mLRrM&w=1200&h=865&q=me sons%20elementary%20particles&ved=2ahUKEwjpo8PK0-j1AhXEjKQKHcVDBOIQMygAegUIARC3AQ.

4.11. THE HISTORY OF ANTIPARTICLES In 1927, he developed the Dirac equation, which demonstrated the existence of a free electron with energy in a version of quantum physics known as relativistic quantum physics, or QQP. Dirac attempted everything he could think of, but his model was unable to provide any insight into the strange nature of negative energy. Anderson’s positron, which is an electron twin that is positively charged, was discovered in 1931 and named after Anderson. You can look at Feynman’s description of how to get rid of negative energy from a couple of different perspectives. We get the same result when we combine special relativity and quantum physics, which holds true for both matter and antimatter (Figure 4.11).

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Figure 4.11. An image of an antiparticle. Source: https://www.google.com/imgres?imgurl=https%3A%2F%2Fupload. wikimedia.org%2Fwikipedia%2Fcommons%2Fthumb%2Fc%2Fcd%2FPa rticles_and_antiparticles.svg%2F1200px-Particles_and_antiparticles.svg. png&imgrefurl=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FAntiparticle &tbnid=Pj-_5uh6_fOVUM&vet=12ahUKEwj62uLu0-j1AhUSQ8AKHTELDGMQMygAegUIARDAAQ.i&docid=opbjfZ2Vh4ta9M&w=1200&h=1178&q=a ntiparticles%20&ved=2ahUKEwj62uLu0-j1AhUSQ8AKHTELDGMQMygAegUIARDAAQ.

4.12. THE EVOLUTION OF NEUTRINOS To explain what happens to an atom when it is destroyed, let us first consider how the neutrino was discovered and how it solved a new difficulty for physicists. Beta decay occurs when there is a mismatch between the electron energy that is expected and the electron energy fluctuation that is actually observed throughout the decay process. Physicist Wolfgang Pauli hypothesized that the beta decay of an electron could produce a particle that is not electrically charged. Neutrinos are particles that do not contain any atoms but do have atoms on their surfaces (McKenzie, 2014). They are extremely difficult to detect since their charge is neutral and their mass is so small that it is nearly impossible to detect them. How can you tell the difference between a neutrino and an antineutrino that is produced during a reaction? In the same way that every particle has an antiparticle, the neutrino has an antineutrino, and every particle has an antiparticle. They were unable to locate one at this time. When the lepton number of one was established in 1953, it was discovered that the electron, muon, and neutrino were all

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particles with the same lepton number. On the other hand, the positron, positive muon, and antineutrino all have a lepton number of one, as does the neutrino. All of the other particles have an L value of zero, as do all of the others. We need to change how we talk. Observing the next reaction doesn’t demonstrate that there is another problem: this reaction doesn’t happen even when no conservation laws are breached! In spite of the fact that this reaction has been seen, what is the difference in this case? A new sort of neutrino, called a muon neutrino, has been found for the first time (Figure 4.12).

Figure 4.12. A neutrino as seen on the telescope. Source: https://www.google.com/imgres?imgurl=https%3A%2F%2Fcdn.mos. cms.futurecdn.net%2FTiGR9cagP5nwBtZ6obwFk6.jpeg&imgrefurl=https% 3A%2F%2Fwww.space.com%2Fpacific-ocean-neutrino-detector-p-one-conc ept&tbnid=CnOG8q7brEuPEM&vet=12ahUKEwjVooaK1Oj1AhVJ86QKH fUnDWgQMygDegUIARDYAQ.i&docid=UR9qThtqfxJeKM&w=2048&h=1272&q=neutrinos&ved=2ahUKEwjVooaK1Oj1AhVJ86QKHfUnDWgQMyg DegUIARDYAQ.

4.13. HISTORY OF STRANGE PARTICLES When Rochester and Butler looked at cosmic rays, they discovered that a Kaon particle was present, which confirmed their hypothesis. Powell went to see it in 1949. Positive baryons that are members of the baryon family and satisfy the baryon number conservation rule decay, which led to the discovery of lambda in 1950. The unusual particles were named after the newly discovered heavy baryons and mesons, which were responsible for their discovery. These particles are referred to as “strange particles” because they change at a very slow rate over time (Macklin et al., 2014). Strong interactions have a unique number associated with them known

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as the “strangeness number,” which is the same in both strong and weak interactions but not in between the two types of interactions. This is not the same number for both of them. To add to the bizarreness of the situation, they are referred to as “strange particles” (Figure 4.13).

Figure 4.13. An image listing some strange particles. Source: https://www.google.com/imgres?imgurl=https%3A%2F%2Fi mages.ctfassets.net%2Fvrrt8fsfwf0e%2F7fG3ATNHc44Oe62PGOk2h 0%2F46de4bb1970535917088b6f357b64275%2Fstrange_particles_1. svg&imgrefurl=https%3A%2F%2Fwww.chegg.com%2Flearn%2Fphysi cs%2Fintroduction-to-physics%2Fstrange-particles&tbnid=hxL6Wf61M iaw2M&vet=12ahUKEwi1i_K31Oj1AhVdg_0HHZ2ZBZcQMygBegUIA RDGAQ.i&docid=HH5d5fRM0fRlIM&w=367&h=497&q=strange%20 particles&ved=2ahUKEwi1i_K31Oj1AhVdg_0HHZ2ZBZcQMygBegUIARDG AQ.

4.14. THE EIGHTFOLD METHOD The eightfold technique was used to classify baryons and mesons into groups based on their charge and strangeness, with the charge being the most important factor. It is composed of the eight lightest baryons arranged in a hexagonal pattern with two particles at the center of the structure. In addition, there is an ameson octet that is present as well. Particles with the same charge are clustered together in the diagonal lines that descend,

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and particles with the same strangeness number are clustered together in the vertical lines. Other particle groups can be represented in a number of different ways. Gell-Mann anticipated that particles would be present in these vacant spaces. We discovered the eight-fold predicted particles, which filled up the gaps left by the other particles. The eightfold method is used by physicists to predict how the missing particle will act (Figure 4.14).

Figure 4.14. An image showing the Eightfold method. Source: https://www.google.com/imgres?imgurl=https%3A%2F%2Fupload. wikimedia.org%2Fwikipedia%2Fcommons%2F3%2F3a%2FMeson_octet. png&imgrefurl=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FEightfold_ way_(physics)&tbnid=YynLgsJBb_QEHM&vet=12ahUKEwir2rrU1Oj1AhW JCsAKHaWVBT4QMygAegUIARC2AQ.i&docid=7H39IwyeExsP2M&w=64 7&h=461&q=the%20eighfold%20method&ved=2ahUKEwir2rrU1Oj1AhW JCsAKHaWVBT4QMygAegUIARC2AQ.

It was necessary for these particles to fit inside the decuplet, and then something truly incredible occurred. This is exactly what occurred. Only nine out of the 10 particles have ever been observed in the lab prior to this discovery. Prior to this discovery, no other particle with the same characteristics had ever been observed in a laboratory environment before. In fact, Gell-Mann predicted that such a particle would exist and provided the scientists with the procedures they needed to follow in order to create one. In 1964, Gell-Mann anticipated that the omega-minus particle would be discovered, and he calculated the particle’s mass at the time (Lyons, 2012). Because of the finding of the omega-minus, no one has given any thought to whether the Eightfold Way was genuine or wrong. Every hadron discovered during the next decade was found in one of these supermultiplets. Another sort of baryon is available if you wish to experiment with something

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else. It is called an “antibaryon” and has the opposite charge and strangeness of the baryons. With mesons, the antiparticles are located in the same supermultiplet as the particles, but they are in the opposite direction of each other in the supermultiplet. It makes sense that both words are used in the same way because the antiparticle of the pi-plus and the antiparticle of the pi-minus are the same thing. Some believe that the Eightfold Way marked the beginning of particle physics in the modern age, although not everyone is convinced of this.

4.15. HISTORY OF QUARK MODEL According to Gell-Mann and Zweig, all quarks are composed of more fundamental constituents. It is possible to categorize quarks into three categories. It is composed of quarks and antiquarks that are organized into an eight-fold triangle pattern. In the quark model, each meson and baryon are made up of two constituents: quarks and leptons. The first is referred to as a quark, and the second is referred to as an antiquark. The Pauli Exclusion Principle is not followed by a particle composed of three identical particles at this point, which brings us to our final conclusion (Figure 4.15).

Figure 4.15. Illustration of the quark model. Source: https://www.google.com/imgres?imgurl=https%3A%2F%2Fmedia. springernature.com%2Foriginal%2Fspringer-static%2Fimage%2Fchp%25 3A10.1007%252F978-3-319-92195-2_4%2FMediaObjects%2F462053_1_ En_4_Figa_HTML.png&imgrefurl=https%3A%2F%2Flink.springer. com%2Fchapter%2F10.1007%2F978-3-319-92195-2_4&tbnid=5CDkJyVME EU0DM&vet=12ahUKEwiy2oX11Oj1AhXCtCoKHX0JBoYQMygBegUIARD

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WAQ.i&docid=yfrbZyhyK9MQPM&w=705&h=628&q=quark%20model&ve d=2ahUKEwiy2oX11Oj1AhXCtCoKHX0JBoYQMygBegUIARDWAQ.

In 1964, the physicist Greenberg proposed the theory that each quark has its own color. This indicated that the three quarks were not identical to one another. It is not a color, but rather a representation of another property, such as charge or strangeness. This isn’t a hue in and of itself, but rather a symbolic representation of something. A single quark is not possible in this situation, but we can obtain a colorless mixture of quarks. Every one of the eightfold ways supermultiplets occurs by chance in the quark model, which is based on the reality of quantum mechanics. They all have the same quark combination: delta-plus and proton both have two u’s and two d’s; pi-plus and rho-plus both have two u’s and two d’s; and so on. It is similar to how multiple energy levels exist within the hydrogen atom and how a group of quarks can be bound in a variety of different ways. Among the many differences between the electron/proton system and the quark, system is that the latter has several different energy levels that are separated by a considerable distance, whereas the former has just one. Most of the time, we think of them as independent particles (Long et al., 2021). Atom/proton systems, on the other hand, have many energy levels that are close to each other, and we think of them all as hydrogen since they are all at the same energy level. We could create an infinite number of hadrons with only three quarks and no other elements. The quark model, on the other hand, restricts your ability to accomplish certain things. It has been a long time since these “exotic” particles have been the topic of extensive investigation. In the event that they are discovered, it would be disastrous for the quark hypothesis. No matter how hard people have tried, they have been unable to locate a single quark. It is possible that the quarks might erupt if you struck the proton hard enough if it were composed of three quarks. In a basic Millikan oil drop experiment, you would be able to tell them apart because they would have the obvious mark of a fractional charge on their bodies, which would make them easy to distinguish. Quarks should be incredibly simple to create, recognize, and store, but no one has ever discovered one that meets these criteria. Many scientists were skeptical of the quark idea after investigations in the late 1960s and early 1970s revealed that they were unable to produce isolated quarks in the laboratory. Those who were under the impression that

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quark confinement was true attempted to conceal their disappointment by claiming that quarks were trapped in baryons and mesons. Even though they tried, they were unable to extricate themselves from the situation. First and foremost, this does not provide an explanation for our dissatisfaction. The fact that quarks can be investigated even when they are contained within a hadron is a key point that hasn’t gotten nearly enough attention so far. Rutherford experimented with firing items into the center of an atom while researching the inner workings of the atom. The proton can be used in the same way as the neutron can be used. The Stanford Linear Accelerator Center conducted these kinds of experiments in the early 1960s with the help of a high-energy electron generated by the facility (SLAC). It was in the early 1970s when neutrino beams and protons were utilized at CERN to simulate the appearance of the neutrinos that had been discovered in the early 1970s (Liu et al., 2017). When anything is introduced, the vast majority of it passes through without a hitch, but a few of them bounce back forcefully. Deep inelastic scattering tests turned out to be extremely comparable to Rutherford’s findings, which was a pleasant surprise. According to these findings, the proton’s positive charge appears to be concentrated in the nucleus, similar to what Rutherford discovered when he investigated how an atom was constructed. However, the proton appears to be composed of three lumps rather than a single one, as opposed to the neutron. Those who believe in the quark hypothesis will be pleased with this development, but it will not be enough to make them happy on its own. Finally, a theoretical difficulty with the quark model was raised: it appears to violate the Pauli Exclusion Principle, which is a fundamental property of quantum mechanics. When Pauli initially proposed the exclusion principle, he came up with the idea of excluding two electrons from the same quantum state. This is the idea behind the exclusion principle.

4.16. THE NOVEMBER REVOLUTION In 1974, a mysterious psi meson was discovered. It has a huge mass in comparison to the rest of its group and lives for a longer period of time than other hadrons in its mass range. After much deliberation, the date for the “November revolution,” or the finding of the psi meson, has finally been agreed upon by all parties involved. It took some time for Glashow and Bjorken to realize that there were only four leptons and three quarks in the universe. As you may have heard, there was a revolution in November. At this point, it became possible to complete

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the quark model. After the discovery of new leptons in 1975, the symmetry between leptons and quarks was broken, resulting in the discovery of new quarks. Due to the presence of a neutrino in tau, there are now six leptons. It is true that mesons and baryons are created out of quarks if all of them are present in the universe. In the following years, Glashow, Iliopoulos, and Maiani came up with the concept of a fourth quark. However, the idea that quarks and leptons are the same is one of those ludicrous theories that turned out to be truer than its inventors could have expected when they first proposed it (Abdelrahman and Sohaly, 2018). As a result, when the particle was discovered, quark theory was doomed. This is the reason why. This response had a wide range of ramifications. As a result, if there is more than one quark, additional baryons and mesons of different sorts should be created. Glashow’s symmetry was shattered in 1975 when a new lepton was discovered and named after him. It is due to the discovery of the tau neutrino that we now have six leptons and four quarks, rather than the original three leptons and one quark. There was also a new heavy meson discovered two years later, and it contained a fifth quark because it was “beautiful,” according to the researchers. Soon after, the search for hadrons that exhibit “naked beauty” began. People didn’t trust the quark model at first, and its folly serves as a constant reminder of that. The fact that Glashow had six quarks and six leptons meant that it didn’t take a genius to figure out that a sixth quark would be discovered in the near future. The top quark, on the other hand, was extremely heavy and difficult to come by. There was no high-energy electron–positron colliders available at the time, and we now know that the top quark does not have enough time to interact with other quarks to create bound states. With the help of evidence gathered by the Tevatron the year before, the existence of the top quark was proven beyond a reasonable doubt in 1995, putting an end to speculation.

4.17. INTERMEDIATE VECTOR BOSONS

Physicists couldn’t apply the same method that Yukawa used to find out how far the weak force could travel and how heavy its mediator was since the weak force and its mediator were not the same thing. They couldn’t do this since the weak force doesn’t have a bound state like the nucleus, so they couldn’t. Glashow-electroweak specifically, according to Weinberg’s hypothesis, there will be three intermediate vector bosons, two of which

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will have a charge on them and one of which will have no charge at all (Leader, 2016). The mass of bosons was discovered at CERN in 1983 to be approximately 100 times greater than the mass of a proton (Figure 4.16).

Figure 4.16. Illustration of the intermediate vector boson. Source: https://www.google.com/imgres?imgurl=https%3A%2F%2Ffisi ca.usac.edu.gt%2Fpublic%2Fcurccaf_proc%2Fgarcia%2Fimg293.gif& imgrefurl=https%3A%2F%2Ffisica.usac.edu.gt%2Fpublic%2Fcurccaf_ proc%2Fgarcia%2Fnode12.html&tbnid=S6ecJWyRxrR8pM&vet=12ah UKEwi1m_em1ej1AhUnx4sKHVymBSoQMygBegUIARC5AQ.i&docid =5Zv8NyzCtDyAUM&w=460&h=287&q=intermediate%20vector%20 bosons&ved=2ahUKEwi1m_em1ej1AhUnx4sKHVymBSoQMygBegUIARC5AQ.

The model that has been used in the past is leptons, quarks, and mediators are described as the three sorts of particles that make up matter in accordance with conventional theory. A mature theory should be capable of explaining the values of the SM, just as we are able to do for the elements of the Periodic Table. The values of the SM are just the outcomes of tests. It is impossible to have more than 20 arbitrary parameters in a “final” theory, and the SM has nearly 20 of them. For electroweak mixing, it takes into consideration three angles and a phase in the Kobayashi–Maskawa matrix, the same number of leptons, and the Weinberg angle. It makes no difference if we still don’t understand how the SM works in its entirety. The absence of the Higgs particle is the most obvious issue that the SM fails to account for. With each new hunt for the Higgs particle that has yet to be discovered, the expected mass of the particle has increased. Since the cancellation of the SSC, the LHC has become our greatest hope for discovering this difficultto-find particle, which is probably too powerful for any other accelerator to detect. Between now and then, there exists a plethora of theories that go beyond the SM but are not supported by empirical evidence. The grand unified theories (GUTs), which connect strong, electromagnetic, and weak interactions, are commonly regarded as the most effective way to think about

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them in terms of their connections. Supersymmetry, which would connect each fermion with a boson and the other way around, would result in twice as many particles as there are currently in existence. These connections would be made by the “sleptons” and the twins of the mediators, which would be made by the leptons and quarks. If subquarks or supersymmetric particles are discovered in the future, the fundamental laws of basic particle physics will be altered. This will pave the way for a new era of exploration and discovery. However, except for a few erroneous alerts, there has been no evidence of either of these (Lasserre, 2014). The Superstring theory, which was first postulated in 1984 and has since attracted the attention of particle physicists as well, another way of putting it is that superstrings not only make it possible to reconcile quantum mechanics and general relativity, but they also make it feasible to develop an all-encompassing unified theory of everything (TOE) from which the entire field of particle physics would flow naturally. Despite having had a happy and adventurous upbringing, the field of string theory has yet to achieve all of its major objectives and objectives.

4.17.1. Leptons It possesses a distinct charge, electron number, muon number, and tau number, all of which are unique. They begin by creating six antileptons from the six leptons, after which they divide into two groups.

4.17.2. Quarks Quarks are classified into six categories. Each one carries a distinct charge and a peculiar weirdness about it. There are six antiquarks for every six leptons, which is the same as the number of leptons.

4.17.3. Mediators In the interaction of two things, photons, Wand Zbosons, and gravitons all have a role in what is happening between them. How do hadrons and quarks engage in violent conflict with one another? Who is the person who lends a helping hand in this quark-quark exchange? In this scenario, there are eight gluons acting as mediators, and the gluons themselves are colored to distinguish them from one another. Gluons and quarks should not be considered different entities from one another.

CHAPTER

5

PARTICLE INTERACTION IN ELEMENTARY PARTICLES

CONTENTS 5.1. Fundamental Interaction ................................................................. 118 5.2. Strong Nuclear Force ...................................................................... 119 5.3. The Electromagnetic Force (EMF) .................................................... 123 5.4. The Weak Nuclear Force ................................................................. 129 5.5. Gravitational Force ......................................................................... 133 5.6. Hadron Interactions ........................................................................ 136 5.7. Mesonic Interactions....................................................................... 139

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Particle interaction in elementary particles describes the physics of particle collisions and illustrates how the particles can interact with each other. Relating to attraction and repulsion, bonding, and clustering, it shows how they spread out over distance to form a potential in which new interactions can occur. While this chapter will be useful to those new to the physics of elementary particles and beam interaction, it assumes some familiarity with elementary particle physics and accelerator physics (Kibble, 2015). Particle physics is the study of the fundamental laws of nature governing the structure of matter and energy. Elementary particles are theorized to be the most basic units of existence from which matter is formed. It is the fascinating interactions between particles, such as those between an electron and a positron, or between quarks. In particular, it deals with the interaction of fermions with gauge bosons and with one another, or with other types of particles such as quark-antiquark (Figure 5.1).

Figure 5.1. A diagrammatic illustration on particle interaction in elementary particles via the sub-=atomic components. Source: Image by Wikimedia Commons.

In particular, it deals with the interaction of fermions with gauge bosons and with one another, or with other types of particles such as quarkantiquark. The motivation behind this study is the fact that most of the experimental results in particle physics are obtained from measuring the events in which a particle interacts with another particle. To understand the phenomenon better, it is necessary that we study the basic elements of such an interaction, namely the scattering and absorption processes. This book presents an introduction to the interactions of hadrons, leptons, and mesons. The elementary particles or fundamental particles are the constituents of all matter. They are classified according to their spin as fermions, which obey the

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Fermi–Dirac statistics and bosons that obey Bose–Einstein statistics. In the past 25 years, we have witnessed tremendous progress in our understanding of the weak, electromagnetic, and strong interactions (Kohls and Mele, 2018). Combining results from many different experiments performed over this period has led to a remarkably detailed and consistent theory, known as the SM of particle physics. Despite its success, it is not complete, as it does not include gravitation or predict why neutrinos are so light. In this context, there is a major interest worldwide in developing new theories seeking to go beyond the SM (Figure 5.2).

Figure 5.2. The difference between fermions and bosons can be illustrated by the elementary table regarding leptons and quarks. Source: Image by Forbes.

Basic interaction of elementary particles is described by means of effective operator theory. Particles exchange virtual particles. Virtual particle is described as an alternative solution to the mathematical equation – Poisson equation. There is a full range of particle interaction in the postNewtonian regime. The approach is twofold: the description and estimation of the underlying microscopic physics is given first, followed by the derivation of a macroscopic theory. Particle interactions are at the core of particle physics, and a glimpse into this fascinating field can be gleaned by observing the tracks that individual particles leave in our silicon detectors.

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Many interesting experiments have served as milestones in the study of this fundamental topic, such as Rutherford’s gold foil experiment—which established the existence of the nucleus—and Chadwick’s neutron source— which revealed the existence of neutrons and marked the beginning of nuclear physics studies (Kahle et al., 2016). Elementary particles, such as quarks and gluons, have always been the stuff of theory and conjecture. But the launch of the relativistic heavy ion collider (RHIC) brought experimentalists a frontrow seat at one of the most interesting laboratories in the Universe. This chapter describes in clear terms the nature of particle interactions—with an emphasis on matter-antimatter annihilation and quantum chromodynamics (QCD)—and highlights their implications for future collider studies and for cold atomic systems, respectively. Elementary Particle Physics Studies the fundamental constituents of everyday objects using experimental and theoretical tools: The force carriers are said to be the elementary particles. They are basic building blocks of the known matter in all its various forms. Elementary particles represent contemporary physics, showing deep connections among diverse areas such as gravity, quantum field theory and string theory. This thesis investigates the elastic and inelastic scatterings of elementary particles using the framework of QCD. The QCD production cross-section for 7 TeV pp collisions at sqrt(s)=8 TeV is measured using di-hadron correlations. Two sets of data corresponding to production times lower than 7 ns and ranges between 5 fm and 1.1 fm were collected at LHCb. Differential cross section measurements are performed for various observables within the invariant mass windows from 60 GeV/c–115 GeV/c. Particle interaction will in this case focuses on how these vertices interact and behave amongst each other. The study can be quite difficult to comprehend at times because it requires an advanced knowledge of mathematics and general physics. However, through thorough research one may be able to comprehend the relationship between the atoms according to their mass, velocity, and energy, as well as their total angular momentum as described by angular momentum coupling (Figure 5.3).

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Figure 5.3. The QCD framework for Production and reaction processes. Source: Image by ResearchGate.

This chapter deals with the particular phenomenology of hadrons and mesons and the electromagnetic force (EMF). This chapter proceed from short-distance, or weak, interactions to long-distance, or strong, interactions – with discussions of both gauge theory and quantum electrodynamics (QED). Being the smallest known structures of the universe, this chapter describes the general principles of interaction, and the phenomenological formulas that determine the interaction rate of particles (electrons, protons, neutrons, photons… etc.). It combines elementary, physical insights with the basic theories of quantum field theory and statistical mechanics which are necessary for explaining statistical phenomena in the interactions of elementary particles. In that sense it considers all aspects of elementary particle physics in a unified framework (Alexandre, 2011). Elementary particles undergo a plethora of interactions, including scattering, absorption, and emission. In many cases, the elementary particles involved are identified by the types of force fields through which they travel. Inspired by data from the ZEUS experiment at HERA, we used event-byevent simulation to study particle in mixed final states through $x^+Jpsi$ scattering. Energy and momentum conservation as well as diagrams up to next-to-next leading order were incorporated into a likelihood analysis framework that identified $(\rm{d}\overline{\rm{s}})$ mesons most suppressed in any kinematic variable by measurement. The particle

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interaction between elementary elements can be identified as fundamental interaction.

5.1. FUNDAMENTAL INTERACTION Fundamental interactions—the forces of nature governing the particles that make up you and everything in your environment—are irreducible. Fundamentally, they do not need to be explained further. That is, they lack factors that account for their existence as a whole. The four forces (gravitational, electromagnetic, weak nuclear forces, and strong nuclear forces) simply are. Our quest to understand the fundamental physics of nature has revealed a rich collection of physical phenomena to explore with sophisticated experiments that probe smaller and smaller distances and stronger fields. It has been a spectacular journey so far. Fundamental interactions are physical forces that act between elementary particles and are responsible for most of the physical phenomena we experience in our daily lives. For example, when a magnet is placed on a metal surface, or two magnets attract or repel each other due to their magnetic charges, several fundamental interactions are involved. Perhaps the best-known example is visible light, which is actually a form of electromagnetic radiation. Electromagnetism is one of four fundamental interactions in nature; others include the strong and weak nuclear force and gravity. The fourth primary interaction is the weak interaction. The three fundamental forces are sometimes described as the “constituents” of all matter, since these forces are thought to be the causes for all other forces that can be measured (Jaeckel and Ringwald, 2010). Fundamental Interactions provide the force through which elementary particles interact. The different types of fundamental interactions explain the behavior of forces between ordinary objects, such as a proton and an electron into a hydrogen atom or the attraction of a magnet for steel. Based on a core of curved steel wire, Fundamental interaction recalls the fabric of a magnetic field connecting two poles. The expressive form is inspired by the mathematical equation used to describe this fundamental physical force, and is made to hang vertically as a solitary object or grouped with other Madsen wall objects. These basic interactions cannot be described in terms of other simpler interactions. Fundamentally, they represent the different operations or actions that a quantum field can perform. An example is the strong interaction that binds together quarks to form hadrons (baryons and mesons). These four forces (the strong, weak, electromagnetic, and gravitational forces) appear to be very different in their manifestations in daily life and most easily observed on Earth. However, at high energies all

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four forces become essentially two forces: one electromagnetic (of which visible light is a manifestation), and one nuclear—strong force. These interactions do not appear to be reducible to more basic interactions. Currently, as stated above, the best known and most familiar of these fundamental interactions are the EMF, between electrically charged particles such as the proton, neutron, electron, and photon; the strong interaction, between two quarks or gluons; and the weak interaction, between a quark, an antiquark, and a W boson. All other interactions are considered to be due to either one or a combination of these forces. This chapter will survey the fundamental interactions of nature-with emphasis on both their physical characteristics and their rich mathematical structures (Ishimori et al., 2010). The chapter also explores topics in both particle physics and condensed matter (solid state) physics that illuminate topics related to the fundamental interactions. Physics determines that particle interaction in elementary particles can be expressed in four fundamental forces. These forces in order of decreasing strength include: • • • •

Strong nuclear force; Electromagnetic force; Weak nuclear force; Gravitational force.

5.2. STRONG NUCLEAR FORCE The strong nuclear force is the strongest force operating between particles in the universe. It binds together atomic nuclei at the heart of all the planets and stars and holds atoms themselves together, accounting for their characteristic rigidity. It is responsible for binding protons and neutrons (collectively known as nucleons) together into atomic nuclei. The strong force inherently has a very short range, but can become stronger with increasing distance due to zero-range. The strong nuclear force (also called the strong force or nuclear strong force) is the mechanism by which subatomic particles called hadrons that make up nuclei can remain together against the repulsive jostling of their constituent protons. It is the strongest of the four fundamental forces of nature, with a strength of about 1,038 times that of electromagnetism and 100,642 times that of gravitation. The strong interaction is observable at two ranges, on a larger scale (over about 2–3 femtometers) as a force between nucleons, and on a smaller scale (less than about 0.8 femtometers) as the short-range constituent of the nuclear force carrying particle, called the gluon (Figure 5.4).

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Figure 5.4. The strong nuclear force in action. Source: Image by Energy Education.

It is also responsible for behavior observed in atomic nuclei, at the subatomic level, it appears to act on itself in mediating the internal properties of hadrons. It holds these together (by conferring mass), as well as pions to form nuclei. The strong nuclear force is responsible for binding protons and neutrons together into nuclei, hence its name. The strong nuclear force governs the processes involved in radioactive decay (and thus radioactivity itself), which dominate over other processes by their contribution to the binding energy of nuclei and thus to their stability. At the range of 10–15 centimeters from a nucleus, the strong force is approximately 137 times as strong as electromagnetism; this is about as one would intuitively expect from elementary considerations (Humbert-Droz et al., 2019). As with other fundamental forces, it has a crucial role in keeping together the atomic nucleus and in binding the components of nuclei together. The strong interaction between particles manifests itself not only through the creation of the atomic nucleus, but also through the fusion of nuclei when extremely high temperatures or pressures are achieved. The strong nuclear force or strong interaction is the mechanism responsible for the strong nuclear reaction (strong nuclear Fermi interaction), which mediates the so-called strong interactions, that is, fundamental interactions that occur between quarks or other baryons. It is one of the four known fundamental forces of nature, with a range and strength intermediate between those of the weak interaction and EMF. It allows the fundamental

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building blocks of nature to exist and keeps them together in a very stable form. It is estimated to be 1000000000000000000000000000(1099) times stronger than the EMF. With its application in elementary particles, it is also responsible for binding quarks and leptons into hadrons. It is strong, over 100 times stronger than the electric force, and as a result has been witnessed in only a few reactions of particle scattering. QCD, which is the theory that describes the nuclear force, has provided good explanations for many previously unexplained phenomena, such as high energy particle scattering in the “forward direction,” the mass of some strange quark states, and large asymmetries in particle production rates at high energies (Figure 5.5).

Figure 5.5. Elements required for a nucleus reaction. Source: Image by lbl.gov.

NB-Hadron and Mesons interaction will be discussed later in this chapter. The strong nuclear force is an element of nuclear physics. Atomic physics studies the electronic structure of atoms, as well as emission processes, whereas nuclear physics is focused on the nucleus itself: its description, structure, dynamics, interactions with matter and decay. This chapter will provide an overview of the region of physical properties that concern both atomic and nuclear systems. The strong nuclear force is in quantum field theory, the basic laws of which were introduced in 1928 by Enrico Fermi and later jointly formulated with Edward Teller, among others. The strong nuclear force, symbol G for the grand unifying theory, is shown as a medium-sized gold sphere. This force is actually carried by gluons which interact with quarks: the strongest interaction possible in nature. The strength of the strong interaction between nucleons is measured by high energy physicists in units of 0, 1, 2, and 3 followed by a decimal point, e.g., 0.885 for the interaction between two protons, 0.138 for the interaction

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between an unpaired proton and an unpaired neutron and 0.510 for the interaction between two neutrons (Heckman, 2010). The residual strong force is responsible for binding quarks within protons (in a process known as color confinement). Within a nucleus, it is not possible to bind light nuclei in this way because they have no net electric charge to serve as handles on which the strong force can act (Figure 5.6).

Figure 5.6. Quantum electrodynamics; the theory used to explain the strong nuclear force. Source: Image by Wikipedia.

There are theories that discusses how physicists from all over the world are conducting experiments that attempt to discover new phenomena beyond the SM of particle physics and discover more about the strong nuclear force. We are all familiar with how strong electromagnetic and weak nuclear forces can be utilized to generate electricity, heat our homes, and run machines. However, in order to truly understand these forces, it is important to know the science behind them. For a long time, physicists were puzzled by the somewhat bizarre property of QED that this force was only felt at very short distances, the so-called range of attraction or the Yukawa length. The term strong is in contradistinction to the other 3 fundamental forces which act over all but astronomical distances of 1,011 cm and longer (Graña and Herráez, 2021). All 4 forces are related by symmetries several postulates about them including Noether’s theorem. In particle physics σ denotes the probability density for finding a nucleon with its (unknown) position given by r and velocity given by v. In our presentation here, we’ll talk about the science behind this nuclear force before presenting an explanation of how to calculate it in QED. Yet indeed, if you’ve ever wondered why the sun can burn without disintegrating, why the world is made of matter and not

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antimatter, or why we all have different amounts of mass, The Science of Strong Nuclear Force will clear things up. The strong nuclear force is the strongest force in nature and it’s at work whenever a nucleus-the tiny core at the heart of every atom-contains more protons than it can hold. The protons repel each other because they are positive charges, but they are held together by even stronger forces that physicists have struggled to understand since the dawn of their science. The story of where this force came from is a fascinating and suspenseful one, with clues dating to ancient Greece and medieval Islam. There is Enrico Fermi’s famous decades-long battle against Wolfgang Pauli. Pauli was convinced that there must be an unknown particle to carry this radioactive decay away from nuclei, one which we now know as a neutrino. Then there were two international crises that led directly to our discovery of what holds these untold numbers of protons together: Tsung-Dao Lee’s Nobel Prize winning work on parity violation using hot polar molecules trapped inside gas spectrometers. While history may not clear things up, the deep connection between the structure of these nuclei and their chemical, electrical, and physical behavior is emphasized, in order to give a holistic view of superheavy element research. These facts about superheavy elements will be very useful for future planning regarding their usefulness as future materials and for a better understanding of Big Bang nucleosynthesis and astrophysics. By reviewing concepts such as QCD confinement, confining SU(3) symmetry, QED vacuum structure constant, QCD chiral fermions, Gell-Mann matrices, SU(3) chiral Lagrangians and SSB formalism, one will gain a thorough understanding of why the strong force is so powerful (Fraser, 2011). This force is more of the force between nucleons, subatomic particles that are the heavy atomic nucleus, or protons and neutrons. Protons are positively charged and magnetic while neutrons have no charge or spin. When nuclei contain an uneven number of protons and neutrons, they can be unstable, leading to radioactive decay and eventual disintegration.

5.3. THE ELECTROMAGNETIC FORCE (EMF) The EMF between two charged particles is an example of a dipole-induced dipole interaction. It is the second strongest force that acts on particle pairs, after the strong force. The EMF arises from the fact that like charges repel and unlike charges attract. Namely it depends on the product of their charges, so it is long-range and its strength declines with increasing distance. The EMF is one of the four fundamental forces of nature and is responsible for

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electromagnetic interactions between elementary particles. It affects all electrically charged particles, and is one of the most powerful. The EMF is one of the four fundamental interactions (originally postulated as three: gravitation, EMF, and weak interaction) in nature. The EMF is one of the most universally present forces in nature since it binds together atoms and molecules in the universe, giving all matter on Earth its tangible properties. The word “electromagnetic” means “relating to magnetism, electricity, and the propagation of light.” The EMF affects all matter the atoms and subatomic particles that make up matter are affected by it (Figure 5.7).

Figure 5.7. An illustration of how the electromagnetic force helped build and form matter. Source: Image by the University of Chicago.

The EMF is one of a relatively few fundamental forces in nature. It can be detected between electrically charged particles and is responsible for numerous interactions, including those that hold atoms together, bend radiation (such as light), and cause the formation of magnetic fields. It is also part of the interaction between the matter particles that make up protons so that the basic unit of matter – the proton – that can exist by itself. According to a widely accepted theory, the EMF acts between two charged elementary particles, such as the electron and the proton, in the nucleus of an atom. The strength of this force is one of the most comprehensive forces in nature, resulting in many different reactions and interactions (Francescon et al., 2013). The EMF holds atoms together by creating bonds between their electrons and nuclei when they collide. It is also called Coulomb’s force or electric force. The EMF is a rarely used scientific term for an intermolecular force, i.e., a force created by the interaction of two or more molecules. Unlike

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the strong force and weak force, both of which are generated by elementary particles that have rest mass, the EMF pertains to the class of physical interactions that occur between any two particles. When a charged particle accelerates, it generates an electromagnetic field. When another charged particle enters this region of electromagnetic field, it gains acceleration. Since electromagnetic fields depend on the relative motion between charged particles, and cannot exist at rest, they are referred to as transient fields. Interactions mediated by transient electromagnetic fields are listed under “electrodynamic forces.” The strong and weak nuclear forces keep the constituents of an atom together. They cause the inter-atomic attractions and repulsion between substances, which is essential in chemistry. The EMF is second only to the weak force in strength, but it is more wide-ranging and acts on smaller objects than the weak force does, affecting atoms and their component particles, such as protons and electrons. The EM field has a value of zero in empty space and is responsible for holding all matter together as well as attracting all charged particles with each other. The term “electromagnetic force” refers to the interaction between particles with an electric charge, and includes both the electromagnetic attraction (when two charged bodies are moving towards each other) and repulsion (when they are moving away from each other) interactions (Figure 5.8).

Figure 5.8. Electromagnetism – a branch of physics necessary for the electromagnetic force. Source: Image by Pinterest.

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This force falls under electromagnetism. Electromagnetism is the branch of physics that studies the EMF, a type of physical interaction that occurs between electrically charged particles. Moreover, the EMF plays an important role in astronomical systems, including stars and galaxies, and also plays an important role in everyday life since electromagnetism influences living organisms in many ways such as the mechanism by which nerve cells communicate with other cells. Unlike gravity, it affects all particles—matter as well as antimatter. It is responsible for many phenomena seen in daily life, especially those associated with magnetism. The magnetic and gravitational forces both have a long range: attraction to an electrically charged particle can occur a meter away and gravitational effects extend throughout the universe. There is evidence that a particle known as the graviton also carries gravitational force between molecules. All objects are currently known to possess either a positive or a negative electric charge and interact through the EMF. Its strength is approximately 10–13 times that of the weak force, 10–36 times that of the gravitational force, and 10–8 times that of the strong force (Boyle and Farnsworth, 2014). All particles and hence all matter, both visible and invisible, have electromagnetic fields associated with them. Centuries before the development of quantum theories, the nature of the EMF was well understood by James Clerk Maxwell’s equations for electromagnetism which showed that electricity, magnetism, and light are all manifestations of the same phenomenon manifested in different ways. Initially discovered in the late 19th century by Michael Faraday, the EMF plays a major role in determining the internal structure of most objects encountered on a daily basis, whether inorganic or living. Its effects are prominent not only in electrical phenomena but also in electromechanical phenomena, such as magnetism and electromagnetic induction (Figure 5.9).

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Figure 5.9. James Clerk Maxwell; one of the first brains behind the electromagnetic force. Source: Image by Biography.

The science behind the EMF is the subject of not one but two new Science Museum exhibits. Magnetism makes the world go round, so it has been applied it to both fun and learning. Throughout history, people have been captivated by two things: the mysteries of space and the secrets of electricity. Few people understood that these two seemingly unrelated worlds are connected by an invisible force called the EMF-until now. New York Times best-selling author Dr. Tony Phillips unravels the story behind this ubiquitous but little-known force in The Science behind the EMF, bringing readers face to face with scientists who discovered its workings, as well as the electric motors, generators, transformers, and other devices they imagined. Be it known, the EMF is a fundamental interaction, used to describe everything from the gravitational force of the sun and moon on the earth to magnetic fields around permanent magnets (Figure 5.10).

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Figure 5.10. Electromagnetic force is used to light a bulb. Source: https://www.sciencefacts.net/electromotive-force.html

Around 100 years after the discovery of this force, we still don’t fully know how it works. The EMF explores how we first discovered the two types of electric and magnetic forces, the EMF, and the weak nuclear force. What is the exact mechanism behind this physical phenomenon? Science fiction has given us many ideas, but in reality, no one knows what the true nature of EMF is. The fact that certain materials can be magnetized while others cannot, and that the magnetism remains even after the magnet is removed, was first recorded by the Greek scientist Thales of Miletus. The English scientist William Gilbert went further in 1,600 and demonstrated that the Earth itself is a giant magnet, as are all matter’s varieties of ferromagnetic material: if a piece of some such material is freely suspended and allowed to turn toward the north and south poles of a magnet placed nearby, it will always line up – pointing in the same direction – with an axis parallel to the magnetic field (Feroz et al., 2009). The EMF pushes on other electrically charged particles, providing the force that causes atoms to hold together and gives rise of the phenomena of electricity and light. Fascinating Electromagnetic experiments include: Attraction at a distance is replaced by repulsion between two like charges – charged metal balls attract paper clips, yet repel each other – moving

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charged magnets can create electric current. The EMF lets the charges of objects interact with one another. This force is what holds atoms together, and affects the motion of objects made of charged particles, called electrons. Every atom has a positively charged nucleus at its center, and at least one positively charged particle flying around it. Electrons have negative charges and must be balanced by a nearby positive charge. Without this force, there would be no chemistry… no matter. It is why you are here now reading these words. It is similar to a magnetic field, only that it has no magnetic poles. The EMF field is both an electric force and a magnetic force that acts on electrical charges in the same manner as the gravitational field. When an electron moves through a conductor, it creates a magnetic field. This is because moving electrons create an electric current that generates a magnetic field. Electrons moving through a wire creates an electric current and generates a magnetic field around the wire. The movement occurs in two opposite directions due to the nature of electricity being a dual wave form (think of water going up and down in wave form), a magnet itself can be made by taking two similar ends of wires and wrapping them in opposite directions, one facing each other. With this configuration you will have both positive charge on one side, and negative charge on the other side. But what if you took the same 2 wires and wound them together tightly, with equal numbers of the same charges each time, you will now have composite wave form where both positive and negative charges are present at all times, again this is due to the way electricity behaves as an oscillating wave, not an actual line or particle. The composite wave form is also a constant changing wave where electrons are constantly changing direction. There are also other forces at play here such as Inductance which is when an electric current passing through a wire creates a magnetic field that affects another moving electrical charge close by it.

5.4. THE WEAK NUCLEAR FORCE The weak nuclear force (related to the radioactive decay of atomic nuclei) is actually the third strongest force in nature. It takes place due to the process of fusion of quarks and other elementary particles that causes transformations of elementary particles from one state into another. The theory of electromagnetism, describing electricity and magnetism, appears to be almost completely successful, with only a handful of unexplained phenomena. The weak nuclear force was named to reflect its perceived weakness, compared to the strong nuclear force. Perhaps the most important

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is the puzzle of beta decay, which begins with the weak nuclear force. The weak nuclear force is only weaker than gravity and electromagnetism (Farnsworth and Boyle, 2015). The weak nuclear force is responsible for radioactive decay as well as the fusion processes in stars. It is carried by elementary particles known as gauge bosons which are also responsible for mediating the EMF. The weak force has a very short range, even shorter than the strong force, and is responsible for radioactive decay. A much more common interaction encountered in daily life is this force’s subtle influence on our world in forms such as background radiation. Its effects are easily observable at the level of individual particles (where it is called the force of radioactivity or radioactive decay), and in certain other systems, such as neutron stars (Figure 5.11).

Figure 5.11. An illustration of the working of the weak nuclear force. Source: Image by Medium.

The weak nuclear force or weak force is the mechanism responsible for radioactive decay, which plays an essential role in nuclear fission. The weak force has both long-range and short-range aspects, and is one of four fundamental forces (along with the strong force, electromagnetism, and gravitation) described in the standard model (SM) of particle physics. The weak force is so named because it is only really evident at very small (subatomic) distances, where other forces are averaged out, and because it only comes into play under certain circumstances (El Naschie, 2009). The strong force allows large, stable particles to exist. It holds the protons and neutrons in the atomic nucleus together, despite their electrical repulsion from each other – because of this power, as well as its own stability and longevity within the nucleus, it is also called the strong interaction. The weak force plays a crucial role in the functioning of cell and essentially

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controls the stability of the atom. It defines the decay and transformation of elementary particles such as proton. Its importance can be explained in terms of the fact that it is involved in radioactive beta decay, which allowed for the determination of a precise value for the mass ratio between a neutron and a proton (muon decay has not proved successful here). It also allows for the production of neutrinos through muon decays. It has an extremely short range (distance), and a very small effect on everyday life. It is responsible for radioactive decay, which can reverse unstable atomic nuclei back into stable, more abundant forms of the same element. Although initially estimated to be weaker than the strong force and EMF, studies show that it is about 10^39 times as much weaker than electromagnetism and 10^36 as much weaker than the strong nuclear force, making it about 10^32 times as strong as gravity (Figure 5.12).

Figure 5.12. A diagrammatic representation of radioactive beta decay. Source: Image by Shutterstock.

The weak force is responsible for radioactive beta decay, an example of radioactive decay as well as the continuous decay of some isotopes from parent isotopes to daughter isotopes. This is a natural process of radioactivity resulting from the structure of atomic nuclei. The theory behind the weak interaction is often referred to as quantum flavordynamics (QFD), which is part of the SM of particle physics. The weak interaction was discovered in 1956 simultaneously by two groups of physicists, working independently: one was led by C. D. Anderson (Lawrence Berkeley National Laboratory) and the other by T.D. Lee (Brookhaven National Laboratory: BNL).

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The weak interaction has a short range; the force carriers, the W and Z bosons have a mass of 80.4 GeV/c2 and 91.2 GeV/c2, respectively. The W boson is the carrier of the electromagnetic interaction when transformed into the corresponding gauge boson in Fermilab experiments, while the Z boson is responsible for the nuclear weak force between nucleons. From this evidence it may appear that the electromagnetic and nuclear interactions are very similar, but with different carrier particles; this is not entirely correct because of the two-dimensional character of electromagnetic propagation and its divergence (the magnetic part diverges too) (Dubois-Violette and Todorov, 2019). The weak nuclear force (also known as the weak force or weak nuclear interaction) is a force that acts between atoms. This is the force responsible for certain cancers, such as those of the breast and prostrate, as well as muscle wasting in AIDS. The weak nuclear force is carried by three particles called neutrinos. These particles are nearly massless, but when a neutrino strikes an atom, it may transfer energy to it. The atom recoils from the strike. This energy is what causes damage to cells from radiation sickness and cancer. While the EMF binds electrons and protons together into atoms, and gravity attracts objects with mass, the weak nuclear force is a very shortrange interaction that actually changes the properties of matter at an atomic level. The weak nuclear force is responsible for some types of radiation, but also for holding neutrons and protons together as part of atoms. There are several particles that are involved in this force. These include the W+, W-, Z (neutral), and the neutron. Scientists aren’t sure why there are four fundamental forces in the universe, but all three of them are critical to understanding how the universe works. In some theories, all the forces were once one force. Forces operate over different ranges of sizes and influence familiar properties that make up our world. A better understanding of this force and its effects will allow for further advancement in modern medicine. The Weak Nuclear Force is a power that has never been observed directly but plays a crucial role in the Universe. It is responsible for interactions between exotica such as neutrinos, quarks, and gluons, without which life would be impossible. And despite its key role, The Weak Force has a surprisingly simple operating mode. The weak nuclear force, or “weak force,” plays a role in the creation of matter. This force acts as an agent for radioactive decay, enabling atoms

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and molecules to break down in the process of radioactive decay. The weak nuclear force furnishes energy for various lighter atomic nuclei to change into other lighter atomic nuclei, or smaller parts of these nuclei. How does a beta particle switch from a negative electron to a positive neutrino, without losing energy? This is the question that researchers from the world’s biggest particle collider are now aiming to answer. The weak nuclear force is responsible for many of the natural processes we see in our universe. It is so weak that it does not bind atoms together, yet it has fundamental effects on how atoms behave and how we react with our environment! The origin of this force was theoretically established by Makoto Kobayashi and Toshihide Maskawa in 1965; as one of the four fundamental forces of nature. By then it was the EMF exerted by one proton on another. It has a strength of about 10–14 N, which is not very strong in comparison to the strong or EMFs. However, it played a huge role in the formation of subatomic particles, and can also lead to nuclear fission and fusion.

5.5. GRAVITATIONAL FORCE Gravitational force is the weakest force. It is the sole force that can have attraction between elementary particles. It can act upon the particle weakly. Gravitational force is not an action at a distance because of which there are many phenomena like, Coulomb’s law, Atom, and so on. It is this force that shapes galaxies and reveals black holes. Even when the universe was created, it depended on gravitational force. Gravitational force helps particles to attract each other. They have a strong gravitational field and when they come close to each other it starts showing their strength and helping them to attract each other’s mass. Gravitational force is the weakest force present in nature (with an extremely low value in contrast to other forces), which attracts matter with mass toward matter with mass. Gravity is a fundamental phenomenon, not an interaction of any kind. It is the weakest natural force acting between two objects as it has infinite range. It also affects the mass of an object as well, making it heavier. This force is responsible for interactions between particles and is the cause of spherical planetary motion, including orbital period and speed around the Sun. The gravitational force between two bodies depends on

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their masses and distance between them. If you drop a mug, it will fall to the ground (attraction by gravity), same happens to planet earth with objects such as planets or stars (Beringer et al., 2012). Gravitational force was not proposed as a hypothetical fundamental force until after Isaac Newton’s work on classical mechanics, when Joseph Louis Lagrange developed Lagrangian mechanics and began considering “frictional forces,” which were proportional to the velocities of the interacting objects. Thus, Newton’s theory of gravity was replaced by general relativity, which does not predict gravitational forces as an inherent property of space-time, but instead predicts them based upon local effects described by that theory. Considered as the weakest force, it is present even in the empty space in field theory and to a limited extent in quantum field theory. Gravitational forces originate hence from the properties of space-time (general relativity). Gravitational force is a fundamental interaction that acts between all things with mass and determines the strength of all gravitational interactions (falls, weights, springs). The gravitational attraction of the original matter particles created the development for new particles: the messenger photon, the gluon and eight types (Dubbers and Schmidt, 2011). Gravitational force is described by Newton’s law of gravity which says: “every particle attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them.” In its simplest form, it defines the way in which two nuclei attract one another. Gravitational attraction is the most familiar of all physical forces and manifests itself as the agent responsible for many observable effects in everyday life. Gravitational force is an idea invented to explain not only the falling of normal material bodies, but also the motions of celestial bodies such as planets and rationalize in this way the disruption of their orbits around the Sun. Gravitation is most familiar as the agent that gives weight to objects with mass, and plays a major role in the dynamics of the Earth and other planets. Gravity has been an important concept in a wide range of fields, including physics, philosophy, and religion; its effects are observable in many different everyday phenomena, from athletic performance to microscopy (Figure 5.13).

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Figure 5.13. Gravitational force as discovered by Isaac Newton acts on the same way as in elementary particles. Source: Image by Online Science Notes.

Gravitational force is the weakest of all four fundamental forces, the other three being EMF, or electroweak force (the combination of electromagnetism and the weak interaction), Strong nuclear force, and Weak nuclear force. The gravitational force is approximately 1,036 times weaker than the EMF, 1,038 times weaker than the strong nuclear force and 1,039 times weaker than the weak nuclear force. The gravitational attraction between two objects with mass results from a combination of their masses and separation, which is a function of their distance for example (DuboisViolette, 2016). Gravitational force is a central prediction of general relativity. Gravitational attraction between objects arises from discrepancy in their gravitational potential. This forms an invisible bond between any two objects and is central to our understanding of how systems as complex as galaxies, solar systems, planets, and even atoms can be held together. This force is analogous to the electromagnetic interaction that governs the structure of atoms and molecules, though much weaker in strength. Gravitational force was discovered in the last century and has come to play an essential role in forming understanding of the Universe. Gravitational force is a mutual interaction, between anything having mass and everything else. This force plays a key role in keeping the earth, moon, and other celestial bodies in orbit around the sun and each other. Gravitational force is responsible for keeping the planets orbiting the sun in their elliptical orbits. In the case of

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gravitational force between two bodies or particles with significant mass, gravitational force causes them to either attract each other as in the case of celestial bodies or objects with mass or fall towards each other if they apply weak attractive forces on each other. In everyday life, gravity interacts with other physical quantities such as human ambition, but these only account for minute fractions of the phenomenon. A graviton is a hypothetical elementary particle that mediates the force of gravitation in the framework of quantum mechanics. Gravitons have not been directly observed or detected, and their existence is speculative and disputed. When two particles that are neutrally charged are accelerated by a gravitational field is relative to each other, they experience a net force, as described by Newton’s law of gravitation. The acceleration is directly proportional to the product of the two masses and inversely proportional to the square of the distance between them. This is sometimes referred to as action-at-a-distance.

5.6. HADRON INTERACTIONS Hadronic Interactions is the first non-perturbative treatment of the interplay of QCD at low energies and hadronic systematics. Opening up an entirely new area of hadronic physics, it has fundamentally changed our understanding of strongly interacting matter. Combining the latest data on cosmic rays with our improved event generators, hadron interactions is studied in the inner track of a muon or an electron in particles (at rest or produced in p-Ray– gamma recoil) leading to resonant state hadrons. We calculate the ratio of branching fractions for production of a vector meson from quark decays from the same initial state, compared to vector meson production with QCD radiation effects included. The results show that QCD radiation does not make any contribution for mesons that decay into two quarks after internal gluon emission, but it does for those that decay into a quark and an antiquark (Figure 5.14) (DeMille et al., 2017).

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Figure 5.14. A sample hadron-hadron interaction. Source: Image by ResearchGate.

In a hadronic interaction, the constituents of the interacting particles (called hadrons) may just scatter elastically after one or more given number of impacts although they do interact due to the exchange of gluons in the first place. In this way, the original interaction can be understood as a collision between constituents of the two hadrons with subsequent separation of these constituents. QCD is the theory of strong interactions, one of the four known fundamental interactions in nature. It describes the dynamics of quarks and gluons as they participate in the strong interaction. In order to uniquely define a quark–gluon plasma (QGP; a quark–gluon fluid), it is essential to evaluate hadron interaction in the heavy-ion collisions. Because QCD is a non-perturbative theory, there are several theoretical difficulties. The Hadron and Lepton Number Constraint, which are invariance principles in the gauge sector of QCD, have been related to the mirror symmetry of matter and antimatter. The ‘Solar Model’ of the Sun and solar neutrinos is related to the ‘Stardust Model’ of starlight and cosmic rays, which are however not at odds with the cosmological data that contradict such models. The ‘constrained minimal supersymmetric SM,’ exhibiting the smallest number of free parameters among supersymmetric models, is also a restricted version thereof. This book will provide a description of the elementary particle physics necessary for understanding our current

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knowledge, as well as an overview of the theoretical approaches to unification. Hadronic interactions are best described in terms of “probing hadronic matter with light, watching for the nuclear shadow of a strong interaction with non-zero angular momentum.” Hadronic Interactions describes the scattering amplitudes of all inclusive, one loop inclusive and exclusive, and two loop hadronic interactions in the SM. It is intended for researchers from all backgrounds in particle physics who want to learn more about these interactions. Hadronic interactions are a class of nuclear processes that take place primarily through the exchange of virtual hadrons. Proton–proton, or pp, collisions, which result from the scattering of two nuclei with a small relative momentum transfer, are particularly relevant in simulation work. At the highest energies available at the LHC, the prime simulations involve pp collisions. Hadronic interactions are the basic physical processes that occur between the elementary particles which form the matter we see in our everyday environment. These processes, governed by the laws of quantum physics, involve the emission and absorption of hadrons, or particles containing quarks. At certain energies, two or more hadrons can combine to form a meson. All matter particles (such as quarks and leptons) have corresponded antiparticles and all antiparticles have corresponding matter particles (Bellotti, 2011). The hadronic interactions arise from high-energy collisions of the quarks and gluons inside the proton and neutron. They are described by the non-Abelian gauge theory called QCD. Quark-gluon plasma, which is created in heavy-ion collisions at very high energy, behaves in many respects like a perfect fluid. It is interesting from both fundamental physics and astrophysical viewpoints since it has unique properties which are different from water or other fluids studied in hydrodynamics. At the conceptual level, hadronic interactions have been in use for many years. Even so, it can be argued that they are not yet part of the culture of quantum field theory. (Strange as it may seem, this statement is evident in the fact that hadrons are still treated as elementary particles!) On the theoretical side, hadronic interactions should in fact provide insights into some of the deep questions of our time: The nature of strongly-interacting matter, effective field theories that are nonrenormalizable, chiral symmetry breaking, and the top quark mass puzzle. This Festschrift volume is dedicated to gathering these insights from subsequent generations of physicists and putting them in a form that can serve as a resource for future researchers.

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Understanding the internal structure of protons and neutrons is key to elucidating a broad range of fundamental problems in particle physics, nuclear physics, atomic, and molecular physics, condensed-matter physics, and astrophysics.

5.7. MESONIC INTERACTIONS Mesonic interactions are short-range nuclear forces between nucleons and mesons. They were discovered in experiments involving cosmic ray muons and nuclei around 1961, and described theoretically by Alexei Abrikosov in 1964. This discovery made it possible to understand why certain particles are more stable than others, and also why nuclei hold together. Meson theory refers to quantum field theory of the strong interaction. Mesons are hypothetical particles that mediate the strong interaction, more specifically the process of quark-hadron particle conversion, a key component of proton decay (Bass, 2020). Mesons are subatomic particles that form the building blocks for matter. They were discovered in cosmic ray experiments in the 1930s and 1940s, but their behavior was not fully explained until a quarter-century later. In 1947, Hideki Yukawa predicted the existence of mesons as carrier particles of the short-range nuclear force that binds nucleons together within atomic nuclei; with empirical verification of this prediction in 1949. However, until 1970 it was still unclear how poions interacted to form mesons. It is now understood that mesons arise from the exchange of quanta of the strong force between neighboring. Mesons are subatomic particles composed of one quark and one antiquark. The best-known mesons, called the pion, kaon, and the muon are unstable, having lifetimes less than 10 seconds. Despite their short lifetimes, mesons play an important role in the dynamics of the universe that can be seen as a result of their important interactions with other particles. The meson is the collective name for subatomic particles whose quantum numbers add up to zero. The most well-known examples are the pions and kaons, which participate in strong interactions of fundamental particles. They also mediate the weak force between quarks, by converting from one flavor to another through the weak interaction. Mesons are part of the hadron particle family, characterized by having zero spin and integer (positive) parity, i.e., they cannot be polarized along any axis when traveling at a speed slower than light. They are subatomic particles that participate in strong interactions of fundamental particles (Figure 5.15).

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Figure 5.15. Mesonic corrections of three-quark (baryon) currents where the quarks interact while the meson is in flight. The dashed line denotes an external photon or other operator. Source: Image by ResearchGate.

CHAPTER

6

PARTICLE COLLISION IN ELEMENTARY PARTICLES

CONTENTS 6.1. Examples of Mechanisms Put in Place to Test Particle Collision in Elementary Particles................................................... 144 6.2. Working.......................................................................................... 147 6.3. Experiments Sites Inside the Hadron ............................................... 157 6.4. Discoveries From Colliding Particles ............................................... 165 6.5. Calculations of the Dynamics of Collision ...................................... 168

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Particle collision in elementary particles is one kind of reaction that highly energetic elementary particles have. In elementary particle physics, collisions with energy above the center of mass energy threshold are used to probe for new physics at higher energies. These reactions can be thought of as being a collision between the two particles and both may be annihilated to create new particles, or they could scatter off each other. Particle collision has played an essential role in many elementary particles in accelerating. Particle collision in elementary particle experiments is usually used to refer to the newly produced elementary particles in the process of particle collision (Capelle and Campo, 2013). The study of these newly produced particles helps us better understand the particles and forces that govern our universe. Some of the mechanism used to test particle collision in elementary particles will be discussed in the course of this chapter. This chapter provides an introduction to the scattering of quantum particles including a thorough discussion of the concept of quantum particles, the tools for describing them and their interactions, as well as the concepts needed for describing and interpreting experiments (Figure 6.1).

Figure 6.1. An illustration of particle collision as illustrated by quantum computing. Source: Image by Softpedia News.

Particle collision in elementary particles is a subfield of particle physics which studies the dynamic properties of elementary particles. The phenomenon of particle collision in elementary particles is discussed with

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regard to the correlations between momenta, angles, and time of collision. Particle collisions are an important phenomenon in which particles change their energy and direction as a result of the collision. This is a process in which two subatomic particles collide, transferring energy between them in an elastic or inelastic collision. This includes collisions of electrons and positrons, single photons, protons, antiprotons, neutrons, and antineutrons, pions, muons, and other leptons. This chapter examines elementary particle collision from the historical perspective of new particles discovered in colliding beams, and current experiments searching for new particles. Experiments involving high-energy protons, antiprotons, and leptons are discussed as well as detectors used to study the new particles. These collisions may occur in particle detectors, or they may naturally occur while the particles are in the universe long after they were created. Particle-antiparticle collisions are also possible. The calculation of the cross section for a given collision is exceedingly complex, so in most practical applications the relevant data is obtained from experimental measurements and collated in a database (Dolenec et al., 2017). Every field of physics which uses interacting particles to further our understanding of how the universe works: particle physics, nuclear physics, solid state physics and others, depends on databases of particle collision data. Some databases are specific to one application, while others attempt to be generic and cover a range of applications (Figure 6.2).

Figure 6.2. Illustration of a particle detector; in most cases, this is where the collision may be observed. Source: Image by ResearchGate.

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A particle collision is a process in which two or more particles, coming from different directions, collide to produce a new set of products. The energy of the incoming particles can be measured in the lab frame, and momentum is conserved in the collision. Particle collisions are indispensable tools for the study of fundamental interactions in physics, as they allow to probe the structure of particles and test theories about their nature. In this sense, particle colliders such as the large hadron collider (LHC) at CERN, the Tevatron at Fermilab, RHIC at Brookhaven National Laboratory (BNL), and LEP at CERN can be considered as a discovery machines. The collision may be elastic (the incident particles just bounce off each other, with their original directions, speeds, and energies) or inelastic (the particles become part of one or more new subatomic particles). In particle physics, two particles can collide by means of a single force carrier, such as electromagnetic force (EMF), or QCD force. The theory is the theory of elementary particles that describes three of the four forces of nature: electromagnetic, weak, and strong interactions. It is therefore a so-called gauge theory which also applies to strongly interacting massless particles and forces between fermions when expressed in terms of preons. Collision of a particle with another particle (most often an electron in which case this is electron capture) or with a nucleus (in which case this is a nuclear reaction) (Calvo et al., 2016). The decay products of a nucleus formed during the collision can be observed and these can then be identified as a new particle. Most modern experiments are designed to detect just such new particles. However, it is not always the case that the observed decay product can be unambiguously attributed to the formation of a new particle during the collision. Numerous evaluation criteria have been developed to reliably determine which collisions result in the production of new particles.

6.1. EXAMPLES OF MECHANISMS PUT IN PLACE TO TEST PARTICLE COLLISION IN ELEMENTARY PARTICLES 6.1.1. The Large Hadron Collider (LHC) The large hadron collider (LHC) is the world’s largest and most powerful particle accelerator. It took about a decade to design and build, and cost approximately €10 billion (US$ 9 billion) (Dolenec et al., 2017). It is

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operated by the European Organization for Nuclear Research (CERN), has a circumference of 27 kilometers (17 mi) and crosses the border between Switzerland and France at four points. It first started up on 10 September 2008, and remains the latest addition to CERN’s accelerator complex. The LHC consists of a 27-kilometer ring of superconducting magnets with a number of accelerating structures to boost the energy of the particles along the way. Inside the accelerator, two high-energy particle beams travel at close to the speed of light before they are made to collide (Zimmermann, 2018). The beams travel in opposite directions in separate beam pipes – two tubes kept at ultrahigh vacuum. They are guided around the accelerator ring by a strong magnetic field maintained by superconducting electromagnets. The electromagnets are built from coils of special electric cable that operates in a superconducting state, efficiently conducting electricity without resistance or loss of energy. This requires chilling the magnets to –271.3°C – a temperature colder than outer space. For this reason, much of the accelerator is connected to a distribution system of liquid helium, which cools the magnets, as well as to other supply services” (Figures 6.3 and 6.4).

Figure 6.3. A section of the LHC. Source: Image by Firstpost.

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Figure 6.4. A disassembled section of the LHC. Source: Image by The Conversation.

Following an upgrade, the LHC now operates at an energy that is 7 times higher than any previous machine and with 10 times more collisions per second. It was built by the CERN between 1998 and 2008 in collaboration with over 10,000 scientists and hundreds of universities and laboratories, as well as more than 100 countries. It lies in a tunnel 27 kilometers (17 mi) in circumference, as deep as 175 meters (574 ft) beneath the Franco–Swiss border near Geneva, Switzerland. Its first research run took place from 30 March 2010 to 13 February 2013 at an initial energy of 3.5 teraelectronvolts (TeV) per beam (7 TeV total), almost 4 times more than the previous world record for a collider, rising to 4 TeV per beam (8 TeV total) from 2011. On 23 February 2015 it was restarted with 1.6 times its previous energy level (Woithe et al., 2017). It reached 13 TeV per beam (6.5 TeV per nucleon pair), breaking the previous record by around a factor of two, with the goal exceeding that of covering previously unexplored areas of particle physics like the search for supersymmetric particles and extra dimensions.”’ The LHC is used by physicists to study the smallest known particles – the fundamental building blocks of all things. It will revolutionize our understanding, from the minuscule world deep within atoms to the vastness of the Universe. The LHC is the most powerful particle accelerator ever built, by humanity, using a number of features designed to enable the LHC to accelerate two beams of protons to an energy of 7 TeV (3.5 TeV per beam) and smash them into each other head on, with a combined energy equivalent

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to a flying mosquito. At the LHC, protons (the core of ordinary hydrogen atoms) will travel at 99.999999% of the speed of light – nearly 186,000 miles a second – and smash together, creating conditions like those just after the Big Bang. Scientists will investigate these collisions to answer some of the most fundamental questions about our universe. The LHC is also expected to provide major contributions to medical research, computing, and telecommunications as an outgrowth of its research program (Figure 6.5).

Figure 6.5. An aerial scientific view of the LHC with its experimental sections. Source: Image by UCI sites.

The LHC is named after LHC Engelke, who played a significant role in the initial design of the accelerator. When the LHC was first turned on, it was the largest scientific experiment in history. The current particle accelerator is 4 miles in circumference and required the collaboration of 10,000 scientists from over 100 countries. The aim of the science project was to recreate conditions similar to that of the Big Bang by colliding together protons at high speeds. CERN’s mission statement is outlined with a focus on ‘building scientific knowledge and understanding’ in an open and collaborative environment (Wood and Heyde, 2016).

6.2. WORKING The LHC is a titled circular tunnel built in the countryside between France and Switzerland, initially with the hope of finding the so-called Higgs Boson particle. This sub-topic will explore the operating principles of the LHC. The LHC is a high-energy particle collider located beneath France and Switzerland. Each LHC experiment involves more than 2,000 scientists, engineers, and technicians from institutes around the world, who work together to operate these experiments. This sub-topic will be an introduction to topics such as how subatomic particles are accelerated, how they collide,

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and how physicists analyze the data from these collisions. Accelerating protons with unprecedented energy, the LHC smashes them into each other head-on in four enormous detectors. With the analysis of LHC data, a new era of high energy physics will begin.

6.2.1. Injector An injector is a device used to introduce a stream of item into something. In particle physics, and specifically in a hadron collider, an injector is a chain of accelerators that inject bunches of particles into the main ring. Injectors are used in hadron colliders such as the LHC to accelerate elementary particles. These injectors can include different types of pre-linac accelerators such as linacs and synchrotrons. Description of specification, design, and performance of injectors to hadron colliders. The text is intended to provide a balanced view on the detailed requirements, techniques, and parameters that are required for design, construction, commissioning, and operation of injectors to hadron colliders. The text addresses acceleration physics, ionization cooling and beam manipulation schemes that are most pertinent to the injector design. Moreover, the text also reviews conceptual designs of high energy heavy ion collider designs that employ various injector types (Figure 6.6) (Wallace, 2011).

Figure 6.6. LHC injector complex. Source: Image by ResearchGate.

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Injector systems ensure the availability of high-quality particle beams for the experiments in hadron colliders. A wide range of different electron and proton accelerators provide the high-intensity particle beam to the LHC. They share common accelerator technologies, such as superconducting magnets, but have very specific requirements and technical solutions to perform the challenging task of injecting a few bunches into the rings filled with thousands of other bunches. In particle accelerators that collide particles, a large number of particles is needed to make collisions eventful. This number can be created by injecting a small particle bunch from an injector and then accelerating it several times. Hadron colliders use two intersecting beams of protons or ions traveling in opposite directions. Each beam needs its own injector system, which usually consists of several linacs. These linacs are used for different processes such as pre-injection, bunch compression and injection into the main ring (Figure 6.7).

Figure 6.7. In hadron colliders, particles are injected, accelerated, and collided. Source: https://science.howstuffworks.com/science-vs-myth/everyday-myths/ large-hadron-collider.htm

Injectors of hadron colliders are usually synchrotrons with frequency doublers (FDs) for the production of polarized protons. Radio frequency quadrupoles (RFQs) and/or Linac are used as injector and for pre-accelerating of beams up to the energy level where the frequency doubler system starts producing polarized protons. Alternative options, like linacs or other ECR sources, can provide a high energy proton beam (~1 GeV), but they don’t produce polarized proton. Hadron colliders are among the most difficult machines to set up and run, not only due to their enormous energy but also because of the high degree of control needed to store and collide bunches of protons and ions (Viaux et al., 2013). A large number of particles need

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to be injected into the collider from source, transported, and accelerated in a synchrotron, and finally renewed every few hours when they are lost by interaction with residual gas in the vacuum chamber. These requirements are particularly stringent for the ions in RHIC and LHC where, unless replaced by new ones, they would cause catastrophic chamber erosion within a few minutes. Colliders are the heart of high energy particle accelerators. They inject, accelerate, and collide particles, or beams of particles, which then decays into other particles. The evolution of such collisions process is recorded by sophisticated detectors that measure characteristics such as momentum and charge of the resulting particles to produce a contextual record of the experiment. Hadron colliders (protons and ions) rely on multi-step accelerators, called injectors, to accelerate them to the energy required for successful collision. These particles are shot into a full-size circular accelerator, such as the LHC, which continues the process of accelerating and colliding the hadrons in a ring. The injectors play a critical role in maintaining high intensity beams at high energy. High-energy hadron colliders have a need for a high average beam current to efficiently produce collisions. The average beam current must be much higher than the natural beam current, due to rapid loss of particles during cool-down and beam conditioning. Injectors are used at the lower energy stages to acquire this large number of particles. High energy hadron colliders require a large number of bunches in order to achieve the desired luminosity. We describe extensions to the standard procedures used in injectors for electron-positron colliders and their implementation in the injector chain of the LHC. This has been achieved using a sophisticated machine control system that provides real time beam processing. The high intensity beams are maintained while meeting increasingly stringent environmental regulations, with significant injection losses of order 1% due to constraints on radiation doses and cryogenic inventory in the transfer lines. Electron and positron accelerators are needed at the front end. A proton or an ion collider would be of little use without an electron and a positron injector. However, the electron and positron beams have to be brought into collision as well. Usually, an accomplished phase detector will do for this purpose. The injectors are initially the most important part of a hadron

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collider as they are responsible for creating the beam that will be used throughout the rest of the machine (Volovik, 2015). Free electron lasers are one of new generation of equipment and are used to produce high power coherent radiation in the ultraviolet, visible, and infra-red wavelength regions. The free electron lasers have applications not only in the traditional research areas but also in industry where they become efficient tools. Two examples of practical uses can be mentioned: CO2 laser welding (efficient technique for manufacturing sophisticated parts) and plasma generation (used in nuclear fusion research). These machines need high quality electron or positron beams with very low emittance. The aim of this project is to study a high brightness injector using energy recovery linear accelerator. The LHC contains two types of injectors, the Linac 2 and most recently, Linac 4.

6.2.2. Linac 2 vs. Linac 4—Roles and Difference The LHC is the most important and advanced particle accelerator in the world. Within this complex system are several smaller linear accelerators (Linacs) that play a key role in prepping particles for the 27 km long LHC ring. Linac 4 and 2 are two of these four Linacs. Learn more about their function in the layout of the LHC, their differences and shared roles with our sister linac, Linac 2. Usually when CERN hires international students for their summer student program, they explain the difference between Linac 2 and Linac 4. As others have said, Linac 2 is the accelerator that produces 400 AMeV beam (i.e., at 400 AMeV) energy to inject into proton synchrotron (PS) Booster and PS respectively to accelerate higher energy while Linac 4 produces 160 MeV beam energy to inject into RFQ, a linear accelerator and then it follows by accelerating in MEBT (low energy beam transport), LEBT (medium energy beam transport) and high energy part of PSBOoster to get higher energy beams. The Linac 2 and Linac 4 both accelerate hydrogen ions to full energy (Van Noorden, 2012). They shoot the ions from the injector into the main ring of LHC where heavy ions experience additional acceleration to 7 TeV per nucleon for lead-based ion beams. It rotates clockwise and consists of several accelerating elements that successively increase ion kinetic energy up to 54 MeV, after which extraction from Linac 2 occurs to enter a linear particle accelerator in Linac 4 (Figure 6.8).

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Figure 6.8. A section of the Linac 2. Source: Image by CERN.

Linac 2 accelerate the protons to low beam energy before injecting into Linac 4 for up to 400 MeV. This helps prolong the Linac 4 RF structure lifetime. The Linac 4 also provide the beam during injection/extraction session of the LHC as well as when no beam is stored in LHC (between “fill” and “empty”). Linac 2 consumed less power than Linac 4. LHC is collider, meaning that it accelerates two beams of particles. The particles in the beam, called protons and their antiparticles the anti-protons, are accelerated from very low, practically zero energy and brought up to an energy of 4 TeV by a series of accelerators… Linac 2 injects each beam into the PS Booster ring for further acceleration. Linac 4 is currently under construction and will replace Linac 2 as part of LHC upgrade (Figure 6.9).

Figure 6.9. The new and most recent Linac 4. Source: Image by CERN.

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Before Linac 4 development, The LHC starts its journey in a linear accelerator called Linac 2. In Linac 2 the particle energy is increased using a radio-frequency (RF) field. The protons are accelerated from their rest mass to an energy of 80 MeV (mega-electron volts). This is just enough to take them into the next accelerator, PS Booster, where they are further accelerated. Most importantly, The LHC accelerator is composed of a chain of accelerators. This chain starts at the proton synchrotron booster (PSB), which feeds protons into the PS, which then feeds protons into the super proton synchrotron (SPS) and finally, into the main ring of the LHC. All these accelerators can be regarded as one large accelerator, or as three distinct accelerators that feed protons into the SPS which in turn feeds them into the LHC. The first link in this chain is Linac 2. The role of this linac is to accelerate the H-ions from 0 eV to 10 MeV for injection into the PSB.” Linac 2 is a large complex of electronics and machinery with four main operational areas, cryogenics, radio frequency sections, focusing sections and systems to cool, vacuum, and pulsed-power waveform all come together to accelerate protons from 20 MeV to 50 MeV. Linac 4 will use normal conducting copper RF cavities operating at 352 MHz accelerating H– from 20 keV to 5 MeV in 52 cells over 62.4 m (Ünel and Sekmen, 2018). We may think of two situations for these two linacs: First case: the beam should go to them around the same time so that they have enough protons to launch accidents! Second case: one may launch accidents while other linac gets back accurately so that it doesn’t miss the beam this time!!! The main difference between the two is the energy of the particle beam they can provide; Linac 2 can deliver a beam of 50 MeV while Linac 4 can deliver a beam of 160 MeV. The higher energy Linac 4 will be used to deliver protons to fill the LHC with circulating beams, while the lower energy Linac 2 will be used to feed injector synchrotrons, producing beams for experiments. Linac 2 is the main injector. It brings proton bunches to an energy of 50 MeV. On the other hand, Linac 4 is and upgrade of Linac 2 with a higher performance and with more flexibility to match different operating conditions. Two years ago, the LHC was deemed inactive and not running, why so? To answer this, there seemed to be a problem with one of the linacs most likely triggered a shutdown. This is because each proton beam in the LHC is accelerated to its final energy of 7 TeV by two different accelerators: Linac 2 and Linac 4. Each linac consists of a linear accelerator driven by a pulse from a modulator and some additional accelerating modules. To allow for

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global monitoring, both linacs are located outside the tunnel and send their high-energy pulses through transfer lines connecting them to the chain of accelerators at CERN.

6.2.3. The Main Ring The design of the 27 km main ring of the LHC was performed in close collaboration of leading international institutes. A major challenge was the special requirements for vacuum, magnetic stability, and field quality. The 27 km main ring of the LHC follows the natural topology of the terrain and appears in section as an ellipse. It is split into two sectors – east and west – by a broad flat valley, each sector being further subdivided into two. The ring surface is divided three ways, a middle third for the surface return current to circulate, and two outer thirds for the beam pipes. The accelerator is located at a depth ranging between 50 m depending on the geographical location (Tluczykont et al., 2012). The main ring consists of a big ring of magnets to make protons collide very fast and produce data for scientists to study. Moreover, it entails superconducting dipole and quadrupole magnets to guide the protons, cryostat sections to keep the magnets and other lowtemperature components at –271°C, connectors to join the cryostats together and provide cabling access, thermal shields to insulate from the warm tunnel environment (Figure 6.10).

Figure 6.10. Diagrammatic representation of the main ring including its components. Source: Image by ResearchGate.

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As the largest scientific instrument in the world, the components of this machine involve almost every aspect of physics and engineering. The design, production, and assembly of approximately 10,000 magnets and close to 100,000 associated electronic sub-systems required a huge effort from thousands of people. These are arranged into more than 8,000 subassemblies which were brought together in the final stages before installation at point 1 (see right) to make up the full 120-meter-long dipole sections. The dipole sections are the most fundamental components of an accelerator since they are responsible for steering and focusing the particles in their orbit by means of a magnetic field (Shlomi et al., 2020). The LHC overcomes key technical limits of previous accelerators by using high magnetic fields, ultra-precise control of the particle trajectories, novel superconducting radio frequency technologies and design optimizations that minimize synchrotron radiation losses. These innovations, together with improved materials and low electrical resistance, make the LHC 20 times more powerful than any previous accelerator and will allow physicists to study collisions at higher energies than ever before. The ultimate aim is to understand and exploit the properties of the universe at its smallest scales, which are currently inaccessible.

6.2.4. Role of Dipole and Quadruple Magnets Inside the Ring The role of dipole and quadruple magnets inside the ring is not just to confine a beam, but rather to manipulate its phase space distribution, i.e., its shape and size in order to achieve optimum performance (luminosity). For this purpose, other magnetic elements are needed to “sculpt” the phase space. Dipole magnets deflect the beam of particles through an angle as they pass from one section to the next. The beam is deflected either towards or away from the center of a circular particle accelerator depending on the sign of their pole. In addition, quadrupole, and sextupole magnets are used to focus the beam in order to keep particles bundled and on track in the accelerator ring (Figure 6.11).

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Figure 6.11. Cross-sectional view of the LHC main dipole. Source: Image by ResearchGate.

The magnets placed inside the ring convert rotational energy into electricity, which is stored in batteries. Inside the ring, there are dipole and quadruple magnets, they are placed all around the ring to capture momentum of the user’s finger. Every time someone moves their finger, it will help charge the batteries in your phone if you are using our ring. Moreover, the dipole and quadrupole magnets focus the proton beam within the accelerator. The role of dipole magnets is to bend the beam around a curve and the role of quad magnets is to focus the beam into a small size while aligned in a straight line (Seshavatharam and Lakshminarayana, 2013). In the LHC at CERN, superconducting dipole and quadrupole magnets are used to accelerate and focus two beams of protons traveling in opposite directions. The beams pass through two adjacent beam pipes that are held in place by a strong vacuum, with one beam moving clockwise and the other anticlockwise. Powerful magnetic fields created by superconducting coils guide and control the proton beams as they travel at nearly light speed inside the accelerating cryostat. These magnets are made of neodymium, a rare earth material. The dipping and quadruple magnets each do two specific tasks. The dipole magnets are used to steer the beam of charged particles, while the quadrupole magnets focus the beam along the circular path in the accelerator. The magnetic steering forces on each particle are very small, so the ring needs hundreds of magnets. With innovation in progress, this 13th generation fusion device

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will include three major improvements with respect to its predecessors: an extremely high value of the magnetic field on the plasma axis (15 T), a doubling of its diameter from 2 to 4 m and a significant increase of the plasma current, beyond 3 MA. Using an experiment to test a difference between electromagnetic and scalar resonance coupling we designed a simple circuit. There are two parts of circuit. On first one, the input part of circuit, there is a scalar generator with two coils L1 and L2. The resonance frequency for both can be changed by changing the DDS frequency. The phase between them can be adjusted by using capacitors C3 and C4 connected in parallel to both coils. Both coils have same inductance but different number of turns. In experiment described here, we made 120 turns on L2 coil and 360 on L1 coil. Both coils L1 and L2 generate standing waves on their plates. On second part of circuit there are resonators whose output voltage is visualized in scope pictures below. We put two inductors (L3 – primary coil and L4 – secondary coil) into one single coil without magnetic coupling between them so they should not influence each other at all if they. There are 1,232 dipole magnets (magnets for bending the beam path) and 1,241 quadrupole magnets (magnets for keeping the beam focused).

6.3. EXPERIMENTS SITES INSIDE THE HADRON 6.3.1. ALICE The ALICE experiment is one of several particle physics detector experiments at the LHC, a powerful particle collider and the largest machine in the world. It was built by an international collaboration consisting of more than 1,000 physicists and engineers from 100 institutions and 35 countries. The ALICE (A Large Ion Collider Experiment) experiment site inside the LHC, before the start of the 2010 proton run at 7 TeV. The ALICE experiment site is located around point 3 in the image. The detector used at this experiment is called the ALICE time projection chamber (TPC). This has a diameter of 6 m and a height of 4 m; this makes it the largest ever TPC to be built. This image shows the ALICE detector installation inside the LHC tunnel at CERN, in Switzerland, with a member of the collaboration posing for scale (Radovic et al., 2018). The experiment consists of a huge central barrel and several

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smaller sub-detectors moving around it in concentric circles. The innermost part is formed by layers of silicon detectors surrounding the main tracking detector at the center, which is a large cylinder filled with gas. Charged particles are flying through this gas leave trails of gas that can be detected. Outside this going outwards is a much larger cylindrical TPC, which detects charged particles moving through its gas. Following this are two cylindrical tracking devices; one called the inner transition region detector (ITR), and one called the time-of-flight (TOF) detector. This lies alongside several chambers that detect neutrons, photons, and electrons created in collision events in various parts of the central barrel (Figure 6.12).

Figure 6.12. The ALICE experiment. Source: Image by Wikipedia.

The ALICE experiment uses the LHC to collide protons and lead ions in order to study fundamental properties of matter at extreme energy density, temperatures, and pressures. The ALICE detector, suspended from the L3 magnet, is lowered into the underground experimental area at Point 5 of CERN’s accelerator complex. The detector had to be completely dismantled in order to be moved and reassembled inside the tunnel. ALICE is optimized to study heavy-ion collisions at a center of mass energy of √sNN = 2.76 TeV per nucleon pair (7 TeV proton-proton collisions). The resulting temperature and energy density are expected to be enough to produce quarkgluon plasma, a state of matter wherein quarks and gluons are freed. The experiment is named after Alice from Lewis Carroll’s classic novel Through

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the Looking-Glass, as a reference to the Wonderland depicted by the LHC experiments (Pitkänen, 2011). The main experimental chamber of the ALICE detector is located inside the LHC. The LHC consists of a 27 km ring-shaped tunnel in which hydrogen gas atoms are collided at high energy. These collisions produce many different types of particles, including protons, neutrons, and electrons and also rare exotic particles that are not found in nature on Earth but may have been present shortly after the Big Bang. The ALICE experiment is positioned close to the point where the counter-rotating proton and lead ions will cross. The collision region is located inside a detector which consists of several sub-detectors, each with different functions. The ALICE detector is built to study what happened in the first moments after the Big Bang, by studying lead ion collisions at the LHC. It is particularly designed to detect and measure QGP, a state of matter thought to have occurred just after the Big Bang.

6.3.2. ATLAS ATLAS (A Toroidal LHC ApparatuS) is one of seven particle detector experiments constructed at the LHC, a 27-kilometer (17 mi) ring-shaped synchrotron at CERN, which straddles the Franco-Swiss border near Geneva. The ATLAS experiment is one of two large general-purpose particle physics detectors built on the LHC. It is designed to take advantage of the unprecedented energies and to lead the way in charting the unknown, in searching for new discoveries in the head-on collisions of protons of extraordinarily high energy. When the LHC is operating at maximum luminosity, it will produce tens of millions of proton-proton collisions every second. The ATLAS experiment will record about a million of them for further analysis (Pashkin and Leitenstorfer, 2014). From these recorded collisions, ATLAS physicists hope to extract a handful that may reveal new physics, such as the Higgs Boson. The ATLAS detector at the LHC is among the largest and most complex machines ever built. It examines a huge variety of particle collisions so we can discover more about the fundamental nature of matter and the basic forces that shape our universe. ATLAS is one of the two particle detectors for the world’s largest scientific experiment, the LHC. Since 2009, it has been hunting for new particles that could give us a deeper understanding of how our universe works (Figure 6.13).

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Figure 6.13. The ATLAS experiment subsystems. Source: Image by ResearchGate.

The ATLAS detector is four stories high. The central solenoid magnet, which has four concentric superconducting coils, is 15 meters long and weighs about 7,000 tons. Inside the solenoid are three large detector systems that help identify the properties of particles produced in LHC collisions. In February 2013, the ATLAS and CMS collaborations at CERN announced that they had observed a new particle in the mass range around 125–126 GeV. It is hoped that collisions of protons in the LHC will simulate the conditions just after the Big Bang, and thus result in the production of new and exotic particles which may confirm or disprove current theories” The ATLAS experiment at CERN’s LHC discovered the Higgs Boson particle in 2012. It is hoped that it will shed light on new theories of particle physics beyond the standard model (SM). Following a competition among European laboratories, a design by a group at the (CERN) was selected in 1992. Funding for ATLAS was approved by the CERN Council of Members on May 29, 1993 and construction began in 1994. The ATLAS experiment is designed to take advantage of the unprecedented energies and flux of many different types of particles produced in the collisions of protons of extraordinarily high energy. It will learn about their properties, looking for new discoveries in the head-on collisions of protons of extraordinarily high energy.

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6.3.3. CMS The compact muon solenoid (CMS) is a general-purpose detector. One of the two large multipurpose detectors built on the LHC at CERN in Switzerland and France, it was designed to investigate a wide range of physics, including the search for the Higgs boson, extra dimensions and particles that could make up dark matter. The CMS experiment searches for new physics beyond the SM such as extra dimensions and particles that could make up dark matter. The collision point of the LHC is located inside a separate experimental hall on a platform 30 m below the top of C-Collar. The platform dimensions are about 64 m x 32 m, with a height of 6 m. It can accommodate up to 2,500 tons of CMS detector, services, and infrastructure. CMS is one of the two general purpose experiments at the LHC. Operating in a restricted area, the CMS and ATLAS experiments each have access to 6,500 m2 of floor space and 20,000 m2 of underground cavern space. The detector components are assembled in several very large halls close to their point of installation at their final operational locations (Figure 6.14) (Olive et al., 2014).

Figure 6.14. The compact muon solenoid (CMS). Source: Image by Wikipedia.

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The CMS detector is housed in a cavern inside the LHC tunnel. It is 41 meters long, 21 meters wide, and 16 meters high, approximately 1 cubic hectometer. The height and width allow it to fit snugly around the LHC beam pipe, which does not exceed 17 cm in diameter. The construction of the CMS detector was completed in September 2008 and it is currently operational for data taking. The CMS experiment is a general-purpose, forward-backward symmetric detector. It has a compact, cylindrical geometry and covers nearly 4 pi steradians in solid angle. It is designed specifically to address the physics goals of the LHC. CMS consists of layers of various particle detectors, surrounds the collision point. The various layers detect different sorts of particles, for a range of momenta, and also work together to identify particles as electrons, photons, muons, or hadronic jets. The outermost shell of CMS is a hadron calorimeter (HCAL) consisting mostly of heavy steel plates with small sensor gaps interleaved with plastic scintillator tiles. Inside this are electromagnetic calorimeters (ECAL) composed of brass plates with lead radiators and plastic scintillator bars arranged in projective towers inside the HCAL; these instruments provide precise directional measurements of electrons and photons. For momentum measurement in the central region, there are three different technologies: drift tubes (DT), cathode strip chambers (CSC), and resistive plate chambers (RPC). The DTs measure track coordinates along the tubes. The CSCs act as threedimensional tracking devices by measuring track trajectories. The CERN logo is a visual expression that captures the essence of Meyrin campus, the CMS experiment site inside the LHC and the energy of discovery. It symbolizes CERN’s unique diversity, with its 13 member states, but, above all, its unity in scientific endeavor. Each element represents one of CERN’s experiments or sites and all are brought together in a delicate and off-centered balance by the charged particle beams circulating in the LHC. The supermassive metal detector takes up a large part of the 27 km circumference LHC and measures over 14 m in height. The energy of the particles passing through the CMS are measured with precise sensors and triggers, which are constantly updated to get valuable data.

6.3.4. LHCb The LHCb (large hadron collider beauty) experiment at CERN is dedicated to studying the differences between matter and antimatter, which is believed to hold the key to our understanding of what happened in the very early universe (McKenzie, 2014). The LHCb experiment is the only LHC

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experiment devoted to the study of what happened after the Big Bang that allowed matter to survive and build the Universe we inhabit today. LHCb will learn about the fundamental asymmetries between matter and antimatter by studying the decays of b-hadrons, particles containing a bottom quark (Figure 6.15).

Figure 6.15. Schematic view of the LHCb. Source: Image by ResearchGate.

LHCb (Large Hadron Collider beauty) is one of seven particle physics detector experiments collecting data at the LHC at CERN. LHCb is a specialized b-physics experiment, designed primarily to measure the parameters of CP violation in the interactions of b-hadrons (heavy particles containing a bottom quark). Such studies can help to explain the Matter– antimatter asymmetry of the Universe. The detector is located at point 8 on the LHC tunnel close to Ferney-Voltaire, France just across the border from Geneva, Switzerland. It was constructed between 2003 and 2008 by an international collaboration of about 1,500 scientists and engineers from 71 institutes in 19 countries. LHCb is a specialized b-physics experiment, designed primarily to measure the parameters of CP violation in the interactions of b-hadrons. These parameters are fundamental to understanding why there is more matter than antimatter in the Universe, and why the matter that we do observe has a lifespan far longer than initial expectations (Macklin et al., 2014). The LHCb experiment is a single-arm forward spectrometer that performs precision measurements of CP violation and rare decays of beauty, charm, and strange hadrons. The LHCb, in absence of the supersymmetric

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particles and no sign of the Higgs boson after searching through more than 500 trillion proton-proton collisions generated by the LHC, announced its first observation of pentaquarks. It collects data at the LHC at CERN. The experiment is designed primarily to detect and measure heavy flavor baryons (Lambda_b, Xi_b,). The experiment will focus on the differences between particles and antiparticles, on the violation of CP symmetry (an apparent symmetry between matter and antimatter) and on measurements of heavy-quark production. The LHCb detector is a single-arm forward spectrometer. The physics program of LHCb comprises the study of: rare decays of beauty and charm hadrons, Open charm production in proton-proton collisions, CP violation in the B_s and D meson systems, rare decays of B mesons, associated production of Gauge Bosons, Forward physics including diffraction. The experiment is located on the surface and consists of four main sub-detectors: a vertex detector, a spectrometer, a calorimeter, and a muon detector. The main physics goal is to study the slight differences between matter and antimatter, specifically to find out if CP symmetry has been violated. Such studies can help to explain the Matter-Antimatter asymmetry of the Universe. The detector is on the LHC ring close to the ATLAS and CMS experiments, around point 8, shortly after one of the two collision points where proton bunches collide at very high energies. It is sited at one of four experimental areas set far enough apart to allow safe operation while minimizing accidental coincidences between nearby proton collisions. LHCb is an international collaboration of more than 850 physicists and engineers, 286 of which work permanently in 17 institutes, located in 12 countries (of which 61 work in France) and is supported by around 570 engineers and technicians (Lyons, 2012). It might seem surprising that a detector designed to study the particles produced in high energy proton-proton collisions lies beside one that studies high energy lead-lead collisions. Yet there is an advantage: because these collisions are rarer than proton collisions, there is not enough lead circulating in the LHC at any one time to fill it with lead beams. The LHCb detector is a single-arm forward spectrometer covering the pseudorapidity range 2 to 5. A type-II superconducting quadrupole magnet with a pole tip field of about 12 T provides a key component in the design of the LHCb detector: it focuses particles having the same momentum but originating from primary and secondary vertices, which are separated along the beam line.

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6.4. DISCOVERIES FROM COLLIDING PARTICLES 6.4.1. Top Quarks Top quarks were discovered independently at Fermilab in Illinois and the European Center for Nuclear Research or CERN in Geneva, Switzerland, in 1995. At a mass (when at rest) roughly 175 times greater than that of a proton, it is by far the heaviest known elementary particle. Because the top quark decays so quickly, it can be detected only in high-energy collisions between elementary particles. Scientists from around the world continue the particle discovery at Fermilab’s Tevatron collider. The search for the Top Quark, a 27-year quest, may have found its end with the CDF and DZero collaborations’ reporting of simultaneous observations of the particle. Top quarks were first postulated in the SM of particle physics. They were finally confirmed to exist on March 2, 1994, by the CDF and DØ experiments at Fermilab. As such, they are a relatively recent discovery in the realm of subatomic particles. A top quark (also known as an anti-top quark) is a subatomic particle that is most elementary particles are created and destroyed when two other particles collide with each other. The top quark is one of only two particles discovered that have never been observed to change into another form (Figure 6.16).

Figure 6.16. Top quark. Source: Image by Wikipedia.

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The top quarks had no charge, spin equal to 1/2, and could decay or annihilate into other particles. It was theorized that the most abundant particle at the Higgs Boson should be the Top Quark (top quark mass), but it was a difficult particle to find due to its short lifespan and disfavored decay modes.

6.4.2. Bottom Quarks The fundamental building blocks of matter and our universe, a subatomic particle colliding with its antiparticle at the world’s largest and most powerful particle accelerator reveals an unexpected new form of matter. By combining insights from several experiments and computer simulations, scientists have discovered that bottom quarks, part of the third generation of quarks in the Periodic Table of Particles, do not always act as expected. The result shows that bottom quarks can sometimes form excitons – tightly bound subatomic particles that behave like atoms – as they pass through a superfluid liquid (Amsler et al., 2008). The project initially involved creating a proton-proton collider that would eventually reach extremely high energies, allowing for the creation of heavy particles. The physicists spent months at the Fermi lab in Batavia, Illinois, directing events with massive subatomic particles. They created an instrument called a spectrometer specifically designed to detect bottom quarks before they dissolved again into electrons, which are elementary particles. In 1969, they detected their first quark. What used to be called ‘beautiful’ in particle physics is now referred to as the “bottom quark,” and you’ll find this new particle inside every type of atom in our universe. The discovery of the bottom quark in 1977 with the help of a high-energy particle accelerator at Fermi National Accelerator Laboratory was significant because it made it possible to understand what matter is made of at such a small scale. The very existence of bottom quarks demonstrates that the universe could transform in a way that creates new, heavy particles, transforming energy into mass. Bottom quarks are produced frequently in high-energy collisions of other particles, resulting in a down quark and an antibottom quark. Since bottom quarks have a much longer lifetime than the timescale of typical particle experiments, they appear as jets of hadrons without any accompanying leptons. Two bottom quarks are required in the “flavor diagram” synthesis reactions to form lithium-8 and beryllium-8, although unstable beryllium-8 decays almost instantaneously into two alpha particles. According to quantum chromodynamics (QCD) theory, when a proton collides at such high energy

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with another object (in this case, a gold nucleus) that it “dissolves,” the quarks and gluons that make up the protons and neutrons are free to interact with each other in a way they usually do not. These interactions lead to the creation of new particles: jets of hadrons and single particles which can crash with other particles in the detector and create even more.

6.4.3. Charm Quarks Charm quarks; a particle initiated by assigning matter and antimatter to a negatively charged particle. An initiator in the search for whether there is an asymmetry between matter and antimatter. The discovery of quarks and charm quarks, introduced a new concept in elementary particle physics. Two Nobel Prizes have been awarded for the discovery of charmed particles. “Charm Quarks; a discovery of colliding particles” provides information on the study of particles. Charm quarks play an integral role in the SM of matter, accounting for a wide range of subatomic particles, from kaons to charmed mesons to D-Omegabarions, and are thus responsible for the fact that objects can hold together. They are also essential to our current theory about how the Universe began. Charm plays a role in the transition of quarks (the building blocks of the protons and neutrons that make up atoms). The existence of charm was first predicted in 1964. By 1968, it was known to exist and by 1974 it was possible to detect its effects.

6.4.4. W&Z Bosons W boson (W-BOS’un), also called intermediate vector boson is a heavy subatomic particle that mediates the weak force (weak interaction). The weak force, one of the four fundamental forces, is responsible for radioactive decay and for some type of nuclear fusion in stars. The W boson has a positive charge, which it can impart to other particles when it decays. In 2008, at the LHC in CERN, Switzerland, the world saw the discovery of colliding W and Z bosons. These subatomic particles exist both in the SM and in unified theories of Weak and Electromagnetic Interactions (Long et al., 2021). The discovery of W and Z bosons, respectively, in the 1983 and 1984 experiments at CERN represents one of the landmarks in 20th century physics. For a period long after their observation, there were many numerous challenges to their existence. Today, they are considered to be among the most significant discoveries associated with that research center. The W and

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Z bosons are elementary particles that mediate the weak interaction; their symbols are W+, W–, and Z. The discovery of the W and Z bosons in 1983 and their properties were fundamental to further development in particle physics, such as the unification of electroweak interactions. Particle collisions are key to understanding the nature of matter, and this new discovery will bring us closer to unraveling what it is.

6.5. CALCULATIONS OF THE DYNAMICS OF COLLISION

The complexity in calculating the dynamics of the collision is that it is necessary to take into account the role of many factors: collisions occurring, the material of the colliding bodies, etc. The calculations are separated by the regulation of elastic collisions and inelastic. The most common mechanical problem in physics is an elastic collision between two bodies of relatively small mass. The equation for calculating the initial speed of one body after collision depends on two factors: coefficient of restitution and angle at which the velocity vector of one body intersects with the velocity vector of another; for calculation you need to know: initial velocities bodies before impact, mass, coefficient of restitution and corner reflection, depending on what you want to calculate or find unknown value (Abdelrahman and Sohaly, 2018).

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Accident reconstruction calculations typically involve the dynamics of collision between motor vehicles using the principles of physics. An understanding of the basic physical principles involved, coupled with a knowledge of collision reconstruction methodology, can be used for the purpose of determining how and why an accident occurred. The equations of motion are used to determine the velocity and position of a body or bodies at any time after impact. Calculations are typically carried out in one dimension, as well as two dimensions whenever applicable. The collisions of particles are studied. The objective is the problem of collisional capture of the satellite by an endeavor. It is carried out numerical calculation of the dynamics of collision and analysis of the results. It is shown that in the favorable conditions, that lead to the formation of stable motion, occurs in a very short time interval. This permits you to use a simplified description. The system includes a method for calculating the energies of impact, dynamical parameters of collision (the coefficient of restitution, coefficient of friction and tangential impulse), which approximates to a first order.

CHAPTER

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NEW DISCOVERIES IN PARTICLES

CONTENTS 7.1. Parity Violation in Weak Interactions ............................................... 174 7.2. Cp Violation.................................................................................... 176 7.3. Implications of the Discovery of CP Violation ................................. 180 7.4. Neutrino Masses ............................................................................. 181 7.5. Heavy Quack Symmetry ................................................................. 185 7.6. Effective Field Theory (EFT) ............................................................. 187 7.7. Feynman’s Paradox ......................................................................... 188 7.8. Hadrons.......................................................................................... 190

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New small elementary particles are being discovered. Progresses in elementary particles reveal how the universe works and adapts to changes. In the 1960s and 1970s, physicists discovered four fundamental forces: gravity, electromagnetism, and the “strong” and “weak” nuclear forces. All four are described by gauge theories, analogous to the way that electromagnetism is described by Maxwell’s equations. In the early 1970s physicists found a way to unify three of these early into a single theory called the standard model (SM) (Liu et al., 2017). Since the SM of particle physics was first proposed, there has been a torrent of findings that have led researchers to believe that an unknown element—dubbed “dark matter”—accounts for about 85% of all matter in the universe (Figure 7.1).

Figure 7.1. The large hadron collider where particles discoveries are made while they break the known laws of physics. Source: Image by National Geographic.

The discovery of the Higgs particle a few years ago was an important step forward in our understanding of elementary particles. However, many questions remain unanswered. One big question center on the nature of dark matter, which makes up more than 80% of the mass in the universe but has so far eluded detection. Much of current research in high energy physics centers around detecting signatures for dark matter and understanding what it can tell us about our universe. Another line of research is devoted to understanding why elementary particles have mass, a property that is still not fully understood 50 years after its introduction in the theory of weak interaction. A whole new set of experiments is currently being constructed whose aim is to further our understanding of the SM (which describes

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elementary particles and their interactions) and search for signs of new phenomena beyond it. Particle physics continues to be the gateway through which we confront a great many puzzles of physical reality. While relating these developments and challenges faced, the emphasis is on science (rather than politics) and on physics insights rather than painstakingly detailed discovery chronicles. These discoveries are a basis of elementary particles (Leader, 2016). Elementary particles are subatomic particle which are most important constituents of matter and radiation. Yet indeed, there has been a revolution in elementary particle physics in the last 75 years. It began with a theory by Dirac of quantum electrodynamics (QED) and developed into the theory of quarks and gluons, which has been so successful that it is generally thought that the major advances in this field are over (Figure 7.2).

Figure 7.2. Subatomic particle disintegration: The basis of particle discovery. Source: Image by SciTechDaily.

On November 21, the Nobel Assembly at Karolinska institute decided to award the 2019 Nobel Prize in Physics with one half to James Peebles for theoretical discoveries in physical cosmology, and the other half jointly to Michel Mayor and Didier Queloz for the discovery of an exoplanet orbiting a solar type star. For the last 75 years there has been a revolution in elementary

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particle physics. It began with a theory by Dirac of QED and developed into the theory of quarks and gluons, which has been so successful that it is generally thought that the major advances in this field are over. There are four possible areas of new discoveries: (a) CP violation, which is better understood theoretically than experimentally; (b) neutrino masses; (c) heavy quark symmetry; and (d) effective field theory (EFT). Discoveries in elementary particles is the subfield of particle physics which has been most rewarded with Nobel Prizes, including almost half of all Physics Prizes. While the first discoveries were made in a wide range of topics, there were two major themes: hadrons (1993) and parity violation (1995), each receiving its own prize during 1995. Since the 1960s, the foundations of physics were shaken by two discoveries that were completely unexpected (Lasserre, 2014). The first was the discovery of parity violation in weak interactions in 1956. The second, which took over a full decade to be realized from the first hints in 1964, was CP violation, discovered in a series of experiments culminating in the work of Cronin and Fitch at Brookhaven National Laboratory (BNL) in 1964.

7.1. PARITY VIOLATION IN WEAK INTERACTIONS The discovery of parity violation in weak interactions was of fundamental importance in elementary-particle physics. In 1956, Tsung-Dao Lee and Chen-Ning Yang published papers proposing that parity was not conserved in the weak interactions. The discovery of non-conservation of parity in weak interactions actually happened in summer 1956 at the BNL in New York by T. D. Lee and C. N. Yang, but only became broadly known in 1957 after work by Madame Chien-Shiung Wu, who performed a decisive test of their hypothesis at Columbia University. Parity non-conservation came as a complete surprise to most physicists at that time, since it violates an intuitively reasonable symmetry between the left and right sides of space (Figures 7.3 and 7.4).

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Figure 7.3. Sketches of conceptually parity violation in beta decay. Source: Image by ResearchGate.

Figure 7.4. The BrookHaven National Laboratory; where the discovery was made. Image by Brookhaven National Library.

Parity violation in elementary particle physics is a phenomenon in which there is a difference in physical processes that occur for particles of opposite spin and handedness (chirality) on the basis of their weak interactions

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with other particles. By 1954, most scientists expected that subatomic interactions were symmetrical – that is, an interaction would look the same if you reversed all its variables. This symmetry was based on the idea that a particle’s spin was irrelevant to its properties. Theoretical physicist ChenNing Yang disagreed with those expectations (Kibble, 2015). He and his colleague Tsung-Dao Lee proposed a very rare scenario in which the spin would matter: their equations showed that a decay between two beta particles might be possible only if one of them moved left-handedly, not spherically, since spin is a form of angular momentum. The fact that it appeared certain particles have “handedness” was puzzling and revolutionary, but in 1957 experiments supported Yang and Lee’s prediction. In elementary particle physics, parity non-conservation is a violation of the mirror symmetry of the laws of physics. This means that mirror symmetry does not hold for every physical law: if a physical system is exchanged with its mirror image, the resulted mirrored system can behave differently from the original system.

7.2. CP VIOLATION Cronin and Fitch observed CP Violation in 1964. This observation was due to an asymmetry in particle decays through the neutral K meson decay mode that violates the rule of charge parity conservation. The Nobel Prize was awarded to them in 1980. The discovery was made in a series of experiments at BNL. It changed our fundamental understandings regarding the basics of particle motion. CP Violation violations were both a puzzle for physicists and a key to their understanding of how matter developed following the big bang (Kohls and Mele, 2018). The discovery of CP violation in 1964 changed the field of elementary particles profoundly. It was one of the first evidences for physics beyond the SM and motivated model-building for decades. It is also a major ingredient in many problems in cosmology, and of current interest because of inconsistencies between measurements, which might point to new physics (Figure 7.5).

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Figure 7.5. CP violation – the different types. Source: Image by SlideToDoc.com.

CP violation is a fact of life. We may worry about its consequences for the stability of matter, but CP violation is seen as a new phenomenon that illustrates the richness of phenomena to be found in nature. CP violation affects many different areas of particle physics. Its presence in the decay of the neutral kaon system was an important discovery, which won the 1980 Physics Nobel prize. It is based on the fact that elementary particles and antiparticles react differently to a combination of the charge-conjugate transformations C and parity reversal P. CP symmetry arises when the laws of physics are the same if a particle is interchanged with its antiparticle (charge conjugation C) while its spatial coordinates are inverted (parity inversion P). Violation of CP symmetry manifests itself in various ways, most clearly as a difference between matter and antimatter particle decays; this is most evident in the decays of neutral kaons into pions (Figure 7.6).

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Figure 7.6. CP violation discovery at 3 σ fraction. Source: Image by ResearchGate.

When the mass of a neutral K meson (composed of a down quark, antiup quark, strange anti quark) is heavier than that of an anti-neutral K meson (composed of a down anti quark, up quark, strange anti quark) or vice versa, the CP symmetry is said to be violated. Indeed, in 1964 physicists Christenson and Cronin showed the asymmetry between both particles when observed long after their decay. They couldn’t know at the time that this would lead to one of the greatest discoveries in elementary particle physics: the violation of CP symmetry with enormous implications for modern physics. It relates to the fact that in 1960s we knew that K-meson was composed of both antimatter and matter, but the decay was asymmetric with time. Which means K would decay faster to π+. As a result, the antimatter decays slower than the matter (K⁰) itself. This led to the find of CP-violation observation. This project is an experiment to measure the CPT-symmetry violation from entangled particle within a magnetized container. C.P. violation was discovered in neutral kaons many years ago (Kahle et al., 2016). The discovery played a major role in the understanding of elementary particles and their interactions and motivated the development of theories beyond the

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SM that have some experimental evidence now. In this talk I will discuss aspects of C.P. violation in particles, some connections to cosmology and the SM as well as discuss what implications of such a discovery might bring to our understanding of physics beyond the SM. CP violation continues to be a subject of great interest since its discovery by Cronin and Fitch in 1964. After more than 40 years of research at high energy laboratories, yet more detailed studies of CP violation have become possible with the recent upgrade at the BNL that has resulted in an increase in the intensity of polarized anti-protons and polarized protons by about four orders. Future experiments at this laboratory may lead to greater surprises. If such turns out to be the case then these are likely to have great relevance for our understanding of cosmology and for satisfying some of the many questions still outstanding in elementary particle physics (Figure 7.7).

Figure 7.7. Discovery of CP violation in charm particles. Source: Image by LHCb Experiment.

CP violation is a small but measurable difference between reactions in which all particles behave as though their spin, electrical charge and other similar properties were reflected in a mirror and reactions in which all the particles’ properties are the same as those of their mirror image particles. CP symmetry is a fundamental symmetry of the laws of nature that states that it takes the same amount of time for a process to occur as for the time-reversed process to occur (Jaeckel and Ringwald, 2010). In particle physics, CP violation is a violation of charge conjugation parity symmetry: the combination of C-symmetry (charge conjugation symmetry) and P-symmetry (parity symmetry). CP-symmetry states that the laws of physics should be the same if a particle were interchanged with its antiparticle (C symmetry) while simultaneously swapping left and right (P symmetry). The discovery of CP violation in 1964 in the decays of neutral kaons resulted in

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the Nobel Prize in Physics in 1980 for its discoverers James Cronin and Val Fitch. It plays an important role both in the attempts of cosmology to explain the dominance of matter over antimatter in the present Universe, and in the study of weak interactions in particle physics.

7.3. IMPLICATIONS OF THE DISCOVERY OF CP VIOLATION The discovery of CP Violation was important because it provided a clue to the puzzle that particle physicists were busy piecing together, aiming to bring order out of chaos and demonstrate that the elementary particles are not merely fundamental entities at random. If no CP violation could be observed or predicted, then the only expectation of physics would be a completely symmetric universe. This universe would also be composed of equal amounts of matter and antimatter and all reactions would be perfectly symmetric. The fact that there has been a slight difference between how matter and antimatter behave has opened up new lines of research into our understanding on what happened at the very beginning of the universe (10– 43 seconds after the Big Bang) (Figure 7.8).

Figure 7.8. The significance with which CP violation can be discovered as a function. Source: Image by ResearchGate.

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CP violation, which is a difference between the behavior of matter and antimatter, had been predicted to occur in nature. It was first discovered in 1964 in the decays of neutral kaons. For this discovery, Cronin, and Fitch were awarded the 1980 Nobel Prize in Physics. Many years of work were required to understand these phenomena. The Story of CP Violation explains how these discoveries were made and what they mean, both for particle physics and more generally. It focuses on a small number of key ideas that have shaped our understanding of CP violation and its implications for cosmology. Aimed at graduate students, it can also be used by practicing physicists wishing to review this exciting field.’ This discovery is responsible for the matter-dominated universe we live in today. Continuous search for further manifestations of CP violation is going on at several laboratories all around the world. Discovery of CP violation beyond two Kaon (pion) decays would imply that our knowledge about particles and fundamental forces is far from complete, thus stimulating new ideas and possibly new theories beyond the SM for elementary particle physics (Ishimori et al., 2010). It is suggested that the result can be accommodated in a theory in which the weak-interaction mass eigenstates are not purely up or down, but have a small component of opposite-helicity states. This discovery is an important step towards understanding how the universe evolved after the Big Bang. It gives theoretical astrophysicists a new tool to test whether they really understand what happened when it all started, and therefore how the universe looks today. We do not know why our universe is made out of matter but not antimatter.

7.4. NEUTRINO MASSES The knowledge of fundamental particles has been considerably extended in recent years by the discovery of neutrino oscillations. We demonstrate that this qualifies as a second discovery of neutrino masses. The first discovery was made in neutrinoless double beta decay. The two discoveries are complementary and can be made with very different types of (future) experiments and with different techniques of data analysis with the present result, we show that there is no theoretical or practical reason for not applying the same criterion for discovery to both cases. We further propose an operative definition for the term ‘probable’ in particle physics, which specifies measurable outcomes and experimental requirements to guarantee that a claim to have discovered something new is substantive and reproducible. The Noble Prize in Physics was recently awarded to the

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discovery of neutrino mass. We show how this discovery has opened up a new era in elementary particle physics and cosmology that could lead to a deep understanding of the Universe (Figure 7.9).

Figure 7.9. A graphical view of neutrino mass. Source: Image by Wiley Online Library.

The discovery of neutrino masses, the first in elementary particle physics and a unique discovery in the field since quarks and gluons, is proposed to be considered as a result deserving the 2020 Nobel Prize. The temperature spectrum of the cosmic microwave background radiation and measurements of cosmological parameters, suggesting relatively large effective number of neutrinos N_ {eff}, may reflect new physics beyond the SM with light sterile neutrinos; while the (3+1) mass scheme is favored by neutrino oscillation data, which also indicate a normal ordering of neutrino masses (Figure 7.10).

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Figure 7.10. Neutrino mass eigenstate flavor composition and mass pattern in the two cases of normal (left) and inverted (right) hierarchies. Source: Image by ResearchGate.

The existence of neutrino masses is a long-time puzzle in elementary particle physics. The reasons are, first, that the three species of known light neutrinos are all massless in the SM of particle interactions and second, that a massive neutrino would contradict the observed quenching of the solar electron neutrinos. If a neutrino is large enough to be noticed by measuring something else, it must be virtually at rest because it moves so slowly. If a large object is moving close to the speed of light, its momentum becomes so great that its velocity does not vary much from the speed of light. This mass cannot be measured by observing its momentum, but it can be detected by measuring some other property that depends on it. Neutrinos, born as massless particles in the hot big bang, developed into massive particles as the universe evolved. It is thus with great excitement that we learned about the discovery of nonzero neutrino masses through the observation of oscillations in a variety of experiments. This chapter is both a review of this exciting field and an attempt to place it in the context of modern elementary particle physics (Humbert-Droz et al., 2019). We use three main examples: nuclear beta decay; the solar neutrino problem;

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and atmospheric neutrinos. Although these phenomena were initially quite puzzling, they all now provide strong evidence for nonzero neutrino masses and have opened up new research areas with profound implications for both cosmology and particle physics beyond the SM. The Foundation recognizes the discovery as one of the most important discoveries and breakthroughs in modern physics. This is the first evidence that neutrinos are massive particles and may have equal mass, which provides answers to new questions in elementary particle physics and draws attention to the new direction of research. In particular, this discovery raises the question of how neutrinos got so little mass; physical theories that can answer such questions can potentially solve many other problems, including explaining the nature and origin of dark matter. Despite more than half a century of intense experimental work, neutrinos have remained enigmatic. There is now convincing evidence for tiny neutrino masses, which cannot be understood within the SM. If confirmed, these neutrino ‘oscillations’ will be seen as a tragedy or a triumph in particle physics. It would mean that either the theory has to be abandoned, or else… Since the observation of neutrino oscillations in 1998, neutrino physics has come of age. It has truly become a precision science, revealing yet another layer of organization of matter at the smallest scales (Heckman, 2010). While matter is organized according to particle charges and the strong or weak nuclear force, its mass structure is governed by a new symmetry associated with neutrinos. This symmetry can be broken by a small amount through vacuum expectation values of scalar fields. Experimental evidence for neutrino masses has been amassed over the past 20 years and is now as compelling as that for quarks and leptons. Neutrino oscillations have shown that neutrinos must be massive, a discovery that has required small and non-zero mass differences between the different neutrino species. Neutrinos form the lightest massive particles of the SM. In combination with cosmology and big-bang nucleosynthesis, oscillations measure their absolute masses to be less than about 0.5% of the electron mass. This is a remarkable finding, as it is far below any other mass scales in the theory. We shall not only review experiments but also propose new scenarios for measuring neutrino masses, which offers prospects on physics beyond the SM. Abstract Neutrinos are the most elusive of all elementary particles, and undoubtedly one of the most numerous. Their initially mysterious absence was first experimentally established in 1956 by Reines and Cowan, who

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received the 1995 Nobel Prize for this discovery. Certainly, over the years this weakly interacting particle sometimes assumed a rather uncertain status among nuclear physicists. Its mass was not predicted but only postulated in 1931 by Pauli. Many attempts to confirm its existence failed until 1957 when Rebsamen and Miethe (1955) found evidence for it in electron capture decay of tritium for which they shared the 1977 Bruno Pontecorvo Prize with Ledermann et al. The discovery of neutrino oscillations in 1998 by Fukuda et al.; Weinheimer et al.; and Bahcall finally demonstrated that neutrinos are massive and influenced the title of this talk. In fact, short thereafter it was finally proven that neutrinos were not massless by Kajita, McDonald, and Pontecorvo who were awarded the 2015 Nobel Prize for their proof that neutrinos oscillate. The mystery lives on: Neutrino masses cannot be explained within the currently favored model of elementary particles as they would require fundamental.

7.5. HEAVY QUACK SYMMETRY In recent developments, the Quack Theory has received a great deal of support. Assuming that Heavy Quacks exist, new predictions have been made and verified to within 1% accuracy. This theory supersedes the SM, opening a new paradigm in elementary particle physics. It is proposed that Heavy Quark symmetry is not just an approximate but, rather, an exact symmetry of the strong interactions. Under heavy quark symmetry, all heavy flavors transform identically; heavy quarks with different spin and/or space projections can be interchanged. This is based on new evidence from recent experimental results where the transverse momentum dependence of the masses of D (+) D (–), D (0) over bar, Lambda(c) (+) and (c) over bar baryons have been explored (Graña and Herráez, 2021). In addition, we show that Heavy Quark symmetry predicts a set of sum rules which are constrained by current experimental data to within errors of order 15%. A new discovery by theoretical physicists that means the universe contains many more elementary particles than previously believed (Figure 7.11).

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Figure 7.11. Symmetry and asymmetry which led to the formation of the universe. Source: Image by Big Think.

Although quarks are among the most famous theoretical particles, there are few experimental studies of hadrons containing two quarks. One such system is the “di-quark,” in which experiments show a fermion with two valence quark colors. Each valence quark has the same mass, spin, and flavor label. In the present chapter we show that there is an unknown property that can distinguish between any two valence quarks called “heaviness” that can be determined by combining Poincaré symmetry and renormalizable quantum field theory. A symmetry of the forces is presented that is a generalization of the SM and can account for gravitation. The motivation for its development was an attempt to identify an underlying cause for mass generation in elementary particles, a problem that remains unsolved in the SM. The symmetry called Heavy Quack was discovered after several attempts to build quark models based on simpler symmetries failed. Heavy Quack turns out to be exceptional, because it leads naturally to a coupling constant that is priori reasonably close to experimentally measured values. Furthermore, Heavy Quack symmetry can be built upon the basic tenets of special relativity, which has been important in the growth of physics in the last century (Fraser, 2011). Lastly, it is shown that Heavy Quack symmetry leads to a viable and natural candidate for dark matter whose masses are determined as part of

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successful fits made here to quark and lepton masses. The Heavy Quark Symposium (“HQS”) is an international conference for the discussion of experimental and theoretical problems related to heavy quarks (charm, top, and beauty) and the physics of heavy-flavor states. Its purpose is to facilitate the exchange of information among researchers who use various techniques, such as e+ e– annihilation, deep-inelastic scattering, fixed target experiments, colliding beam experiments and methods such as perturbative QCD, lattice QCD and phenomenological models. It is held biannually in odd-numbered years.

7.6. EFFECTIVE FIELD THEORY (EFT) Effective field theory (EFT) is an approach for constructing quantum field theories that emphasizes the physics of a particular energy scale, such as those probed by a specific particle accelerator experiment. It achieves this focus by integrating out fields associated to higher energy scales, leaving behind an effective Lagrangian that describes only the lower-energy modes (Figure 7.12).

Figure 7.12. An illustration of effective field theory. Source: Image by MIT OpenCourseWare.

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In the 1940s theoretical physicists were using Quantum Field Theory to describe particles. In the 1970s theorists used EFT to describe nucleons. These theories used the same math and were often taught in the same courses. But by the 1990s some theorists began to talk about two different discoveries: Elementary Particles and Nucleons. This did not mean relabeling old discoveries but rather involved new insights about particles and nucleons. The discovery of a new physics in elementary particles, testing in high-energy collisions, has led to a paradigm shift in the interpretation of experimental results and our understanding of the mechanisms underlying collisions at high energies. The new physics is presented here, utilizing a new theory (EFT), which is mathematically and physically distinct from previously available theories (quantum chromodynamics (QCD) or quantum electrodynamics (QED)). In the theory of fundamental interactions, a model called effective field theory (EFT), and is used to describe elementary particles. The model has been considered effective by scientists, and led to many discoveries in the field of elementary particles. EFT is the extension of quantum field theory to systems with a large separation of scales (Francescon et al., 2013). It provides an approximate low-energy description of physical systems in which the fundamental physics responsible for a phenomenon appears at high energies and can only be observed indirectly. EFT has been applied in many areas of physics, including particle and nuclear physics, condensed matter physics, and cosmology. It is also a useful tool in analytical calculations in quantum field theory it has inspired progress in a number of new fields including dimensional analysis and numerical methods for effective field.

7.7. FEYNMAN’S PARADOX Feynman’s paradox is a causal relation mechanism between elementary particles, which to date has been considered only an analogy. However, as shown in this chapter on the basis of QED, Feynman’s interaction is true and exists. Its underlying principles come from the superposition principle of quantum mechanics. Furthermore, the underlying principle of Feynman’s interaction is a new discovery in elementary particles physics (Figure 7.13).

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Figure 7.13. An insightful quote by Richard Feyman. Source: https://www.azquotes.com/quote/1040427.

In statistical mechanics, Feynman’s paradox is a thought experiment devised by American physicist Richard Feynman to illustrate and challenge the second law of thermodynamics. The second law is often stated as follows: In an isolated system that is not in thermal equilibrium, any variant of a given process will cause a spontaneous process toward thermal equilibrium. In the experiment, one uses a box containing an imaginary ideal gas perfectly partitioned into two halves by two walls (each wall has an open door). One fills up one half with the maximum concentration of molecules and keeps the other half empty, so that there is no question about which way heat will flow. The door to each half is then shut and the two compartments are left alone for very long periods. After a period of time, when one opens the doors, instead of molecules having flowed only from one compartment to the other, they will have become scattered almost randomly among both compartments. Feynman’s paradox arises in the study of the Compton Effect, where light is scattered by electrons. The theory of QED can be used to predict the scattering probability for any given incident photon energy, but this requires computing an infinite series of diagrams of increasing complexity. Feynman realized that a simple argument based on Newtonian physics could provide an extremely crude approximation to the QED result, and that this approximation would become exact in a specific limit: low photon energy, intermediate scattering angle and weak coupling constant (Feroz et al., 2009). For these conditions the QED prediction diverges from the non-

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relativistic result by only 20%, which Feynman interpreted as a probable experimental discovery of a new particle with a mass roughly equal to that of the electron. It is now known that our best physical theories support Feynman’s conclusion. Feynman’s idea of a charged particle propagating towards an infinite plane, perpendicular to the field lines, is a paradox that is derived from the known effects of all integrals. This idea has never been explained in great detail before, but it is shown that all integrals that do not include all possible values of velocity or acceleration, are subject to the same line of reasoning as is used here.

7.8. HADRONS In early 2012, a team of scientists led by Dr. Fernando Tavera of the Instituto Superior Tecnico in Lisbon, Portugal, and including researchers from Portugal, Italy, Germany, and the United States probed deep beneath the Earth’s surface at a facility called Gran Sasso in Italy with an instrument called OPERA that, over a three-year period, was able to detect particles known as hadrons that originated from deep space. These particles are known to be generated from the decay of neutrons (from other galaxies) at extreme energy levels. Hadron theory has been long advocated by scientists who study the Higgs Boson (the so-called God particle) as a way to probe deeper into the known universe for evidence of new life forms. Hadrons are elementary particles. In the list of full particles, there are 34 types of elementary particles. All hadron consists of two or more quarks. Hadrons appeared as a new discovery in elementary particles. According to their structure, all existing hadrons are divided into two groups: the baryons and the mesons. Baryons have spin 3/2, the mass is higher than that of mesons, and they participate in nuclear reactions together with protons and neutrons (except anti-protons, which can be annihilated in particle accelerators). Mesons have spin 1 and a mass much lower than that of protons or neutrons; they are less stable than baryons and decay into electrons, positrons, and neutrinos in a very short time. These particles show the characteristics of different properties depending on the degree of freedom. Scientists explain these properties in terms of three types of quarks: up, down, and strange. However, this model is not enough to explain certain properties of particles, so we introduce a new particle named with quarks: charm (c) or bottom (b) which are called fourth generation particles. Hadrons are one type of elementary particles that include, mesons (2 quarks), baryons (3 quarks),

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anti-hadrons (2 anti-quarks and 1 quark or vice versa) (Farnsworth and Boyle, 2015). In resolving unprecedented puzzles generated by the interactions of hadrons, theoretical physicists and experimentalists were driven to conclude that model-independent evidence now clearly indicates a paradigm shift in our understanding of these subatomic particles. This paradigm shift sets hadrons apart as a new class of elementary particles whose discovery is only now being widely acknowledged. Elementary particles are the final building blocks in all matter.

CHAPTER

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APPLICATIONS OF ELEMENTARY PARTICLES

CONTENTS 8.1. Introduction .................................................................................................. 194 8.2. Applications of Elementary Particles .............................................................. 194 8.3. Use of Elementary Particles in the Sakata Model............................................ 195 8.4. Application of Elementary Particles in Measurement Problems ...................... 197 8.5. Application of Elementary Particles in Muon Precession Frequency ............... 198 8.6. Antineutrino Energy Spectrum ....................................................................... 199 8.7. Application of Elementary Particles in More Discoveries of Physics ............... 200 8.8. Application of Elementary Particles in Nanoparticle Tracking......................... 201 8.9. The Photo-Sensor Panel Technology............................................................... 202 8.10. Application of Elementary Particles to the Problem of Compositeness ......... 204 8.11. Application of Elementary Particles in the Control of Airborne Infectious Disease ....................................................................... 205 8.12. Application of Elementary Particles in Organic Chemistry ........................... 206 8.13. Application of Elementary Particles in Controlling Covid-19 in Ventilation Systems ................................................................................ 208 8.14. Application of Elementary Particles in Quadratic Time................................. 209 8.15. Application of Elementary Particles in Transferable Dynamic Molecular Charge ...................................................................... 211 8.16. Application of Elementary Particles in Neutron Imaging Experiments .......... 212 8.17. Application of Elementary Particles in Quark-Gluon Plasma ........................ 213 8.18. Application of Elementary Particles in Tomographic Imaging of Laser-Plasma Structures ......................................................................... 214 8.19. Application of Elementary Particles in Multistage Geminate Reactions ........ 215 8.20. Application of Elementary Particles in Modern Circulating Accelerators ...... 215

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8.1. INTRODUCTION The tiniest core foundation of the universe are said to be the elementary particles; whose internal structure is yet to be defined, for most scientists have concluded that they are zero-dimensional points that do not occupy space; however, they have mass, they experience change, and they spin. The most common types of elementary particles include: quarks, leptons, antiquarks, antileptons, and antimatter particles among others (El Naschie, 2009). Elementary particles serve several purposes; more so with the fact that they are the smallest building blocks of the universe.

8.2. APPLICATIONS OF ELEMENTARY PARTICLES 8.2.1. Elementary Particles Are Used in the Parton Picture There are numerous ways in which Parton’s hypothesis can be developed further. The first step is to research quantum physics in the infinite momentum zone, which will take several years. This analogy is used to demonstrate how non-relativistic reasoning may be employed in relativistic contexts using the Galilean principle. When utilizing infinite momentum quantum mechanics to compute the radius of a relativistic bound state, it is conceivable to represent space and time as a collection of peripherals and to use the eikonal technique for high energy scattering (Figure 8.1).

Figure 8.1. An illustration of the Parton picture. Source: https://www.google.com/imgres?imgurl=http%3A%2F%2Fwww2. physics.umd.edu%2F~yskim%2Ffeynman%2Fppic%2Fquapar55.

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jpg&imgrefurl=http%3A%2F%2Fwww2.physics.umd.edu%2F~yskim%2Ffey nman%2Fpartons.html&tbnid=3bli0GozkExEFM&vet=12ahUKEwjMorjQhfj 1AhXj8LsIHe_DByoQMygPegUIARDWAQ.i&docid=hHZDZzz7sXNLmM&w =1200&h=1069&q=elementary%20particles%20in%20the%20parton%20pi cture&ved=2ahUKEwjMorjQhfj1AhXj8LsIHe_DByoQMygPegUIARDWAQ.

The most frequently encountered phenomenological uses of the parton model are reviewed and explained in detail. The shrinking photon effect, deep inelastic electro production, and heavy lepton pair production are only a few examples of what is possible (Dubois-Violette and Todorov, 2019). A parton model incorporates the hadronic string model into an infinite momentum frame, thus it is called a parton model. In this chapter, the distribution of parton spins and currents in a hadronic string is investigated. Several properties of the lattice can be linked to the meson spectrum, and we propose that this is a good way of thinking about hadrons. The spin lattice concept can be used to improve the performance of deep inelastic electron and neutrino scattering experiments. Structure functions are expected to be predictable in their behavior during these operations. With the use of the string model, we are able to explore the formation of multiparticles. When accelerating at different rates of acceleration, this data can be utilized to determine longitudinal and transverse momentum distributions as well as charge per secondary and secondary system correlations. The consideration of an altogether new class of phenomena, one that is not explained by the string model, is being considered. “Hard Parton effects” is the term used to describe this phenomenon. Among the secondary effects in this category are the development of large transverse moments and the logarithmically increasing total cross sections, to name a few examples.

8.3. USE OF ELEMENTARY PARTICLES IN THE SAKATA MODEL All interactions, including electromagnetic interactions, are classified using a simple subgroup of the 3-D unitary group, which is defined as follows: There are many various types of interactions that can take place, but these are the only ones that take place (Dubbers and Schmidt, 2011). When this technique is applied to leptons, there is no direct electromagnetic mu-e decay, which is detrimental to their survival in the universe. Plans for lowering the degeneracy of the mu-e mass are examined, as are the applications of these proposals.

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8.3.1. Single-Particle Spectroscopy Cesium halide perovskites, which are light-emitting materials, are very good at masking structural flaws. They have become a good starting point for many different types of light-emitting devices due to their near-unity photoluminescence, high quantum yield, and narrow emission linewidth across the whole visible spectrum. In recent years, lower-dimensional perovskites have gotten greater attention than three-dimensional perovskites. They are more thermally, photochemically, and chemically stable than three-dimensional perovskites, for example. External size quantization and internal octahedron organization, among other strategies, can be used to study and use multiple-dimensional electrical properties. Despite the fact that research into the underlying charge carrier dynamics of lower-dimensional perovskites has been going on for quite some time, it has not kept up with the massive effort to use them in optoelectronics. Recent progress in the research of excitonic complex dynamics in Cs-based perovskite Nano crystals is discussed, as well as future directions in the field. We use single-particle time-resolved PL spectroscopy and photon correlation measurements, among other approaches, to analyze the mobility of the complexes (Dubois-Violette, 2016). Recombination routes can only be examined in unprecedented depth via statistical analysis of single photons, and charge carriers can only be discovered where they are supposed to be, allowing for the identification of hitherto unknown charge carriers. It also explains how various materials, such as small perovskites, could have a common source of PL release, as well as the processes that generate this release. A specific example demonstrates the proper course of action. Single particle spectroscopy could be a useful tool for gathering important data in vast, unknown areas (Figure 8.2).

Figure 8.2. An illustration of the Sakata model. Source: https://www.google.com/imgres?imgurl=https%3A%2F%2F media.springernature.com%2Fm685%2Fspringer-static%2Fimage%

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8.4. APPLICATION OF ELEMENTARY PARTICLES IN MEASUREMENT PROBLEMS The reasonable elucidation of estimations, common among analysts and engineers, suggests that estimation permits them to set up observationally a few objective properties of bodies or forms or their relations. Objectivity is caught on to cruel that these properties do not depend on the sees and convictions of the individual taking the estimations, nor on the methods used. This approach infers that there exist a few genuine amounts, and amid the estimation their approximate values are assessed. Such understanding is certainly based on the thoughts of logical positivists and empiricists that experimental information could be an unbiased provider of truths on which theoretical developments are grounded, as well as on the arrangements of logical authenticity, which state that objects, forms, and their properties portrayed by logical hypotheses exist objectively, regardless of one’s state of intellect (Figure 8.3).

Figure 8.3. An illustration of the nuclear scale used in solving measurement problems. Source: https://www.google.com/imgres?imgurl=https%3A%2F%2Fimageio. forbes.com%2Fblogs-images%2Fstartswithabang%2Ffiles%2F2017%2F09%

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The combination of the previously mentioned sees leads to the expectation that, on the one hand, the estimation values of amounts can be obtained independently of hypotheses of marvels and, on the other hand, the measured amounts compare to objective substances and indicate their inexact values (DeMille et al., 2017). The investigation of the claim around the presence of mind-independent objects and forms involves a metaphysical understanding of the estimation alongside the thought of the precision of the estimation as an understanding of the result with the “true” meaning. With the realistic approach, the estimation mistake is additionally caught on in this sense. To contend for their position, realists often point out that with advancements in estimation innovation, the accuracy of estimations increments which distinctive strategies for measuring the same esteem lead to consistent comes about.

8.5. APPLICATION OF ELEMENTARY PARTICLES IN MUON PRECESSION FREQUENCY Since more than 50 a long time the electron and muon inconsistencies, characterized in terms of the gyromagnetic calculate for particles, have given a profound knowledge into the quantum structure of rudimentary particles. They have been, and proceed to be, a turning point for the improvement of the Standard Demonstrate of Molecule Material science against which all modern hypotheses got to be compared. For nearly 20 a long time, the test values have appeared a tantalizing disparity from the hypothetical forecast making it required for experimentalists to move forward the current result, ruled by the. The Muon try at Fermilab will utilize the same capacity ring strategy utilized, with the objective of decreasing by a factor of four on the current error, which is able permit for a better comparison with the hypothetical forecast (Figure 8.4).

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Figure 8.4. Graphs on muon precession frequency. Source: https://www.researchgate.net/figure/Frequency-spectrum-ofmuon-spin-precession-in-UBe13-in-a-transverse-magnetic-field-B-1_ fig1_257028387

8.6. ANTINEUTRINO ENERGY SPECTRUM The expectation of reactor antineutrino spectra will play a significant part as reactor tests enter the accuracy time. The positron vitality range of 3.5 million antineutrino converse beta rot responses watched by the Daya Inlet test, in combination with the parting rates of fissile isotopes within the reactor, is utilized to extricate the positron vitality spectra coming about from the parting of particular isotopes. This data can be utilized to create an exact, data-based forecast of the antineutrino vitality range in other reactor antineutrino tests with distinctive parting divisions than Daya Inlet (Figure 8.5).

Figure 8.5. A graph on antineutrino energy spectra. Source: https://www.google.com/imgres?imgurl=https%3A%2F%2Fwww. researchgate.net%2Fprofile%2FVirginia-Strati%2Fpublication%2F26941

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7607%2Ffigure%2Ffig4%2FAS%3A667090264539150%40153605812152 1%2FAntineutrino-energy-spectra-expected-at-JUNO-Geoneutrino-energyspectrum-green-is.jpg&imgrefurl=https%3A%2F%2Fwww.researchgate. net%2Ffigure%2FAntineutrino-energy-spectra-expected-at-JUNO-Geoneutrino-energy-spectrum-green-is_fig4_269417607&tbnid=90hC0Z1Gg_ uqJM&vet=12ahUKEwjYwq2Xh_j1AhVQgaQKHWPyCbQQMygAegUIA RC0AQ.i&docid=VrVOEBPS7Inm_M&w=850&h=601&itg=1&q=antin eutrino%20energy%20spectrum&hl=en&ved=2ahUKEwjYwq2Xh_j1AhVQgaQKHWPyCbQQMygAegUIARC0AQ.

The positron vitality spectra are unfurled to get the antineutrino vitality spectra by expelling the commitment from locator reaction with the WienerSVD unfurling strategy. Steady comes about are gotten with other unfurling strategies. A method to develop a data-based expectation of the reactor antineutrino vitality range is proposed and explored. Given the reactor parting divisions, the procedure can anticipate the vitality range to a 2% exactness (Dolenec et al., 2017). In expansion, we outline how to perform a thorough comparison between the unfurled antineutrino range and a hypothetical demonstrate forecast that maintains a strategic distance from the input demonstrate predisposition of the unfurling strategy.

8.7. APPLICATION OF ELEMENTARY PARTICLES IN MORE DISCOVERIES OF PHYSICS The disclosure of a clear standard model (SM)-like Higgs at the Sweeping Hadron Collider couriers the start of an unused time in atom fabric science. While the Higgs marks the completion of the Standard Illustrate framework, it offers far off more openings inside the looked-for fabric science past the Standard Appear. The Higgs boson raises a pressing speculative issue known as the chain of command issue such as: why is a simple scalar particle so light when quantum alterations tie its mass to the foremost critical imperativeness scales? The Higgs additionally gives an uncommon test opportunity as a bellwether of advanced fabric science: it may be fair the essential of many states inside the electroweak symmetry breaking portion, while its era and decays may provide uncommon demonstrate for additional particles. Questions approximately reinforced by this allow utilized the Higgs boson to investigate cutting edge fabric science from both heading, making novel approaches to handling the movement issue posed by the Higgs boson and direct utilizing the Higgs as an unused instrument for revelation. Given that invalid comes around at the LHC and other tests have begun to risk standard

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approaches to the pecking arrange issue, ask around maintained by the allow recognized one-of-a-kind courses of action to the chain of command issue wherein the lightest degrees of adaptability securing the Higgs boson carry no Standard Appear quantum numbers and, in this way, evade existing looks. The PI’s approach combined standard rebellious of quantum field theory with novel applications of the orbifold reducing of tireless symmetries to characterize the framework of “unbiased naturalness” and examine its exploratory comes about over the essentialness, concentrated, and interminable unsettled areas (Calvo et al., 2016). In utilizing the Higgs particularly as a device for revelation, ask around maintained by this allow verbalized a deliberate approach to seeking out for developments of the Higgs division at the LHC and looked for after four key streets through which the Higgs can be utilized to uncover cutting edge fabric science over a run of tests: as a arrange final state test; as an circuitous test through its couplings; as an entrance to states fair underneath the Standard Appear; and as a source of captivating shapes in evacuated spoils.

8.8. APPLICATION OF ELEMENTARY PARTICLES IN NANOPARTICLE TRACKING From the granular and broken subsurface environment to exceedingly outlined polymer movies utilized in pharmaceutical filtration, penetrable materials are ubiquitous in nature and mechanical applications. In particular, porous media are utilized broadly in shapes tallying water treatment, pharmaceutical sterilization, food/beverage planning and heterogeneous catalysis, where destroyed mass transport is either essential to the strategy or a basic, but undesirable limitation. Shockingly, there are as of presently no all-comprehensive models competent of anticipating mass transport based on a depiction of the penetrable texture since honest to goodness permeable materials are complex, as a result various coupled lively disobedient allow rise to the observed doubtlessly unmistakable transport wonders. Whereas classical methods, like atomic attractive reverberation and energetic light scrambling, give valuable data around mass transport in permeable media at the gathering level, they give constrained knowledge into the tiny instruments that grant rise to complex wonders such as odd dissemination, ruined pore-space openness, and startling maintenance beneath stream, among numerous others (Figure 8.6).

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Figure 8.6. An illustration of the nanoparticle tracking analysis. Source: https://www.google.com/imgres?imgurl=https%3A%2F%2Fwww. azonano.com%2Fimages%2FArticle_Images%2FImageForArticle_3936(1). jpg&imgrefurl=https%3A%2F%2Fwww.azonano.com%2Farticle.aspx%3FAr ticleID%3D3936&tbnid=epa6z-gogO-pnM&vet=12ahUKEwjavLbmh_j1AhV MwOAKHSI9B7sQMygAegUIARC1AQ.i&docid=ov16vSKXGMPjFM&w=3 95&h=320&q=nanoparticle%20tracking&hl=en&ved=2ahUKEwjavLbmh_ j1AhVMwOAKHSI9B7sQMygAegUIARC1AQ.

Concrete cases of nanoparticle transport in porous materials are depicted from two perspectives: understanding pivotal fundamental atom transport shapes in penetrable media, checking pore accessibility and misery escape, which compel transport in porous media; empowering applications in mechanical shapes, e.g., by understanding the rebellious of atom fouling and remobilization in filtration movies. A perspective of openings related with investigating other sorts of mass transport in kept circumstances utilizing single-particle taking after procedures, checking electrophoretic and selfpropelled development are given.

8.9. THE PHOTO-SENSOR PANEL TECHNOLOGY The first crucial value of the Board is to serve as a ‘distributor’ of the electric field among the person ABALONETM units settled inside the closely stuffed system on the best of the Board. Our one of kind orchestration was to optimize the Board arrangement through numerical entertainment. Inside the course of this work, we luckily realized that there’s an unambiguous and sensible way of arranging the electron optics of the ABALONETM

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Sheets, to be particular a “rapid prototyping” procedure that incorporates the make of a tremendous number of Board models made of distinctive sensible plastic materials specialist of entwined silica (Capelle and Campo, 2013). That has allowed us to screen the position of the photoelectron bar on the scintillator by a CCD camera. They have found great assentation with the numerical desires, but for a difference credited to space charge (Figure 8.7).

Figure 8.7. An illustration of some photo-sensor panel technologies. Source: https://www.google.com/imgres?imgurl=http%3A%2F%2Fwww.lanbaosensor.com%2Fuploadfile%2F2018%2F1108%2F20181108010933754. png&imgrefurl=http%3A%2F%2Fwww.lanbaosensor.com%2Findex.php%3Fm%3Dcontent%26c%3Dindex%26a%3Dcatlists%26catid%3D82%26ccatid %3D83&tbnid=BRcDDXZjv1rOIM&vet=12ahUKEwibiK6IiPj1AhVQiIsKHQ ILC5EQMygBegUIARC_AQ.i&docid=oavlZh4_aosxeM&w=1920&h=1080& q=photosensor%20panel%20technology&hl=en&ved=2ahUKEwibiK6IiPj1A hVQiIsKHQILC5EQMygBegUIARC_AQ.

Person Modules bolt into each other, side-by-side, to make expansive photosensitive regions of custom shapes. The patented baseline Board plan could be a sandwich composite board, with a lightweight inflexible cell material epoxied between two printed circuit sheets. An encapsulation of the standard Board design was tried at UC Davis in a few simple models, whose primary reason was to illustrate the capability of a composite board to have a closely pressed network of ABALONE Photo sensor units and to supply the tall voltage and the ground potential at the same time to all units (Bass, 2020). An especially vital advantage of the ABALONE Photo sensor Innovation is the moo level of radioactivity that comes at no extra taken a toll on the gathering handle – in case intertwined silica, components are utilized. At the same time, combined silica gives straightforwardness to UV light. Both benefits are pivotal for the proposed venture.

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8.10. APPLICATION OF ELEMENTARY PARTICLES TO THE PROBLEM OF COMPOSITENESS A novel theoretical approach to the issue of the compositeness of a resonation or bound state is made on the introduction of the crave values of the number directors of the free particles inside the continuum. This formalism is remarkably sensible for compelling field speculations in which the revealed simple states are arranged out but that gives rise to resonation and bound states when executed in nonperturbative calculations. It is outlined that for finite-range energy-independent possibilities, either standard or specific. A non-trivial case for an energy-dependent potential is talked about approximately where it is showed up that it is independent of any sort of cutoff controller utilized. The generalization of these strategies to relativistic states is made. It in addition clarified how to urge an imperative compositeness concerning the open channels for resonances, undoubtedly in case, it is complex in a to start with turn, by making utilize of sensible phasefactor changes. Characterizing elementariness, they decide on an unused comprehensive premise for the elementariness of a bound state. Along the same lines, a crucial condition for a resonation to be qualified as simple is given. The application of the formalism here made may be of noteworthy down to soil charmed (Figure 8.8).

Figure 8.8. An illustration of both elementary particles and composite particles. Source: https://www.google.com/imgres?imgurl=https%3A%2F%2Fwww. researchgate.net%2Fprofile%2FRalf-Farkas%2Fpublication%2F3281453 85%2Ffigure%2Ffig1%2FAS%3A679443806826510%401539003435702% 2FRelations-between-elementary-and-composite-particles-in-the-StandardModel-of-Elementary.png&imgrefurl=https%3A%2F%2Fwww.researchgate. net%2Ffigure%2FRelations-between-elementary-and-composite-particles-in-

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the-Standard-Model-of-Elementary_fig1_328145385&tbnid=IO-OcuudvCX4J M&vet=12ahUKEwiGmsmriPj1AhXS-qQKHb1zC-cQMygBegUIARCGAQ.i& docid=hTMQRhBVdevxyM&w=850&h=518&q=compositeness%20in%20elementary%20particles&hl=en&ved=2ahUKEwiGmsmriPj1AhXS-qQKHb1zC-cQMygBegUIARCGAQ.

8.11. APPLICATION OF ELEMENTARY PARTICLES IN THE CONTROL OF AIRBORNE INFECTIOUS DISEASE The progression of SARS-CoV-2 disease has come approximately in variations likely to be more expeditiously transmitted through respiratory fog concentrates, underscoring the extended potential for indoor characteristic controls to calm risk. Utilize of tight-fitting go up against shroud to trap overwhelming vaporized in breathed out a breath and diminish internal breath presentation to sullied talk about is of essential noteworthiness for contamination control. Definitive controls tallying the heading of inhabitance and interpersonal isolating are as well imperative, though appearing social and monetary challenges (Bellotti, 2011). Indoor building controls checking ventilation, weaken, talk about stream control, filtration, and sanitization by germicidal shinning brightening can diminish reliance on unbending inhabitance confinements. In any case, the impacts of controls-individually and in combination-on reducing powerful vaporized trade interior remain to be characterized to the degree required to support distant coming to execution by building operators (Figure 8.9).

Figure 8.9. An illustration of the transmission of airborne infectious disease.

Source: https://www.google.com/imgres?imgurl=http%3A%2F%2Fd attmedi.com%2Fblog%2Fwp-content%2Fuploads%2F2019%2F07%

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2FScreenshot-2019-07-08-at-11.14.59.png&imgrefurl=https%3A%2F %2Fdattmedi.com%2Fblog%2Fdiseases-that-spread-through-air-airborne-diseases%2F&tbnid=8jaPul1EFwU2zM&vet=12ahUKEwj1tK3O iPj1AhWF_IUKHQXoCfMQMygAegUIARC0AQ.i&docid=YkT8hhjfQ_ HE7M&w=555&h=435&q=airborne%20infectious%20diseases&hl=en& ved=2ahUKEwj1tK3OiPj1AhWF_IUKHQXoCfMQMygAegUIARC0AQ. The audit of aero biologic and epidemiologic prove of indoor natural controls against transmission and display a quantitative airborne exchange situation outlining relative contrasts in a presentation at the closeinteractive, room, and building scales. We recognize an overarching require for speculation to execute building controls and assess their adequacy on disease in well-characterized and real-world settings, bolstered by particular, methodological signs of progress. At long last, made strides understanding of building control viability guides execution at scale whereas considering inhabitant consolation, operational challenges, and vitality costs.

8.12. APPLICATION OF ELEMENTARY PARTICLES IN ORGANIC CHEMISTRY Robotic ponders have generally played a key part in the disclosure and optimization of responses in natural and organometallic chemistry. Be that as it may, indeed clearly straightforward natural and organometallic changes may have shockingly complicated multistep instruments, expanding the trouble of extricating this unthinking data. The coming about response intermediates regularly constitutes a small division of the whole response blend, for case, making a long-term expository challenge of discovery. This challenge is especially articulated in cases where the positions of intermediates on the response vitality surface cruel that they don’t build up to the amounts required for perception by conventional gathering explanatory devices. Hence, their presence and single-step rudimentary reactivity cannot be examined straightforwardly. Unused approaches for getting this otherwise-missing robotic data are hence required (Beringer et al., 2012). Single-turnover, single-molecule, single-particle, and other sub ensemble fluorescence microscopy methods are in a perfect world suited for this part because of their affectability and spatiotemporal determination. Motivated by the strong advancement of single-molecule fluorescence microscopy apparatuses for examining chemical catalysis, our research facility has created practically equivalent to fluorescence microscopy methods to

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overcome robotic challenges in manufactured chemistry, with affectability as tall as the single-complex, single-turnover, and single-molecule level (Figure 8.10).

Figure 8.10. An illustration of subatomic particles and their respective masses. Source: https://www.google.com/imgres?imgurl=https%3A%2F%2Fwww.priyamstudycenter.com%2Fwp-content%2Fuploads%2F2019%2F02%2Fsubat omic-elementary-particles-of-atom.png&imgrefurl=https%3A%2F%2Fwww. priyamstudycenter.com%2F2019%2F02%2Felementary-particles.html& tbnid=VkHC9abeCOU7jM&vet=12ahUKEwjDmJ-Hifj1AhUISEEAHclH ASAQMygAegQIARBq.i&docid=WdqbgVTfvP8reM&w=500&h=400&q =application%20of%20elementary%20particles%20in%20organic%20 chemistry&hl=en&ved=2ahUKEwjDmJ-Hifj1AhUISEEAHclHASAQMygAegQIARBq.

These methods free the experimenter from the past limitation that intermediates must build up to amounts required for discovery by outfit expository instruments and are suited to frameworks where synchronization through streak photolysis or halted stream would be badly arranged or blocked off. In this handle, the strategies change certain already unobservable intermediates and their basic single-step re-activities into observable ones through delicate and particular ghostly handles. Our program has centered on imaging responses in small-molecule, natural, and polymer engineered chemistry with an emphasis on the reactivity of atomic move metal complexes and catalysts. To empower imaging, they began with fluorophore determination and advancement, overcame challenges with imaging in natural solvents,

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and created methodologies congruous with air-sensitive chemistry and concentrations of reagents by and large utilized in the small-molecule union. These thinks about developed to incorporate characterization of already obscure organometallic intermediates within the blend of organozinc reagents and the coordinate thinks about their elementary-step reactivity. The capacity to specifically watch this behavior produced prescient control for selecting salts that quickened organozinc reagent arrangement in the blend, counting salts that had not, however been detailed artificially. In 2017 the primary single-turnover imaging of atomic catalysts was created, which through the technique’s spatiotemporal determination uncovered suddenly time-variable polymerization energy wherein atomic ruthenium ring-opening metathesis polymerization catalysts changed rates freely from other catalysts. Person catalytic turnovers, each compared to one single-chain-elongation response emerging from the addition of single Frolic monomers at person Grubbs II atomic ruthenium catalysts, were spatiotemporally settled as green flashes in developing polymers (Boyle and Farnsworth, 2014). The talk on the improvement of this method from thought to application, counting challenges overcome and techniques made to picture engineered natural and organometallic atomic chemistry at the most elevated levels of location affectability. We too depict challenges not however unraveled and give a viewpoint for this developing field at the crossing point of microscopy and synthetic/molecular chemistry.

8.13. APPLICATION OF ELEMENTARY PARTICLES IN CONTROLLING COVID-19 IN VENTILATION SYSTEMS COVID-19 constrained the human population to reexamine its way of living. The risk postured by the potential spread of the infection by means of an airborne transmission mode through ventilation frameworks in buildings and encased spaces has been recognized as a major concern. To moderate this risk, analysts have investigated distinctive advances and strategies that can evacuate or diminish the concentration of the infection in ventilation frameworks and encased spaces. In spite of the fact that numerous innovations and strategies have as of now been investigated, a few are right now accessible on the showcase, but their viability and security concerns have not been completely explored (Alexandre, 2011). To obtain a broader see and collective viewpoint of the current inquire about and advancement status, a talk on a comprehensive audit of different workable innovations

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and strategies to combat airborne infections, e.g., COVID-19, in ventilation frameworks and encased spaces is done. These innovations and strategies incorporate an increment in ventilation, high-efficiency discuss filtration, ionization of the discussion, natural condition control, bright germicidal illumination, non-thermal plasma, and responsive oxygen species, channel coatings, chemical disinfectants, and warm inactivation (Figure 8.11).

Figure 8.11. The COVID-19 ventilation system explaining how it operates. Source: https://www.thelancet.com/journals/ebiom/article/PIIS23523964(22)00052-4/fulltext

8.14. APPLICATION OF ELEMENTARY PARTICLES IN QUADRATIC TIME Time subordinate quantum issues characterized by quadratic Hamiltonians are unraveled utilizing canonical changes. The Green’s work is gotten and a comparison with the classical Hamilton–Jacobi strategy leads to vital geometrical experiences like outside differential frameworks, Monge cones and time subordinate Gaussian measurements. The Wei–Norman approach is connected utilizing unitary changes characterized in terms of generators of the related Lie bunches, here the semi-direct item of the Heisenberg

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bunch and the symplectic gather. An unused unequivocal connection for the unitary changes is given in terms of a limited item of basic changes (Figure 8.12).

Figure 8.12. A graph on time complexity simplification. Source: https://www.google.com/imgres?imgurl=https%3A%2F%2Fres. cloudinary.com%2Fpracticaldev%2Fimage%2Ffetch%2Fs--LwdH0L3f-%2Fc_imagga_scale%2Cf_auto%2Cfl_progressive%2Ch_420%2Cq_au to%2Cw_1000%2Fhttps%3A%2F%2Fdev-to-uploads.s3.amazonaws. com%2Fi%2Farh0q6t4946tyuhknrjf.png&imgrefurl=https%3A%2F%2Fdev. to%2Fnashmeyah%2Ftime-complexity-simplified-3io7&tbnid=vi-VqfezXAyB OM&vet=12ahUKEwjs5fnuifj1AhVVnFwKHdgPDjEQMygAegUIARC4AQ.i& docid=8y4HQDAJPND5tM&w=1000&h=420&q=quadratic%20time&hl=en &ved=2ahUKEwjs5fnuifj1AhVVnFwKHdgPDjEQMygAegUIARC4AQ.

The successive application of satisfactory sets of unitary changes leads normally to a modern division of factors strategy for time subordinate Hamiltonians, which is appeared to be related to the Inönü–Wigner compression of Lie bunches. The modern strategy permits moreover distant a much better; a higher; a stronger; an improved and higher understanding of association particles or coupled modes and opens an elective way to analyze topological stages in driven frameworks (Alexandre, 2011). Some of the highlights include: correct unitary change diminishing time subordinate quadratic quantum Hamiltonian to zero; Modern division of factors strategy and concurrent uncoupling of modes. • Express illustrations of changes for one to four-dimensional problems; Modern common advancement condition for quadratic shape within the activity, separately Green’s work.

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8.15. APPLICATION OF ELEMENTARY PARTICLES IN TRANSFERABLE DYNAMIC MOLECULAR CHARGE The capacity to precisely and proficiently compute quantum-mechanical fractional atomistic charges has numerous commonsense applications, such as calculations of IR spectra, examination of chemical holding, and classical drive field parameterization. Machine learning procedures give a conceivable road for the effective forecast of nuclear fractional charges. Present-day machine language progresses within the expectation of atomic energies; that is, the progressive association molecule neural arrange has given the fundamental demonstrate system and engineering to foresee transferable, extensible, and conformationally energetic nuclear halfway charges based on reference thickness useful hypothesis recreations. Utilizing HIP-NN, we appear that machine language charge forecast can be exceedingly exact over a wide extent of particles, both little and expansive, over an assortment of charge dividing plans such as the Hirshfeld, and NBO strategies (Figure 8.13).

Figure 8.13. An illustration of molecular dynamic simulation. Source: https://www.google.com/imgres?imgurl=https%3A%2F%2Fmedia. springernature.com%2Ffull%2Fspringer-static%2Fimage%2Fart%253A10.1 038%252Fs41598-019-56052-3%2FMediaObjects%2F41598_2019_56052_ F i g 1 _ H T M L . p n g & i m g r e f u r l = h t t p s % 3 A % 2 F % 2 F w w w. n a t u r e . com%2Farticles%2Fs41598-019-56052-3&tbnid=xss5caZJ_7-nTM&vet=12a hUKEwiJzbWTivj1AhUCkFwKHd8xDSoQMygAegUIARCwAQ.i&docid=Gm ght9OdJsLPgM&w=1640&h=932&q=dynamic%20molecular%20charge&hl =en&ved=2ahUKEwiJzbWTivj1AhUCkFwKHd8xDSoQMygAegUIARCwAQ.

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Usually surprising since this benchmark contains two proteins that are multiple times bigger than the biggest particles within the preparing set. An application of our nuclear charge expectations on non-equilibrium geometries is the era of IR spectra for natural atoms from dynamical directions on an assortment of natural particles, which appear great assertion with calculated IR spectra with reference strategy (Alexandre, 2011). Basically, HIP-NN charge forecasts are numerous orders of greatness quicker than coordinate DFT calculations. In conclusion, these combined comes about give advance prove that ML gives a pathway to incredibly increment the run of attainable reenactments whereas holding quantum-level exactness.

8.16. APPLICATION OF ELEMENTARY PARTICLES IN NEUTRON IMAGING EXPERIMENTS An intuitively web-based instrument has been created at Oak Edge National Research facility to direct the end-user test arrangement for neutron imaging tests. The instrument is able of evaluating transmission through the test utilizing the cold neutron range at the Tall Flux Isotope imaging beam line. It can moreover foresee the position and stature of the reverberation crests at the Spallation Neutron Source SNAP beam line when performing neutron reverberation imaging with neutron energies high. This device gives vigorous and user-friendly test input and utilizes a simulated pillar range at comparing beam lines for precise transmission calculations. By utilizing this instrument, clients who are curious about neutron imaging can test their thoughts expeditiously and can superiorly get ready tests for their tests (Figure 8.14).

Figure 8.14. An illustration of the neutron imaging method. Source: https://www.google.com/imgres?imgurl=https%3A%2F%2Fm edia.springernature.com%2Foriginal%2Fspringer-static%2Fimage%2

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Fchp%253A10.1007%252F978-0-387-09416-8_11%2FMediaObjects% 2F978-0-387-09416-8_11_Fig1_HTML.jpg&imgrefurl=https%3A%2F%2Flin k.springer.com%2Fchapter%2F10.1007%2F978-0-387-09416-8_11&tbnid=j 6tUzcv6sRmghM&vet=12ahUKEwi5zL63ivj1AhUkCBAIHdVvDpkQMygIegU IARDbAQ.i&docid=UfPPy9pTF61SxM&w=505&h=204&q=neutron%20ima ging&hl=en&ved=2ahUKEwi5zL63ivj1AhUkCBAIHdVvDpkQMygIegUIARD bAQ.

8.17. APPLICATION OF ELEMENTARY PARTICLES IN QUARK-GLUON PLASMA A change in fundamental atom fabric science happened with the approach of the parton illustrate from revelations in Significantly Inelastic electronproton Scrambling at SLAC, neutrino tests, hard-scattering observed in collisions at the CERN ISR, the change of QCD, and SLAC, and the clear recognition of tall transverse drive planes at the CERN SPS collider. These and other revelations in this period driven the affirmation of QCD as the theory of the strong instinctive (Figure 8.15).

Figure 8.15. A quark-gluon plasma. Source: https://www.google.com/imgres?imgurl=https%3A%2F%2Fphysicsw orld.com%2Fwp-content%2Fuploads%2F2021%2F06%2Fparticle-collision1063275902-iStock_Girolamo-Sferrazza-Papa.jpg&imgrefurl=https%3A% 2F%2Fphysicsworld.com%2Fa%2Fquark-gluon-plasma-flows-like-watercalculations-suggest%2F&tbnid=LuLE0vUGdKVqkM&vet=12ahUKEwiX3 fnZivj1AhVT04UKHXLnAXsQMygBegUIARDWAQ.i&docid=P2M8ZCMR_ gTfEM&w=1200&h=800&q=quark%20gluon%20plasma&hl=en&ved=2ah UKEwiX3fnZivj1AhVT04UKHXLnAXsQMygBegUIARDWAQ.

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The need to induce nuclear fabric science at a tall thickness such as in neutron stars driven to the application of QCD to this issue and to the figure of a Quark-Gluon Plasma in centers at tall vitality thickness and temperatures. This in the long run driven to the improvement of the Relativistic Overpowering Molecule Collider at BNL to observe superdense nuclear matter inside inquire about the office. Exploratory methodologies come around which affirmed QCD at the essential hadron collider, the CERN ISR, played a basic portion in tests at the essential overpowering molecule collider, RHIC, driving to the revelation of the QGP as a come full circle liquid as well as divulgences at RHIC and the LHC which continue to the appearance day (Alexandre, 2011).

8.18. APPLICATION OF ELEMENTARY PARTICLES IN TOMOGRAPHIC IMAGING OF LASER-PLASMA STRUCTURES The interaction of unequivocally brief laser beats with ionized gasses, or plasmas underlies unmistakable applications such as speeding up of clear particles, period of imperativeness by laser combination, period of x-ray and far-infrared terahertz beats for obliging and materials testing, more removed recognizing of explosives and hurts, and time of enabling stars. Such laserplasma cleverly makes unassuming electron thickness structures internal parts the plasma inward parts the shape of waves, bubbles, and strands that move at the speed of light, and enhancement as they prompt. Prior to an in spite of the fact that a brief time afterward works by the PI of this recommendation, point by point data of such structures came since it was from really computer redirections. Portrayals of these precarious, light-velocity structures can be taken inside the investigate facility utilizing a lively variety of holography, the procedure utilized to provide ID cards and DVDs, and a lively variety of tomography, the procedure utilized in pharmaceutical to picture inward genuine organs. These fast visualization procedures are crucial for understanding, advancing, and scaling the above-mentioned applications of laser-plasma cleverly. In this amplify, we wrapped up three things: They took holographic pictures of a laser-driven plasma wave inside the act of enlivening electrons to tall essentialness, and utilized computer reenactments to urge it the pictures. Utilizing comes almost from this test to optimize the execution of the animating specialist, and the brightness of x-rays that it transmits.

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8.19. APPLICATION OF ELEMENTARY PARTICLES IN MULTISTAGE GEMINATE REACTIONS Particular two-stage reversible response of the rot of species C reactants by two free move channels is considered on the premise of the common hypothesis of multistage responses of disconnected sets of reactants. It is accepted that at the starting moment of time, the responding framework contains as it were reactants C. The utilized common approach has made it conceivable to consider, within the common case, the inhomogeneous beginning conveyance of reactants, and dodge application of demonstrating concepts of a reaction framework structure; that is, of the structure of reactants and their atomic versatility (Alexandre, 2011). Abating of multistage reaction vitality as compared to the vitality of simple stages is set up and physically deciphered. To test approximations utilized to form an all-comprehensive engine law, a broadly utilized specific illustrate of circular particles with isotropic reactivity diffusing in course of action is associated. With this particular illustration as an outline, the extraordinary vitality of the chemical alteration of reactants is inspected. The address concerning the profundities of chemical alters at which longterm asymptotes are come to be inspected.

8.20. APPLICATION OF ELEMENTARY PARTICLES IN MODERN CIRCULATING ACCELERATORS Molecule quickening agents are machined to quicken and store charged particles, such as electrons or protons, to the vitality levels for different logical applications. A collection of charged particles more often than not shapes a molecule bar. There are three fundamental sorts of molecule quickening agents: direct quickening agents, storage-ring or circular quickening agents, and recycling quickening agents. In a linac, particles are quickened and pass through once along a direct or straight beamline. Storage-ring quickening agents impel particles around a circular track and monotonously add vitality to the put-away pillar. The third sort, moreover the foremost later one in chronology, the recycling quickening agent, is planned to quicken the molecule pillar in a brief area of linac, circulate the pillar, and after that either proceed to quicken for vitality boost or decelerate it for vitality recuperation. The pillar properties of a linac machine are set at best by the starting molecule sources. For capacity rings, the bar equilibrium is instep decided by the general machine plan. The cutting-edge recycling

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machines share with linacs the points of interest to both quicken and protect the bar with tall pillar quality, as well as productively reuse the quickening components (Figure 8.16).

Figure 8.16. An illustration of modern circulating accelerator. Source: https://www.google.com/imgres?imgurl=https%3A%2F%2Fmedia. springernature.com%2Foriginal%2Fspringer-static%2Fimage%2Fchp%25 3A10.1007%252F978-3-030-34245-6_1%2FMediaObjects%2F440481_1_ En_1_Fig1_HTML.png&imgrefurl=https%3A%2F%2Flink.springer. com%2Fchapter%2F10.1007%2F978-3-030-34245-6_1&tbnid=fudZjys4ERg cSM&vet=12ahUKEwiru-WAi_j1AhXZNOwKHRbZDw0QMygBegQIARAe.i& docid=n5DfygFk3eid1M&w=713&h=625&q=modern%20circulating%20acc elerators&hl=en&ved=2ahUKEwiru-WAi_j1AhXZNOwKHRbZDw0QMygBegQIARAe.

The beamline orchestrate in such a machine course of activity can be that since it may be much more complicated than that of linacs. As cutting-edge enlivening pros pushed toward the high-brightness or high-intensity wild by inquiring particles in an exceedingly charged bunch to concentrate in an ever-decreasing bar organize space, the interaction among particles through their self-generated electromagnetic zones can conceivably lead to coherent dangers of the column and along these lines posture basic challenges to the machine organize and operation (Alexandre, 2011). A magnetized bar in common highlights non-zero canonical exact vitality, in this way considered to be a transversely coupled column. A novel thought of utilizing magnetized column transport was proposed for alter of cooling adequacy and conceivable control of collective impacts. A concern of MBI with regard to this arrange

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was considered and maintained a strategic distance from. The broad transverse column appraise related with the column magnetization is found to help cover MBI by implies of the transverse-longitudinal relationship.

8.21. CONCLUSION There exists so many areas in which knowledge on elementary particles can be applied in; to help in solving the millions of problems in the world.

CHAPTER

9

CONSERVATION LAWS AND SYMMETRY OF ELEMENTARY PARTICLES

CONTENTS 9.1. Conservation of Mass and Energy ................................................... 222 9.2. Conservation of Energy ................................................................... 223 9.3. Mass–Energy Equivalence ............................................................... 224 9.4. Mass Conservation .......................................................................... 225 9.5. Conservation of Linear Momentum ................................................. 229 9.6. Angular Momentum Conservation .................................................. 231 9.7. General Considerations .................................................................. 233 9.8. Charge Conservation ...................................................................... 236 9.9. Symmetries in Elementary Particle Physics ...................................... 236 9.10. Symmetries ................................................................................... 237 9.11. Symmetries and Particle Physics.................................................... 238 9.12. Local or Gauge Symmetries .......................................................... 241 9.13. The Standard Model (SM) .............................................................. 243 9.14. Spontaneous Symmetry Breaking (SSB) ......................................... 245

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A conservation law in physics says that a specific observable attribute of an independent physical system does not change as the system changes over time. Precise conservation laws cover mass and energy conservation, linear momentum conservation, angular momentum conservation, and electric charge conservation. There are numerous approximation conservation rules that apply to quantities such as mass, parity strangeness, lepton number, baryon number, hypercharge, and so on. Some classes of physics processes conserve those quantities, although not all (Alexandre, 2011). A local conservation law is typically described theoretically as a continuity equation, a partial differential equation that expresses a relationship between the amount of a quantity and its “transport.” It asserts that the amount of a conserved quantity at a position or within a volume may only vary by the amount of a quantity flowing in or out of the volume. Every conservation law is related with a symmetry in the supporting physics according to Noether’s theorem. Conservation rules are essential to the comprehension of the physical universe because they specify which processes in nature can and cannot occur. The conservation law of energy, for example, stipulates that the entire quantity of energy in a closed system does not vary, despite the fact that its form may change. In general, physical processes do not modify the overall quantity of the property controlled by that law. Conservation rules in classical physics include the conservation of energy, matter, linear momentum, angular momentum, and electric charge. In particle physics, particles may only be formed or destroyed in pairs, one of which is an ordinary particle and the other an antiparticle. In terms of symmetries and invariance concepts, three specific conservation laws connected with inversion or reverse of space, time, and charge have been defined (Figure 9.1).

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Figure 9.1. Mass near the M87* black hole are converted into very energetic astrophysical jet, stretching 5,000 light years. Source: https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence#/ media/File:M87_jet.jpg.

Conservation law, often known as the law of conservation, is a principle in physics that asserts that a specific physical attribute does not change over time inside an independent physical system. This sort of law governs energy, momentum, angular momentum, mass, and electric charge in classical physics. Other conservation principles apply in particle physics to features of subatomic particles that are unchanging during interactions. Conservation laws provide an important role in that they allow us to forecast the macroscopic system behavior without need to analyze the microscopic intricacies of the progress of a physical process or chemical reaction (Zimmermann, 2018).

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Conservation laws are regarded as fundamental principles of nature, with broad applications in physics as well as chemistry, biology, geology, and engineering. In the extent that they correspond to all feasible processes, most conservation laws are accurate or absolute. Some conservation laws are incomplete in the sense that they apply to some processes but not others. The Noether theorem, which asserts that there is a one-to-one connection between each of them and a discrete symmetry of nature, is an especially significant finding involving conservation laws. The conservation of energy, for example, emerges from physical systems’ time-invariance, while the conservation of angular momentum comes from the notion that physical systems act the same irrespective of how they are orientated.

9.1. CONSERVATION OF MASS AND ENERGY The conservation of energy, like the conservation of momentum, is a universal principle in physics that applies to any interaction. In contrary, the classical conservation of mass is compromised in some relativistic conditions. This idea has been demonstrated experimentally in a variety of different ways, such as the conversion of mass into kinetic energy in nuclear processes and other interactions involving elementary particles (Woithe et al., 2017). While current physics has abandoned the term “conservation of mass,” in earlier language, a relativistic mass can also be characterized as being comparable to the energy of a moving system, accounting for relativistic mass conservation. When the energy involved with a particle’s mass is changed into another type of energy, like kinetic energy, thermal energy, or radiant energy, mass conservation disintegrates. Likewise, kinetic, or radiative energy can be employed to generate particles with mass while maintaining total energy and momentum (Figure 9.2).

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Figure 9.2. The world line: A diagrammatic representation of spacetime. Source: https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence#/ media/File:World_line.svg.

9.2. CONSERVATION OF ENERGY The law of conservation of energy asserts in physics and chemistry that the total energy of an individual system stays unchanged; it is said to be conserved across time. This law, suggested, and tested by Émilie du Châtelet, states that energy cannot be generated or destroyed, but can only be converted or moved from one form to another. When a piece of dynamite explodes, for example, chemical energy is transformed to kinetic energy. If all types of energy produced in the explosion are added together, such as the kinetic and potential energy of the fragments, and also heat and sound, the precise drop in chemical energy in the burning of the dynamite is obtained. Historically, energy conservation was separate from mass conservation. Special relativity, on the other hand, demonstrated that mass is connected to energy and vice versa by E = mc2, and physics now believes that massenergy is indeed conserved. In theory, this means that everything having mass can be transformed to pure energy and vice versa. This is thought to be conceivable only under the most extreme physical conditions, such as those

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that likely occurred in the cosmos right after the Big Bang or even when black holes release Hawking radiation (Wood and Heyde, 2016). Noether’s theorem logically proves energy conservation as a result of continuous time translation symmetry; such that, the notion that the laws of physics do not change across time. A perpetual motion machine of the first sort can exist as a result of the law of conservation of energy; that is, no system lacking an external energy source can send an infinite quantity of energy to its surroundings. It is possible that conservation of energy cannot be defined for systems that do not have temporal translation symmetry. Curved spacetimes in general relativity or time crystals in condensed matter physics are two examples.

9.3. MASS–ENERGY EQUIVALENCE Atoms and what constitutes atoms are what matter is made of. Matter possesses intrinsic mass, often known as rest mass. It was discovered that certain rest mass is conserved in the restricted range of acknowledged experience of the 18th century. Einstein’s 1905 special relativity theory demonstrated that rest mass equates to an identical quantity of rest energy. This implies that rest mass can be transformed into or out of similar amounts of (non-material) energy such as kinetic energy, potential energy, and electromagnetic radiant energy. Rest mass, unlike total mass or total energy, is not conserved when this occurs, as shown in modern research. Every type of energy contributes to total mass and total energy (Wallace, 2011). An electron and a positron, for example, both have rest mass. They can die together by turning their total rest energy into photons with electromagnetic radiant energy but no rest mass. Whenever this happens inside a closed system that does not emit photons or their energy into the surrounding environment, neither the system’s total mass nor total energy will vary. The electromagnetic radiant energy created adds just as much to the system’s inertia (and any weight) as the rest mass of the electron and positron prior to their deaths. Similarly, non-material types of energy can be converted into matter, which has a rest mass (Figure 9.3).

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Figure 9.3. The interactions of hadrons. (a) Bubble chamber photograph; (b) sketch that represents the photograph. Source: https://opentextbc.ca/universityphysicsv3openstax/chapter/particleconservation-laws/.

Thus, energy conservation (total, including material or rest energy) and mass conservation are one (identical) law. In the 18th century, these existed as two separate laws.

9.4. MASS CONSERVATION The law of conservation of mass, also known as the theory of mass conservation, asserts that for any system sealed to all exchanges of matter and energy, the mass of the system will stay constant throughout time, because the system’s mass cannot change, and hence quantity can’t be added or subtracted. As a result, the amount of mass is conserved through time (Viaux et al., 2013).

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According to the law, mass cannot be generated or destroyed, but it can be reorganized in space or the entities linked with it changed (Figure 9.4).

Figure 9.4. In the 19th century, several novel discoveries were made as a result of Antoine Lavoisier’s discovery of the law of conservation of mass. Antoine Lavoisier’s discoveries spawned Joseph Proust’s law of definite proportions and John Dalton’s atomic hypothesis. Lavoisier’s quantitative tests demonstrated that burning used oxygen rather than phlogiston, as previously supposed. Source: https://en.wikipedia.org/wiki/Conservation_of_mass#/media/ File:Antoine_laurent_lavoisier.jpg.

In chemical processes, for example, the mass of the chemical components prior to the reaction equals the mass of the constituents after the reaction. Therefore, in an isolated system, the total mass of the reactants, or starting materials, must equal the mass of the products throughout any chemical reaction and low-energy thermodynamic processes.

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Mass conservation is a theory that is widely employed in numerous domains, including chemistry, mechanics, and fluid dynamics. Traditionally, Mikhail Lomonosov separately proved mass conservation in chemical reactions, which was later confirmed by Antoine Lavoisier in the 1790s. The development of this law was critical in the transition from ancient chemistry to the modern natural science of chemistry. In fact, mass conservation applies only roughly and is regarded one of a set of assumptions in physical laws. Under the concept of mass-energy equivalence, which asserts that energy and mass comprise one conserved quantity, the law must be adjusted to meet with the laws of quantum physics and special relativity. The conservation of mass-only is proved not to hold for particularly intense systems, as in nuclear reactions and particle-antiparticle destruction in particle physics (Volovik, 2015). In open systems, mass is not frequently preserved. This is true when different types of energy and matter are permitted into or out of the system. Until radioactivity or nuclear reactions are implicated, the quantity of energy exiting (or joining) these systems as heat, mechanical work, or electromagnetic radiation is probably too small to be quantified as a drop (or gain) in the system’s mass. General relativity must be considered for systems with huge gravitational fields; consequently, mass-energy conservation becomes a more complicated idea, subject to various interpretations, and neither mass nor energy is as purely and simply preserved as in special relativity. With the emergence of special relativity, the law of conservation of mass was called into question. Albert Einstein proposed an equivalence between mass and energy in one of his Annus Mirabilis articles in 1905. This concept indicated various statements, such as the notion that a system’s internal energy may add to the total mass of the system, or that mass can be turned into electromagnetic radiation. Nevertheless, as Max Planck noted out, a change in mass as a consequence of chemical energy extraction or addition, as described by Einstein’s theory, is so minuscule that it cannot be detected with the existing instruments and cannot be offered as a test of special relativity. Einstein hypothesized that the energies connected with recently found radioactivity were substantial enough, in comparison to the mass of the systems generating it, to allow their change of mass to be detected when the energy of the reaction was withdrawn from the system (Van Noorden, 2012). This was later proven to be possible, but it was the first artificial

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nuclear transmutation process, shown by Cockcroft and Walton in the 30s, that revealed to be the first successful demonstration of Einstein’s hypothesis linking mass loss with energy gain (Figure 9.5).

Figure 9.5. Methane combustion reaction where 4 hydrogen atoms, 4 oxygen atoms, and 1 carbon atom are present before and after the process. The overall mass after the reaction is the same as it was before it. Source: https://en.wikipedia.org/wiki/Conservation_of_mass#/media/ File:Combustion_reaction_of_methane.jpg.

The law of conservation of mass and its counterpart, the law of conservation of energy, were eventually overridden by a more comprehensive notion known as mass–energy equivalence. Special relativity also reinvents mass and energy, which can be employed interchangeably and are specified relative to the reference frame. For uniformity, other quantities, like a particle’s rest mass and relativistic mass, have to be specified. The latter is a less commonly used term. If the system is open and energy leaves, the conservation of mass does not hold in special relativity. It does, though, apply to completely closed systems. A system’s mass can’t reduce if energy cannot exit. According to relativity theory, any sort of energy that is kept within a system has mass (Ünel and Sekmen, 2018). Furthermore, mass must be distinguished from matter, because matter may not be fully conserved in closed systems, whereas mass is always conserved in these kinds of systems. Even so, in chemistry, matter is so now almost conserved that violations of matter conservation were not assessed until about the nuclear age, and the premise of matter conservation continues to be a crucial practical concept in most systems in chemistry and other sciences that do not encompass the high energies characteristic of radioactivity and nuclear reactions.

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9.5. CONSERVATION OF LINEAR MOMENTUM Linear momentum, translational momentum, or simply momentum is the product of an object’s mass and velocity in Newtonian mechanics. It is a vector quantity with magnitude and direction. If an object’s mass is m and its velocity is v (also a vector quantity), then its momentum p is: P = mv. The kilogram meter per second (kgm/s) is the unit of momentum measurements in the International System of Units (SI), which is identical to the newton-second. According to Newton’s second rule of motion, the pace of change of a body’s momentum is equivalent to the total forces applied on it. Momentum varies depending on the reference frame, but it is a conserved quantity in any inertial frame, which means that if a closed system is not impacted by foreign influences, its total linear momentum does not vary (Tluczykont et al., 2012). Momentum is maintained in special relativity (with a revised formula), as well as in electrodynamics, quantum mechanics, quantum field theory, and general relativity (in a customized version). It is a representation of translational symmetry, which is one of the essential symmetries of space and time (Figure 9.6).

Figure 9.6. A pool break-off shot. Source: https://en.wikipedia.org/wiki/Momentum#/media/File:Billard.JPG.

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Modern formulations of classical mechanics, such as Lagrangian and Hamiltonian mechanics, provide for the selection of coordinate systems with symmetries and constraints. The preserved quantity in these systems is generalized momentum, which is not the same as the kinetic momentum mentioned above. In quantum mechanics, the principle of generalized momentum is transferred over as an agent on a wave function. The Heisenberg uncertainty principle connects the momentum and position operators. A momentum density can be defined in continuous systems such as electromagnetic fields, fluid dynamics, and deformable bodies, and a continuum variant of the conservation of momentum gives rise to formulae like the Navier–Stokes equations for fluids or the Cauchy momentum equation for non-rigid solids or fluids (Shlomi et al., 2020). The total momentum stays unchanged in a closed system (one that does not interchange matter with its environment and is not operated on by external forces). Newton’s principles of motion imply this principle, referred to as the law of conservation of momentum. Consider the case of two particles interacting. The forces between them are identical in magnitude but opposing in direction, as stated by the third law. The second law asserts that F1 = dp1/dt and F2 = dp2/dt if the particles are numbered 1 and 2. Therefore,

with the minus symbol showing that the forces are opposed. Equivalently,

If the particle velocities are u1 and u2 before the interaction and v1 and v2 after the interaction, then: This law is true regardless of how intricate the force between particles is. Similarly, if there are multiple particles, the momentum transferred between each pair of particles equates to zero, resulting in a total change in momentum of zero. This conservation law pertains to all interactions, even those induced by explosive forces. It can also be extended to circumstances where Newton’s rules do not apply, such as in relativity theory and electrodynamics.

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9.6. ANGULAR MOMENTUM CONSERVATION Angular momentum (also known as moment of momentum or rotational momentum) is the rotating analog of linear momentum in physics. It is significant in physics since it is a conserved quantity—the total angular momentum of a closed system stays unchanged. Both the direction and magnitude of angular momentum are conserved (Seshavatharam and Lakshminarayana, 2013). Motorcycles and frisbees all benefit from angular momentum conservation. Because of the conservation of angular momentum, hurricanes have spirals and neutron stars have fast rotating rates. In essence, conservation restricts a system’s conceivable motion but does not specify it precisely (Figure 9.7).

Figure 9.7. This gyroscope remains upright while spinning due to the conservation of its angular momentum. Source: https://en.wikipedia.org/wiki/Angular_momentum#Conservation_of_ angular_momentum.

The three-dimensional angular momentum of a point particle is a pseudovector r × p, which is the cross product of the particle’s location vector r (relative to some origin) and momentum vector; the latter is Newtonian physics’ p = mv. Angular momentum, unlike momentum, is affected by where the origin is chosen, because the particle’s position is measured from it.

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As with angular velocity, an object’s angular momentum is classified into two types: spin angular momentum and orbital angular momentum. Spin angular momentum is the angular momentum around the object’s center of mass, while orbital angular momentum is the angular momentum about a selected point of rotation. The Earth has orbital angular momentum because it revolves around the Sun, and spin angular momentum because it rotates about the polar axis on a daily basis. The sum of the spin and orbital angular momenta is the total angular momentum (Radovic et al., 2018). Since angular momentum is transferred to a small but significant extent among the planets and the Sun, the total angular momentum of the solar system is the principal preserved quantity in the instance of the Earth. A point particle’s orbital angular momentum vector is parallel and linearly proportional to its orbital angular velocity vector, where the constant of proportionality relies on both the particle’s mass and its position from the origin. A rigid body’s spin angular momentum vector is proportional but not always parallel to its spin angular velocity vector Ω, therefore the constant of proportionality is a second-rank tensor rather than a scalar (Figure 9.8).

Figure 9.8. Velocity of the particle m with respect to the origin O can be resolved into components parallel to (v∥) and perpendicular to (v⊥) the radius vector r. The angular momentum of m is proportional to the perpendicular component v⊥ of the velocity, or equivalently, to the perpendicular distance r⊥ from the origin. Source: https://en.wikipedia.org/wiki/Angular_momentum#/media/File:Ang_ mom_2d.png.

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Angular momentum is a broad concept; the overall angular momentum of every composite system is the sum of its constituent angular momenta. Total angular momentum for a continuously solid body or fluid is the volume integral of angular momentum density (angular momentum per unit volume in the end as volume drops to zero) through the whole body. Angular momentum is conserved where there is no external torque, analogous to how linear momentum is conserved when there is no external force. Torque, like force, can be described as the rate of change of angular momentum. The net external torque on any system is equal to the total torque on the system; that is, the sum of all internal torques on any system is always 0 (It is essentially the rotational equivalent of Newton’s Third Law). As a result, for a closed system (one with no net external torque), the total torque on the system must be zero, implying that the system’s total angular momentum is fixed (Pitkänen, 2011). Angular momentum is defined as an operator in quantum mechanics, and its one-dimensional representations have quantized eigenvalues. Angular momentum is constrained to the Heisenberg uncertainty principle, which states that only one projection (also known as a “component”) may be evaluated with certain precision at any given time; the other two remain uncertain. As a result, the axis of rotation of a quantum particle is unknown. Quantum particles do have a sort of non-orbital angular momentum known as “spin,” but it does not correlate to a spinning motion.

9.7. GENERAL CONSIDERATIONS “In a closed system, no torque can be applied on any matter without the exertion of an equal and opposite torque on some other matter,” is a rotational analog of Newton’s third law of motion. As a result, in an isolated system, angular momentum can be transferred between objects, but total angular momentum before and after such exchange remains unchanged or is conserved. To put it another way, a rotational equivalent of Newton’s first rule of motion could be phrased as “A rigid body continues in a state of uniform rotation unless acted upon by an external effect.” As a result, with no external influence acting on it, the system’s original angular momentum remains constant.

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In investigating central force motion, the conservation of angular momentum is applied. When the total force on a body is always oriented toward a single point, the center, then the body has no torque with regard to the center since all of the force is applied along the radius vector and none is perpendicular to the radius. Torque is defined mathematically. because in this instance because in this case are vectors that run parallel. As a result, the body’s angular momentum about the center is constant (Pashkin and Leitenstorfer, 2014). This is true of gravitational attraction in planet and satellite orbits, where gravitational force is always directed toward the primary body and orbiting bodies conserve angular momentum by trading distance and velocity as they travel around the primary. Central force motion is applied when observing the Bohr model of atoms. An angular momentum is allocated between a planet’s spin and its revolutions in its orbit, and they are frequently transferred by various methods. Because of the tidal tension exerted by the Moon on the Earth, the conservation of angular momentum in the Lunar–Earth system leads in the transfer of angular momentum from Earth to Moon. As a consequence, the Earth’s rotation rate slows to around 65.7 nanoseconds per day, while the radius of the Moon’s orbit gradually increases to roughly 3.82 millimeters every year. The torque produced by the two opposing forces Fg and Fg creates a shift in the angular momentum L in the torque’s direction as a result, the top processes. The angular acceleration of an ice skaters as she pulls her limbs close to the vertical axis of rotation is explained by the conservation of angular momentum. She reduces her body’s moment of inertia by moving a portion of her body’s mass relative to the axis. Since angular momentum is the sum of moment of inertia and angular velocity, the angular velocity (rotational speed) of the skater has to rise if the angular momentum remains unchanged (is conserved) (Figure 9.9).

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Figure 9.9. A figure skater in a spin uses conservation of angular momentum – decreasing her moment of inertia by drawing in her arms and legs increases her rotational speed. Source: https://en.wikipedia.org/wiki/Angular_momentum#/media/File:Cup_ of_Russia_2010_-_Yuko_Kawaguti_(2).jpg.

When compact stars (such white dwarfs, neutron stars, and black holes) are produced from much larger and slower rotating stars, the same mechanism causes them to spin incredibly quickly. When the size of an object is reduced n times, its angular velocity increases by a factor of n2. Conservation is not necessarily a complete explanation for a system’s behavior, but it is a critical restriction. A spinning top, for example, is subject to gravitational torque, which causes it to lean over and change its angular momentum about the nutation axis; however, ignoring friction at the point of spinning contact, it has a conserved angular momentum around its spinning axis and another about its precession axis (Olive et al., 2014). Furthermore, in any planetary system, the planets, star(s), comets, and asteroids can all travel in a variety of sophisticated ways, but still only so that the system’s angular momentum is conserved. According to Noether’s theorem, all conservation law is related with a symmetry (invariant) of the physics involved. Rotational invariance is the symmetry connected with angular momentum conservation. The idea that a system’s mechanics remains constant when rotated by any angle about an axis means that angular momentum is conserved.

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9.8. CHARGE CONSERVATION The principle of charge conservation in physics states that the total electric charge of a closed system remains the same. The net quantity of electric charge, defined as the sum of positive and negative charge in the cosmos, is constantly conserved. As a physical conservation law, charge conservation states that the change in the quantity of electric charge in any volume of space is precisely equal to the amount of charge coming into the volume subtracted from the amount of charge traveling out of the volume. Charge conservation, in principle, is an accounting relationship between the quantity of charge in a region and the movement of charge into and out of that area, as defined by a continuity equation between charge density and current . This does not preclude the creation or destruction of individual positive and negative charges. Subatomic particles like electrons and protons carry electric charge. In elementary particle processes, charged particles can be generated and eliminated. Charge conservation in particle physics indicates that in reactions that produce charged particles, an equal number of positive and negative particles are always produced, maintaining the net amount of charge constant. Likewise, when particles are annihilated, they remove an equal number of positive and negative charges. All empirical findings to date confirm this characteristic with no exception (McKenzie, 2014). Although conservation of charge demands that the total amount of charge in the universe be constant, it does not specify what that quantity is. The majority of evidence suggests that the universe’s net charge is zero; that is, there are equal amounts of positive and negative charge.

9.9. SYMMETRIES IN ELEMENTARY PARTICLE PHYSICS Several decades of high-energy physics experiments have yielded an exceptionally rich and extensive collection of information on elementary particles, the most significant of which are presented in the 700-page Particle Data Book. The particle designated as the K meson, for instance, is unstable and can dissolve into a group of lighter particles in approximately 70 different ways. Many observations have been conducted for each decay mode, such as the nature, velocity, and directions of the particles generated. How does one make sense of such a richness of data? The goal of theoretical particle physics is to discover the regularities concealed in data and to

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develop rules and laws that offer an explanation of the information in the most simple and exact way possible. The most powerful feature in this endeavor is symmetry, which is discussed further below. Symmetries have enabled an extraordinarily compact synthesis of all particle physics knowledge: the SM. This synthesis has now been subjected to a slew of extremely precise testing. Below is an explanation of how the strong, weak, and electromagnetic forces (EMFs) emerge as a result of three symmetries; the symmetries, in fact, define the exact structure of these three interactions (Macklin et al., 2014). These symmetries, however, lead to an astonishing—and apparently incorrect—prediction: all basic particles should be without mass. To solve this riddle, the symmetries must be “broke,” which indicates that new forces must exist that are still to be found. These new forces are linked to a theoretical particle known as the Higgs boson in the SM. The interactions of the Higgs boson with other particles produces particle masses but does not offer a true comprehension of the observable mass pattern. Furthermore, such a hypothesis may be expected to produce particle masses that are significantly heavier than measured. The masses of fundamental particles constitute a critical clue in interpreting the final theory of nature, and there is still much detective work to be done. With all of its triumphs in organizing the amount of evidence from highenergy particle collisions, the SM raises a whole new series of puzzles. What defines this theory’s particles, symmetries, and mass scales? Could they have been drastically different, fundamentally altering the nature of the world we live in? Physicists can explain the physical cosmos with astounding simplicity and precision, but they have little grasp of why this is so. Several theoretical theories that augment the SM to tackle, in particular, the issue of particle masses is examined later. Other difficulties, such as the function of gravity, are not even addressed by these ideas.

9.10. SYMMETRIES Although symmetry arguments have a rich and respectable history in physics, they have only recently come to dominate our knowledge of fundamental physics. Only when such ideas were represented mathematically did their entire power and beauty become clear. The committee, on the other hand, intends to express the essence of this topic by presenting some of its key physical principles (Lyons, 2012).

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What exactly do we imply when we state that physical laws are symmetric? When a square is rotated through 90° around its center, it is symmetric. This operation results in an orientation that is identical to the initial one—this is what we mean when we state that a symmetry operation renders an item invariant. A rotation via any angle leaves a circle unchanged (invariant). It has more symmetry since it provides for more symmetry operations. In essence, an item is considered to be symmetrical if there are operations on it that may have affected its look but do not. Physical laws, like all other rules, contain symmetry. One of the fundamental principles of physics would be that the laws of physics are the same as in one area as they are in another, and at one moment as they are in another. This idea is akin to symmetry: whether we change our perspective from one location to another or from one moment to another—the rules of physics remain invariant. Another well-known example of symmetry is rotation. Consider a laboratory to be a windowless free-falling spaceship free of electric and magnetic forces, in which an experimentalist has some equipment to verify a given physical law. Assume the experimenter takes a measurement, the spacecraft rotates, and the identical measurement is taken again. The outcomes of the two results are always the same: No need to indicate the direction of the laboratory while stating the rules of physics. It is not required to define the speed of the laboratory—the principles of physics do not vary if the test is carried out, for instance, on an aircraft. This final symmetry principle was the deciding factor in Einstein’s development of special relativity. The need that physics be symmetrical under the operations mentioned leads to all of the stunning conclusions of special relativity, like the equivalence of mass and energy and the inability to travel faster than light.

9.11. SYMMETRIES AND PARTICLE PHYSICS There is a variety of ways that the symmetries of space and time, known as space-time symmetries, affect particles and their interactions. Firstly, there is a clear implication for the very composition of elementary particles. Because of rotational symmetry, elementary particles acquire a new property known as spin. Electrons, for instance, exist in two types: left-handed and righthanded (Long et al., 2021). The distinction can be visualized by imagining the quarterback’s view of a football’s spin as seen by the quarterback who threw the pass. When thrown by a right-hander, the football spins clockwise, while when thrown by a left-hander, it spins counterclockwise. Photons have

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the same two types of spins, but other particles have three spin orientations yet others are spinless. The laws by which all particles interact are also constrained by the symmetry of space and time. It is crucial not to lose sight of why it is critical to comprehend these connections. Every physical process, has its underlying basis in these interactions. Materials’ qualities, from cement to quicksand, are ultimately determined by the characteristics of elementary particles. Consider the collision of two electrons depicted in Figure 9.10. The electrons 1 and 2 near one other, clash, and then exit as the electrons 3 and 4. According to quantum mechanics, there is no such thing as a unique outcome: Electrons are deflected by big and small angles at different times. The laws of physics can be expressed in terms of probabilities in this quantum realm. The representation is complete if the laws predict the probabilities for all potential outcomes. The issue is that the probabilities are determined by the speeds, orientations, and spins of the four electrons, each of which has an infinite amount of potential values. The significance of symmetry can now be recognized: Probabilities are governed by symmetries and rely on particle velocities, orientations, and spins. In principle, symmetries impose significant constraints on the nature of interactions between elementary particles. Despite the fact that there are many alternative initial and ultimate configurations, probabilities can be defined in terms of a few quantities (named parameters).

Figure 9.10. Collision of two incoming electrons, 1 and 2, into two outgoing electrons 3 and 4. Source: https://www.nap.edu/read/6045/chapter/5#36.

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As physicists identified more fundamental particles, they recognized that patterns in their behavior could be explained using mathematical symmetries. These more recent symmetries frequently operate in more abstract, socalled interior spaces. Early research on protons and neutrons, for instance, demonstrated that, despite their different electric charges, these particles are essentially comparable and their strongest interactions are identical. This striking resemblance sparked the idea of a two-dimensional “internal” space in which protons and neutrons correspond to various orientations. The closeness of their behavior becomes the assertion that physics remains constant when one turns in this fictitious interior space. This operation is deemed to be internal symmetry if it does not modify the rules of physics. As more particles were identified, the usefulness of this method of thinking became clear. Each has to be positioned within the confines of the building (Liu et al., 2017). If only a portion of the picture was available, apparent asymmetries in the arrangement of known particles inside internal space would occur. The existence of particles required to finish the symmetric pattern, as well as some of their attributes, may thus be anticipated. The detection of the omega-minus (Ω) particle, which was anticipated ahead of time to cover the gaps in the symmetrical pattern illustrated in Figure 9.11, was an early illustration of this.

Figure 9.11. Pattern of particles that allowed prediction of the Ω-particle. Particles in the same row have similar masses: Particles with the same electric charge (shown by superscripts) also lie on straight lines. Source: https://www.nap.edu/read/6045/chapter/5#36.

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9.12. LOCAL OR GAUGE SYMMETRIES The most fundamental and powerful physical law symmetries revealed to date are known as local or gauge symmetries. Even Einstein’s theory of general relativity and the SM of strong, weak, and electromagnetic interactions are based on such symmetries. The majority of matter on Earth is made up of only two quarks, up, and down quarks, indicated by the letters u and d. Because of internal symmetries, each of these quarks has three variants, which are identified by color: ur, ug, and ub represent the red, green, and blue up quarks, respectively. If the colors of quarks are switched, for example, ur, and ug, physical principles remain constant. A local symmetry, in reality, indicates that physical rules remain unchanged even though different interchanges are made at different points in space. In one portion of the laboratory, for example, ur may be replaced by ug, while ur could be replaced by ub in another. There are an endless number of such local activities, and requiring the laws to remain constant for any of them is exceedingly restrictive (Leader, 2016). Local internal symmetries necessitate the existence of particles (referred to as force carriers) whose interactions are the source of the forces. The strong force that binds quarks into nuclei is caused by the local symmetry that works on the three hues. Returning to the collision of two electrons, we can obtain insight into this foundation for comprehending forces. If it appears in a theory with a local internal symmetry, the circular blob represents the real interaction between particles and is extremely limited. If one could examine within this blob under great magnification, such a theory would suggest that the interaction is caused by the exchange of a force particle, which in an electromagnetic interaction is known as the photon, as represented below. In addition, the interplay of a photon with two electrons is severely restricted by local symmetry. Regardless of the particle speeds, orientations, or spins are, just one parameter—the electric charge of the electron—is required to characterize this interaction. It’s the same single parameter that underlies all of the electron’s electromagnetic interactions, such as the bending of an electron’s path in a magnetic field and the electron’s binding to an atomic nucleus (Figure 9.12).

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Figure 9.12. Collision of two electrons resulting from exchange of a photon. Source: https://www.nap.edu/read/6045/chapter/5#38.

This is the same one parameter that affects all of the electron’s electromagnetic interactions, such as the bending of an electron’s path in a magnetosphere and the electron’s bonding to an atomic nucleus. The electromagnetic interaction is depicted diagrammatically below as a vertex where the three particles collide. Local symmetries are also called gauge symmetries, and the corresponding force particles, like the photon, are called gauge bosons (Figure 9.13).

Figure 9.13. Electromagnetic vertex of an electron: The electron emits a photon with a probability, in emissions per second, proportional to the electron’s charge. Source: https://www.nap.edu/read/6045/chapter/5#38.

It’s mind-boggling to discover that the seemingly limitless range of chemical characteristics and interactions of atoms and molecules all stem from one electromagnetic vertex. The photon’s existence, as well as the shape

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of electric and magnetic interactions, is a result of local electromagnetic symmetry. Although it is obvious that symmetries are the most potent tool physicists have for interpreting particle properties and interactions, we could only discover the symmetries nature contains by meticulous investigation. Although many symmetries have been postulated, measurements are the sole certain guidance. Future investigations will seek to find more of nature’s symmetries, while theoretical physics will keep on trying to comprehend why nature selected these symmetries.

9.13. THE STANDARD MODEL (SM) The creation of quantum field theories—theories of particles and their interactions that combine the probabilistic rules of quantum mechanics, special relativity, and the symmetries outlined above—has been a key advance in theoretical physics this century. This venture began shortly after the late 1920s discovery of quantum mechanics. The electron and photon were described in detail by the quantum field theory of electromagnetism, which was completed in the late 1940s, although ideas including larger local internal symmetries were not grasped until the early 70s. Quantum field theories are the fundamental tools used by theoretical particle physicists. There are numerous similar theories, and the wide range of occurrences that they can explain is the focus of ongoing research. The standard model (SM) describes all observable particle phenomena in a succinct and accurate manner (Lasserre, 2014). In nature, three local internal symmetries have been found: They are named from the three forces that they offer ascent to: strong, weak, and electromagnetic. The gluons, g, are force particles of strong interactions caused by strong symmetry. This force is felt by matter particles known as up and down quarks, u, and d, which exist in red, green, and blue versions. The up-quark’s gluon vertex is depicted below. A quark of one color enters the interaction and emerges as a quark of another color, but its other attributes remain same. Quantum chromodynamics, or QCD for short, is the mathematical theory of quarks and gluons that underpins this vertex. The gluon interaction strength is denoted by the letter g3. It is enormous, resulting in a strong QCD interaction. The matter particles that are not affected by this strong force are known as leptons, which include the electron, e, and its neutrino,

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ve, as well as its second- and third-generation equivalents, the muon and tau, and their corresponding neutrinos (Figure 9.14).

Figure 9.14. Quark triplets and the gluon vertex. Source: https://www.nap.edu/read/6045/chapter/5#38.

The W and Z bosons, the force particles of the weak interaction, are highly heavy, resulting in a force with a very narrow range—much far less than size of a proton. The electromagnetic interaction, on the other side, has a massless force particle, the photon, and an endless spectrum of interaction, permitting humans to see all the way to the other side of the cosmos. The intensity of the weak interactions is described by a single parameter g2, whereas the intensity of the electromagnetic interaction is described by g1. The weak symmetry has an unusual feature. Only quarks and leptons spinning counterclockwise are affected by the weak force. One of the numerous concerns about the constitution of forces for which we have no good solutions is why nature regards left-handed and right-handed objects differently. As previously stated, symmetries govern both forces and the multiplet architecture of particles that experience these forces. Figure 9.15 illustrates how the three forces resulting from local internal symmetries connect to the four fundamental kinds of matter particle. The elements for strong and weak forces reflect the size of the multiplet of particles interacting with the associated force particles (Zimmermann, 2018). The strong force operates on quark triplets (three colors), transforming one into the other; the weak force operates on quark and lepton doublets, transforming one into the other. Because there is nothing to transform into, a “I” entry suggests that there is no interaction. The EMF operates on all particles save neutrinos (which

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do not change their composition), thus the entry in Figure 9.15 shows the electric charges of the particles. Figure 9.15 shows the current limit in the search for a basic explanation of particle interactions. This knowledge poses several problems, none of which are addressed by the SM: Why do certain particles feel the strong force while others do not? Why are the bad interactions always left-handed? Why don’t there exist multiplets with more than three components? In a nutshell, why are matter particles what they are, and why do they interact with force particles in the manner depicted?

Figure 9.15. Forces and symmetry. Source: https://www.nap.edu/read/6045/chapter/5#38.

The four matter particles examined thus far (u, d, e, ve) are part of the first particle family, or generation. Three generations of particles of this type have been discovered. The only apparent variation between the three generations is their mass—in particular, the force particle vertices of the heavier generations are comparable to those shown in the pictures for the lightest generation. Some believe that the reproduction of particles indicates the existence of a new internal symmetry that is accountable for the distinct generations.

9.14. SPONTANEOUS SYMMETRY BREAKING (SSB) Whereas the interactions of force particles are constrained by the three local symmetries, the measured masses of quarks are constrained by the strong symmetry. Components of weak doublets, such as ve and e, do not have the same mass as ur, ug, and ub. Nonzero masses of elementary particles are considered to violate electroweak symmetries. This appears to be unsatisfactory—certainly, all aspects of a theory should have the same symmetry. In truth, scientists believe that the theory’s equations do have electroweak symmetry at first, but something inside the theory leads the solution to the calculations to violate the symmetry. The previously cited illustrations of the square and circle show this fundamental phenomena of random symmetry breakdown (Woithe et al., 2017). Remember that these

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shapes are symmetrical when turned 90° around their centers for the square and any angle for the circle. We have violated the symmetry if we design a square and a circle on an elastic sheet and then stretch the sheet in one direction, elongating these figures into a rectangle and an oval. When the rectangle is rotated 90°, it no longer matches the shape that corresponds to its initial position. This stretching is a simple model for spontaneous symmetry breakdown in particle physics theories. The first stage is to deduce from information what stretching is occurring—this is well understood—and the second step is to identify what is driving the stretching. There are some suggestions here, but the correct solution is not yet discovered. The symmetry of the square and circle are not fully destroyed when the sheet is stretched: The ensuing rectangle and oval are both symmetric with regard to 180° rotations about their centers. Likewise, not all electroweak symmetries are lost; the local electromagnetic symmetry remains intact. An essential implication of precise local symmetry is that the mass of the associated force particle must vanish. This helps to illustrate why gluons and photons have no mass. W and Z particles, on the other end, which correlate to the broken sections of the electroweak symmetry, are not required to be massless. In truth, they are so hefty that it wasn’t until the 80s that accelerators reached high enough energy to make them. So, in physics, the notion that the characteristics of particles including such atoms and molecules stay constant despite a range of symmetry changes or “operations.” Ever since beginnings of natural philosophy (Pythagoras in the sixth century BCE), symmetry has provided clarity into physical rules and the nature of the universe. In a significant manner, the two outstanding theoretical discoveries of the 20th century, relativity, and quantum physics, include conceptions of symmetry (Wood and Heyde, 2016). The implementation of symmetry to physics gives rise to the important summary that certain physical laws, especially conservation laws regulating the conduct the behavior of objects and particles, are unaffected when their geometric coordinates—including time, when considered as a fourth dimension—are transformed using symmetry operations. As a result, the physical laws apply everywhere and at all periods in the cosmos. In particle physics, symmetry concerns can be utilized to develop conservation laws and to specify which particle interactions can and cannot occur (the latter are said to be forbidden). Symmetry is also used in many other fields of physics and chemistry, such as relativity and quantum theory, crystallography, and spectroscopy. Likewise, the quantity and kind of symmetry operations that

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may be done on crystals and molecules can be used to characterize them. Group theory is the quantitative study of symmetry. Valid symmetry operations are those that can be performed on an item without affecting its appearance. The quantity and nature of such procedures are determined by the geometry of the object to which they are applied. Consider a square sitting on a table to show the significance and diversity of symmetry operations. Valid operations for the square include: (i) rotation about its center through 90°, 180°, 270°, or 360°; (ii) reflection through mirror planes perpendicular to the table and running through any two opposite corners of the square or the midpoints of any two opposing sides; and (iii) reflection through a mirror plane in the plane of the table. As a conclusion, there exist nine symmetry operations that provide an outcome that is unrecognizable from the initial square. A circle is considered to have greater symmetry if it can be rotated through an unlimited number of angles (not simply multiples of 90°) to produce an identical circle. Subatomic particles have a variety of characteristics and are influenced by symmetrical forces. Parity is an important feature that offer ascent to a conservation law. All constituent particles and atoms in quantum mechanics can be represented using a wave equation. This wave equation is considered to have even parity if it stays unchanged following simultaneous reflection of all coordinates of the particle via the origin of the coordinate system. If such concurrent reflection produces a wave equation that varies only in sign from the initial wave equation, the particle is shown to have odd parity (Wallace, 2011). The overall parity of a group of particles, like a molecule, is discovered to be constant across time during physical processes and reactions; this phenomenon is referred to as the law of conservation of parity. Nevertheless, at the subatomic level, parity is not retained in weak force reactions. Internal symmetry is another term for elementary particles; these symmetries are helpful for identifying particles and contributing to selection criteria. The baryon number, which is a characteristic of a type of particles known as hadrons, is an example of such internal symmetry. Hadrons with a baryon number of zero are referred to as mesons, whereas those with a number of +1 are referred to as baryons. By symmetry, another group of particles with a baryon number of one must exist; these are the antimatter equivalents of baryons known as antibaryons. All through nuclear interactions, the baryon number is conserved.

CHAPTER

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FUTURE OF ELEMENTARY PARTICLES

CONTENTS 10.1. Ghost-Hunting Machines .............................................................. 250 10.2. Further Exploration of the Sky ....................................................... 252 10.3. Upgrades in the LHC .................................................................... 254 10.4. Different Thinking ......................................................................... 256 10.5. New Observations ........................................................................ 257 10.6. The Muon’s Moment ..................................................................... 258 10.7. Going Bigger ................................................................................ 259

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The future of elementary particles is bright with scientists making new advancements. There could also be development of new theories to explain further on particles. There is a lot of area to discover under elementary particles as there are some unresolved mysteries. Some of these mysteries include why there is a large percentage of matter in the universe compared to anti matter, the true identity of dark matter and why ultra-weak neutrino particles ended up ghostly (Viaux et al., 2013). Most scientists are excited about this as there are several ideas and several experiments that could be conducted to evaluate the ideas. There are several projects that could’ve undertaken making the prospect for discovery very real. The high number of experiments means that there is a greater potential of solving the mysteries and also uncover several clues (Figure 10.1).

Figure 10.1. The future of elementary particles involves several discoveries being made. Source: https://depositphotos.com/stock-photos/elementary-particle.html.

10.1. GHOST-HUNTING MACHINES Among the area of elementary particles that has posted a challenge to scientists is the study of abundant particles in the universe. Among these particles is the neutrino which is also called the ghostly. These particles

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have posed a challenge with regards to studies as they weakly interact with regular matter. Few studies done have led to the discovery that the particle comes in three separate flavors and also three separate mass states. It was also noted that the mass states to not correspond to the flavors as each of the flavors is formed through the combination of the three mass states. Scientist are looking to learn more about these masses, establish their values and the order they appear in when they combine to make up the flavors. KATRIN is an example of the experiments done in German to measure the masses (Volovik, 2015). For the next five years, the experiment will be taking data. Some side effects were noted with the mass of a neutrino. When the masses travel though space, they are seen to oscillate between the flavors. There are experiments that will be used to understand and get more information on the oscillations. The Jiangmen Underground Neutrino Observatory in China has been involved in experiments of on oscillations and is scheduled to take data on neutrinos emitted from nuclear power plants. In Japan, the Super-Kamiokande has been taking the data and making some observations (Figure 10.2).

Figure 10.2. There is limited information on neutrino particles. Source: https://www.forbes.com/sites/startswithabang/2020/12/14/8-factsabout-the-suns-most-ghostly-particle-the-neutrino/.

In the United States, construction is underway on a neutrino beam as well as a corresponding detector. The facility is known as the Long-baseline neutrino facility and Deep Underground Neutrino Experiment. The facilities will be located in Illinois and South Dakota respectively. The LBNF/ DUBE experiments received international funds of 1.5 billion dollars and is

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expected to be online in 2024 and fully operational in 2027. There are other experiments that have been founded to deal with the neutrino mysteries. In Tennessee there is the PROSPECT at Oak Ridge National Laboratory and Illinois the Short-Baseline Neutrino Program at Fermilab (Figure 10.3).

Figure 10.3. Fermilab has actively been involved in several experiments on new particles. Source: https://news.fnal.gov/2020/12/major-upgrade-to-fermilab-accelerator-complex-gets-green-light/.

There is more to neutrinos than their innate properties. At the South Pole there is an underground Icecube neutrino observatory that measures neutrinos traveling through the earth. Recently, the IceCube cracked the mystery of the source of ultra-high-energy cosmic ray particles. There is construction of an underwater neutrino telescope that will be employed in the hunting of similar neutrinos from the Mediterranean Sea. The facility is called the KM3NeT and is expected to be in operation in 2025.

10.2. FURTHER EXPLORATION OF THE SKY There are three things that influence the manner in which the universe evolves and looks. They include mysterious dark energy, mysterious dark matter, and ordinary matter. This is clear indication that elementary particles are found in areas other than earth as fundamental physical properties may

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leave their mark on structures of the cosmos. For this reason, most of the experiments lean towards the use of telescopes rather than particle detectors in providing answers on the unexplained physics mysteries. The greatest mystery is the nature of dark energy (Van Noorden, 2012). This is the mysterious energy that permeates the cosmos and causes the acceleration of the expansion of the universe. Energy is composed of particles. Therefore, by understanding the energy the particles in it could be accounted for. Recently, the Dark Energy Spectroscopic Instrument began its survey. To help with its work, it is expected that the National Science Foundation/ Department of Energy’s Large Synoptic Survey Telescope located in Chile will be conducting surveys in 2022. Its operations began in 2020. A spacebased telescope, The Wide Field Infrared Survey Telescope, was launched in 2020 after the deadlines were met (Figure 10.4).

Figure 10.4. Scientists are working to establish the source of dark matter. Source: https://earthsky.org/astronomy-essentials/definition-what-is-dark-matter/.

Experiments conducted by the facility are expected to make use of data obtained from surveying the universe and observing several galaxies. The obtained data is used to understand whether dark energy is caused by unaccounted-for math in present-day theories of gravity, innate feature of the universe of by particles. Other than observing dark matter, the dark matter-hunting telescopes are also used in probing other anomalies including mysterious drop in the number of high-energy electrons reaching

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the Earth’s surface, extra gamma rays from the center of our galaxy, excess antimatter from space and strange patterns in the signals from distant hydrogen. Most scientists speculate that dark matter could be used to explain the noted observations though there are other potential causes include g spinning neutrons, pulsing or wrong theories (Ünel and Sekmen, 2018). It is anticipated that further research will be useful in explaining these anomalies through the generation of data. According to Rebecca Leane, Collider-based experiments collide things at high energy. The outcomes are the observed. These processes have been noted to occur for the duration of the universe. It was noted that high-energy events make cosmic rays to collide with everything in space. This knowledge can be used to discover new particles and check whether there are new things happening from the already established physics (Figure 10.5).

Figure 10.5. Dark matter-hunting telescopes have been used in most research facilities. Source: https://astronomy.com/news/2019/04/scientists-use-lhc-to-hunt-darkmatter-siblings.

10.3. UPGRADES IN THE LHC A large amount of the information on particle physics throughout the century were produced by the large hadron collider (LHC) in Geneva Switzerland. The facility is known for the Particle physics’ Hallmark experiment. There are hopes that scientists will be able to squeeze more information from the machine. The machine was shut down for a period of time till 2021 for maintenance work. Afterwards the company began its activities and is expected to continue run and deal with slightly high energies until 2023. The machine is expected to receive major upgrades. It is expected that the upgrades will be completed in 2026. The High Luminosity-LHC is the billion-dollar upgrade. The upgrade may increase the number of

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collisions produced by the machines per second. It is anticipated that the number of collisions could double by 2030. Of the produced collisions, it is anticipated that it could produce new violations or particles to the laws of physics as theorized (Tluczykont et al., 2012). An Increase in the luminosity or collision rate causes an increase in the statistics available for physicist search. It also enables them to get precise values of the masses of particles and the frequency at which the particles decay into other particles. This makes each particle collision a different kind of experiment and therefore it has its own potential outcome. There are cases where scientists will have to conduct the experiment a number of times as the experiment could yield new data or similar data to other experiments. By repeating the experiment, scientists are able to ascertain whether what they were getting is what they were expecting (Figure 10.6).

Figure 10.6. The Large Hardon Collider has provided much knowledge in particle physics. Source: https://www.nytimes.com/2007/05/15/science/15cern.html

Presence of more statistics enables physicist prove whether theoretical particles decay exist as predicted. If they are found not to, then the scientists are able to look into other lines of inquiry. The LHCb detector spotted one rare decay that seems to be a variation from predictions from current theories. More statistics are used in determining whether the variance is statistically significant; whether it is highly unlikely to appear by chance and a potential sign of physical forces or unknown particles. In the experiments, scientists mat tries to produce as many Higgs boson and study the many properties while compared to the standard models (SMs). All deviations were noted.

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10.4. DIFFERENT THINKING James Beacham a particle physicist at the ATLAS Experiment at the large Hardon Collider stated that LHC is a marathon and should therefore be run for longer durations of time. Adoption of this methodology enables something that may show up with a tiny bump gets a chance to peep through the noise. This is the vision of LHC in a span of 10 years. While using the LHCs scientists are hoping to fully utilize it for all its worth. This involves shifting of data in new ways or building of new detectors that will enable physicist to access physics theories that old detectors can’t. Currently, HLC detectors are being used to hunt particles that leave a signature in the dew meters outside the initial collision. The question most scientists seek to answer is whether there are particles that drift the way out of the detectors before they are detected (Shlomi et al., 2020). Other than the HLC detector, there is the MilliQan and the MoEDAL. These detectors are used to find longer-lived particles. To aid with the research, MATHUSLA called for an airplane hanger-sized, air-filled chamber above the ground and far from collision points. This will enable the trapping of potential wanderers. There are those who argue that collection and observation of HLC data should be done from a different point of view. Recently, the LHCb detector has been used to look for particles called dark photons. This is achieved when the system that determines whether data should be thrown out or not is tweaked. There is plenty of data to be weed through in HLC. Most physicist are busy dealing with that from HL-LHC (Figure 10.7).

Figure 10.7. Various detectors have been used to detect the presence of particles in the atmosphere. Source: https://www.sciencephoto.com/media/976/view/h1-particle-detector.

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10.5. NEW OBSERVATIONS A major part of conducting research is waiting for something to happen. With dark matter, there is a lot of mystery surrounding its source. LHC is yet to detect a particle that can explain the source of dark matter. Dark matter is said to be five times more than regular mass. Scientists do not have sufficient information on the composition of dark matter. The weakly interacting massive particles is the most recent and popular theory. There are several experiments across the globe that are lying in wait, buried deep underground in various locations and scientists are hoping that their sensitive detecting medium will interact with the weakly interacting massive particles (Seshavatharam and Lakshminarayana, 2013). This enables the generation of a visible signal. Most of the experiments have not yielded much or useful information. Results from the experiments have also ruled out potential WIMO candidates. Though it is discouraging for scientists to conduct research but not get meaningful results, there are hopes that in the next decade, there will be upgrades in the experiment making them more sensitive. In Italy, there is the XENON-nT experiment handling enormous vat of liquid xenon deep underground is being brought online allowing research activities. In Ontario, there is the suoerCDMS SNOLAB involved in taking data as it has suoer-sensitive ultra-cold semiconductor detectors. When using these detectors, scientists can look into dark matter candidates other than WIMPs. In some experiments, suoer-low-mass particles called axions were noted. They are likened to slowly tuned radios waiting to hear a telltale signal. Less mysterious physics makes use of giant underground detectors. Most of these devices are extremely sensitive particle detectors and are used by scientists when measuring incredibly rare radioactive decay events. Most scientists are looking towards observing the neutrino less double beta decay the makes two neutrons from an atom’s nucleus undergoing simultaneous decay into protons leading to the production of a neutrino and an electron. The products meet other neutrinos and annihilate. If scientists were able to prove that the reaction existed then it proves that neutrinos are their own antiparticle. It indirectly bolsters another theory of the early universe explaining why there’s more matter than anti matter. The LEGEND-200 experiment is among the experiments dedicated towards hunting this reaction. The experiment is expected to be taken online in 2021.

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10.6. THE MUON’S MOMENT Among the most celebrated achievements is the Fermilab’s experiment that measures the muon g-2. Among the various kind of particles known to be in existence are the muons. They are electron like with the same electric charge but a larger mass. Muon’s have a magnetic moment. The magnetic moment enables the muons to twist and react when applied in a magnetic field. The g-factor is the measure of this moment and is equal to two or more quantum prices. To measure the g-2, scientists are using a 50-footwide electromagnetic. Form the currently generated information, the g-2 value has been noted to differ from the SM of particle physics’ predictions. In the extra piece, g-2, has extra information on other particles that may interact with muons (Radovic et al., 2018). This means that the discrepancy could be caused by a new unexplained behavior or a new particle. When the differences between experiment and theory are consistent, they are considered as clues that will answer big questions of particle physics. However, there is no statistical significance of the discrepancy of the g-2. By conducting more studies, researchers are hoping to measure the value with high levels of precision that may make the discrepancy clearer or eradicate it. The current run at Fermilab is anticipated to give more answers (Figure 10.8).

Figure 10.8. Further research is expected to give more information on muons. Source: https://nmi3.eu/service/print-template-artid=150.html.

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10.7. GOING BIGGER While conducting various experiments, scientists are looking towards development of next-generation colliders. This goal is at the top of the myriad particle projects. In China, there is a consortium that plans to begin construction of a particle collider. The particle collider will be called the Chinese Circular Electron Positron Collider and is expected to be functional non 2022. Other than the consortium, CERN also has plans to build a particle collider expected to be fully operational in 2040. Particle collider currently used have not generated any new evidence for new particles at high energy ranges of the proposed colliders. There are those who have shared their skepticism about the giant machines being built. The challenge with science experiments is that it is hard for a scientist to in is whether it can be used to discover new things unless the device is built and it is explored (Pitkänen, 2011). There are different kinds of colliders with different sizes and make that can be used by physicists in different ways. In the United States, there are colliders that require upgrades. The upgrade would make the colliders to be electron-ion-colliders. When upgraded, these colliders could act as microscopes for protons that make up atoms. Some countries have made collaborations enabling them upgrade their colliders at a cheaper price. This is the case for the International Linear Collider, linear Collider in Japan. Linear colliders enable physicist to make accurate measurements of particle masses like the Higgs boson. This enables more discovery beyond the SM of particle physics. The results could also indicate that there are other potential physics. Building of most of these projects requires a lot of commitment, support, and time. ILC has been able to make it as Japan has not withdrawn its support for the experiment. However, there are doubt whether the project is worth funding. There are those who worry that the colliders such as the FCC are too costly and too big. They also point out that there are smaller experiments that can be used that has different funding from other often-strapped science budgets. Sabine Hossenfelder, a physicist also stated that if they had reasons to think that the collider could be useful in finding new particles then they would opt to build and use them (Pashkin and Leitenstorfer, 2014). Among the challenges faced is that they have built a single particle collider and it measures constant for more than one digit. Though the achievements gotten form the collider may be worthwhile for scientists, it may not be the same case for those involved in making the purchases. This is what Science entails. Major risks are taken. Currently used economic models make it difficult for scientists to justify experiments

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that may not guarantee big discoveries. Most Science projects have been done with the aim of getting information rather than profit (Figure 10.9).

Figure 10.9. Some projects have not been achieved due to lack of funds. Source: https://www.scientificamerican.com/article/long-awaited-muon-measurement-boosts-evidence-for-new-physics/

By making more discoveries on particles, scientists will be able to create an environment for future success. This is considered an anthropocentric perspective on science as science is viewed to work more for us. Most scientists suggest that the future may involve more radical thinking and several experiments may be done that may not reveal something new. There is still hope that there will be a shift in the society so that larger numbers of people will value science enough to an extent that they will take on greater experimental endeavors with less focus being placed on getting Nobel prizes or compromising smaller experiments. Though there is hope for future changes, it does not mean that the changes will come drastically. This gives scientists more time to learn more physics and generate new and better ideas. There is hope that there may be profound physics discoveries made in the future that may shed light on the true nature of dark matter, what is the fate of the universe, new particles in the atmosphere and why the universe looks the way it does. More discoveries on elementary particles may involve governments and relevant stakeholders being more financially invested. Researchers may also have to look into more ground and uncovered areas. This presents an opportunity for scientists to learn, to

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fail in some experiments and come up with new technologies that can be used in some experiments (Olive et al., 2014). Particle physics make use of technological advancements. These technologies have led to the discovery of other particles that have been used in various fields such as aerospace, the internet and medicine. The experiments may lead to advancements of their own and may eventually be used in quantum technology. More research will enable researchers to answer the numerous questions they have concerning various matters. The future of elementary particles involves scientists dealing with some of the challenges they faced when using colliders among other tools in particle physics (Figure 10.10).

Figure 10.10. Research may require improvement of techniques used. Source: https://phys.org/news/2020-07-cern-physicists-discovery-unique-particle.html.

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INDEX

A Abstract Neutrinos 208 accelerator 168, 170, 171, 173, 174, 175, 177, 178, 179, 180, 182, 190 aether 87 aluminum 87, 104 analogy 212 angular momentum 59, 60, 63, 77, 83 angular momentum conservation 244, 255, 259 antimatter 109, 126 antiprotons 167 astrophysics 147, 163 atmospheric neutrinos 208 atoms 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 50 B Bardeen-Hill-Lindner theory 121 baryon number 244, 271 Big Bang nucleosynthesis 147 bonding 138 Bose–Einstein (B–E) statistics 61

Brookhaven National Laboratory (BNL) 168 C Cesium halide perovskites 220 classical physics 26 clustering 138 collisions 166, 167, 168, 170, 171, 172, 173, 174, 179, 182, 183, 184, 188, 189, 190, 192, 193 composite particle 56, 57, 75 Compton Effect 213 computing 166, 171 conservation law 244, 254, 259, 260, 271 Conservation rules 244 continuity equation 244, 260 Copper 27 cosmology 197, 200, 203, 204, 205, 206, 208, 212 D Dark matter 278, 281 dark photons 280 distribution system 169 dust 56

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E

H

Earth’s atmosphere 109 effective field theory (EFT) 198, 212 Effective field theory (EFT) 211 electric charge conservation 244 Electricity 110 electromagnetic 57, 59, 71, 72, 73, 78 Electromagnetic force 143, 152 electromagnetic force (EMF) 110 electromagnetic radiation 142 electron 26, 29, 31, 32, 33, 34, 35, 36, 38, 43, 47 Elementary particles 108 energy conservation 244, 247, 248, 249, 251

Hadron colliders 173, 174 hadronic string 219 hadronic string model 219 hadrons 138, 141, 142, 143, 144, 145, 160, 161, 162 Hard Parton effects 219 Heavy Quack symmetry 210 heavy quark symmetry 198, 209 Heavy Quark Symposium (\“HQS\”) 211 high-energy collisions 212 high quantum yield 220 hypercharge 244

F Fermi–Dirac (F–D) statistics 61 fermion 60, 61, 62, 63, 68, 77, 83 Feynman’s paradox 212, 213 flavors 89 fluid water 26 frequency doublers (FDs) 173 G gamma rays 278 gases 26, 36, 40 gas particles 56 gauge theory 168 gluons 87, 90 Grand Unified Theory 111 Gravitational force 143, 157, 158, 159 graviton 110, 116 gravity 110, 111, 112, 116, 117

I injector 172, 173, 174, 175, 177 interpersonal isolating 229 K kinetic energy 246, 247, 248 L large hadron collider (LHC) 86, 120, 168, 278 lepton number 244 Leptons Model 90 light-emitting materials 220 light neutrinos 207 Linac 173, 175, 176, 177 linear momentum conservation 244 liquid helium 169 logical authenticity 221 M macroscopic theory 139 magnetic moment 282

Index

magnets 169, 173, 178, 179, 180, 181 mass conservation 246, 247, 249, 251 mathematical equation 139, 142 Maxwell–Boltzmann (M–B) statistics 61 medical research 171 mesons 138, 141, 142, 160, 163 momentum 168, 174, 180, 186, 188 multiparticles 219 mysterious dark energy 276 mysterious dark matter 276 N neutral kaons 201, 202, 203, 205 neutral kaon system 201 neutrino mass 206 neutron 33, 49 Newtonian physics 213 Noether’s theorem 244, 248, 259 nuclear beta decay 207 nuclear decay 27 nuclear physics 114, 116, 117 O ordinary matter 276 P parity non-conservation 200 parity strangeness 244 partial differential equation 244 Particle collision 166 particle energy 177 particle interactions 58, 66 Particle physics 56 particular isotopes 223 parton model 219 Parton’s hypothesis 218

271

photons 26, 31, 37, 39, 47 plasma 26, 27 Point particles 117 Poisson equation 139 positron vitality spectra 223, 224 preons 117, 118, 119 proton synchrotron booster (PSB) 177 proton synchrotron (PS) 175 Q quantum chromodynamics (QCD) 90, 117, 140 quantum electrodynamics (QED) 141 quantum fields 56 quantum field theory 58, 62, 72, 73, 78 Quantum gravity 116 quantum particle 116 quantum statistics 60 Quarks 89, 92 R radiant energy 246, 248 radiation 56, 57, 71, 72, 80, 82 Radio frequency quadrupoles (RFQs) 173 radio-frequency (RF) field 177 rapid prototyping 227 relativistic heavy ion collider (RHIC) 140 rudimentary particles 222 S scattering 138, 141, 145, 162 selenium 87 shrinking photon effect 219

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solar electron neutrinos 207 spin 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 72, 73, 74, 75, 76, 79, 82, 83 Standard matter 57 standard model (SM) 27 String theory 116, 117 strong interactions 139, 144, 161, 163 Strong nuclear force 143, 159 substance 26, 38, 40, 41, 45, 47 suoer-low-mass particles 281 super proton synchrotron (SPS) 177 supersymmetric theory 113 supersymmetry 90 T technicolor 90 telecommunications 171

teraelectronvolts (TeV) 170 theory of everything (TOE) 59, 112, 136 thermal energy 246 thermodynamic equilibrium 61 U ultra-high-energy cosmic ray particles 276 V vanilla 89 virtual particles 108 W water vapor 26 waves 26, 27 Weak nuclear force 143, 159 Wei–Norman approach 233