The Neutrino Story. One Tiny Particle’s Grand Role in the Cosmos 9783030518455, 9783030518462

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RABINDRA N. MOHAPATRA

The

Neutrino Story One Tiny Particle’s Grand Role in the Cosmos

The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos

Rabindra N. Mohapatra

The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos

Rabindra N. Mohapatra Department of Physics University of Maryland College Park, MD, USA

ISBN 978-3-030-51845-5 ISBN 978-3-030-51846-2 (eBook) https://doi.org/10.1007/978-3-030-51846-2 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Cover image: © Lynette Cook / Science Photo Library This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

To Manju

Preface

Among the particles in the universe, the neutrino is the tiniest and the one with the weakest interactions, yet it has a disproportionately outsized influence on the creation of the universe that is our home today. That is why the story of the neutrino is a fascinating one. Starting with how it entered the discussion of science in 1930 to how it was discovered and how its properties were uncovered as time evolved, the neutrino’s story has been laced with curiosity, suspense, hard work, and the thrill of discovery of the unanticipated. So is its promise for great societal applications in the future. The discoveries are still evolving with new investments on the international scale. The pursuit of a more complete knowledge of the neutrino is one of the most diligent scientific endeavors in the world today. Scientists are going out, all decks on hand to learn as much about this tiny particle as possible. They have set up “nets” in most unlikely places, from the deep cold Antarctica to the warm ocean floors and places around the globe. They have built instruments deep underground to catch the neutrinos from the sky, supernovae, the Sun, and the center of the galaxies. Everyday new knowledge is pouring in and being analyzed in sophisticated computer networks. This book is an attempt to provide only a partial glimpse of the decades-long story of the neutrino, starting in 1930 when it first came into the scientific stage as a mere idea. Originally thought to be far-fetched, its existence was confirmed in the 1950s. Today many of its properties are known, uncovered by difficult experiments and scientific perseverance. Much still remains to be learned. My attempt to convey the excitement around the neutrino necessarily requires some knowledge of the basic rules of the game in the field of the sub-atomic physics, as well as some familiarity with the various stages in the evolution of the universe. The book tries to summarize them in arguably accessible vii

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terms, hoping that they can be followed without too much additional help. An attempt has been made to avoid the appearance of mathematical equations in the description of the various ideas except for one or two essential ones. The book is presented in four thematic parts, which we shall take a look at in Chapter 1: Introduction. College Park, MD, USA May 2020

Rabindra N. Mohapatra

Acknowledgements

The book is a distillation of my knowledge of the neutrino gained from numerous discussions and collaborations with many colleagues and students, to all of whom I am extremely grateful. They are too numerous to mention here. I am extremely grateful to my wife, Manju, for carefully reading the entire manuscript, and making many suggestions for improvement of the text. Without her help, the book would have been much less readable. During the time of writing of this book, the author was supported by grants from the US National Science Foundation No. PHY-1620074 and PHY1914731 and a sabbatical leave from the University of Maryland. The author is deeply grateful for these supports. The author also thanks Ms. Hannah Kaufman for guiding the book to publication at Springer Nature and Clement Wilson Kamalesh for help with processing the manuscript. College Park, MD, USA May 2020

Rabindra N. Mohapatra

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Contents

Part I 1

Introduction

2

Particles as Building Blocks of Matter 2.1 Protons and Electrons 2.2 Add the Neutron 2.3 Particle Spin 2.4 Particle Helicity 2.5 Stable and Unstable Particles 2.6 Matter and Anti-Matter from Einstein’s Theory of Relativity: The Power of an Algebraic Sign

3

4

From Protons and Neutrons to a Zoo of Particles 3.1 Looking Inside Protons and Neutrons with High Energy Colliders 3.2 Particles from Cosmic Rays Order in the Zoo and Quarks 4.1 Eightfold Way and Quarks Inside Baryons and Mesons 4.2 Baryons Have Their Own Markers, the Baryon Number (B)

1 3 7 8 12 13 14 15 16 21 21 24 27 27 30

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4.3

Leptons Have Their Own Marker Too: The Lepton Number (L)

31

5 Forces That Keep the Universe Together 5.1 Gravity 5.2 Black Holes and Gravity 5.3 Electromagnetic Force 5.4 Nuclear Force 5.5 Weak Force

33 33 36 37 38 38

6 Forces Are Also Caused by Particles 6.1 Photon, Mesons, and Forces 6.2 Had the Force Strengths Been Different?

43 43 46

Part II

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7 The Neutrino Is Born as an Idea 7.1 Missing Energy Puzzle in Beta Ray Emission 7.2 December Night Ball and Pauli Letter

51 52 53

8 From Idea to Reality: The Neutrino Story Unfolds in Slow Motion 8.1 Fermi Theory of Beta Decay 8.2 Can the Neutrino Be Found?

57 58 59

9 The Neutrino is Discovered 9.1 How to Detect a Neutrino 9.2 From Hanford to Savanna River 9.3 The Years That Followed the Neutrino Discovery 9.4 More Neutrino Types Found 9.5 Charged Weak Force Comes Accompanied by Neutral Weak Force 10

Standard Model of the Particles and Forces 10.1 How Charming was the Charm Quark? 10.2 The Quark Family and Their Interaction 10.3 Leptons and the Monogamous Neutrinos

63 63 64 65 69 70 71 71 73 75

Contents

11

12

13

14

Forces in the Standard Model and Symmetries 11.1 Are the Weak Forces Also from Gauge Symmetry Like the Electric Force? 11.2 Where Did Mass Come from? 11.3 Symmetries and Symmetry Breaking 11.4 Spontaneous Symmetry Breaking 11.5 Higgs Mechanism 11.6 The Theory of Strong Force More Physics Beyond the Standard Model or the End of Physics Now? 12.1 Future Colliders and New Physics 12.2 Non-Accelerator Probes of Physics Beyond the Standard Model Neutrinos Oscillate and Hence They Weigh 13.1 From Oscillating Swing to Oscillating Neutrino 13.2 Quantum Mechanics and Neutrino Oscillations 13.3 Detecting Neutrino Oscillations 13.4 Ray Davis and Catching of Solar Neutrinos 13.5 Super-Kamiokande Experiment 13.6 Atmospheric Neutrino Oscillation 13.7 Neutrino Oscillations Confirmed by Accelerator and Reactor Neutrinos 13.8 Understanding the Sun Using Solar Neutrinos What Have We Learned about Neutrinos from Neutrino Oscillation Experiments? 14.1 Who Is Heavy and Who Is Light: Mass Ordering of Neutrinos 14.2 Refraction of Neutrinos in Matter 14.3 Do Neutrinos Decay? 14.4 Long Distance Communication Using Neutrinos 14.5 Using Neutrinos for National Security Purpose 14.6 Worldwide Effort to a Fuller Understanding of Neutrino Mass

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77 79 80 81 82 82 84

87 88 89 91 91 92 93 95 98 100 102 103

107 107 110 111 112 112 113

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14.7 14.8

Can Neutrino Be Sensitive to Magnetic Forces: The Neutrino Magnetic Moment What Oscillation Experiments Do Not Tell Us

113 114

Part III

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15

Mendeleev’s Periodic Table

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16

A Brief Overview of the Big Bang Theory of the Universe 16.1 Big Bang Theory vs. Steady State Theory 16.2 Big Bang Theory Wins 16.3 Major Events in the Universe’s Past

123 123 125 126

17

The Inflationary Universe 17.1 Inflation: One Beginning Before Another Beginning 17.2 Beginning of the Hubble Era after Inflation

129 129 132

18

From Quarks to Protons and Neutrons and Then to Helium and Beryllium and the Dance of Atoms 18.1 Big Bang Nucleosynthesis 18.2 Formation of Galaxies 18.3 Cosmic Microwave and Neutrino Backgrounds

135 135 138 138

19

Stars as the Cooking Pots for Heavy Nuclei 19.1 Stellar Nucleosynthesis 19.2 Still Heavier Elements

141 141 145

20

Neutrino Mass Hints at Mirror Symmetry in Nature 20.1 Back to Symmetries 20.2 Mirror Symmetry and Weak Force 20.3 Mirror Symmetry and Neutrinos 20.4 Mass and Helicity 20.5 Mirror Reflection and Neutrino States and Nature of Weak Force

149 149 150 150 151 153

Contents

21

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Mirror Symmetric Weak Force and Neutrino Mass 21.1 Neutrino Mass-Mirror Symmetry Breaking Connection 21.2 Majorana Neutrinos 21.3 Seesaw and Majorana Neutrino Mass 21.4 Testing Majorana Nature of Neutrinos in Experiments

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155 156 158 160 162

Hints of Other New Physics from Neutrino Mass 22.1 Mirror Universe Versus Left–Right Symmetry: Two Paths to Parity 22.2 Grand Unification of Forces and Matter 22.3 What if Neutrinos Are not Majorana Fermions?

165 165 167 169

23

The Origin of Matter and Neutrinos 23.1 Enter Sakharov 23.2 The Search for Baryon Number Violation 23.3 Neutrino Seesaw and Baryon Asymmetry

171 172 174 177

24

Dark Universe 24.1 Dark Matter and Galaxies 24.2 What is the Dark Matter? 24.3 Is There a Parallel Universe? 24.4 Are There Sterile Neutrinos? 24.5 Can We Communicate with the Mirror World?

179 181 182 184 185 187

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Neutrinos from Heavenly Sources 25.1 Why Look for Neutrinos from Extra-Solar Sources and Extra-Galactic Sources 25.2 Supernova Neutrinos 25.3 Neutrinos Observed in the IceCube Experiment in the South Pole

189 190 191 192

Part IV

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26

197 197

Anthropic Principle 26.1 Why Go Anthropic?

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26.2 Many Universes and the Anthropic Principle 26.3 Other Examples

199 200

What Lies Ahead? 27.1 “Near” Future: The First Ten Billion (∼1010 ) Years 27.2 One Hundred Billion Billion (∼1020 ) Years 27.3 Far Future: Beyond the Next Million Trillion Trillion Years ∼1030 Years

203 203 205 205

28 Epilogue

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References

209

Index

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Part I

1 Introduction

What is this world made of? Where did life come from? How did we get to where we are? Galaxies, planets, stars shining at night; water, trees, and a whole world of animals; how did they originate? Why does time so regularly repeat day into night and night into day, turning summer to winter and winter to summer in endless succession for billions of years, not missing a beat? Will it continue like this forever or stop and fall to a different rhythm? What, then, will happen to life and to the universe? When will that happen, if that happens? How much time do we have? What is time anyway? Does it move only in one direction or it also goes back and forth in a cycle similar to day and night? These were likely some of the questions that came to the minds of wise humans who came many centuries before us. Through their perseverance and deep intellect, they gave some of the answers that are at the heart of modern science. The story however remained incomplete then and it remains incomplete now. The ancient Greek philosophers, and the Hindu philosophers thousands of years before them, were known to be among the earliest to think seriously about the universe and understand as much about it as possible. Few concepts had appeared then: the concept of infinity may have been in the Vedas of ancient Hindus, as may have been the concept of atoms. In ancient Greece, philosophers like Thales of Miletus, Aristotle, Pythagoras, Zeno, and Socrates tried to make their mark with new ideas, some of which have been built upon in subsequent centuries. Democritus postulated that all matter were composed of tiny particles, a concept which has endured the test of time and still remains at the foundation of physics. The famous Archimedes principle, which says that objects have apparent weight in water (or any liquid) that is less than their © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2_1

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weight in empty space, was given by the Greek Mathematician and physicist by the same name. It endures until today and is in all undergraduate text books. Euclid, considered the founder of geometry, and Pythagoras, known for his famous theorem for triangles, gave mathematical results which have survived the test of time. About 300 BC, Greek philosopher Aristarchus tried to understand the lunar eclipses and concluded that it is caused by the shadow cast by Earth on the moon as the Earth goes around the Sun. That is a stunning realization, considering the prevailing wisdom at the time that the Sun went around the Earth rather than the other way. This may have been the first known heliocentric model of the solar system. The concept of four basic elements, fire, water, Earth, and air put forth by Empedocles during those ancient times (and to which Aristotle added the aether as the fifth one) did not however survive the test of time. We now know that they are not the fundamental objects of which matter is built but derived from other more basic constituents. Nonetheless, they represented deep insightful thinking that prevailed before Christ. Similar were the thinkings in ancient Hindu philosophy circa 1000 BC about the nature of the cosmos. Even though bits and pieces of new ideas were trickling down over the ages, well organized physics that we practice today seems to have originated around the seventeenth century. Pioneers like Copernicus, Galileo, Tyco Brahe, Kepler, and others, derived knowledge and wisdom from direct observations of stars and planets in the sky. Telescopes that helped in some of these were invented by German–Dutch lens maker Hans Lippershey in 1608. Isaac Newton was one of the earliest pioneers. He wrote down a definitive law that told us in more concrete terms why an apple falls to the ground and does not go upward to the sky, and also, at what speed it falls. His equation enunciated in “Principia Mathematica,” published on 5th July, 1687, could explain the Keplerian laws of Planetary motion, discovered several decades before Newton published his laws. It provided a unified way of understanding two diverse and apparently unrelated phenomena—an apple falling from the tree and the planet going around the Sun in the sky. His proof of Kepler’s laws of planetary motion pretty much dispelled the last remaining doubts about the heliocentric view of the planetary motion. Earth was no more the center of the universe; the geocentric view of Ptolemy from second century AD was past its time and no more part of science, superseded by the heliocentric view of Nicolaus Copernicus. Newton in England, and Gottfried Leibniz in Germany, also independently invented the new form of mathematics, called calculus, around the same time. This became a primary mathematical tool in the discussion of physical laws at

1 Introduction

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the time of Newton and later. For a while, there were great disputes about who invented calculus first. The so-called calculus controversy began simmering in 1699, and broke out into full force in 1711. Leibniz published it first, in 1684, but Newton claimed that he started working on it as early as 1666. Leibniz died a frustrated man for not getting any credit during that time, although nowadays credit is given to both of them. About a century later came Charles Augustin de Coulomb, and in the following century came Michael Faraday and James Clark Maxwell, who explained what makes the sky fill up with lightening. Gravity, electricity, and magnetism were the only kinds of phenomena known at that time. So for example, they could not tell us what makes the sun shine every day and helps it keep on shining without ever shutting down, or whether it will ever shut down. That was a matter of great interest in the nineteenth century. For example, Lord Kelvin and Herman Helmholtz pursued the idea that it could be due to gravitational contraction, but found that that could only help the sun shine for some ten million years, and not the billions of years that it has been shining for. Uncovering the actual mechanism took several more decades, far into the twentieth century. The answer to this question is intimately tied to the subject of this book, the neutrino. We discuss it later on. We now know almost completely the answer to this question and also to the question: will the sun ever stop shining and if so when? We will delve into this towards the end of this book. The sun, like other stars, was born from the cosmic dust, four and a half billion years ago, when the universe was filled mostly with hydrogen, helium, Lithium, and little else. The sun now also pretty much contains the same elements. The story of the cosmos before and after the formation of hydrogen and helium is a fascinating one that we go into later in the book. The Earth and other planets were born from the disc around the sun by accreting and processing “dust” from nearby matter (so the theory goes). But Earth has a lot more stuff than hydrogen and helium. The Earth, which was a dust ball, became solid and developed an atmosphere that has a lot of nitrogen, oxygen, carbon dioxide along with other gases. This is a story that partly involves our topic, the neutrino. The neutrino in many ways helped to make Earth a comfortable place to live with all various chemical elements. Also in our daily life, we use chemical elements much heavier than hydrogen and helium— such as carbon, iron, nickel, etc. Where did they come from? How did a dusty universe that in its first few minutes of “life” was full of only hydrogen and helium, end up producing these heavier elements, so artfully organized in the periodic table of Mendeleev? The answer to many of these questions appears to be held by the tiny elusive particle, the neutrino. The birth and growth of the

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field of neutrino science as a serious field is a testament to human ingenuity and scientific prowess. The technical developments that have occurred have taken the later part of twentieth century and the early part of the twenty first by storm. The more we learn about this tiny particle and its interactions with the universe of particles, the more insight we gain into the inner workings that led to the creation of the universe as we know today. And more likely, it would tell what is in store for us in the far future. A word about the title of the book: the universe started out as a cosmic soup of hot plasma of quarks and leptons—and it is gently (or often not so gently) guided through various phases till it reached the stage of what we see today, which is a vastly more complex and ordered system. A major actor that helped the universe in reaching its current state is the neutrino. Although, it must be made clear that the neutrinos had nothing to do with how the universe began—at least, nobody suspects so. The fate of the universe, however, would have been very different if this particle had not been part of the drama and if it behaved differently from what we know about its behavior today. Very simply put, we would not be here. In that sense the story of the evolution of the Cosmos as we know it is in large part the story of the neutrino. The book is organized as follows: Part I of the book describes some of the background in which the intellectual birth and growth of the neutrino story occurs. The many laws and particles known before the idea of the neutrino appeared are summarized to help set the background for the understanding of the neutrino story that follows. The second part deals with the dramatic way the idea of the neutrino appears on the scene and where, starting from the idea of the particle to deep skepticism about its existence to its final discovery in a laboratory experiment. This part also includes the most recent developments in the field which have established that the neutrino has a tiny mass, contradicting decades of belief that it is massless, the later idea being an integral part of the successful standard model of forces and particles. In Part III, I discuss what the implications and future prospects are for the field following the transformational neutrino discoveries of the past two decades. I outline some scenarios for physics beyond the standard model of forces and matter implied by the neutrino mass discovery and its possible connection to the dark matter of the universe, another hot topic in physics and astronomy today. Part IV deals with two speculative ideas of the anthropic principle, i.e. an alternative approach to understanding why some or all of things are the way they are and what the future holds for the universe given what we know about the laws of nature currently.

2 Particles as Building Blocks of Matter

With the exception of dark matter and dark energy, scientists now have an almost complete idea of what this universe is made of and what keeps it together. There are fundamental building blocks and forces constantly at play. If we think of the universe as a stage of space and time, the building blocks are particles, who are like the “actors” in this stage. They play their role by using the forces to communicate with each other. The neutrino happens to be one of these particles, the tiniest among them that has emerged as a crucial actor in this story. It has not only rescued the laws of physics when they were in danger of falling apart under the weight of observations but it has also ushered in a new era of understanding to observations on both cosmic and earthly scale. This book is the story of this particle. To understand the role of the neutrino in the evolution of our understanding of the Cosmos, we need to have a broad knowledge of what those observations were and the background in which they related to the three parts to the universe (space-time, particles, and forces). This and the following beginning chapters of the book portray the key historical scenes in this drama, each encapsulating years of dedicated scientific research that went in to building this picture and how the neutrino had to make its appearance to keep the rules of the drama coherent and consistent. It slowly became clear that the neutrino not only lent consistency to the story of the universe but it also played a key role in building it to its present stage. This is an amazingly profound story for a particle that is so tiny and so elusive.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2_2

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2.1

Protons and Electrons

All matter we see around us is built out of three “fundamental” building blocks: the proton, electron, and neutron. It took years to realize that the protons and neutrons in turn are made out of more basic constituents called quarks. There is no evidence today for anything more fundamental than quarks and electrons. How did this particle picture of matter emerge? Below we give a brief historical perspective on the development of these concepts. Democritus of ancient Greece suggested the existence of the atom, but it took almost two millennia before the atom was placed on a solid ground as a fundamental object in physics. It goes back to John Dalton (1766–1844), who used his own analysis of chemical reactions to conclude that matter must be composed of tiny particles and suggested that they must be the atoms suggested by Democritus. Microscopist Robert Brown, who in 1827 was looking at pollen of plant Clarkia Pulchella under a microscope, found them emitting such tiny particles. This random motion of particles in the liquid became known as Brownian motion (after Robert Brown). The theory of how these particles jiggle around incessantly because they were colliding with the atoms and the molecules in the medium was given much later by Albert Einstein in one of his five famous papers in the miracle year 1905, and the idea was subsequently verified by Jean Perrin 3 years later. The atomic picture kept getting more refined and detailed as J. J. Thompson observed the cathode rays and discovered the electron, and Rutherford scattered alpha particles, against atoms and established the existence of atomic nucleus. In 1886, Eugene Goldstein observed that while cathode rays traveled from the cathode to the anode, there were also rays traveling from anode to cathode. Those were the hydrogen nuclei (protons) although Goldstein did not know what they were or if they had a wider role in understanding the atom. Also, these experiments made it clear that electrons are negatively charged and the other rays (to be known later as protons) are positively charged. Already since the work of Charles Augustin de Coulomb in 1785, it was known that opposite charges attract each other and like charges repel, a fact that was used to determine that the cathode rays which were moving towards the anode had negative charge. They were the negatively charged electrons, and anode rays traveling in the opposite direction were positively charged and were the protons (the hydrogen nucleus). Rutherford gave the name proton to the hydrogen nucleus and argued that they are part of all atomic nuclei. Protons had positive electric charge but Rutherford also suggested that there might be other heavy particles in the nucleus, which had no electric charge or were

2 Particles as Building Blocks of Matter

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electrically neutral. Those were identified more than two decades later and called neutrons (see below). Ernest Rutherford was a New Zealand-born physicist who pioneered the Rutherford model of the atom, which posits that the mass of an atom is concentrated in the center of the nucleus. Thus was born the basic picture of the atom and its nucleus, which persists today. He is rightly called the father of nuclear physics. Born in the year 1871 in rural Brightwater in New Zealand’s south island, he learned to invent new ways to keep himself occupied in the midst of the limited means of his parents. His mother was a school teacher who believed that knowledge was power, and his father, a hard working flax-miller. At age 19, he was awarded a scholarship to attend the Canterbury College in Christ Church, New Zealand. By age 24, he was already in Cambridge where he worked with such giants of the field of physics as Sir J. J. Thompson studying X-rays. X-rays were discovered only months before, by Wilhelm Conrad Rontzen. Working independently when Thompson was working on the electron, Rutherford discovered what he called the “alpha” and “beta" radiation. The latter consists of electron, a basic constituent building block of matter, and the former is the nucleus of the helium atom. The alpha radiation was used in the famous “gold foil experiment” by Rutherford to establish that inside each atom there was small volume where most of the atom’s mass was concentrated. A clearer picture of the constituents of the atom was emerging. Soon after, Rutherford moved from England to Canada and then to the University of Manchester after that. On 7 March, 1911, Rutherford attended a meeting of the Manchester Literary and Philosophical Society, where he announced the discovery of the atomic nucleus. The American Physical Society has decided to mark this date as the beginning of a century of elementary particle physics [102]. At Manchester, Rutherford continued studying the atomic nucleus and established that the entire mass of the atom was concentrated in the nucleus. He showed this by hitting the atom with alpha particles, which bounced back as if there was a solid object at the center of the target. This led to the Rutherford model of the atom which replaced the so-called plum pudding model of the atom proposed by his one time mentor J. J. Thompson. The plum pudding model, as the name suggests, said that the atom was like a pudding and the electrons and protons were embedded in it at random. Works of pioneers like Rutherford and Thompson were giving a clearer picture of the atom but a lot remained to be discovered in the early 1900s. More details of Dalton’s atomic conjecture of 1803 were coming into shape. Dalton made several prophetic conjectures about the atom and its role. They were:

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(a) Everything is composed of atoms, which are the indivisible building blocks of matter and cannot be destroyed; (b) All atoms of an element are identical; (c) The atoms of different elements vary in size and mass; (d) Compounds are produced through different whole-number combinations of atoms; (e) A chemical reaction results in the rearrangement of atoms in the reactant and product compounds. All of the above conjectures were eventually verified. Rutherford’s model made clear what was going on inside the atom, and combined with Thompson’s 1897 discovery of the electron, the picture emerged that the center of the atom had all the mass and was called the nucleus. The electrons in their incredible lightness were simply floating around the nucleus. How they were floating inside the atom came only to be understood with the proposal of Niels Bohr, who was trying to understand the observed light emanating from hydrogen atoms. This eventually led to the foundation of a new field called quantum mechanics, which has far reaching conceptual as well as technical implications (e.g., from laser scanners in the grocery stores to an MRI machine in the hospital, to name just two). Born in Copenhagen in 1885, Bohr was interested in physics from his very early days. He received his Ph.D. in 1911, in Denmark, working on the electron theory of metals. Electrons were the fascination of the physicists in those days since their discovery by J. J. Thompson. After getting his Ph.D., Bohr went to work in the group of J. J. Thompson in 1912. Thompson was not very impressed by Bohr. So Bohr went to join the group of Thompson’s former colleague Ernest Rutherford in Manchester. Rutherford’s findings had overturned the “plum pudding” model of Thompson for the atom and he had already received his Nobel Prize in chemistry in 1908. While Rutherford’s theory that the central part of an atom was the nucleus and had almost the entire weight of the atom and the electrons were swarming around it only to make it electrically neutral, there was a puzzle that was brewing with the model. In Rutherford’s model, all electrons would eventually spiral towards the nucleus of positive charges under the attractive electric force and emit light which would be a continuous band of colors (or frequencies; each color goes with a frequency of the vibration of the electromagnetic wave). Scientists had, however, found that light emitted by atoms, such as hydrogen, did not have continuous frequency (or color) as predicted by Rutherford model. Rather, it was found that only when objects are hot do they give out light in all mixed colors or continuous colors. But at colder temperatures, they

2 Particles as Building Blocks of Matter

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showed a peculiar characteristic of emitting only a discrete set of colors, the kind of colors depending on the material. For example, if the atoms giving light are hydrogen atoms, the light is red and for other atoms the color is different. A Swiss mathematics teacher named Johann Balmer, who at age 60 was studying the pattern of hydrogen light, concluded that a mathematical formula using only integers could fit the observed colors. This became known as the Balmer series. This formula was later generalized by Johannes Rydberg. A continuous spectra would hardly require only integers to describe them, and the presence of the integers in the formula for atomic emission was quite a mystery, until Niels Bohr made a single simple but radical hypothesis to solve this puzzle. In 1913, Bohr wrote three papers totaling 70 pages in the Philosophical Magazine. He suggested that the electrons inside atoms move in fixed orbits characterized by integers. Note that there are gaps between integers (for example, between one and two, you can have many fractional numbers, but in the absence of the fractional numbers, there will be a gap). To get the radius of the orbit of an electron in the atom, Bohr realized that out of a mass and electric charge, he could not get a length. So he invoked the Planck’s constant, suggested by Max Planck in 1900, to understand the properties of Black body radiation. He suggested that the angular momentum of an electron (which characterizes the electron’s rotational speed around the proton) in an orbit must be an integer times Planck’s constant. The second fundamental proposal of Bohr was that the light would be emitted when an electron jumps from a higher to a lower radius orbit. The frequency of light would have nothing to do with the orbital frequency of the electron but would be the difference in the energies of the electron in the two orbits. These were revolutionary and bold suggestions and were quite contrary to the classical thinking at the time which would have related the frequency of emitted light to the orbital frequency. The same integer that was used to describe the orbital angular momentum of the electron describes the spectral characteristic found by Balmer. Bohr’s theory proposal was quite different and indeed quite radical. For atoms, however, the idea of using discrete set of orbits was quite foreign to scientific thinking in those days. In classical physics before the time of Bohr, continuity was central to all physical laws except for two discoveries made the previous decade. The idea of things being discrete in physics was entertained by Albert Einstein in describing photoelectric effect, the emission of electrons from certain metals when light impinges on it. The second example was by Max Planck who described radiation from objects known as black bodies, which absorb all radiation in discrete units. Not too many physicists working on the atomic theory of matter paid much attention to these ideas as being relevant in the world of atoms, until Bohr made his monumental suggestion to

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explain light emission from hydrogen using discreteness. Naturally, old guard physicists like Thompson, Lorentz, and Rayleigh were very skeptical of Bohr’s idea, but it turned out to be decisive in later years, leading to the birth of a whole new subject called quantum mechanics. Soon afterwards, Bohr’s model of the hydrogen atom received confirmation from observations using other atoms and acquired firmer footing. This picture was supplemented by the exclusion principle for electrons suggested by Wolfgang Pauli in 1924, which said that no two electrons could occupy the same space-time point or same energy and momentum. This is known as the Pauli exclusion principle and it helped explain the atomic structure from hydrogen and helium to heavier atoms. Soon it would also play an important role in understanding the chemical properties of various elements. The protons and electrons were slowly taking their well deserved place in the pedestal of physics as two fundamental building blocks of matter. Is that then the end of the story? Fortunately not quite. People were pouring into details of what actually was going on inside the atom and discovering new things that would guide the future direction of physics and provide many new revelations.

2.2

Add the Neutron

As Ernest Rutherford had speculated, there is more mass in the core of the atomic nuclei than only protons can account for. The number of protons is after all fixed by the fact that atoms are neutral, and therefore must contain an equal number of protons and electrons to cancel each other’s electric charge. Also, Rutherford’s argument made it clear that whatever else is there in the atomic nucleus in addition to protons must be electrically neutral to keep the atom as a whole neutral. Proton and electron were discovered due to their motion in electric fields resulting from their electric charge. The fact that the remaining heavy stuff had no electric charge made it impossible to use electric field methods to uncover its nature. In 1932, James Chadwick, working in the Cavendish laboratory, bombarded Beryllium nucleus with alpha particles and found a new kind of radiation which was not deflected by electric field, which meant that it is electrically neutral. This kind of radiation was also observed by Bothe and Becker but they concluded that the emanating radiation was gamma rays (or energetic photons), which was the only neutral particle known at the time but the photon was too light to satisfy the energy– momentum conservation in this reaction. In fact, it was the use of the principle of energy–momentum conservation that helped Chadwick conclude that the new electrically neutral particle that was emitted in the Beryllium plus alpha

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particle collision had the same mass as proton. He called it the neutron. Thus the picture of elementary particles changed from just protons and electrons to protons, electrons, and neutrons, all of which were present in all atoms except hydrogen. Chadwick was awarded the Nobel Prize for this fundamental discovery in 1935. This pretty much established the roadmap of nuclear physics for the coming decades. Born in Manchester England, Chadwick was a shy child. While doing research under Hans Geiger in Germany, he spent 4 years in a prison camp for being a British citizen in Germany during the World War I (all British citizens living in Germany were detained in prison camps in Germany during World War I). His discovery of the neutron shaped the future of an important field in physics with many implications for science and society. Understanding as much about the neutron as possible was the next big task. There was an urgency to this, since it was a big part of every atomic nucleus. The neutron had no electric charge, but what else did it have? Soon after it was discovered, it was found that it behaved like a tiny magnet and in the physics language, it had a magnetic moment, like a bar magnet, but tiny in size. The magnetic moment was much too large for an electrically neutral particle— since electrically neutral particles are not supposed to have magnetic moment. On the other hand, the neutron’s magnetic moment was almost as big as that for the proton but was pointed in the opposite direction to that of the proton. That was a strange feature. As we note later, it was explained by the quark substructure of protons and neutrons.

2.3

Particle Spin

Particles are always characterized by how much they weigh and that is a characteristic of their kind, i.e. all electrons have the same mass and so do all protons. Is there any other property that is intrinsic to the particles of the same kind? It turns out that each kind of particle has another intrinsic property called spin. That is as if the particles are like soccer balls that are spinning, except that the particle spin does not mean the body of the particle is actually turning at a rapid rate—but only that the particle behaves like it is. Moreover, just like the Bohr model had discrete orbits for the electron around the proton in the hydrogen atom, the discreteness is also a property of spin, i.e. the spin orientations go in steps rather than continuously. For example, electron spins have only two possibilities, either up or down and nothing in between; so do protons and neutrons. These particles are said to be carrying spin half. The number of spin orientations is given by twice the value of spin plus one.

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Thus if a particle has spin half, two times half plus one is two and hence two orientations for spin half particles. There can be particles which have three spin orientations—they are supposed to have spin one, etc. A particle can have no spin—that will be said to have spin zero. This idea of spin was suggested by George Uhlenbeck and Samuel Goudsmit in 1925 at Leiden University to explain certain properties of atomic spectra. Atomic spectra indeed played a crucial role in unraveling the mysteries of the atomic world. The mathematical theory of spin was worked out by Wolfgang Pauli in 1927. There were found to be two kinds of particles in the universe: particles that had spin 1/2, 3/2, etc. (half odd integral) and particles that had spin zero, 1, 2, …(integral). These two classes of particles were fundamentally different—the former set were called fermions and the latter bosons. When more of them are together, the fermions behave very differently from bosons. As already noted, at a given point, there cannot be two identical fermions by the principle called the exclusion principle. This explains the stability of matter and also stars made out of neutrons and other massive objects in astronomy. The bosons on the other hand have no such restrictions and can congregate together at one place in large numbers. This is called a Bose condensate, named after Satyendra Nath Bose who suggested how the bosons behave when they are in large numbers. This was discovered experimentally by Eric Cornell, Carl Wieman, and co-workers at JILA on 5 June 1995, and Wolfgang Ketterle at MIT in 1996. Cornell, Weiman, and Ketterle were awarded Nobel Prize for this discovery in 2001.

2.4

Particle Helicity

Closely associated with spin of a particle is the concept of particle helicity. As we just discussed, spin comes in discrete orientations—spin half comes in 2 orientations, spin one comes in three orientations, etc. To understand helicity, imagine a clock. We describe clockwise or anti-clockwise movement of the hands, depending on which way the hands are moving, as we are looking at the face of the clock. If we look at the clock from its back, what was clockwise would be anti-clockwise and vice versa. Thus, to define clockwise, you need to know from which side you are looking. The same way, to define helicity, we need a direction. It is chosen as the direction of motion of the particle. Thus if a particle is moving in some direction and its spin is pointed along the same direction, the particle is defined to have right-handed helicity (i.e., looking along the direction of motion, if the particle is spinning clockwise, it is a right-handed helicity) and left handed if it is aligned the opposite way to its motion direction. These two helicity states become more distinct if the

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particle is moving at the speed of light, as all zero mass particles do. As we will see later, in the case of a particle with mass, by moving to different reference frames, we can change from one helicity to another, whereas we cannot do the same for a massless particle. The massless particles move at the speed of light, hence, their direction of motion cannot be changed. In other words, a massive particle needs two helicity states in nature, whereas a massless spin half particle needs only one helicity state. This concept has profound implication for the neutrino, which was thought to be massless for a long time, as we discuss later.

2.5

Stable and Unstable Particles

A stable particle stays like it is forever, whereas an unstable particle disappears into other less heavy particle in a certain amount of time. The time it takes for a particle to decay to roughly one third of its original amount is called its lifetime. Of the many particles discovered to date using different methods like colliders or cosmic rays, there are very few which are absolutely stable. For example, we know that protons and electrons are the only two absolutely stable elementary particles. Neutrons are unstable, and they decay to a proton, electrons, and anti-neutrinos, in a little under 15 min. As we will see, this decay unleashed a huge research area known as weak interactions, and eventually led to the rise of the standard model, as the theory of all forces and particles except for gravitational forces. It turns out that once the neutron is inside a nucleus, it becomes part of the nucleus and often becomes a stable particle. That is because it effectively loses part of its mass (relative to its mass when it is free) to the binding by nuclear force. As a result, it does not have enough energy to decay to a proton, electron, and neutrino. This is due to the fact that “all processes in nature must conserve the total energy,” which is a cardinal principle of physics and is a law known to be absolutely valid. The loss of mass of the neutron inside a nucleus is called its binding energy. If a particle is unstable, it will decay to some other particles as noted and that provides a gold mine of information about both the particle that decays and those that come out in the final state and the nature of the force that causes this. For instance, how it decays tells us about the interaction of the particles. Similarly, accounting for all the states it decays to gives a fuller detail about the interaction of the particle in question.

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Matter and Anti-Matter from Einstein’s Theory of Relativity: The Power of an Algebraic Sign

Protons, neutron, and electrons were fundamental to understanding the atomic nucleus. As noted, the existence of the neutron was already suspected by Rutherford and was discovered by Chadwick in 1932. Are there any other kind of particles in nature and, if so, what are they? To understand this further, we need to understand the other key developments in physics in the early 1900s. In 1905 one of the five papers that Albert Einstein wrote was entitled “On the Electrodynamics of Moving Bodies,” where the cardinal concepts of the theory of relativity were introduced. Einstein was a patent clerk when he wrote these papers. The theory of relativity provided a unified approach to space and time which until then were thought to be two separate components of physics thinking. The long held concept was based on the experience about time behaving so differently from space. For instance, time flows in one directions— past goes to future through the present but never the other way, whereas in space, we can go backward and forward, as well as up and down. Einstein’s theory was therefore a radical departure from this common experience. Einstein came to this conclusion in a strange way. He had been thinking about light from his very early years. A lot was known about light in Einstein’s time. Light is a special kind of wave. It was known to travel at finite speed ever since Danish astronomer Ole Christenson Roemer measured its speed in 1676. The speed of light is now known to be about three-hundred thousand kilometers per sec (actual measured value is 2.99792458 × 108 meters per second). This is a huge speed but not infinite as people had thought before Roemer. Einstein’s thinking about light can be summarized as follows. A moving car or moving train moves at finite speed like light does. Is there then a difference between a moving train or car and a traveling beam of light? Imagine two trains traveling side by side. If one of them is traveling next to the other at the same speed, for a passenger in one train, the other train will look like it is standing still or moving at zero speed relative to this train. In other words, the relative speed between the two trains is zero. Einstein always wondered if a train traveled at the speed of light next to a beam of light, will a light beam also stop moving like the train traveling in the previous example? In other words, does a traveling light beam next to a moving train behave the same way as a train traveling next to a moving train? An attempt to answer this question came from two American physicists, Albert Michelson and Edward Morley, working

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in 1887 at what is now the Case Western Reserve University in Cleveland. They conducted an experiment which looked at two light beams, one traveling along the direction of Earth’s motion, and the other perpendicular to it. They wanted to observe if light in the former case traveled with a different speed due to the moving Earth, compared to the other. The thinking at that time was that light travels in a medium, called ether, and the ether will be dragged along the Earth’s motion like any fluid through which a rigid body is moving. Michelson and Morley thought that this effect should change the speed of light along the direction of Earth’s motion, compared to the one perpendicular to it. But they found no difference between the two light beam speeds, which meant that regardless of the motion of the medium, light speed always remains the same. That was an astounding result which established light as having remarkably different property from all other moving objects like the train. Einstein took the bold step to postulate that the speed of light remains the same no matter how fast a frame from which you are measuring the speed moves. No matter how fast the train moves next to a beam of light, the light wave never slows down and always moves at the same speed. Einstein’s genius connected this amazing and unique property of light to the peculiar property of time and proposed the theory of relativity. The theory of relativity revolutionized the thinking in physics prior to 1905 about time and space. It posited that nature of time in a moving train is different from that in a train standing still. Things that look simultaneous in a moving train will not look the same if viewed from the ground at rest. At the basis of the theory of relativity was the result that light speed is independent of the speed of the object where the source of light is located. It is claimed that this theory was so revolutionary, that at one point only a few people other than Einstein understood it. The story goes that the well known British physicist Arthur Eddington, when asked in 1919 whether it was true that only three people in the world understood the theory of general relativity, [Eddington] allegedly replied: “Who is the third?” Slowly the theory of relativity became part of the physics discussion and its incredible impact on how things behave started to emerge. One important consequence among many of the theory of relativity is that the relation between energy and speed of objects gets fundamentally altered. For example, prior to the theory of relativity, mass and energy were considered separate, whereas theory of relativity implied that mass can be converted to energy and 2 vice versa. Instead of E = mv2 as the relation between energy, mass, and speed for slowly moving particles, the relation in the theory of relativity became E 2 = p2 c2 + m2 c4 . Here the variable p is the momentum of the particle

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defined in Newtonian mechanics as p = m v , c is the speed of light which enters many equations in physics and begins to play a major role. Max Planck is believed to have said “The velocity of light is to the Theory of Relativity as the elementary quantum of action is to the Quantum Theory: it is its absolute core.”.1 For a particle at rest, Einstein’s formula for energy says that there is an equivalence between mass and energy given by the formula E = mc2 , (which nowadays appears on t-shirts). It is at the core of many applications of nuclear energy. In nuclear reactors, when one nucleus transmutes to one nucleus in beta decay or to two nuclei, the difference in their mass gets transformed into energy and is available as nuclear energy, all due to the E = mc2 relation of Einstein. The difference between the two formulas for energy above, the one for slow moving particles (non-relativistic) and the other one for fast moving particles (relativistic), may not appear so fundamental at first sight, but there is a hidden aspect of this which had far reaching implications. The point is that in the first non-relativistic formula the energy is always positive as we commonly understand—however, in the second formula, which involves energy square, the energy E can be positive or negative. This is because of the peculiar mathematical property of a square root of a positive number, which can be either positive or negative, i.e. the square of both +2 or −2 is +4. What is the meaning of the negative value of energy? When we run, we have energy and it is always a positive number. No moving object has negative energy. But it appears that in the theory of relativity, there are states with negative energy! How to make sense of the negative energy? Should we just discard the negative value as being unphysical? That is certainly one possibility, but that would be rather arbitrary since it comes out of a perfectly sensible equation in relativity. It would appear that we have no choice but to accept these states as real states in nature. The true significance of energy being negative was first realized by British physicist Paul Andre Maurice Dirac in 1928. Dirac was a deep thinking, quiet man. This author has been in lunch gatherings at Stonybrook where Dirac was a visitor in the early 1970s. At the end of the lunch, the person who talked the least was Dirac. In 1928, Dirac was trying to construct a theory of the electron within the relativistic framework (for fast moving electrons) generalizing the work of Erwin Schroedinger. Schroedinger wrote down the equation, describing quantum mechanical motion of slower moving particles. 1 Incidentally

elementary quantum of action (which is defined as energy times time) is denoted by the symbol h and is the smallest quantum of action of an atomic system. This is known as Planck’s constant. All actions are integral multiples of this fundamental quantum.

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Since Dirac was generalizing this to relativistic energies, he had the same square root problem as described in the previous paragraph. Dirac pointed out that if the negative energies are taken to exist like the positive energy states, this will have disastrous implications. To see this, recall Bohr’s suggestion that in a hydrogen atom, an electron at a higher level always drops down to a lower level state and light is emitted. In Dirac’s theory, since there are always negative energy states which lie lower than the usual positive energy electron states of atoms, the electrons would drop to the negative energy states and the atoms would disappear. For the electron not to disappear into the negative energy states, Dirac postulated that the negative energy levels must be filled up with electrons so that Pauli’s exclusion principle will prevent the electron from falling from a positive energy state to a negative energy state. By this time, Pauli had enunciated his celebrated principle (he did so in 1925) to explain the pattern of light emission in atoms. Pauli’s exclusion principle states that two identical particles with spin half, like electrons or protons, cannot occupy the same point in space. This simple hypothesis explained a lot about atomic spectra and also explained why matter is stable and does not collapse into a ball. Pauli received Nobel Prize for this suggestion in 1945. Application of the Pauli principle implied that if the negative energy levels were filled by electrons, a positive energy cannot fall to this state and would go on behaving like a normal electron without disappearing. The same is supposed to happen for all spin half particles (say a proton or neutron), etc. Filling of the negative energy states just to save Dirac’s theory was dubbed as the Dirac sea, and as an idea, it looked pretty contrived. However, once Quantum Field Theory was invented, the Dirac sea was reinterpreted to mean that there is a new kind of matter (called anti-matter) which has exactly opposite property to matter. For example, an unoccupied negative energy state for electron would mean that it is its anti-particle with a positive charge (opposite to the electron charge) and with positive energy. That would be an electron’s anti-matter. This particle is known as the positron and was discovered by Carl Anderson in 1932 while he was analyzing the cosmic rays in a cloud chamber. He found an electron-like particle which bent in the opposite direction to the electron in a magnetic field, proving that it had opposite charge to the electron but same mass. That was a major discovery for which Anderson got Nobel Prize in 1936, at the very young age of 31.

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Just as the positron appeared as the anti-particle of electron, the same would happen for each particle that we know since we can apply the theory of relativity to all known particles when they move very fast. Thus was born the concept of anti-matter. It is interesting that a simple mathematical sign ambiguity led to a ground breaking concept of a whole new world of particles in physics, i.e. all matter is accompanied by anti-matter. When matter and anti-matter meet, they destroy each other and give a burst of light, carrying the same energy as the total mass of matter and anti-matter particle together. The anti-particle of a proton is called an anti-proton and similarly for each particle. There also appeared a new class of particles which are their own antiparticles. For example, the photon is its own anti-particle. We come back to this question when we discuss the mass of the neutrino. There is also another profound implication of the energy formula of theory of relativity: if a particle has mass, it can move at any speed less than the speed of light, whereas if it has no mass, it can move only at the speed of light, a realization that did not exist before the theory of relativity came along. This will play a significant role as we try to understand the mass of the neutrino and its implications for new physics.

3 From Protons and Neutrons to a Zoo of Particles

Physics research took us one layer down from atoms to nucleus and electrons and then from the nucleus to its substructures which are protons and neutrons. Is this the end of the road in the search for fundamental matter or is there another layer below this? This piqued the curiosity of scientists during the 1950s and 1960s. To appreciate the next stage of the development in the quest for building blocks of matter, let us summarize the rapid discoveries that were taking place both in the experimental technology and theoretical analysis. Both preceeded the breath-taking sequence of events in the 1950s. In this search, the cosmic ray studies and accelerator experiments went hand in hand, the first preceding the latter. We do not necessarily follow the developments in historical sequence in what follows. Rather, we follow them in conceptual sequence.

3.1

Looking Inside Protons and Neutrons with High Energy Colliders

To see if there is another layer of matter below the protons and neutrons, we have to look at distances smaller than their size. How do you probe the inner substructure of a proton or neutron? The basic idea is not hard to follow. If you throw a small stone with great force at a rock, the small stone will break apart and will reveal what is inside it. The faster the stone is thrown, the more pieces it breaks up into, and the more we see of the inside of it. For subatomic particles, the principle that allows us to probe deep inside is similar, © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2_3

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and is called the uncertainty principle of quantum mechanics. This principle enunciated by Werner Heisenberg in 1927 says that neither the location of a particle nor its speed can be simultaneously determined with unlimited accuracy. The limit to this accuracy is set by a tiny number known as Planck’s constant. This implies a complementarity between speed and distance, i.e. the faster you travel, the shorter distance you can probe. This principle has served the physicists well. The idea is to speed up the protons and electrons and collide them against various kinds of particles including protons and electrons, and find new things that result from the break-up of particles in such a collision. How do you accelerate a sub-atomic particle? If the particle has electric charges like the electron and proton, one can use the electric field to speed them up by the electric force they experience in an electric field. One then needs a machine which can do it in an efficient way. The first such machine was built by Cockroft and Walton who accelerated protons using 200 kV capacitor plates. The two capacitor plates had opposite charges and had an electric field between them which accelerated the charged particles. Then came Robert Van de Graaf who built the so-called Van de Graaf generator which could generate higher voltages (up to 750 kV) and could accelerate the protons to even higher speeds. Soon it became clear that to go further, one needed bigger space. That became a difficulty which needed to be overcome. To proceed further with such accelerating machines, the scientists had to find a way to use smaller electric fields and do it in the limited space of the laboratory. The first such compact accelerator that speeds up the sub-atomic particles like the electron and proton was the cyclotron, which is a circular machine invented by Ernest O. Lawrence in 1929. It was a major step forward. Ernest O. Lawrence was born to Norwegian parents and after his Ph.D. from Yale university contributed to the making of the atom bombs in Los Alamos. His idea was to make charged particles go round in spirals as they gain more and more speed within a confined space. The new ideas used here were first to realize that moving charged particle move in circular paths in a magnetic field. This was used to make the circular beams of charged particles. They were then allowed to pass through gaps between two semicircular “dishes” which had an electric field. The electric field came from the two faces of the gap being electrically connected to the two terminals of an alternating current source. The electric field accelerates them in opposite directions in each gap, if the time it takes for the charged particle from one gap to the other is such that, it matches the half period of the alternating current. This would effectively add to the previous speed. A steady magnetic field makes the beam go around in a circle as just noted. Thus it made very clever use of alternating currents (oscillating fields) and magnetic fields to build beams of highly energetic

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Fig. 3.1 Original drawing of the cyclotron by its creator Ernest O. Lawrence. Source: Wikipedia.org

protons and electrons, starting with slow beams. This could now be done within the limited space of the laboratory using only lower electric fields. The electric fields in the gaps need not be huge to achieve this goal. The magnetic fields make the charged particles go around. The electric field would speed up the electron or proton and the magnetic field would bend it around a circle so the particle can be subjected to the same electric field over and over again. Very clever and very efficient indeed. See a picture of the arrangement in a cyclotron in Fig. 3.1. However, this has also a limit since once the particles start moving really fast, as the magnetic fields need to be larger and that put a limit on how high in energy could the cyclotron push the particles. Once a high energy beam of electron or proton was created in a cyclotron, the resulting beams could be made to collide with protons, neutrons, and nuclei to study the inner workings of the target object. This is a much more sophisticated version of Rutherford’s colliding of alpha particles with nuclei. In the beginning, they were used to study the inner structure of nuclei. Slowly things improved and the cyclotron was superseded by synchrotrons in the 1950s, which uses newer techniques to push particles to even higher energies. They are still in use for particle acceleration as well as medicinal purposes. Scientists started using these more energetic beams of particles to conduct new experiments and started looking deeper and deeper inside the nucleus, so that they could see what was going on inside it. That is how the fact that there are smaller constituents called quarks inside the proton and neutron was established, as we discuss below.

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Over the years, colliders proved invaluable in exploring the sub-atomic world and discovering new particles. This provided a deeper understanding of what was known about sub-atomic particles. To go deeper, the speed of the colliding proton or electron had to get larger. That meant devising clever schemes without taking too much space and spending too much resources. People used linear colliders to avoid having to use extremely high magnetic fields to bend energetic beams of electrons. Bending very high energy electrons would also cause huge energy loss, since electrons lose energy by radiating light as they bend. A classic linear collider machine was the Stanford Linear Accelerator. At the same time, a circular electron positron collider was built at CERN in Geneva, Switzerland. Proton accelerating higher energy machines were also built in Brookhaven National Laboratory and Fermilab. The most energetic such machine is the famed Large Hadron Collider (LHC) at CERN Geneva. The LHC spans 17 miles in circumference and uses a huge amount of electricity when it is running. That is why it is made to stop running during cold weather when there is need for more electricity for public use. Built at a cost of nearly seven billion dollars, this machine represents true international collaboration in science. Only 2 ng of hydrogen are used each day to make intense and energetic proton beams, one from each side, and they collide at four intersection points around the machine. At the point of collision, the fleeting temperature is 100,000 times the temperature in the core of the Sun. The protons travel at very close to the speed of light. The discovery of the Higgs boson (see later) is one of its shining achievements.

3.2

Particles from Cosmic Rays

The magnetic and electric fields that are naturally present in space can accelerate particles with electric charge and produce new energetic beams of them as they fly in from distant astrophysical sources to Earth. They are known as cosmic rays. Victor Hess won the 1936 Nobel Prize for his discovery of the cosmic rays, although others made comparably significant contribution to this discovery. Theodor Wulf may have been the first to make the discovery in 1910 [11]. Cosmic rays come from Sun, but mostly they originate in our galaxy and outside of it. They could be coming from stellar explosion, known as supernovae, or possibly from other sources, such as active galactic nuclei at the center of the galaxy. It is not clear yet what the actual sources are for cosmic rays. What we know is that they come and collide with the atoms and nuclei in the Earth’s atmosphere to generate cascades of other particles (see Fig. 3.2) which are observed at the Earth’s surface and also in sky-borne detectors.

3 From Protons and Neutrons to a Zoo of Particles

Fig. 3.2

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Cosmic ray showers. Source: Wikipedia.org

Several particles were discovered in the cosmic rays before the accelerators became the major players in particle searches. Particle collision experiments using accelerators such as cyclotrons and synchrotrons were preceded by experiments studying the collisions involving the cosmic rays. There were also advances in technologies for detecting particles. The cloud chamber discovered by Charles Wilson, a Scottish physicist, was a primary instrument for detecting particles that result from the collision of high energy particles, both in the laboratory as well as those in cosmic rays. It led to the discovery of new particles beyond the protons, electrons, and neutrons, as mentioned. For example, the positron, the anti-matter partner of the electron was discovered in 1932 in the cosmic rays by Carl Anderson, which provided a spectacular confirmation of Dirac’s prediction of anti-matter. This was the first new particle discovered. Anderson also discovered a new particle called the muon in 1936. We will discuss more about the muon later. A few years later, George Rochester and Clifford Butler working at the University of Manchester used the cloud chamber in 1947 to discover another new kind of matter in cosmic rays, the K-meson. The cloud chamber was superseded by the bubble chamber invented by Donald Glaser in 1952. Glaser was awarded the Nobel Prize for this discovery in 1960.

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In 1947, Cecil Powell and collaborators working at the university of Bristol, England, discovered another new particle in the cosmic rays, called the pimeson. This particle was already proposed by theorist Hideki Yukawa in 1935 as the carrier of nuclear force that binds the protons and neutrons in the nucleus (see the next chapter). They used photographic emulsion pictures of the cosmic rays to make this discovery. A different kind of new particle called Lambda hyperon (denoted by the Greek letter ), which turned out to have the combined property of both neutron and K-meson, was discovered by Melbourne physicists D. Hopper and S. Biswas in the cosmic rays. Then came the discovery of sigma hyperons () and many more particles, and the particle zoo kept getting more and more crowded. What were all these particles and what did they mean for the nature of the sub-atomic world? One suggestion was to introduce the concept of strangeness as conceived by Y. Nambu, K. Nishijima and Y. Yamaguchi, and independently by S. Oneda in 1951, and by A. Pais in 1952. The introduction of the new quantum number strangeness was required to explain the observed properties of the hyperons and the K-meson. The K-meson and the  and  hyperons were unstable particles; however, they took longer to decay. That seemed to suggest that they had a new quantum number, the strangeness (S) that prevented them from decaying via strong forces to lighter particles, such as pions and neutrons and protons, which have no strangeness, in a prompt manner. Prompt decays would have been an indication of the strong force mediating the decay. So there must have been something new about these particles that prevented the direct decay, and if the strangeness is conserved in strong interactions, but violated by a weak force (see later), that would explain this slowness of the decay. Incidentally, pions and K-mesons have played a major role in understanding the neutrino properties and the nature of weak interactions as we will see in a later chapter. That they would play such a transformational role was not known when these particles were discovered.

4 Order in the Zoo and Quarks

Physics always builds on simplicity of principle. Simple rules and laws often help to explain complicated things as we move towards a fundamental theory. It was therefore unacceptable to physicists that all the members of the zoo of particles are truly fundamental. There must be a simpler set of ideas that would explain them, and the obsession to find this started in the 1950s, and continued to the 1960s. Mathematical techniques, already known to mathematicians as group theory, started to come into the lingo of physicists.

4.1

Eightfold Way and Quarks Inside Baryons and Mesons

The so-called eightfold way was suggested by Murray Gell-Mann and Yuval Ne’eman in 1961, to put order into the particles zoo. The phrase “eightfold way” is derived from Buddhist teaching of eight ways to attain “nirvana” (or salvation). It put eight known particles similar to the proton and neutron and those that are close by in mass together into a group. They were (p, n,  ± ,  0 , , − , 0 ). Similarly, he put the eight mesons (π ± , π 0 , K ± , K 0 , K¯ 0 , η) into another group. Group theory based on a group called SU (3) predicted that all eight particles in the above group would have the same mass but they did not. Understanding the small differences in the particle masses in one group could be achieved using group theoretical methods, suggested by Murray Gell-Mann and Susumu Okubo, in 1962, confirming the eightfold way arrangement further. This went on to provide a © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2_4

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Fig. 4.1

Quark picture of the proton (left) and pion (right). Source: Wikipedia.org

deeper understanding of the particle zoo. A new field of research called particle physics was emerging and starting to get its separate identity from nuclear physics. A major breakthrough came in the works of Murray Gell-Mann and George Zweig in 1964, who suggested that there is an underlying simple picture which can explain this zoo of particles. This model is known as the quark model. They postulated that there are three fundamental particles below the level of baryons and mesons, called quarks and their three anti-particles (called antiquarks). All these mesons, such as pi and K-mesons, etc., and the baryons, such as protons, neutrons, and hyperons, are made of the quarks in various combinations. The baryons are made of three quarks and the mesons are made of one quark and one anti-quark (see Fig. 4.1). This picture provided a simple way to understand the zoo of sub-atomic particles which were known in the 1960s, and predicted many others that were to be discovered subsequently. To understand the variety of baryons and mesons known in the sixties, it was enough to postulate three quarks called (u, d, s) (up, down, strange) ¯ s¯ ) also with electric charges (2/3, −1/3, −1/3) and their anti-particles (¯u, d, with electric charges (−2/3, +1/3, +1/3), respectively. One could then have two different combinations involving them to describe the different known baryons and mesons (see Table 4.1 for mesons and Table 4.2 for baryons). The quarks obeyed very simple symmetry patterns which made possible further explorations into the particle world. The field of particle physics was growing rapidly as time passed. Quarks became the new fundamental particles of the universe, superseding the protons and neutrons. Symmetries became the mathematical tool for discerning this order out of apparent chaos. Slowly quark based models of particles became the acceptable framework. The quark model also explained the anomalous magnetic moment of the neutron in terms of the quark magnetic moments. The quarks have electric charge and therefore have magnetic moment like all charged particles with spin. It was pointed out by Mirza A. Baqi Beg, Benjamin W. Lee, and Abraham Pais that since the neutron is made of three quarks, the quark magnetic moments must be added up to give a magnetic moment to the neutron. This explained another puzzle

4 Order in the Zoo and Quarks

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Table 4.1 Mesons made out of quarks and anti-quarks π+

ud¯

π0

¯ (uu¯ − dd) du¯ us¯ ds¯ sd¯

π− K+ K0 K¯ 0 K− K¯ 0 η

su¯ sd¯ (uu¯ + dd¯ − 2ss¯)

The quark and antiquarks have equal and opposite baryon number and hence their baryon number marker of a meson is B = 0

Table 4.2 Baryons made out of 3 quarks p

uud

n  + 0 − 0 −

udd uds uus uds dds uss dss

The baryons have baryon number marker B = 1

of particle physics. The quark model became successful in describing baryons and mesons. The question that naturally arises is: “where are the quarks?” Have we seen the quarks in the laboratory as we have seen the proton and neutron, as well as its other family members, such as, the pi meson, hyperons (another baryon), etc. using our detecting devices? All these members of hadron family (as pions, hyperons, etc. are called) leave tracks in detection instruments, such as bubble chambers and other devices, invented to detect tiny particles with electric charge. As far as quarks go, the answer to whether we have seen them in particle detector is “no,” and it is one of the profound mysteries of modern particle theory as to why we do not see the quarks. Yet we think they exist and help so succinctly to understand the mesons and baryons made out of

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their combinations. To be sure, there are some indirect tell-tale signs of quarks in the very high energy particle collisions in the form of what is known as jets (a jet is a spray of particles of known varieties such as pions and other mesons, for instance), but no live quarks (unlike neutrons and protons) have been seen yet. It is believed that this mysterious property of quarks is related to the property of nuclear forces, embodied in a theory known as Quantum Chromodynamics, invented by David Gross, Frank Wilczek, and H. David Politzer, for which they got the Nobel Prize in 2004.

4.2

Baryons Have Their Own Markers, the Baryon Number (B)

Another mystery of elementary particle theory is that in any particle reaction, when a particle in one form of baryonic matter (p, n, ..), disappears in the initial state, there appears the original baryon itself or another form of baryonic matter in the final state. We have never seen a baryon (say a proton) vanish, leaving in its trail a bunch of mesons and no baryon. These kinds of observations have led particle physicists to imagine ways which can prevent the baryonic type matter like protons and neutrons from disappearing. One such way is to assign a new quantum number for baryons which would have the property of not changing in any elementary particle reaction. The quantum number assigned for protons, neutrons, hyperons, and other similar particles is called the baryon number, which is supposed to have the property of being indestructible and works as a marker for their core property. Baryon number remains unchanged in any elementary particle reaction. On the other hand, the mesons such as pions, K-mesons, etc. are not supposed to have any such quantum number that remains same before and after a reaction. A single meson can transform to many mesons in a nuclear reaction or even just disappear to other forms of particles. The baryon number never changes, and is like a rule with a slogan T-shirt that says “I am a baryon and you cannot destroy me—you can only change me to another baryon.” In other words, you know a baryon when you see one. Since all objects including planets, stars, mountains, plants, and animals are full of protons, the fact that their identity continues to remain the same during the history of the universe means that the baryon number is crucial to the stability of matter. Because the protons and neutrons have this indestructible attribute called baryon number, we all exist and are stable— we will not suddenly (or over time) disappear. This property of the baryon

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number not changing is called “baryon number conservation.” Thus, the discovery of baryon number non-conservation, which will break this rule, will be a discovery with fundamental significance for physics with far reaching consequences for the fate of the universe. As we will see below, there are theoretical reasons to suspect that the baryon number may indeed be broken very weakly. Many experiments have been carried out in the past 30 years to search for the decay of the proton and oscillation of the neutron to an antineutron, which are both processes that break the baryon number. So far, these experiments have gone without success. However, there is a pervading belief in the theoretical physics community that the baryon number is indeed broken, but it happens so very weakly that we do not yet see it. Incidentally, using Tables 4.1 and 4.2 we see that if we give quarks a baryon number (B) of 1/3 and anti-quarks a B = −1/3, then baryons which contain three quarks have baryon number 1 and mesons, which consist of a quark and anti-quark have baryon number zero in accord with the observations that baryons are stable objects and mesons are not stable objects. Mesons can decay to photons or leptons (electrons and anti-neutrinos, see the next section). Just like the proton, neutrons and hyperons and their baryon number zero cousins, i.e. the pi and K-mesons, could all be understood in terms of a simple quark picture. The next natural question is: does the electron have a complex family (called leptons) and a simpler set of fundamental constituents to explain them? Until the late sixties and seventies, the only family members with similarity to the electron was the muon and a second neutrino known as the muon neutrino. In the late 1970s, a third pair, the tau lepton, and its accompanying neutrino were discovered. The number of similar particles however did not proliferate enough, like the baryon and meson family did, to require a more fundamental constituent description. So far, there is no evidence for such substructure for electrons or muons or neutrinos. Similarly, there is no evidence for any substructure for quarks either. May be we have reached the end of the line as far as a constituent picture is concerned !

4.3

Leptons Have Their Own Marker Too: The Lepton Number (L)

Particles such as electrons, muons, and neutrinos are different from the baryons and mesons and were called leptons. An important observation about leptons is that just as the baryons have their own marker—the baryon number—so do the leptons. They have something called a lepton number which guarantees

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that in any weak force or any known force-mediated reaction process, a lepton never gets destroyed. In other words, if there is a lepton in the initial state, there will be the same or another lepton in the final state; if there is no net lepton number in the beginning state e.g. when there is a lepton and anti-lepton in the initial state, in the final state, either there will be no leptons or a lepton must appear with an anti-lepton so that the total lepton number remains zero. The idea of the lepton number was suggested by E. J. Konopinski and H. J. Mahmoud [68]. If the lepton number was not a good symmetry, the process ν¯ e + n → e− + p should be allowed. This process has been searched for and has not been found. The lepton number conservation is the second reason that the planets, stars, and animals are stable since they all contain elements with many electrons and are therefore stable by virtue of their lepton number. As we will discuss later, there is a strong suspicion that lepton number may not be a good symmetry in nature if the neutrino mass has to be small. Similarly, the proton could also be unstable. These violations of the lepton number (and the baryon number) have to be very weak to explain the stability of the universe. The rate for any such breaking reaction must be much longer than the age of the universe. There are lots of experiments in progress and planning right now to discover the violation of the lepton number. They are looking for a process in which a nucleus decays to two electrons together with a “daughter” nucleus but no anti-neutrinos. Since there are two electrons in the final state and no electrons in the initial state, the lepton number in the final state is two, since the final state nucleus (not the atom) has zero lepton number. If this process is experimentally discovered, that will be a major breakthrough in physics, revealing new forces and new phenomena. Searches to date have revealed that such lepton number violating processes must do so with a chance of less than one in 1026 years, much longer than the age of the universe (few times 109 years) and baryon number violating processes can occur only once in 1034 years.

5 Forces That Keep the Universe Together

Space-time is the stage on which the particles are the “actors” playing their roles. The way the particles communicate with each other and influence each other’s motion reveals another aspect of natural laws governing the universe [83]. They are the various forces operating in nature that are responsible for this inter-communication. The forces communicate the “thoughts” from one actor to the other and affect the development of the “plot” which builds the universe step by step. (“Thought” is the detailed nature and strength of the force and “plot” is the motion of the second particle under the influence of the force.) What the forces are and how they operate is the topic of this chapter. The forces have their own peculiarities and specialties with just the right properties that lead ultimately to a universe that is livable by humans and plants and animals. Is this by “intelligent” design (“anthropic principle”) or some physical restriction on the laws? This is a question that is being debated, and we will touch on the broad aspects of this thinking in a later chapter.

5.1

Gravity

There are four known forces in nature. The first one is the force of gravity, the force that makes the apple fall to the Earth and makes the planets go around the sun. The laws of gravity were discovered by Sir Isaac Newton. He was born in 1642, in Lincolnshire, England. He published his suggestion on laws of gravity in 1685 in a seminal work titled “Principia.” He postulated that gravity is universal and attractive and exists between all objects. Its strength depends on © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2_5

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how massive the objects are. It has infinite range and goes down as the square of the distance between two objects. Now, we know that the gravitational force does not distinguish between matter and anti-matter. In Newton’s time, people did not know about the existence of anti-matter. The discovery of Newton gave a complete understanding of planetary motions observed by Johannes Kepler, and proved once and for all that the Earth was not the center of the universe. It could explain tides in the ocean and trajectory of comets. It also led to the discovery of Neptune. Neptune was not discovered via telescopic observation as many other planets were, previous to that. Applying Newton’s laws of gravity and using mathematics, Johann Gottfried Galle, Urbain Jean Joseph Le Verrier, and John Couch Adams, who all worked independently, helped discover this planet in 1846, more than a century and half after Newton gave his laws of gravity. The way this came about was that astronomers observed discrepancies in Uranus’s observed position, in contrast to its predicted position according to the laws of Newton by the above mathematicians. For a while, people thought that Newton’s laws did not apply to objects at such a large distance. The discrepancy in Uranus’s position could however be explained if a planet— Neptune— was orbiting beyond Uranus. Thus Neptune may have resolved a crisis for Newton’s laws. Einstein proposed the general theory of relativity in 1915, combining the theory of relativity with Newton’s law of gravity. In his theory, known as the general theory of relativity, gravitational force is described in terms of geometry i.e. the gravitational force is equivalent to a curvature of space around the object which is creating the force. It is a very profound and novel concept and the beauty is that it works. He introduced the concept of the metric of a spacetime which describes its geometry as a way to describe the gravitational force in a subtle way. No extra force need be postulated to understand motion under gravity. The metric itself is enough. Imagine a plain page of paper and draw a triangle on it. All three angles of the triangle add up to 180◦ —this is what we learn in high school. If instead, the triangle was drawn on the surface of a spherical vessel, the sum of the three angles would be more than 180◦ . The geometry of the surface of a spherical vessel is different from that of a plain paper. If there was a big source of gravitational force, the space around it would look more like the surface of a spherical vessel, rather than a piece of plain paper. The stronger the gravitational force, the more curved the space around it is. The stronger the gravitational force in a region (for example, due to a large massive object), the more curved the space would be. In other words, gravity changes geometry. If we have a particle that is experiencing the gravitational force from an object, creating the spherical vessel like space around it, the particle will move

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on the surface of the vessel “as a free particle.” The idea, for example, of planets going around the sun due to gravitational force, means in Einstein’s language that, the space around the sun is curved, and the planets are simply following a line path in that curved space. In physics language, the line is called a geodesic. The metric of a space has ten components i.e. ten parts to it. They all depend on each other in an intricate way and affect the motion of particles. The gravitational force is so weak that only if you are standing next to an extremely massive body like the Earth, you can feel it, but if you are standing next to another person or another 100 persons, even though there is gravitational force on you, it is too weak for you to feel. The space around one or 100 persons is not very curved. Every massive object, and in fact any object that has energy, regardless of whether it has mass, will feel the gravitational force with a universal strength. That is how sun is pulling the planets to go around it. Light beams which contain energy but no mass get attracted towards massive heavenly bodies, such as the sun and the stars, as they pass by them on their way from distant stars. That leads to the bending of light, first predicted by Einstein and later observed by Sir Arthur S. Eddington, during a 6 min total solar ellipse in May 29, 1919, confirming the general theory of relativity by Einstein. This observation made Einstein a celebrity overnight. A headline in New York Times read—Lights All Askew in the Heavens—referring to the bending of light. Another major confirmation of Einstein theory came recently with the discovery of gravity waves by LIGO (Laser Interferometer Gravity Observatory) experiment from distant black hole mergers. In fact, there have been more than ten gravity wave signals from black hole mergers starting with the first one in 2015, and one from a binary neutron star merger in 2017. As of this writing, in addition to the detections of gravity wave signals published, there may be others in the process of publication. More gravity wave signals are likely to be detected once several more detectors which are being planned are set up. There already exists the VIRGO gravity wave detector, located outside Pisa, Italy, funded by the Italian and French governments. This has already observed the binary neutron star merger gravity wave. There is the planned LIGO-India, a joint US–India collaboration. There are also plans to set up gravity wave detectors in space, the LISA project, which is a joint NASA and European Space Agency project. These discoveries have launched the new field of gravitational wave astronomy, studying the structure of the universe using not only light but a separate messenger, the gravity wave, which travels un-impeded for much farther distances than light. They could probe the structure of the universe even better than what can be learned using neutrinos. The gravity waves have already revealed significant new facts about the universe, such as the neutron star merger.

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Black Holes and Gravity

According to Newton’s theory, gravity does not have any effect on light. Einstein’s theory introduced the new idea that gravity bends space-time, and all paths, including that of light, follow the curved space (called geodesics). This means that in a space near a massive object, the path of light gets bent (or equivalently, light gets affected by gravity). This follows from the special theory of relativity by Einstein, which says that mass and energy are equivalent and since a light beam has energy, it also gets affected by gravity, just like an object with mass. Extending this idea, one can imagine that if the mass of an object is really large, light can get bent back and will not leave the object. Thus the object will look black since no light is coming from it. Those massive objects from which light ray cannot escape are called black holes. The existence of such objects within Einstein’s theory of general relativity was first noted by Karl Schwarzchild in 1916, and much later, the name black hole was coined by John Wheeler of Princeton. As we discuss later, the end stage of life of certain massive stars is a black hole. Steven Hawking and Jacob Bekenstein pointed out that black holes also emit radiation, like a black body, known as Hawking–Bekenstein radiation. As the black holes radiate, they lose their mass. Hawking–Bekenstein radiation from black holes, however, has not been established experimentally. After a black hole has formed, it can continue to grow by absorbing mass from its neighborhood, like surrounding stars. Thus supermassive black holes of millions of solar masses may form. When a supermassive black hole gobbles up massive stars, it emits a lot of radiation including neutrinos. There is a general consensus that supermassive black holes exist in the centers of most galaxies. An image of the first such supermassive black hole was presented by the Event Horizon Telescope in April, 2019. The black hole, called M87, is at a distance of 16 megaparsecs from us and has a mass of six billion solar masses. This is an exciting finding. The fact that things that were only in our imaginations for so long have been proven to exist is truly gratifying and is a testament to the power of physics. Gravitational waves from as many as ten binary black hole systems have been detected by LIGO as of February 2019.

5 Forces That Keep the Universe Together

5.3

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Electromagnetic Force

The second force known to humankind is electricity and magnetism. The Greeks knew about it in the pre-Christian era. Around 600 BC, they knew that if amber is rubbed against fur, it acquires the property of attracting small pieces of materials, such as feather. Later on, this came to be understood that this happened because of a force called electricity. When amber was rubbed, it became electrically charged and attracted the electric charges in the other small object. They also knew about the attractive property of loadstone, which was later understood as having a magnetic property. It is said that the father of electricity was William Gilbert, a court physician to Queen Elizabeth I, who provided an understanding of these phenomena as being due to electric charges in material. This was in the early 1600, some 2200 years after the Greek philosopher Aristophanes discovered the electric property of amber. William Gilbert studied the properties of loadstone and coined the word “magnetism” and wrote a book entitled “De magnete” as well as other books on the subject. He concluded that the Earth behaves like a big magnet which is responsible for making the compass needle point north–south (which previous to that was believed to be due to the Pole star). Electric and magnetic forces arose from a new attribute of matter known as the electric charge. The electric forces have infinite range and become weaker as we move further away from an electric charge. The electric force law is called Coulomb’s law, after its inventor French physicist Charles Augustin de Coulomb who published it in 1785. Other giants whose pioneering works helped us understand electromagnetism better are British physicist Michael Faraday and Scottish physicist James Clark Maxwell. Their ground breaking works provided a unified framework for electricity and magnetism, i.e., that both kinds of forces are part of one and the same physics. When electric charges are standing still, you only get an electric field, but when they are moving, you get electric current and associated with it are magnetic fields going round the current in circles. The story goes that when Faraday showed some of his experiments on electricity and magnetism to the then British Prime minister, the prime minister asked “Mr. Faraday, what good is what you have done” to which Faraday appears to have replied “I do not know Mr. Prime Minister, but one day you will tax it.” For a particle to feel the electric force, it must have electric charge or some magnetic property that is related to the electric charge. Protons, neutrons, and electrons all feel the electric force and any object that contains them will obviously feel it too.

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Nuclear Force

The strongest force in nature is the nuclear force, which binds the protons and neutrons together in the atomic nucleus. It only extends within the short domain of the nucleus, which is ten trillionths of a centimeter (or mathematically written as 10−13 cm—also called one Fermi in honor of the great Italian physicist Enrico Fermi). The strong force is about hundred times stronger than the electric force and about hundred trillion, trillion, trillion times stronger than gravitational force. Without the nuclear force, we could not exist. The universe would only be filled with hydrogen atoms, and no other elements will be there—no dust, no trees, no animals. This force was discovered in the early part of twentieth century and only came to be understood beginning in the mid-1970s.

5.5

Weak Force

The force that plays a vital role in our daily existence is the weak force, a force which is weaker than the electric and the nuclear forces, but it is stronger by about a trillion, trillion, trillion times than the gravity. Unlike the electromagnetic and the gravitational force however, the weak force is felt only in a very short distance inside the atomic nucleus. The existence of the weak force is responsible for nuclear fusion in the core of the sun that provides us with the warm glow of sunlight and sustenance of all life. As we will see, this force is intimately connected to the main actor in the book, the neutrino, and in fact, the neutrino is the only particle out of the proton, neutron, electron, etc. that exclusively feels the weak force. However, they all feel the force of gravity. Weak force is also different from gravitational and electric forces, in that the weak force can change one particle to another. For example, the weak force acting between an electron and a proton can change the proton to a neutron and electron to a neutrino. In short hand notation, it is written as e− + p → ν +n. By the same token, we can have a neutrino hitting a neutron, converting it to a proton and electron i.e. ν + n → p + e− (see Fig. 5.1). This is very different from the way electromagnetic and gravitational forces work. They preserve the identity of the particles they act on, whereas as we see from the above examples, weak forces change the identity of particles i.e. a neutron to a proton and vice versa. This understanding got expanded in the 1970s, when a new class of processes called weak neutral current processes was discovered.

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Fig. 5.1 Weak force at work in nuclear decays. The left part of figure has only one electron emission which led to the famous energy conservation puzzle that led to the postulate of neutrino by Pauli. The right figure has neutrino accompanying the electron in beta decay. Source: Wikipedia.org

These forces keep the identity of particles unchanged. A typical example of such an interaction is: ν + p → ν + p, ν + e− → ν + e− . They could of course be distinguished from electromagnetic forces by their properties under mirror symmetry, and also by analyzing the detailed property of the protons and electrons after scattering. The way the protons and electrons move after neutral current scattering is different from the way they would move after scattering by electric forces. It is the weak force that can change a nucleus to another nucleus in a radioactive decay process, as happens in a nuclear reactor or a nuclear explosion. For example, in a nuclear reactor, uranium nucleus fragments to two daughter nuclei, which are radioactive and undergo weak decays to give neutrinos. A huge number of uranium nuclei doing the same thing produce a profuse stream of neutrinos, which can be harnessed and used. This is being done in experiments studying neutrinos. These could have many societal applications. For instance, catching these neutrinos from nuclear explosions has been suggested as a way to monitor rogue nations doing clandestine nuclear weapon tests. Even the possibility of oil exploration using neutrinos has been suggested. The reactor source of neutrinos was also used in the early days to prove the existence of neutrino particle as we discuss below. The weak force had another property that distinguished it from all other forces: it did not respect mirror symmetry like other forces did. The weak interaction process does not look the same when reflected in a mirror. See for example Fig. 5.2.

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Fig. 5.2

Beta decay does not respect mirror symmetry. Source: Wikipedia.org

In the table below are listed some examples of dominant weak decay processes of some elementary particles. Note in particular that the weak decays of the pi and the K-meson produce the neutrino as one of the decay products. These neutrinos have played a crucial role in our current understanding of the neutrino’s properties, as will be discussed in Chap. 12. Particle

Decay to

Neutron n K-meson K +

→ p + e− + ν¯ e → μ+ + νμ → π 0 + e+ + νe → π 0 + μ+ + νμ μ+ + νμ → p + π− → n + π0

π+ 

Some other manifestations of the weak force are the muon particle observed in cosmic rays, which also undergoes weak decay to an electron and two neutrinos. A profound observation is that all these processes have similar strengths for the weak force, as deduced from the measurement of the life time of the muon.

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The weak force is what is responsible for light and heat coming from the sun, as already noted. At the core of the sun, there are ionized hydrogen atoms (protons), constantly hitting against each other to fuse into helium atoms, due the dense, hot environment. The temperature of the core of the Sun is nearly 15 million degrees Celsius. In the fusion process, protons and electrons release neutrinos together with the fusion energy, which is emitted as light and heat from the center of the sun. The heat released in the process puts outward pressure on the matter at the core, which is trying to contract inward because of gravitational force. This is much like boiling water in a covered pan that pushes the lid up, despite gravity’s pull keeping it in place. It is therefore a constant tug of war between the gravitational force pulling matter at the solar core towards the center, and the force of nuclear reaction generated heat that is trying to push it outward. We will get into more details of this as the neutrino story evolves.

6 Forces Are Also Caused by Particles

What is the origin of forces? Where do they come from, or were they just there from the beginning of the universe for some mysterious reason?

6.1

Photon, Mesons, and Forces

The mystery of the origin of forces remained until into the 1920s when it was realized that the exchange of a particle, called the photon, between objects, was the source of electric force. The photon as the light quanta had already been postulated by Albert Einstein to explain the photo-electric effect for which he got the Nobel Prize. Hideki Yukawa (1907–1981) was the first to point out that nuclear forces arise due to an exchange of a different kind of particle in much the same way as the cartoon in Fig. 6.1, where the boomerang represents the exchange particle. If you throw a stone at someone, your energy is transmitted via the stone to the “some one” to whom the stone hits and gives him or her a sting (i.e., a force). See Fig. 6.1. Yukawa gave his theory for nuclear forces as arising out of the exchange of mesons, which were later discovered in 1947, in cosmic rays. Yukawa’s suggestion solidified the idea of forces arising out of particle exchange. This meson, called the pion, is created through a temporary violation of conservation of mass–energy and travels from the proton to the neutron or a proton and is recaptured. It is not directly observable and is called a virtual particle. Three pions denoted by π ± , π 0 were soon discovered substantiating Yukawa’s hypothesis. Yukawa was awarded the Nobel Prize for this theory in 1949. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2_6

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Fig. 6.1 Throwing football illustrates how exchange of particles generates force. As the football is received, the receiving boat moves to the left due to the force generated

Fig. 6.2

Picture of W-boson as the source of weak force. Source: Wikipedia.org

In modern physics, therefore, there arose a reinterpretation of the forces, which said that they arise due to the exchange of particles. It culminated with the discovery of the W and Z bosons in the 1980s (Fig. 6.2), which are carriers of the weak force. They were discovered in the colliders at CERN, Geneva. We now believe that all forces are caused by some particle exchange and that those particles can be discovered. Today, the hunt goes on for still other kinds of particles that may be carrying new kinds of forces. Scientists believe very strongly that there are other forces and associated carrier particles, whose discovery will not only broaden our understanding of the universe, but

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also will have a transformational effect on our civilization. The W and the Z boson are examples of particles whose exchange leads to weak forces. Unlike the photon and Z boson, the exchange of the W-boson changes a proton to a neutron. All the particles that carry new forces are believed to be bosons, named after the legendary Indian physicist Satyendra Nath Bose (1894–1974). He first conceived of the fundamental difference between particles with spin zero, one, etc., as compared to particles with spin half, three half, etc. The latter are called fermions, named after Enrico Fermi. Satyendra Nath Bose was a modest man, who discovered the law of bosonic particles while working in Dhaka University (what is now in Bangladesh), far from the main hub of theoretical physics activity, which then was Europe. He sent his manuscript on the subject by post to Albert Einstein with a letter that started with [99]: “Respected Sir, I have ventured to send you the accompanying article for perusal and opinion…” Einstein studied Bose’s paper and recognized the significance and originality of his work. He translated it into German and sent it for publication, while following it up with another paper of his own. In that paper, he applied Bose’s idea to atoms and predicted the existence of the so-called Bose–Einstein condensates. He sent his paper for publication in 1924, and it was published in the Proceedings of the Prussian Academy of Science in January 1925. The first Bose–Einstein condensate was discovered in 1995, by Carl Weiman, Eric Cornell, and W. Ketterle, as discussed before. Bose never received the Nobel Prize, even though half the particles in the universe are named after him and each boson represents a new force in the universe. The two most basic elements in our understanding of the universe are particles with their different spins: half odd integral spin (1/2, 3/2, 5/2 . . .) being matter, and integral spin (0, 1, 2, . . . .) being force carriers. We can call the half odd integral particles (the fermions) the “matter particles,” and the integral spin particles (the bosons) the “force particles.” Every bosonic particle in principle is a force carrier. For a long time, these two different kinds of particles were thought to belong to two different islands of objects with no connection to each other. However, whether they are actually different or not, in the minds of many theorists since 1970s, they have been thought to be two shapes of the same object, and are related to each other by a very new kind of symmetry, called supersymmetry. This is a powerful symmetry, about which we will have very little to say in this book, but whether it is real or not, it is a profoundly important concept, which may connect the gravitational force with all other forces (Fig. 6.2). The theorists were pinning their hope on the

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Fig. 6.3 A side view of the Large Hadron Collider looking for new forces of nature. Source: Wikipedia.org

Large Hadron Collider to find evidence for this new symmetry, but alas, it did not happen. That could simply mean that the LHC is not powerful enough to find this and we may have to wait (Fig. 6.3).

6.2

Had the Force Strengths Been Different?

A force is characterized by two important properties: (1) how strong it is and (2) how far its extends, i.e. its range. We have given roughly how the strengths of different forces stack up, i.e. gravity is much weaker than the weak force, which in turn is much weaker than electricity, which is much weaker than the nuclear force. The arrangement of the universe is a very precise one: it is very sensitive to the strengths and ranges of all the forces. Had they been a little different from what they are, the evolution of the universe could have taken a completely different path and would not have been what it is today. We emphasize it at different points in the book. So what determines the ranges and strengths of forces? Taking this idea to an extreme, one can ask what would have happened if there was no electromagnetic force but only gravity and the strong force. In this case, the strong force would attract the neutrons and protons with equal strength and there would be no distinction between them. In that case, the nuclei that form would be large, depending on the strength of the strong force. For example, a nucleus could easily be two meters in diameter. Such a situation could easily arise for dark matter, about which we know so little, and it could

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therefore easily be that they do not have an electromagnetic-like force, but only a strong force. In which case dark matter would form big blobs. The issue of range is much better understood from fundamental principles, in terms of the masses of the exchange particles. The heavier the exchange particle, the shorter the range. There is a principle called “gauge invariance” which, for example, explains why the electromagnetic forces have infinite range. (See later for an explanation of gauge invariance). Similar is the case for gravitational forces, where Einstein’s coordinate invariance plays the same role. Of course, you could always ask, who decided that these principles must be obeyed in nature? That is the next level question which more fundamental theories like string theory attempt to answer in terms of their own set of fundamental principles. We could of course ask the same question of string theory as to who decided the principles of string theory. These questions could go on. The question of force strength is, however, a different story and it is a big mystery. Why do the different force strengths turn out to be what they are? Is there a fundamental reason behind it, like for the range, which can be uncovered from a set of principles and equations, or is there some “divine hand” which sets them at what they are, so humanity could exist? In other words we do not know any principle like gauge invariance for electricity, which would tell us what the strength of electric force is. The last alternative which is clearly not very satisfactory to a scientific mind is called the “anthropic principle” as mentioned earlier. We will discuss more of this later on in the book. Could it be that there are many universes, in which case, the anthropic picture makes more sense? We do not know the answer to these questions. Thus, we have not made any progress in understanding strengths of forces, even to the first stage of having a principle, as we have for the range of the forces. Even getting to the stage of finding a principle that would determine the strength of forces is a challenge to the human mind and continues to be an obsession to many physicists over the ages. A related question which is often debated is whether over the age of the universe, the strengths of forces change or they have remained same from beginning to the end. If, for example, they changed with time, it would be hard to believe that some unknown hand (or a specific universe) has not only fixed the desired initial value of the strength but also the rate of change of the strength over time. That would be an extra burden on enthusiasts of the anthropic principle and multiverse.

Part II

7 The Neutrino Is Born as an Idea

New ideas that lead to progress in science come in many ways. Often theories follow experiments but sometimes, the reverse can be true. Classic examples of theories following experiments in physics included: Faraday’s law, Oersted’s discovery of connection between electricity and magnetism that established the correct laws governing electricity; Bohr’s atomic theory that led to the whole framework of quantum mechanics; and in more recent times, the idea of no mirror asymmetry in nature enunciated by T. D. Lee and C. N. Yang. In the field of biology, the famous double helix structure of DNA proposed by James Watson and Francis Crick which opened up new frontiers in biology also belongs to the first category. There are also equally illustrious example of experiments following theory. For example, Hertz’s discovery of electromagnetic waves, which is behind radio and TV signal transmission, came following the theoretical suggestion of electromagnetic waves by Maxwell, and the discovery of pi meson followed the suggestion of Yukawa. The pi meson opened up the field of nuclear and particle physics. One could include the discovery of gravity waves as experimental discovery following theory as well. The same pattern of close symbiosis between theory and experiment, with one influencing the other, has continued into the current century. The idea of the neutrino belongs to the first category as we explain below.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2_7

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Missing Energy Puzzle in Beta Ray Emission

“Are there any more fundamental particles beyond the proton, electron and the neutron?” was a question that came to people’s mind in the 1920s. The answer came from some puzzling findings in the early part of this century. Conservation of total energy is one the edifices of modern physics. It is based on sound physical principles and says that in any physical process, the total energy remains constant as the system of particles involved in the process evolves in time. Whatever energy is in the system at the initial stage, the same energy comes out in the final stage. It is a principle obeyed by all physical systems. Are there any systems that do not obey it? No one has found one yet, and if any one does, that would be a profound discovery that would shake up human civilization in many ways. Energy conservation is connected to the somewhat mysterious principle that as we move in time, the system remains unchanged overall. In physics lingo this is called “time translation invariance.” Before Einstein proposed his theory of relativity, total energy was considered to be the sum total of kinetic energy plus the potential energy inside the system. Kinetic energy is the energy of motion, such as a moving car’s energy due to its motion. Potential energy, on the other hand, is the energy in a physical situation even when nothing moves. For instance, if you are holding a stone ten feet above the ground, the stone has the potential to do work when it falls to the ground, even though it was not moving prior to falling. That hidden energy in the stone is called potential energy. Another example of potential energy is when two electric charges are held separated by a distance. After the theory of relativity, the mass of the particles participating in the process was to be added to the total energy, since mass and energy became interchangeable, one converting to the other. As noted earlier, this is a principle that eventually led the construction of nuclear reactors where part of the mass of the nucleus gets converted to energy. This principle became a part of physics after 1905, when Einstein proposed the theory of relativity. Energy conservation has been a useful principle in understanding many observed phenomena in nature. No deviation had been observed until a nuclear process in the early 1890’s was analyzed, which threatened to contradict this sacred principle, as described below. In 1896, French physicist Henri Bacquerel, a descendant of a line of well known physicists, discovered rays similar to X-rays while studying the phenomenon of fluorescence from a compound of uranium. They were also discovered by Rutherford. The discovery of beta rays (as Rutherford called them) generated a great deal of curiosity among physicists who wanted to

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understand as much as possible about these new rays. In 1902, Pierre and Marie Curie showed that beta radiation was nothing more than electrons. Later, it was determined that those electrons come out of the nucleus of the radioactive atoms. Bacquerel was awarded Nobel Prize for that in 1903 (together with Pierre and Marie Curie) for the discovery of radioactivity. In 1914, James Chadwick, another student of Rutherford, was studying the beta rays in the decay of nitrogen and lithium. These rays were supposed to have discrete energy, since they were thought to emerge from a nucleus with the nucleus breaking up into another nucleus and the beta rays. Energy conservation then predicts that beta rays should have a fixed energy corresponding to the difference between the masses of the two nuclei; however, James Chadwick, after many studies of this radiation with Lise Meitner, Otto Hahn, Wilson, and von Baeyer, showed that this is not the case. Rather than being discrete, the electron energy spectrum was continuous. Why it was continuous became a puzzling observation since it flew in the face of the long believed principle of energy conservation. If one particle at rest decays into two particles, then its mass gets divided as two specific fixed energies and does not spread into different energies, as was observed by Chadwick, for beta decaying nuclei. Many people started worrying about this puzzle. Pauli too had been worrying about Chadwick’s beta decay results. In fact, Bohr was arguing that perhaps energy conservation was violated in beta decay but Pauli thought that was too drastic. In his December night letter, he suggested another equally drastic alternative, which he himself called “a desperate remedy” and suggested that another particle not known then, the neutrino, might also be coming out of the nucleus during their beta decay and carrying the missing part of the energy. (Pauli actually called this particle a “neutron” but it was later dubbed as the “neutrino” by Enrico Fermi (see Fig. 7.1)).

7.2

December Night Ball and Pauli Letter

It was a cold December night in 1930, in Zurich, Switzerland, when physicist Wolfgang Pauli, a 30-year-old physicist, wrote a letter to a gathering of physicists in Tubingen that he was unable to attend the conference due to a ball that had must attend in Zurich. He wanted to let them know that he had found a way to resolve the annoying missing energy puzzle in beta decay that has been a crisis in nuclear physics for a long time. He wanted to propose a new particle called the “neutron” (later known as “neutrino”), which has spin half, no mass and resides inside the atomic nucleus. This particle is always emitted with the electron in beta decay, taking away the missing energy, thereby resolving the

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Fig. 7.1

Henri Bacquerel. Courtesy: Wikipedia.org

puzzle. From the tone of his letter, it was clear that he thought of this remedy as extreme. Nevertheless, other resolutions to the above observations were so radical that he just decided to present this idea to the physics community. He was so cautious that he wrote in his letter “. . .only those who dare can win” and surely win he did, when this particle was discovered 25 years later. Wolfgang Ernst Pauli was born in Vienna in the year 1900, to Wolfgang Joseph Pauli and Bertha Camilla Schutz. His father gave his middle name as “Ernst,” after physicist Ernst Mach, well known for Mach’s principle, and revered by Pauli’s father, himself a chemist. Mach was the godfather of Wolfgang. Pauli attended the Döblinger Gymnasium, Vienna, for his early education, and in 1918, went to the University of Munich where he received his doctoral diploma in theoretical physics, summa cum laude, in 1921, under the supervision of Arnold Sommerfeld. At the age of 21, Pauli wrote a book on the theory of relativity. In 1924, Pauli proposed the famous Pauli exclusion principle, which says that two particles with spin half cannot occupy the same position in space, a principle that explains the stability of matter. No deviations from this principle have been observed to date, despite many valiant efforts in recent years. Soon after suggesting the exclusion principle, he suggested a set of matrices to describe spin half particles like the electron, and those matrices bear his name: Pauli matrices. He was recommended for the Nobel Prize for his work on the exclusion principle by Albert Einstein and he received the Prize in 1945. Pauli died at an early age of 58 (Figs. 7.2).

7 The Neutrino Is Born as an Idea

Fig. 7.2

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Wolfgang Pauli. Source: Wikipedia.org

Pauli was having severe personal difficulties during the 1929–30 period. His first wife Kathy Deppner, a cabaret dancer whom he married in 1929, was continuing her previous affair with another man; his mother had committed suicide after being abandoned by his father, and Pauli was seeing Swiss Psychiatrist Carl Jung at the time. It is at this juncture in his life that the idea of the neutrino came to him. Part of the letter he wrote proposing the neutrino, translated from German, is given below: Dear Radioactive Ladies and Gentlemen, As the bearer of these lines, to whom I graciously ask you to listen, will explain to you in more detail, how because of the “wrong” statistics of the N and Li6 nuclei and the continuous beta spectrum, I have hit upon a desperate remedy to save the “exchange theorem” of statistics and the law of conservation of energy. Namely, the possibility that there could exist in the nuclei electrically neutral particles, that I wish to call neutrons, which have spin 1/2 and obey the exclusion principle and which further differ from light quanta in that they do not travel with the velocity of light. The mass of the neutrons should be of the same order of magnitude as the electron mass and in any event not larger than 0.01 proton masses. The continuous beta spectrum would then become understandable by the assumption that in beta decay a neutron is emitted in addition to the electron such that the sum of the energies of the neutron and the electron is constant…

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I agree that my remedy could seem incredible because one should have seen these neutrons much earlier if they really exist. But only the one who dare can win and the difficult situation, due to the continuous structure of the beta spectrum, is lighted by a remark of my honored predecessor, Mr Debye, who told me recently in Bruxelles: “Oh, It’s well better not to think about this at all, like new taxes”. From now on, every solution to the issue must be discussed. Thus, dear radioactive people, look and judge. Unfortunately, I cannot appear in Tubingen personally since I am indispensable here in Zurich because of a ball on the night of 6/7 December. With my best regards to you, and also to Mr Back. Your humble servant, W. Pauli This idea of the neutrino never appeared in any scientific journal. In fact Pauli seems to have regretted suggesting this particle. He said later “I did a horrible thing, which no physicist should do—I suggested a particle that cannot be detected.” In the year 1931, Dirac published the paper on the idea of magnetic monopole. After this, [105] “Pauli told I. I. Rabi: ‘I think I am cleverer than Dirac, I shall not publish it.’?” The “it” here referred to his neutrino hypothesis. Obviously, Pauli thought that Dirac was unwise to have published that year in the Proceedings of Royal Society an article about an undiscovered magnetic monopole. The magnetic monopole has not been discovered yet, but neutrino is now a full blown area of research.

8 From Idea to Reality: The Neutrino Story Unfolds in Slow Motion

The neutrino hypothesis resolved a major puzzle in physics and rescued the sacred principle of energy conservation in physics. But is the neutrino a real particle or just an artifice to satisfy our minds? If the particle were never discovered, it would remain an enigma, and to be sure, there was a lot of skepticism about the neutrino idea. For one thing, according to Pauli’s idea, the neutrino resides inside the nucleus, but how a light particle can stay hidden inside the nucleus was a mystery. Nearly 4 years passed before anyone took the neutrino idea seriously. For theorists, it was a puzzle to understand how the neutrino could stay hidden inside the nucleus. Even if, somehow the neutrino was inside the nucleus, how the nucleus would suddenly “cough” out a neutrino in the process of beta decay was another mystery. The “coughing up” of particles was of course not a new phenomenon, since photons (light) being “coughed out” in electromagnetic processes was already considered before 1930, but the guideline for that was already there in the classical theory of electricity. So, one could use the classical theory as a model for the photon, but there was no such example for the neutrino. Then in 1934, Enrico Fermi wrote a theory of how neutrinos could be emitted from the nucleus. He used his knowledge of the emerging field of Quantum Field Theory to write his theory. Quantum Field Theory before 1930 was applied only to discuss the interaction of light with matter, and Fermi’s genius was to extend it to understand beta decay. This is known as Fermi’s theory of beta decay and the strength of this interaction, denoted by

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2_8

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GF , is called Fermi’s constant (the subscript F being short form for Fermi). It was a major step forward in understanding the neutrino as well as the weak force.

8.1

Fermi Theory of Beta Decay

Enrico Fermi was born in 1901 in Rome, Italy, to Alberto and Ida de Gattis Fermi. His older brother died when he was 14. This had a profound effect on him. His parents diverted his attention to physics to keep him engaged. He went to the Scuola Normale Superiore in Pisa for his university education and graduated in 1922. He then worked with Max Born in Gottingen for some time. He came to America in 1938 after receiving the Nobel Prize. Enrico Fermi wrote his theory of beta decay involving the neutrino in 1933, using the language of Quantum Field Theory. He followed Dirac’s approach to light emission and his own earlier paper on the “Quantum Theory of Light” in Reviews of Modern Physics. He wrote out an interaction where the neutron under the influence of weak force converts spontaneously to a proton, electron, and a neutrino. He wrote this paper after attending the Solvay conference of 1933, where the prime topics were the neutron, neutrino, and beta decay. This conference was attended by Bohr, Chadwick, Rutherford, Pauli, Heisenberg, Dirac among others. After coming from the conference, Fermi used the formulation with creation and annihilation operators, introduced by Jordan and Wigner a few years earlier, to write a theory for beta decay. The revolutionary nature of Fermi theory was that unlike in light emission where the emitting electron remains an electron after emission, the electron and the neutrino get created out of a neutron converting to a proton. This theory gave the first real method to quantitatively deal with the process of beta decay, as well as the neutrino. The story from a paper by C. N. Yang [105] is that Jordan and Wigner, who invented the Quantum Field Theory for spin half particles like the neutrino, did not know how to create a theory for the production of the neutrino in beta decay. Wigner called Fermi’s beta decay theory paper Fermi’s biggest contribution to physics. When Yang asked Wigner why he thought the Fermi paper was so revolutionary, Wigner apparently said [105] “No, no, you do not understand the impact it produced at the time. Von Neumann and I had been thinking about beta-decay for a long time, as did everybody else. We simply did not know how to create an electron inside a nucleus.” Nowadays, Fermi’s theory looks so simple that one wonders how it was not done earlier. But what Fermi did was a major breakthrough in thinking at that time. Fermi first submitted his “tentative” (Fermi’s quotes, see below)

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theory of beta decay to the famous science journal Nature, which rejected it, “because it contained speculations too remote from reality to be of interest to the reader.” This view of Nature journal regarding Fermi’s theory reflected the general attitude towards the neutrino idea in the physics community at the time. Apparently, Nature later admitted the rejection to be one of the great editorial blunders in its history. Fermi then submitted a revised version of the paper to the Italian journal Il Nuovo Cimento, which accepted and published to the Italian in 1933 (Italian title:“Tentativo di una teoria dell emissione diraggi beta?), and the German journal Zeitschrift fur Physik in 1934, limiting a wider dissemination to the international community. The paper did not appear at the time in any primary publication in English. An English translation of the seminal paper was published in the American Journal of Physics only in 1968 [source: Wikipedia.org]. The strength of the beta decay force that caused the neutrino to be emitted is denoted by GF (with “F” for Fermi), as mentioned earlier. This parameter is known to be a very small number, ∼10−5 compared to one for nuclear force. This meant that the nucleus takes a long time to undergo the beta emission process. This should be compared with the nuclear fragmentation time scale, which is miniscule. For example, a free neutron undergoing beta decay takes about 15 min, whereas a nuclear fragmentation time takes 10−24 s.

8.2

Can the Neutrino Be Found?

This is not really a question for physicists in the twenty-first century since there are now copious known sources of neutrinos, both man-made and natural (in the sky). Also, sophisticated experiments are being performed to uncover the various properties of the neutrino. There are even hopes for using them for societal benefits. But in the 1930s, soon after Pauli’s proposal, it was a genuine question as to whether the neutrino exists at all. Nowadays, physicists postulate new particles every day. But in those days, postulating a new particle was a big deal, and even Pauli exhibited a sense of unease for having physicists struggle with his suggestion. However, one person who took Pauli’s idea seriously was Enrico Fermi (Figs. 8.2), and he was serious enough to write a theory for it, as just noted. Soon after Fermi’s paper, more physicists started to get interested and started doing estimates of how many and how fast the neutrinos can be produced, so that they could be looked for in experiments and their existence could be established. Hans Bethe and Rudolf Peierls, who were both at University of Manchester at the time, were among the first to write a paper entitled

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Fig. 8.1

Bethe-Bacher comment on detectability of neutrino

Fig. 8.2

Enrico Fermi: Wikipedia.org

“The Neutrino” where they discussed ways to detect the neutrino particle, basing their estimates on Fermi’s theory. Bethe and Peierls also considered the possibility that the neutrino may have a magnetic moment of its own and thereby can leave an ionization track in the medium. Even though the neutrino was a neutral particle like the neutron, it certainly could have a magnetic moment since the neutron has magnetic moment. The Bethe–Peierls paper was published in Nature in 1934. They claimed that the neutrino interactions were so tiny that it is impossible to detect this particle. A quote from an article by Bethe and Bacher in 1936 can be seen in Fig. 8.1. According to Fermi’s theory, not only does a neutron (discovered in 1932 by Chadwick) decay to a proton, electron, and a neutrino (more precisely the

8 From Idea to Reality: The Neutrino Story Unfolds in Slow Motion

Fig. 8.3

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From beta decay to inverse beta decay

anti-particle of the neutrino), but the same force looked at from a different way also gives the process where an anti-neutrino incident on a proton produces a positron (anti-particle of electron) and a neutron. This process is called “inverse beta decay” (for a connection between beta decay and inverse beta decay see Fig. 8.3). In 1934, two experiments were performed by Chadwick and D. E. Lea, and a second one by M. A. Nahamias, using radium nucleus and a cloud chamber, to discover the neutrino. But they were unsuccessful, further solidifying the then-held belief that neutrinos cannot be discovered.

9 The Neutrino is Discovered

The search for the intriguing particle, the neutrino, caught the imagination of physicists in the 1940s, even though they were aware that it was going to be a difficult task. The first nuclear explosion was carried out on July 16, 1945. It was already known that if Pauli’s hypothesis was correct, the nuclear explosion should produce plenty of neutrinos, since a nuclear decay process was involved in both nuclear explosion and neutrino production. Fermi and Hans Bethe thought the nuclear explosion might be a good place to catch one of the neutrinos emitted.

9.1

How to Detect a Neutrino

The neutrino is an electrically neutral particle. Therefore unlike an electron or proton, if a neutrino flies through a medium, it will not “tear” off charged particles from the atoms in the medium and leave a track. So how does one detect a neutrino? In 1946, Bruno Pontecorvo, an early assistant of Enrico Fermi, who was then in Canada working in the Chalk River reactor, suggested that it may be possible to discover the neutrino using an inverse beta decay reaction. In such a reaction, an anti-neutrino hitting a chlorine nucleus converts it into an argon nucleus, and at the same time emits a positron. The positron would then annihilate with electrons in the detector to produce gamma rays, which can be detected. Pontecorvo had a complex life. Born to an Italian Jewish family, he spent his early research career with Enrico Fermi, working on neutrons. Subsequently, © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2_9

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he worked with Frederic and Irene Curie in Paris., He left for the USA when World War II broke out. He became a fervent communist under the influence of his brother and defected to the Soviet Union in 1950. He did not return to the west for a long time. He was a legendary figure in neutrino physics. He is one of the physicists after whom the neutrino mixing matrix is named, as we will see below. Pontecorvo’s suggestion was to use a nuclear reactor as the source of antineutrinos, which will produce a positron by inverse beta decay. By the same token, one can use the neutrinos coming from the sun to produce an electron by a different inverse beta decay. Both processes must keep the lepton number unchanged between the initial and final states. This principle later was used in the 1960s by Ray Davis to discover the neutrinos from the sun. The general principle of detecting a neutrino was thus laid out and has been used many times since. The only catch is that since neutrinos are so weakly interacting, the detector target must be large, i.e., the more neutrons and protons the neutrinos and anti-neutrinos hit, the better the chance of a reaction happening. The detector must also be underground in order to shield it from the large number of atmospheric neutrinos produced by cosmic ray reactions. The cosmic ray neutrinos also produce charged leptons which can be confused with the neutrino inverse beta decay process. For a detector underground, the overlayer of material can shield from atmospheric charged leptons.

9.2

From Hanford to Savanna River

Fred Reines was born in Paterson, New Jersey, in 1918, to Israel and Gaussie Cohen, two immigrants from a small town in Russia. He received his Ph.D. in theoretical physics from New York University, and was recruited by Richard Feynman to work in the Manhattan Project in Los Alamos. After the war ended, he was employed by the Los Alamos Laboratory. In 1951, he took a sabbatical leave from Los Alamos to think about physics. That is when he decided to search for the neutrino [86], and the neutrino remained his passion for the rest of his career. He and Clyde Cowan teamed up to search for the neutrino, which was still a mystery particle at that time. The first target in their attempt to establish that neutrino was a real particle was to work near a nuclear reactor. Reactors were known to have nuclear weak interactions going on all the time and were assumed to produce neutrinos in vast numbers. Nuclear reactors are used for electricity generation, using energy released in a nuclear reaction that involves weak processes. Essentially, there are four nuclei (235 U,238 U,239 Pu,241 Pu) in reactor fuel that undergo fission, and in the

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process, release nuclear energy which gets converted to heat and subsequently to electricity. The fission products go through subsequent decays. Many of the decays are beta decays that according to Fermi’s theory produce antineutrinos by the reaction such as n → p + e− + ν¯ e . These neutrinos are quite numerous. For example, in 240 grams of uranium, there are about ∼1023 atoms and they result in many neutrinos after beta decay. In a one-gigawatt nuclear reactor, about 2 × 1020 (about two hundred million trillion) neutrinos are emitted per second. They come out with different energies and can be used to undergo inverse beta decay for their detection. The detection process involves the reverse of the beta decay process ν¯ e +p → e+ +n, as suggested by Pontecorvo in 1946. Both the positron (e+ ) and neutron produced in inverse beta decay give spectacular gamma-ray signals, which can be detected and confirm a neutrino reaction event. The first place chosen by Reines and Cowan was the Hanford reactor in the state of Washington. However, an impediment to the plan of Reines and Cowan was the cosmic ray background at Hanford, which produced particles which would look like they came from the neutrino reaction, confusing the whole situation. Thus, Hanford did not fill the bill for neutrino detection. So they had to find another site for their experiment. They found that a more ideal place would be the new Savanna River reactor in the state of Georgia, where the cosmic ray background could be shielded out much better. Savanna River reactor was about a four and a half hours’ drive from Atlanta. There, they decided to look for the anti-neutrinos emitted by the so-called P reactor to cause the inverse beta decay. They were successful in their effort and discovered this reaction and the anti-neutrino in 1956. A particle that has been in the mind of theorists for more than two and half decades was finally detected. Reines immediately sent a telegram to Pauli informing him of their discovery. Pauli responded saying “Everything comes to those who know how to wait” (see Fig. 9.2). So began the saga of the neutrino, with a busy half-century ahead of discovering its properties and uncovering the detailed nature of its participation in the weak force. There was tremendous sense of excitement in the air.

9.3

The Years That Followed the Neutrino Discovery

The discovery of the neutrino was a relief and at the same time groundbreaking. It was a relief since it rescued the sacred principle of energy conservation in physics. It was groundbreaking because it led not only to

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Fig. 9.1

Frederick RTeines who discovered the neutrino

Fig. 9.2 Pauli’s response to Reines telegram informing him of the discovery of the neutrino

a fuller understanding of the weak force but also completely changed our thinking about the evolution of the universe. Two years after the Reines– Cowan discovery, Maurice Goldhaber, Lee Grodzins, and Andrew Sunyar discovered that neutrinos emitted from nuclei had the peculiar property that

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Fig. 9.3 T. D. Lee and C. N. Yang, who proposed that weak interactions violate mirror symmetry (parity)

Fig. 9.4

Handedness of neutrino

their spin vector (see above for explanation of the idea of spin) pointed in the opposite direction (Fig. 9.4) to its motion (called left handed). Goldhaber et al used the Europium nucleus and found that only left-handed neutrinos (and no right-handed ones) were emitted in the weak decay. This suggested something very peculiar about the neutrino and the weak force. Nobody found the counterpart in which the neutrino from a beta decay would have its spin pointed along the direction of its motion. That was odd, but as it turned out, by that time T. D. Lee and C. N. Yang had suggested in a groundbreaking paper in 1956, that mirror symmetry is broken by the weak force, to explain some peculiarities in the decay of the K-meson (Fig. 9.3), totally unrelated to the neutrino. Their suggestion was soon confirmed in an experiment by Ambler, Hayward, Hopson, and Wu, which proved that indeed the Lee– Yang idea was correct. They used the weak decay of a cobalt nucleus and

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found that the emitted electrons in beta decay of this nucleus did not obey mirror symmetry. The Goldhaber et al discovery came the following year and not finding the right-handed neutrino was consistent with mirror symmetry breaking suggested by Lee and Yang. Things were happening at a break-neck speed. Lee and Yang were awarded the Nobel Prize in 1957 (Fig. 9.4). Until the time Lee and Yang proposed the weak forces as being somehow oddly different from other forces and violate parity (mirror symmetry), all forces (including weak forces) were believed to be parity invariant. In other words, they all looked the same in their outcome when viewed in a mirror. In atomic physics, this rule was called La Porte’s rule, named after Otto Laporte, who announced this rule for atomic spectroscopy. The Lee–Yang parity violation idea was completely contrary to Laporte’s rule and was therefore so disturbing to even Lee and Yang that they suggested a way to preserve it. Their idea was that there may be another universe with identical particles and forces as our universe. Parity takes particles and forces of our universe to those in the second universe. As a result, parity would be a good symmetry of forces when both universes are taken together. Since we are doing experiments only in our universe, the weak forces look like they break mirror symmetry. The Lee–Yang parity violation idea was so dramatic that in a letter Pauli wrote to V. Weiskopf in 1957 [42] “Now, after the first shock is over, I begin to collect myself. Yes, it was very dramatic.” In fact, Pauli is reported to have said of parity violation hypothesis that: “I cannot believe God is a weak left-hander [71]”. This idea of a second parallel universe lay dormant for many years and has acquired a lot of traction in the context of dark matter of the universe recently. It will be discussed in a separate chapter in this book. The second universe is called the “mirror universe” in modern parlance. More events came in quick succession after the discovery of neutrino and parity violation in weak forces. New discoveries that shook the field and added to more understanding of neutrinos as well as weak forces followed. In 1957, Bruno Pontecorvo [31] the Italian physicist who defected to Soviet union with his family in 1950, suggested that neutrinos could spontaneously transform to an anti-neutrino in free flight. This is similar to the already suggested and observed transformation of K-mesons in free flight to anti-K mesons (also called oscillations, since the reverse of this, i.e., an anti-K meson transforming to a K-meson, also occurs, giving rise to a back and forth motion, like a swing) by Murray Gell-Mann and Abraham Pais in 1955. K-meson oscillation was discovered soon after by O. Piccioni and collaborators.

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9.4

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More Neutrino Types Found

Reines and Cowan discovered the electron type anti-neutrino (ν¯ e ) that is emitted in nuclear beta decays. In 1962, a new, second kind of neutrino with properties very similar to the previous neutrino ν¯ e was discovered by Lederman, Schwarz, Steinberger and collaborators, that involved the muon. To accomplish this discovery, Lederman et al realized that the neutrino interaction rate depended on how energetic the incoming neutrinos were. The neutrinos emitted from the nuclei that Reines and Cowan used had much lower energy (energies in the few MeV range). Lederman et al employed a new method to create a beam of higher energy neutrinos. They started with faster moving pions in the Alternating Gradient Synchrotron accelerator at Brookhaven National Laboratory to create fast moving pions, which in their decay produced fast moving neutrinos. In the first step, protons were accelerated to high speeds and directed at a target of beryllium nucleus. This produced high energy pi mesons, which in turn produced higher energy neutrinos. These higher energy neutrinos helped to increase the rate at which the inverse beta decay type reaction could take place in the detector. The question then was: were the neutrinos impinging the detector in the Brookhaven experiment of Lederman et al same as the νe discovered by Reines and Cowan? What Lederman et al found is that these neutrinos produced muons and not electrons. This proved that they were a new kind of neutrino, and were called νμ or muon type neutrino. Japanese physicists Ziro Maki, Masami Nakagawa, and Shoichi Sakata proposed that the νe and νμ neutrinos could mix with each other and transform from one to the other kind. This was a revolutionary suggestion, similar to Pontecorvo’s suggestion of a neutrino–anti-neutrino transmutation. The Maki et al suggestion was confirmed in 1998, by the observation of the so-called neutrino oscillations, as we will see below. This discovery altered the landscape of neutrino physics forever. The discovery involved the neutrinos from the atmosphere of the Earth. Collisions of protons in the atmosphere produce neutrinos, as already mentioned. The atmospheric neutrinos were first observed by the joint collaboration of the Tata Institute group headed by Indian physicist M. G. K. Menon, and the Durham group of A. Wolfendale, in Kolar Gold Field in India, in 1965 [4]. The same year that the Kolar Gold field experiment observed the atmospheric neutrinos, a group headed by Fred Reines also discovered the atmospheric neutrinos in an experiment, carried out in the East Rand Proprietary Mine in South Africa [87].

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Ray Davis and colleagues observed the solar neutrinos in 1969 and found a deficit over what was theoretically predicted by John Bahcall, of Princeton. That observation could be interpreted as oscillation of neutrinos coming from the sun (see later for more details), providing support for the ideas of Pontecorvo, Maki, Nakagawa, and Sakata.

9.5

Charged Weak Force Comes Accompanied by Neutral Weak Force

As we mentioned, weak forces were thought in the 1960s to only change a neutron to a proton. They were called charged current weak force, since they change the electric charge. Then in the 1970s, a momentous discovery was made by scientists at CERN who found a new kind of weak force in neutrino scattering off neutrons and protons, where the charge of the nucleus did not change. They were called neutral current weak interactions. It was discovered in 1973 [90] and was the first evidence for a complete theory of weak interactions, suggested by S. L. Glashow, Abdus Salam, and Steven Weinberg. We will discuss this theory further in the next chapter.

10 Standard Model of the Particles and Forces

Experimental evidence to date seems to suggest that the constituents which make up all matter, and particles responsible for known forces in the universe, are now fully understood within the framework of the so-called standard model. This model was invented by Glashow, Weinberg, and Salam in the 1960s. This does not include the recent discoveries involving neutrinos. In this chapter, we give a quick run-down of the basic ingredients of the standard model. We describe the particles in the model in this chapter, and what determines the forces in the following one. In the chapter following the next, we also discuss the mysteries that provide the clue to go beyond the standard model.

10.1 How Charming was the Charm Quark? As already described above, quarks are the fundamental constituents of protons, neutrons, pions, and in fact all known particles that participate in the strong interactions (called hadrons). They made their debut in chapter two. We called them up (u) and down (d) quarks. To explain the existence of Kmesons and hyperons, one needed to introduce another kind of quark, called the strange quark (denoted by the letter “s”). The next quark, the charm quark, had an interesting history. It shows how important hunches based on symmetry can be insightful and decisive. Prior to the discovery of the muon neutrino, Gamba, Marshak, and Okubo noticed a symmetry between the electron, muon, and the electron neutrino © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2_10

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(νe , e− , μ− ) and the three known hadrons (p, n, ) and called it hadronlepton symmetry. The electric charge pattern of the two triplets are as follows: the (νe , e− , μ− ) charges are like (0, −1, −1) and for (p, n, ), they are (+1, 0, 0). In other words, the patterns are the same, meaning the second and the third particles in each group have their electric charges shifted by −1 with respect to the first particle. One could change hadron-lepton symmetry to quark-lepton symmetry as well noticing that (u, d, s) quarks have charges (2/3, −1/3, −1/3) where the d and s charges are shifted downward by −1 compared to the up-quark. As soon as the muon neutrino was discovered, this symmetry looked peculiar since there was no fourth quark to match the muon neutrino. To correct that, James D. Bjorken and S. L. Glashow postulated that there might be a fourth quark to match the muon neutrino. They called it the charm quark (with electric charge 2/3) which restores this symmetry. The charm particles containing the charm quarks were discovered in 1974, in the electron–positron colliders at the Stanford Linear Accelerator Center, and in the proton accelerator at the Brookhaven Alternating Gradient Synchrotron. As we will see, the introduction of the charm quark had a more profound impact on the consistency of the standard model than was imaginable at that time. To realize the significance of the charm quark further, note that there were many puzzles in elementary particle physics in the late 1960s. There were two running philosophies in elementary particle physics. The strong interactions were believed to be understandable by a philosophy called Smatrix theory, whereas Quantum Field Theory was working very well for phenomena involving electricity and magnetism. Neither was very helpful for the weak forces. One of the puzzles involving the weak force was that it was hard to calculate many weak processes using Quantum Field Theory. The only theory known for weak forces was the Fermi theory, which did not work very well for high energies. The Fermi theory was merely a starting point for many processes, but it was not a full theory. So it was customary to use artificial mathematical tools called cut-off energy to make estimates of rates for some processes. The idea behind the value of a cut-off energy is that it suggested the existence of new physics around that energy. One such process was the mass difference between two states of the K-meson (K1 − K2 ). When calculated using crude methods with cut-offs, it was found that the measured number for K1 −K2 mass difference fitted only if the cut-off was a mere four times the proton mass. This fact was pointed out in 1968 by Mohapatra (the author), Robert Marshak, and J. Subba Rao in the USA, and by B. L. Ioffe and E. P. Shabalin in the Soviet Union. This result meant that

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there is some new physics near the cut-off energy (four times the proton mass) that should be added to the Fermi theory for it to make sense. A year later, S. L. Glashow, John Illiopoulos and Luciano Maiani [47] revived the Bjorken– Glashow idea of the charm quark and proposed that the weak interaction cutoff was merely the mass of the hypothetical charm quark near few GeV. The first reference in this paper was to the cut-off paper of Marshak et al., just mentioned. The charm quark had not been discovered in 1970; however, this proved prophetic and the charm quark was discovered in 1974 as discussed above. In the subsequent years, the top (t) and bottom (b) quarks were suggested as part of the standard model, by M. Kobayashi and T. Maskawa, in order to accommodate the possibility of matter–anti-matter symmetry (CP) violation in the standard model. They were discovered much later. So what happened to hadron-lepton symmetry in the presence of top and bottom quarks? As it turns out, two more leptons were discovered within a few years (see below). The discovery of these extra two leptons completed the standard model. Predictions of this theory seem to explain all experiments up to now. Thus the symmetry between quarks and leptons that was a mere elegance requirement indeed became part of the standard model as we know it now. It is essential for the mathematical consistency of the theory, known in physics lingo as “anomaly cancellation.” Kobayashi and Maskawa were awarded the Nobel Prize in 2008, for connecting the top and bottom quark to CP violation. These last two quarks were discovered at the Fermi National Accelerator laboratory in Batavia, Illinois, much later. The current belief is that these six quarks are at the root of all hadrons that exist and are produced in accelerators. The current version of the standard model is based only on these quarks. Of course things could change in future, as happens in physics so often.

10.2 The Quark Family and Their Interaction One of the features of the standard model is that there are three sets of quarks— with almost identical weak interaction properties (see Fig. 10.1). Each set is said to belong to a family, with (t, b) being the heaviest (or third family), (c, s) being the middle heavy (or second) family and (u, d) being the lightest in weight (or the first family). The first question that comes to mind is: do these families live separately without affecting each other or there is some interaction among them (Fig. 10.2)? It turns out that they mix among themselves, which means they transform from one to the other in different circumstances while interacting via the weak force. In other words, a physical strange quark has a

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Symmetry between quarks and leptons in the standard model

Fig. 10.2 Mixings between quarks in the standard model. This is a symbolic representation of the so-called Cabibbo–Kobayashi–Maskawa mixing matrix

little bit of the physical down quark mixed in it, so that part of the time, it behaves like a down quark. A concrete manifestation of this is in the decay like  → p + π − (see Fig. 10.3). To see this, note that the  contains an s quark which has a little bit of down quark in it. This d quark together with the other quarks in the  baryon gives a proton and pion, neither of which has a strange quark. The  is a second generation baryon, whereas the proton and pion are the first generation particles. Thus, unless the strange quark has the ability to change into a down quark, this process should not happen. This is caused by the mixing between strange and down quarks. Similarly, the bottom quark mixes with the strange quark and down quark which makes bottom hadrons decaying to second generation or first generation hadrons. These mixings between generations are symbolically denoted in matrix form in Fig. 10.2. The size of the squares in the matrix is meant to show symbolically how big the mixings are. This mixing matrix consists of a bunch of numbers, some real and some complex. The complex number entry signifies that there is an asymmetry under quark and anti-quarks. This leads to all processes that distinguish between mesons and baryons from anti-mesons and anti-baryons, containing

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0

u

u

d s

d p u

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p– d

Fig. 10.3

Decay of the  hyperon due to quark mixing

quarks and anti-quarks respectively. For mesons, this has manifested in several places. One of them is the decay K 0 → π + π − and also in the mixings ¯ and its anti-particle B¯ 0 (bd) ¯ (Fig. 10.3). between B 0 (bd)

10.3 Leptons and the Monogamous Neutrinos Each family of quarks is associated with two leptons per family for a complete description of all known phenomena including weak interactions. (Incidentally, recall Chap. 2, where we introduced the lepton as a generic name for the electron, electron type neutrino, and its cousins (muons, muon neutrinos)). The leptons do not participate in nuclear forces but participate only in electric and weak force. As a result, they do not bind like the quarks do. Of course, the proton and electron can bind due to the electric force to form a hydrogen atom, but that binding is much weaker than nuclear binding. We can heat up a hydrogen atom using electric discharge and separate the electron from the proton—a process called ionization. It is however not possible to unbind a proton into quarks just by electrically heating it up. So how many kinds of leptons are there? By 1962 when the muon neutrino was discovered, there were four leptons (two charged and two neutral) (e, νe ; μ, νμ ). But a third charged lepton (called τ lepton) was discovered by the group of Martin Perl in 1977. Martin Perl was awarded the Nobel Prize for this discovery in 1995, together with Frederick Reines. The τ lepton, like the muon, decays and emits a separate kind of neutrino—different from νe and νμ , called the τ -neutrino (denoted by ντ ). Thus three charged leptons (e, μ, τ ) and their three accompanying neutrinos (νe , νμ , ντ ), each going with their only partner, became part of the particle zoo of the standard model (Fig. 10.1). An amazing property of the three types of neutrinos in the standard model is that each neutrino type has its specific partner with whom they are faithfully attached in weak reactions (hence the subtitle “monogamous”) i.e. νe with e, νμ with its partner muon μ and tau neutrino ντ with its

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partner lepton τ . This property is used to detect which kind of neutrino is present in a given reaction. In the standard model, each type of neutrino remains strictly “monogamous” with its corresponding partner lepton. Only later, with the discovery of neutrino oscilliations, did there appear to be some cross generational connection “breaking the strict monogamy rule” but that is new physics beyond the standard model, which we discuss later. A couple of facts: the leptons, unlike the quarks, do not experience the strong force. A second interesting fact is that the existence of the tau neutrino was just recently confirmed in an experiment called DONUT based in Fermilab, Batavia, by an international collaboration. Thus all the leptons have now been separately discovered. Each family now has two quarks and two leptons and this is displayed in Fig. 10.1. There is no strict “monogamy” property among quarks in the standard model, as shown by experiments. The quarks mix with each other. Also we note that once the neutrinos are established to have mass (as we see below), their monogamy property is spoiled. They will start mixing with different charged leptons and will not remain monogamous as in the standard model.

11 Forces in the Standard Model and Symmetries

So far we discussed the matter content (the fermions) of the standard model. They describe the constituents of matter and are the fundamental units of all matter. They come in three varieties of quarks and leptons (usually called three generations), as we just saw. Now we turn to the forces acting on them. Recall our earlier discussion that forces are caused also by particles, which are bosonic in nature. Figure 11.1, in addition to containing the matter particles, also contains the particles that carry the forces. They are denoted by the symbols γ (for photon), the carrier of electric force, W ± and Z, the carriers of the weak force, and g (the gluon), the carrier of the strong force. The gravitational force is carried by a boson called a graviton (denoted by G). The photon is one of the earliest force carrier to have been identified by physicists. As soon as the electromagnetic waves were discovered in the last part of the nineteenth century, many experiments were performed with light to understand it better. The photoelectric effect, discovered by Hertz in 1887, was one of them. He found some strange properties which Einstein explained by postulating that the light comes in discrete units called light quanta (also called the photon). That provided a simple way to understand the new features of photoelectric effect found by Hertz. Light, which previously was assumed to be a wave, also came to be called a particle. This dual nature of light was in the spirit of the quantum ideas which became prevalent. Einstein was awarded the Nobel Prize for this suggestion in 1921, and he received the award in 1922. A beautiful aspect of the standard model is that the forces in this theory are not put in by hand to fit what we observe, but are determined by a fundamental physical principle. In some sense, that makes it more believable for the theory © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2_11

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Particles of the standard model. Source: Wikipedia.org

to be the correct one. In addition, the same theoretical principle provides a strategy to go beyond the standard model when needed. To understand this, we note that observations of weak forces during the 1950s and 60s gave an interesting pattern to the strengths of forces. Weak forces had approximately the same strength no matter which particles they coupled to, whether it is changing the neutron to a proton or νe to an electron or νμ to μ, etc. A priori, there was no reason for them to be that way. That was a powerful clue to the theoretical principle that determines the strengths of the weak forces in such an orderly way. The reason it was encouraging is that the electric forces had a similar regularity, i.e. once the electric charge of a particle is given, we know the precise strength of the electric force. This was noticed early in the twentieth century by Herman Weyl, who announced a principle, called gauge invariance, in 1929, which explained this “universality” of the strength of electric forces. It further required that there must be a spin one particle (the photon in this case which mediates the force). The gauge principle dictated that the photon must be massless, i.e. the force must have infinite range which then fitted quite well with the nature of the electric forces. It was therefore well accepted by early 1930s that gauge invariance is intimately connected to electromagnetic forces.

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There was a suspicion that the observed universality of weak forces could also be due to the gauge principle. But there were two fundamental differences between the weak and the electric forces. For one thing, the weak force was short range, and secondly, unlike electricity, weak forces changed electric charge. We needed something a bit different from electromagnetic gauge invariance. Luckily a generalization of Weyl’s gauge invariance principle was given by C. N. Yang and R. L. Mills in 1954. The Yang–Mills theory in technical “lingo” is called non-Abelian gauge symmetry. It did two things: (1) like Weyl’s gauge invariance for electricity, the Yang–Mills theory predicted universal strength of the forces regardless of what matter it coupled to, (2) secondly and more importantly, it allowed for the associated spin one particles to have electric charge, so that when coupling to matter, it could change the electric charge of, for example, a proton and make it a neutron. This is precisely what was required for weak forces. However, unfortunately, it predicted also that the force must be of infinite range, like electromagnetic forces. This is because the mediating particles (and there were more than one spin one particle in the non-Abelian theory) have zero mass. Something still had to be understood if the gauge principle was to dictate the weak forces.

11.1 Are the Weak Forces Also from Gauge Symmetry Like the Electric Force? W , Z, the mediators of weak forces, took a lot longer to make their appearance in Fermi’s theory. The history of their origin could be traced back to 1957, when two Rochester physicists, Robert Eugene Marshak and his graduate student E. C. George Sudarshan, suggested that the theory of weak forces that Fermi proposed but did not specify in detail must have the so-called V − A form. What this means is that the Fermi theory had four fermions joined together to form the mathematical form of weak force. But how are they joined together? First, they must obey the theory of relativity, which allows five possibilities for the interaction if mirror symmetry is respected, and more possibilities if mirror symmetry is not. However, Marshak and Sudarshan, and, Feynman and Gell-Mann, reduced these five to only one form, called (V − A) × (V − A) form. This was a major step in moving towards the modern theory of weak interaction. The gauge theory version, now called the standard model, can only work for V and A type forms due to theoretical constraints. The V − A theory put more definitiveness to Fermi’s theory and was soon confirmed by experiments. This became the standard theory of weak

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interactions, called the four-Fermi theory.1 When Marshak and Sudarshan et al. proposed the V − A theory, the evidence against it was overwhelming— so it took them courage to defy the existing experimental results to propose the theory. Experiments which were against the V − A theory when it was proposed were found to be wrong. The V − A theory was confirmed soon after it was proposed and continued to remain the theory of weak interactions until it became part of the standard model. The V − A theory suggested that there might be spin one bosons, which behave like the light quantum, the photon, but had a large mass that could be mediating the V − A interactions. Do these bosons arise from a fundamental principle, also similar to what gives rise to the existence of photons—the gauge invariance? As just noted, the Yang–Mills generalization of gauge invariance looked just right for weak forces. However, it had the mediating particles W , Z, very similar to the photon, and therefore had infinite range, as noted.The weak forces, however, have a very short range, which means the W , Z must have a mass. A profound theoretical part of the story, i.e. how to assign mass to the W and Z, was still missing.

11.2 Where Did Mass Come from? A very simple way to cure the mass problem of the W and Z is to simply add a mass to the theory and declare that they are massive. Things are, however, not as simple. There are requirements of consistency in a theory. One consistency requirement in Quantum Field Theory is that the theory should be able to produce numbers that can be used to test it. This requirement in physics language is called renormalizability. The adhoc addition of a mass for the W , Z to the Yang–Mills theory may be easy to imagine but hard to make consistent with the requirement of renormalizability. Another way to state the idea is, adding an adhoc mass makes the theory behave badly at high energies. A theory that cannot be tested is not much of a theory and will be soon discarded by the community. A new way of applying mass had to be sought. This is called spontaneous symmetry breaking, discussed in the next section. We start this discussion with an illustration of what symmetry and symmetry breaking mean. 1 The

same year after Marshak and Sudarshan’s theory was announced at a meeting in Venice, Sudarshan and Marshak discussed this theory with Murray Gell-Mann at a RAND corporation meeting. A few months later, Richard Feynman and Murray Gell-Mann derived the same theory using different arguments.

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11.3 Symmetries and Symmetry Breaking What is a symmetry? In any environment around us we see a lot of situations which display symmetries, meaning the system looks the same when looked at in different ways. As a simple example, if you are driving along the road and see a stop sign, it is an eight-sided red polygon with the word “STOP” written horizontally in the middle. Suppose they put up a stop sign without the word “STOP,” then the red polygon would look the same. It will still have symmetry when you rotate it by 45◦ in either direction, as well as if you flip it back and forth along any line joining the middle of two opposite sides. The no “STOP” stop sign has many symmetries. On the other hand, as soon as you put the word “STOP” in the middle as in a regular stop sign, the symmetry is broken. If you now rotate the stop sign by 45◦ , the word “STOP” also rotates and makes the sign look different, i.e. it is not the same as before and that means there is no symmetry. This situation in physics is called “symmetry breaking,” i.e. the symmetry of the eight-sided stop sign is broken by the letter “STOP.” Both symmetries and symmetry breaking play important roles in physics (Fig. 11.2). The symmetry breaking can be of two kinds: (1) explicit and (2) spontaneous. The “stop sign” example is one where the symmetry is broken explicitly. The second way is more subtle and leads to interesting implications, as discussed in the next section.

Fig. 11.2 Eight-angle rotational symmetry of a stop sign without “STOP” (left panel); Once you put the word “STOP,” the sign has no symmetry. This is an example of symmetry breaking (right panel)

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11.4 Spontaneous Symmetry Breaking In 1960 and 1961, Yoichiro Nambu and Jeffery Goldstone, respectively, discovered a profound theorem which arises when symmetry is broken spontaneously (case (2) above). A simple way to illustrate this possibility is as follows: suppose you have a straight stick standing vertically; to an ant sitting on top of this stick, the area around the stick looks the same to it. The stick (and the ant sitting on it) has a symmetric environment, called rotational symmetry. However, because of gravity, such a standing stick will quickly fall to the ground. Then the space around it does not look the same anymore to the ant. The rotational symmetry is now said to be spontaneously broken. This is a crude example of what “spontaneous symmetry breaking” in Quantum Field Theory means. There is no explicit symmetry breaking in this case. Some other pedagogical examples of spontaneous symmetry breaking are the following: suppose there is a round banquet table with glasses arranged at every seat for guests. All the guests sit down. They could pick either glass on the left or right. So before any guest picks up a glass, the table is left– right symmetric but as soon as one guest picks up a glass (say from the right side) to drink from it, all the remaining guests have to pick their glasses also from the right side. The left–right symmetry is spontaneously broken. Another example is that there are two roads emerging from a single road like a fork and are symmetrical with respect to the approaching car. The person in the car approaching the fork sees a left–right symmetric situation but as soon as he/she picks one of the forked roads, the symmetry is broken spontaneously. The analog of these possibilities can be written in terms of Quantum Field Theory.

11.5 Higgs Mechanism The idea of spontaneous symmetry breaking was implemented in the context of symmetries which are space-time dependent, in the year 1964. It was proposed by a group of six physicists and is generally known nowadays as the Higgs mechanism, after one of its proponents, Peter Higgs. The Higgs mechanism has the property which gives mass to the massless gauge bosons of gauge theory. This can be used to give masses to the W and Z boson, making the weak force short range. The same mechanism is responsible for all the masses of the standard model particles, i.e. gauge bosons and fermions.

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It gives every quark and lepton their mass and every force its range and is thus a very fundamental part of the story of the standard model. This mechanism was suggested in three papers, first by R. Brout and F. Englert of the University of Brussels, second by Peter Higgs of Edinburgh University, and in a third paper by Gerald Guralnik, Carl Hagen and Tom Kibble of the Imperial College, London. They showed how a force given by a symmetry operating at every space-time point, independently (called gauge symmetry above), can acquire its short range. Since such a symmetry requires that all forces be long range in the symmetric limit, the symmetry must be broken to give the force a range. In this mechanism, the symmetry is broken by the environment of the theory (like the stick falling due to gravity). These authors put this simple idea into a mathematical framework, which can be used to build theories of the universe. That is a pretty big accomplishment. These ground breaking papers were recognized in 2013. The Nobel Prize awarded to F. Englert and Peter Higgs, after the Higgs boson was discovered in 2012 at the CERN Large Hadron Collider. Robert Brout had died by that time and Guralnik et al were left out, presumably because the Nobel Prize cannot be given to more than three people at a time and their paper was chronologically the last of the three papers. For a detailed discussion of the contribution of Hagen, Guralnik, and Kibble, see [31]. This discovery of the Higgs boson was a major triumph of theoretical as well as experimental physics and a crowning success for the enormous efforts that went into building the Large Hadron Collider, the mammoth machine in Geneva, Switzerland. More than 10,000 physicists from all over the world worked at the LHC on this experiment, constantly monitoring the machine for its performance and analyzing its results. The machine pipes are maintained at a very low temperature and at very high magnetic field, each a major task. In addition to the discovery of the Higgs boson, which was the first success of LHC, it is giving many other extremely valuable pieces of information about a lot of other physics ideas beyond the standard model. The discovery of the Higgs boson essentially confirmed the standard model in all its aspects, and provided for the first time a complete theory that partially unified three of the four known forces of nature. For a long time, it was not clear whether one can do useful calculations using a spontaneously broken gauge theory and make predictions that can test the theory. In a seminal paper, Gerard ’t Hooft showed in 1972 that indeed this can be done and ’t Hooft was awarded the Nobel Prize for this work in 1999, along with his thesis advisor M. T. Veltman.

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11.6 The Theory of Strong Force The standard model also has quarks which bind to form hadrons (protons, neutrons, mesons,…). To understand how quarks bind to form hadrons, more information is needed. It turns out that all the quarks come in three colors, a concept which was first introduced in a paper in 1964 by Oscar Wallace Greenberg of the University of Maryland, when he was a visitor at the Institute for Advanced Study in Princeton. This work was soon followed up in 1965 by Yoichiro Nambu and M. Y. Han, who introduced the method by which forces between the quarks arise from exchange of spin one particles, called color gluons. They act on the color charge to bind the quarks and keep them together to form all hadrons. This is similar to the way electric force is generated by ordinary electric charge to form the hydrogen atom. The color binding is more involved, since the color force, unlike the electric force, can change one color to another. To make this concept accessible, the three colors are often dubbed red, green, and blue, although the real colors have nothing to do with quark colors. The theory of color also arises from the same theoretical principle of gauge invariance. The color gluon is massless according to the Yang–Mills principle, as noted above.This theory was further developed in the early 1970s by David Gross, Frank Wilczek, and H. David Politzer, to what is now called Quantum Chromodynamics. Gross, Wilczek, and Politzer showed a very important property of the color charge theory. They showed that the magnitude of the color charges become weaker and weaker as we move to shorter and shorter distances, as if it is getting screened by other colors. This is opposite to the electric charge which becomes stronger and stronger as we move closer to the charge, since the screening by other charges becomes less potent. Gross, Wilczek, and Politzer used rigorous methods of Quantum Field Theory to prove this. By the same token, the color charges become stronger and stronger as we move to larger distances. One big mystery still remained in 1973, when this property of color theory was discovered. Where were the quarks and the color gluons that carry the strong force? Add this to the mystery of why massless color gluons lead to a short range force. The work of Gross, Wilczek, and Politzer provided a clue. The color force becomes weak at very short distances and by the same token, it becomes strong at long distances. This means that if the quarks are pulled apart to atomic distances, the forces between them become so enormous that they get pulled back in, before anyone can see them using sophisticated instruments. This phenomenon is called color confinement. Any particle, like the quarks, or other particles such as the color force carrier (the color gluons), cannot be

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Fig. 11.3 How a pervading Higgs field gives mass to the fermions of the standard model. The inside of the square is filled with the Higgs field responsible for all masses of matter

pulled out of the nucleus and cannot therefore exist as free particles. This then explains the other mystery as to why nuclear forces are short range. There us various indirect theoretical evidence for this kind of behavior of the quarks and gluons. Final addendum to this chapter: The same spontaneous symmetry breaking mechanism discussed in Sect. 11.5 is responsible for the mass of leptons and quarks (see Fig. 11.3). This completes our description of the standard model.

12 More Physics Beyond the Standard Model or the End of Physics Now?

All the particles and all the physical effects predicted by the standard model have now been discovered, making it an extremely successful and a truly unique theory. So a natural question is: is that the end of physics or could there be some new physics beyond? This kind of situation has emerged at other times in physics. A famous one occurred at the end of nineteenth century when Lord Kelvin is believed to have said “There is nothing new to be discovered in physics now. All that remains is more and more precise measurement.” That was just before the ground breaking discoveries in physics that led to the “Quantum revolution” and a new era with many discoveries and inventions inspired by it. There have been other similar pronouncements by famous scientists predicting the end of physics. Consider for example the 1981 article by Stephen Hawking in “Physics Bulletin” entitled: “Is the End in Sight for Theoretical Physics?” His answer was “maybe” [60]. This was inspired by the rise of the SU (5) theory which was very popular then and was way before the discovery of neutrino mass, which disproved it as the ultimate theory. We of course know that physics did not end then and is unlikely to end soon. Be that as it may, in the same spirit, the answer to this question of whether the standard model is the end of physics is a resounding “of course not,” and there are many reasons for it, the properties of the neutrinos being one of the main ones. A major way progress occurs in science is when people ask why certain things happen. This question leads people to go deeper from what they know to what

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they do not, in the process unraveling the mysteries is: why does it work so well? Some of the “why”s that keep the field active and optimistic are for example: • Why is the Higgs mass what it is, and not much larger or smaller? There have been extensively discussed ideas to solve this problem; they involve novel ideas known as supersymmetry, which is a symmetry between fermions and bosons [85]. Another class of novel ideas use the possibility that there may be extra space dimensions in nature invisible to us [12]. • Why do the neutrinos which are predicted in the standard model to have no weight indeed have weight, confirmed in 1998, as discussed below? • Why are the quark and lepton masses the way they are? Is there a higher level theory that unifies quarks and leptons as well as forces? • Why is there dark matter in the universe, whose story we mention in brief in the later part of the book? • Why does the universe suddenly appear to be accelerating, the theoretical language for this being “why is there a cosmological constant that would have the same effect?”

12.1 Future Colliders and New Physics There are plans for building even more energetic beams of electrons and protons to continue this search for new physics. The maximum energy at the LHC is 14 TeV (fourteen trillion times the mass of the proton). The newer colliders plan to extend this energy to 27 TeV and in future to 100 TeV, using circular tunnels of circumferences as big as 100 km. To accelerate the protons and keep it focused in its path, much stronger magnets are needed. The magnets have to have the strength of as much as 80,000 times the magnetic field of the Earth (8.3 T in physics language). These projects are called FCChh, i.e. Future Circular Colliders using hadron beams. They will use magnets with roughly double the strength of the LHC magnets. Getting such high field strengths for magnets is one of the engineering challenges that has to be overcome. There are also plans for building circular electron–positron colliders at higher energies. Currently being seriously discussed is an International Linear Collider with international collaboration, with Japan taking the lead. Some of these machines once operative can produce as many as ten billion Higgs bosons, allowing more in depth study of Higgs boson properties than LHC can provide. LHC has so far produced ten million Higgs bosons. So we could have thousand times the number of Higgs bosons in future colliders. That

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would reveal more about new physics beyond the standard model and more about the inner workings of the Higgs boson. It is not clear which of them will materialize in the future. Certainly it promises to be an exciting time in particle physics, with prospects for discovery of new physics and far deeper understanding of the forces and matter in the universe.

12.2 Non-Accelerator Probes of Physics Beyond the Standard Model Accelerators are not the only way to push the frontier of physics beyond what we know today. There are many physical processes which are not allowed by the standard model and their discovery will provide a giant leap in our understanding of physics. Examples are processes such as neutrinoless double beta decay, proton decay, and neutron–anti-neutron oscillation, as well as new decay modes of the muon e.g. μ → e + γ decay, etc. Intense efforts are under way to probe all these processes (except neutron–anti-neutron oscillation) at the moment. There is a possibility that n − n¯ oscillation may be searched for at the European Spallation Source facility at Lund, Sweden, in the near future. A great deal of effort is now focused on searches for the axion particle, which provides a solution to the strong CP problem [82], as well as searches for the dark matter of the universe as noted before. So far, both these attempts have not been successful. Then there are exotic possibilities such as searches for the breakdown of Einstein’s theory of relativity [69], electric charge conservation, violations of of Pauli’s exclusion principle, etc. Any evidence for these will revolutionize our thinking about new physics. The reason is that these principles have been used in our understanding of observed physical phenomena with a great deal of success and any deviation will signal rethinking of our standard approach.

13 Neutrinos Oscillate and Hence They Weigh

Oscillation is a day-to-day phenomenon. When you take little children into the park and they go on the swing, the swing goes back and forth and that is called oscillation. The swing oscillates because of the force of gravity pulling it down when it stops at its highest point. Without the force of gravity, the swing, once pushed, instead of oscillating back and forth would just go around the pole in big circles with the strings remaining rigid. That would not be much fun since the child sitting on the swing would be upside down at the top, but would not come down, since there would be no gravitational force to pull him or her down. There always has to be some force for the oscillation to take place. Thus, just like gravitational force makes the swing go back and forth and makes it oscillate, it follows that any oscillation phenomenon is an indication of the existence of a force of some kind.

13.1 From Oscillating Swing to Oscillating Neutrino One could view the up going and the down coming swings as two states of the same swing. The states of coming down of the swing and the up going of the swing can be thought of as the mixing of two states caused by gravity. Hence, gravity can be thought of as converting one state to another. In particle physics (and in quantum mechanics), a particle is represented by a state, and oscillations can therefore be thought of as resulting from two states or two particles when they mix with each other due to a force. In addition, © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2_13

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the principles of quantum mechanics require that certain other mathematical conditions be satisfied for oscillations to occur. One of the conditions is that the two states (or particles) must have their energies (or masses) close to each other, so that the states can get “confused” about their “identity.” According to Heisenberg’s uncertainty principle, energy and momentum cannot be measured precisely in quantum mechanics. As a result, if two particles have masses or energies so close to each other that they cannot be separated by a measurement, they can get confused as the same particle (the same swing) and particle oscillations can take place. The same thing can happen to neutrinos if they have mass and the states of the neutrinos (say νe and νμ ) mix. In other words, the neutrinos mix through their mass. If they are without mass, as is the case in the standard model, then neutrinos cannot oscillate since two states cannot mix with each other. Thus mass mixes one state of the neutrino with another state of the neutrino and oscillations of particles happens if there is a mixing mass.

13.2 Quantum Mechanics and Neutrino Oscillations Although the swing analogy broadly captures some essential aspects of the phenomenon of neutrino oscillation, the basic reason for neutrino oscillation has to do with the quantum nature of sub-atomic particles and not the classical nature of the swing. To understand how quantum mechanics is at the root of neutrino oscillation phenomenon, we note what broad quantum mechanics entails. In physics, there are two classes of descriptions for physical phenomena: one classical and the other quantum mechanical. Classical physics was a well-developed (almost thought to be complete) description of natural phenomena prior to the beginning of the twentieth century. In classical physics, one can use both particles and waves. The first describes motions of solid objects and the second describes motions of sound waves, water waves, etc. There is no overlap between the two. Once we move to atomic and subatomic distances, the two descriptions overlap, i.e. the same phenomenon can be described by waves as well as particles. This is called wave–particle duality and is the basis of quantum mechanics. Two major revolutions in our thinking took place as the twentieth century was unfolding. The first was the theory of relativity, mentioned earlier, which is independent of whether the description is quantum or classical. The second was quantum mechanics. The first as noted earlier referred to situations when

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particles were moving at extremely high speeds and the second when phenomena were taking place in atomic and sub-atomic distances. The full wonder of quantum mechanics cannot be described within the limited space of this book but in a nutshell, quantum mechanics [63] provides a dual description of nature where both the discrete nature of particles and the continuous nature of waves are used for description of the same phenomena. This wave– particle duality grew out of attempts to explain phenomena in atomic spectra that could not be understood on the basis of classical ideas of Newton’s laws and Maxwell’s laws of electricity and magnetism. The observation of discrete light spectra from atoms required physics beyond the old classical laws and it led to Bohr’s groundbreaking suggestion of discrete atomic orbits of Bohr’s and Einstein’s, together with Planck’s ideas of discreteness of light energy, developed into a more elaborate description based on a new kind of mathematics that eventually became quantum mechanics. As just noted, according to quantum mechanics, physical phenomena at atomic and subatomic distances can have descriptions in terms of both waves and particles. To reconcile the particle nature (particles are located at a point) with the wave nature (waves may have infinite spread), the particles are assumed to be described by wave packets. Those are collections of simple plain waves with infinite spread, altogether making a finite size packet within which the particle has a high probability of being found. With this much broad background, one can think of neutrinos as follows: two neutrinos, one of which oscillates to the other, are both described by two wave packets and roughly speaking, oscillation becomes possible if the two wave packets overlap with each other and they get confused about their identity as stated in Sect. 13.1. If they are separated from one another, no oscillation is possible.

13.3 Detecting Neutrino Oscillations What is the experimental manifestation of the oscillation of neutrino states? As the name implies, due to oscillation phenomenon, one neutrino species spontaneously converts to another neutrino species and then depending on the oscillation period, it can convert back to the first neutrino, just like a swing that goes back and forth. If we catch the neutrino state halfway through its oscillation, the intensity of the initial neutrino beam will be less since some of the original beam has oscillated away to the other neutrino. For example, if a source emits ten neutrinos of one kind, five could have oscillated into another kind. This would cause a depletion of the original beam. This is actually the way neutrino oscillation is detected in nature.

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There are two ways to detect neutrino oscillation: one way is as described above, where one looks for depletion of the original intensity of the beam, and a second way where one looks for the appearance of the new kind of neutrino which the original beam turned partially into. Each neutrino produces its partner lepton in a weak force mediated scattering process with a nucleus, i.e. νe produces an electron (e), νμ , a muon (μ), and tau neutrino ντ , its partner lepton τ . The detection of the partner lepton would therefore be the signature of the corresponding neutrino having appeared after oscillation of the νe . The first type of experiment is called a disappearance type of detection and the second is called an appearance type. Both are used in experiments being conducted around the world. The frequency of the oscillation is proportional to the mass difference square between the two neutrinos. It also depends on the energy of the neutrinos. So given the energy, one can adjust the distance where one should observe the neutrinos to detect the oscillation. For a given energy neutrino beam for very small mass differences, the distances are large, and for very large mass differences, the distances are small. The first evidence for neutrino oscillation used natural beams of neutrinos that originate from the Sun. At the core of the Sun, nuclear reactions that give us light are constantly producing neutrinos. The Sun is a perfect sphere of hot ionized gas, at a distance of about 93 million miles from the Earth. It has a surface temperature of about 5800 K. Its core temperature is about 15 million degrees Kelvin. Such high temperature in the solar core causes the nuclear and weak force mediated reactions to take place rapidly. The energy released from The Sun comes from these weak reactions in which four protons and two electrons fuse together to produce a helium atom and two neutrinos, along with 26 million electron volts of energy. This released energy comes to us as sunlight, after the photons, which carry this energy keep bouncing around from the core to the surface and come straight at us. They come at all frequencies, starting from ultraviolet to infrared. The first is responsible for the UV index that we always watch out for when we go out in the Sun, and the second is what we are warned about when we are told not to look at the Sun directly. To see if the oscillation is taking place, one needs to know how many neutrinos are coming from the solar core in the first place. Astrophysicist John Bahcall performed valiant calculations during 1960s to measure the number of neutrinos emitted from the solar core. John Bahcall was born in Shriveport, Louisiana, and got interested in physics when he was a student at the University of California, Berkeley, on a tennis scholarship. He once said that, “Physics changed my life.” He worked with distinguished astrophysicists such as Nobel laureate Willy Fowler, among others, and became a distinguished astrophysicist himself, contributing to many areas of the field. But his first love was solar neutrinos. A

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wonderful book describing the history of physics and research on the Sun and the neutrinos was written by Bahcall in 1989 [16]. Many things needed to be included in getting this calculation accurate. It took several decades to get the final number right, all done by Bahcall and his collaborators. They invented a unit called SNU (solar neutrino unit) and expressed their result in SNUs. It is given by the neutrino flux producing 10−36 neutrino captures per target atom per second. Typically, every second about 10 billion neutrinos pass through every centimeter square of area on the Earth. The detailed numbers, of course, depend on the energy of the arriving neutrino. To detect a single solar neutrino in the detector, one needs to have a lot of target atoms—typically as large a number present in a ton of the detector material.

13.4 Ray Davis and Catching of Solar Neutrinos A key question towards the end of the nineteenth century was, “Where does the Sun get its energy that comes to us as light every day?” This question occupied great minds of the early twentieth century. In 1911, Arthur Eddington wrote a long article on stars for Encyclopedia Britannica. In it, he calculated the energy emitted due to gravitational effect in the Sun and found it to be totally inadequate to explain observed solar luminosity. That then left a new puzzle in physics. Recall, continuous electron spectrum in beta decays was already another puzzle at the time. A clue came in 1920 when Francis Aston showed that the mass of the helium atom was slightly less than the masses of four protons. Physicists knew that solar luminosity had something to do with protons at the core of the Sun. Aston’s observation led Arthur Eddington to suspect that when four protons fuse together along with two electrons to form the helium nucleus, they would have some missing mass, and that missing mass is emitted as energy by Einstein’s mass energy relation E = mc2 . But nobody knew how to calculate the fusion rates in those days to make a reliable prediction of solar luminosity. The Sun is a massive hot star, which has several parts to its structure: the core, the radiative zone, and the convective zone. The core is extremely hot and dense. The radiative zone is the one through which energy generated in the core is transmitted by photons. The convective zone comes after radiative zone and contains gas at relatively low temperature and pressure. The neutrinos are coming from the core where nuclear reactions are taking place. The temperature of the solar core is about fifteen million degrees and it slowly tapers down as one moves outward along the radius. The density of the gas at the core is about 160 g per cubic centimeter. The challenge was, given this

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information, how to quantify the number of neutrinos coming from the core. Once emitted by the core, the neutrinos fly straight out and reach the detectors on Earth since their interactions with matter is so weak. In 1938, the challenge of quantifying the number of neutrinos coming from the core of the Sun was taken up by Hans Bethe and Charles Critchfield, a student of George Gamow. They analyzed the various fusion nuclear processes (a subject on which Bethe was an expert) and ended up with a number, which was too high compared to the known value of the solar luminosity. Bethe was a bit disappointed and called it only an illustrative example. As it turned out, however, the same year a higher solar core temperature measurement was announced, giving a higher luminosity, making the Bethe–Critchfield calculation agree better with observations. In 1967, Bethe was awarded the Nobel Prize for his works on energy production in stars. Incidentally, it is interesting that the Bethe–Critchfield paper makes no mention of the neutrino as a by-product of the fusion reaction. Once the Fermi theory of neutrino reactions was accepted by the community, it was clear that with every four– proton fusion that gives helium, there would be two neutrinos. Since the missing mass between four protons and the helium nucleus was known by that time from solar luminosity measurements, one could calculate the number of neutrinos being emitted by the Sun. It is 70 billion neutrinos per square centimeter per second, passing through the Earth. These neutrinos have different energies. The question then was, could this neutrino emission be confirmed by experimental measurement? A detailed calculation of number of neutrinos from the Sun was needed together with an experiment to measure them. In 1962, Willy Fowler (whose research associate at Caltech was John Bahcall) asked Bahcall, Icko Iben, and Dick Sears to do a detailed calculation of the solar neutrino flux. So began the involvement of John Bahcall with the solar neutrinos, a lifelong interest of his. He teamed up with experimental chemist Ray Davis (Fig. 13.1) in a project to detect solar neutrinos, and history was made with the measurement of the neutrino flux from the Sun. John Bahcall and Ray Davis became the face of the solar neutrino puzzle. An account of their solar neutrino journey can be found in the book written by John Bahcall [16]. Ray Davis was born in 1914 in Washington, D.C., and was trained as a physicist and chemist, receiving his BS degree from the University of Maryland in 1938. His fascination with neutrinos began when he was at the Brookhaven National Laboratory, starting in 1948. He wrote about his getting interested in neutrino research, “Thus began a long career of doing just what I wanted to do and getting paid for it.” He started looking for solar neutrinos in 1965, at a 4850 feet deep mine shaft in Homestake, South Dakota, using 100,000

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Fig. 13.1 Ray Davis who observed the solar neutrinos for the first time and disovered the solar neutrino problem in the underground laboratory in Lead, South Dakota

gallons of dry-cleaning fluid (Fig. 13.1). The neutrinos coming from the Sun would change some of the chlorine atoms in the dry-cleaning fluid to argon atoms. The Argon atoms would then be detected in a chemical process that involved bubbling the chlorine every few weeks and collecting the radioactive atoms formed by neutrinos. That way a very small number (a few tens) of radioactive Argon atoms would be fished out of the 100,000 gallons of chlorine and would prove that solar neutrinos have indeed been detected. This experiment was successful and solar neutrino detection was confirmed in 1968. The number found was, however, smaller than that expected from the calculation of John Bahcall, leading to the so-called solar neutrino puzzle. An obvious explanation was that neutrinos have oscillated away during their travel from the Sun to the Earth. Ray Davis was awarded the Nobel Prize for this discovery, in 2002. This result was confirmed by several subsequent experiments. The first two experiments, the SAGE experiment in Russia and GALLEX experiment in Italy, used radio-chemical detectors that use gallium, a different nucleus, for neutrino detection. Once neutrinos hit gallium, they transform into an electrons and germanium nuclei, respectively. One of the important results of John Bahcall’s solar neutrino flux calculation was that he derived the temperature dependence of the neutrino fluxes in various energy components. So in principle, once all the energy components of the solar neutrino fluxes are measured, the temperature of the core of the Sun can be measured. That is an important piece of information about the Sun.

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13.5 Super-Kamiokande Experiment The Davis experiment was followed by a major experiment in Japan, the Super-Kamiokande experiment, located in Mozumi mine below Japanese Alps, owned by the Kamioka Mining Company. The experiment used purified water instead of dry-cleaning fluid. The 50 kilotons of water in the detector were surrounded by more than 11,000 photo-multiplier tubes that were used to detect light emitted in a neutrino reaction. The idea was that if a solar or atmospheric (cosmic ray) neutrino meets a neutron in the water molecule, it would undergo weak force reaction and produce an electron or muon together with a proton. The electron or muon will be traveling at a high enough speed in water to be relativistic. Inside water, the speed of light is less than in empty space. When that happens, the light produced by the fast moving electron will travel in a cone, called a Cherenkov cone, named after the Russian physicist Pavel Cherenkov, who won the 1958 Nobel Prize for his discovery. An analogous phenomenon happens in a water tank when a duck swims faster than the speed of sound in water. There is a cone, which is similar to Cherenkov cone. See Fig. 13.2. The Super-Kamiokande experiment was a follow-up to the Kamiokande experiment, which was originally designed to search for proton decay. The idea to use a water Cherenkov detector for detecting proton decay was suggested by M. Koshiba, who received the Nobel Prize for this along with Ray Davis in 2002. The Kamiokande detector did not discover proton decay but it discovered the Supernova 1987A neutrino burst,

Fig. 13.2 A typical neutrino detector which was used in the Fermilab MiniBooNe experiment. The Super-Kamiokande experiment is similar but uses water for neutrino detection, whereas MiniBooNe uses mineral oil. Source: Wikipedia.org

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establishing the broad theoretical picture of the supernova as a consequence of stellar collapse. It also put major constraints on new ideas of physics beyond the standard model. For example, it put limits on the magnetic moment of the neutrino, the new interactions of the neutrino, properties of new hypothetical particles called the axion, as well as many others. The light energy collected by photo-multiplier tubes in the SuperKamiokande experiment would signal the arrival of the solar or atmospheric neutrino. The experiment started taking data in 1996. The results for the oscillation of atmospheric neutrino were announced in the bi-annual world Neutrino meeting in Takayama, Japan (Neutrino’98), to an eager audience, which was captivated by the announcement. The 1998 announcement consisted of 2 years of observation. The author of this book was in the audience when this happened. The atmosphere was electric and simply unbelievable. There were announcements in the press by political leaders from all over the world glorifying this result. President Clinton said after this discovery in an MIT commencement speech, “Just yesterday in Japan, physicists announced a discovery that tiny neutrinos have mass. Now, that may not mean much to most Americans, but it may change our most fundamental theories from the nature of the smallest sub-atomic particles to how the universe itself works, and indeed how it expands.” The Super-Kamiokande experiment was a 100 million dollar experiment by Japanese-American collaboration and made the observations that led to the monumental discovery. It transformed the field of physics. The neutrino, which since its birth was thought to have no mass, was now proven to have mass. This was evident that the Nobel Prize–winning Standard model had a flaw in it and it had to be amended. That was big! The Super-Kamiokande experiment was followed by a Canadian experiment in Sudbury mines, known as the SNO experiment (Fig. 13.3), which used 1000 tons of heavy water for solar neutrino detection. The SNO experiment was set up 6800 feet underground in the INCO’s Creighton mine near Sudbury, Canada. Neutrinos from the Sun reacted with the heavy water to produce both electrons due to charged current interactions caused by the exchange of W boson, and neutrinos due to neutral current interactions caused by the exchange of Z bosons. In the neutral current process, the heavy water nucleus deuterium breaks up to a proton and neutron. The neutral current detection by solar neutrinos was a completely new contribution of the SNO experiment. The neutron from the neutral current reaction then wanders around until it gets captured in the heavy water, and when it does, it emits a photon, which is observed by the Cherenkov detectors. Thus, the SNO experiment observed both charged and neutral current processes, whereas the Super-Kamiokande observed only the charged current reaction. They together

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Fig. 13.3

SNO heavy water detector. Source: Wikipedia.org

established that the neutrinos from the Sun oscillate and then undergo both neutral and charged current weak interactions, confirming the three-neutrino picture of solar neutrino oscillations. The SNO experiment established that neutrinos from the Sun were not disappearing into something unknown, but rather simply changing their identity from νe to νμ and ντ due to neutrino oscillations. The leaders of both the Japanese and Canadian teams, Takaaki Kajita and Arthur Mcdonald (Fig. 13.4), respectively, were awarded the Nobel Prize in 2015 for their confirmation of the solar neutrino deficit discovery and the confirmation that the solar neutrinos oscillate to νμ and ντ . These series of experiments are of fundamental importance for unraveling the mysteries of the forces and matter in the universe, as we will see below.

13.6 Atmospheric Neutrino Oscillation Just like the Sun, the Earth’s atmosphere is also a copious source of neutrinos— both muon and electron types. The way they originate is as follows. There are high-energy protons in the cosmic rays, which come from extra-solar sources

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Fig. 13.4 Takaaki Kajita and Arthur McDonald, who won 2015 Nobel Prize for discovering neutrino oscillation. Source: Wikipedia.org

towards the Earth. As they reach the Earth’s atmosphere in their journey, they encounter the thick atmosphere, consisting of all kinds of gases: hydrogen, nitrogen, oxygen, etc. Since the energy of the cosmic ray protons far exceeds the masses of K − and π − mesons, these collisions produce copious amounts of these particles. The following reaction due to strong forces takes place, i.e. p + p → p + (n + π + , n + K + ), etc. The mesons π + , K + then decay to both muon and electron type neutrinos by the following weak force mediated reactions: (π + , K + ) → μ+ + νμ followed by μ+ → e+ + ν¯ μ + νe . This gives rise to twice the number of muon type neutrinos as compared to the electron types. The atmospheric neutrinos have much higher energy than the solar neutrinos (about a thousand times more). In their journey from the atmosphere to the surface of the Earth where the neutrino detectors are located, they undergo oscillations. As already noted, the atmospheric neutrinos were first observed in the Kolar gold field experiment in India and in an experiment in South Africa around the same time, in the 1960s. The first attempts to make a more sensitive study of these neutrinos were made in the 1980s by the IMB experiment in the USA and Kamiokande experiment in Japan, both using water Cherenkov detectors, and by the Frejus and NUSEX experiment in Europe using iron detectors. The Kamiokande experiment was followed up by the Super-Kamiokande experiment already mentioned. The original number of atmospheric muon and electron type neutrinos reaching the Earth (the atmospheric neutrino flux) were calculated by various groups [53]. In 1998, the Super-Kamiokande experiment observed fewer of the muon neutrinos than were predicted by theory, confirming that the muon neutrinos have oscillated to some other species. These neutrinos that νμ oscillate to are the ντ , as is now confirmed from the observation of νμ

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Fig. 13.5 This is what neutrino oscillation looks like. Left panel for atmospheric neutrinos and right panel for Kamland reactor neutrinos

oscillations from accelerators, discussed below. The observation of atmospheric neutrino oscillations is depicted in Fig. 13.5. These oscillations were then confirmed in laboratory experiments using neutrinos from accelerators.

13.7 Neutrino Oscillations Confirmed by Accelerator and Reactor Neutrinos The Ray Davis experiment as well as the GALLEX, SAGE, Super-K, and SNO experiments used naturally born neutrinos in the Sun, and the SuperK also used the neutrinos born in atmospheric particle collisions to confirm the neutrino oscillations. The first five experiments confirmed the oscillations of electron neutrinos to other species, i.e. νe to νμ , ντ , whereas the Super-K experiment using atmospheric neutrinos confirmed the oscillation of muon neutrinos νμ to ντ and some to νe . This meant that there is a force (mass mixing) connecting all three known neutrinos, making the oscillations happen, and that meant that the neutrinos are not massless, a fundamental new piece of information about the neutrino. These experiments were confirmed using neutrinos generated in accelerators. First, a word about how neutrino beams are created in the laboratory: one starts with proton–proton collisions, which via strong forces produce mesons, such as pions, along with two protons since the baryon number

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must be conserved. The mesons then decay and produces neutrinos, i.e. p + p → p + n + (π + , K + ) with (π + , K + ) → (μ+ + νμ , e+ + νe ), which are used in laboratory experiments. This is much like what happens in the atmosphere naturally, as was already mentioned above. The main difference is that the distance from the source to the detector could now be controlled. These neutrinos are allowed to travel an appropriate distance from their source so that some of them would have oscillated to another species of neutrinos whose associated charged lepton produced in the subsequent reaction could be detected. These experiments had names like K2K (an experiment in Japan), MINOS in the USA (Fermilab), and more recently NOVA (also in the USA). They confirmed the νμ to ντ oscillation and thereby the original SuperK atmospheric neutrino oscillation results. Currently there is a major effort involving a new experiment, called DUNE (Deep Underground Neutrino Experiment), which will use neutrinos produced in the Fermilab accelerator and look for matter–anti-matter asymmetry involving the neutrinos, a phenomenon that has been known to exist among mesons (and hence their underlying constituents, the quarks) since 1964. Another important experiment that clinched the case for the conclusions from the solar neutrino observations was the KamLand experiment in Japan. It looked at electron type anti-neutrinos coming from a bunch of reactors, to a detector located at a central place at the right distance, to see oscillations. The results of this experiment confirmed the oscillation pattern of solar electron neutrinos and confirmed again that neutrinos do have a mass and the mass differences concluded from other experiments were correct. This was followed by another set of reactor experiments—conducted using reactor-emmitted anti-neutrinos from the Daya Bay reactor in China, Double CHOOZ reactor in France, and RENO experiment using a South Korean reactor. These setups determined the mixing between the νe and ντ —thus showing that all neutrinos mix among themselves in the most general way with varying strengths. These discoveries will prove invaluable in deciphering the nature of new physics as well as using neutrinos in practical applications.

13.8 Understanding the Sun Using Solar Neutrinos As mentioned earlier, why the Sun shines and how it has been doing it for billions of years without failing remained a major mystery of nineteenth century physics. With the understanding of the atomic nucleus and nuclear

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reactions in the early part of the twentieth century, Bethe and Critchfield’s work made a major advance towards understanding the vast energy supply at the solar core. Yet it was not clear how to test this theory. It came only after solar neutrinos were discovered by Ray Davis and in subsequent experiments at Super-Kamiokande and SNO. They clearly pointed to the correctness of the nuclear reaction picture for solar energy, since according to this picture, neutrinos emitted in the nuclear fusion process are responsible for energy generation in the Sun. However, they only detected the higher energy tail of the neutrinos emitted from the Sun, which is only a small fraction of the neutrinos emitted and a small percentage of the fusion reaction responsible for solar luminosity. By themselves, they cannot therefore confirm the detailed fusion model of the solar energy production. The most dominant energy source in the Sun is the hydrogen–hydrogen fusion part of the nuclear reaction, which produces more than 90% of the solar energy and produces only very low energy neutrinos. There is thus a one-to-one correspondence between the low energy neutrinos and the solar luminosity. To prove this fusion picture in more detail, one needs to measure the low energy part of the neutrino spectrum in as much detail as possible. There are four classes of nuclear fusion reactions going on in the Sun constantly: they are known as (see Fig. 13.6) pp, Be, B, and pep reactions with neutrinos coming out with different energies from them. As noted, the pp reaction is the most dominant source with the characteristic energy of the neutrinos coming from them being in the 0.1–0.4 MeV range. The Ray Davis and Super-K and SNO are only sensitive to the B (Boron) neutrinos, which go from few MeV up to 10 MeV and thus are not sensitive to the most dominant part of the solar energy generation reaction. This important gap was filled by the gallium detector experiments Gallex (Italy) and SAGE (Russia) and by one of the more recent additions to this group, the Borexino experiment in Gran Sasso (Italy) that uses a liquid scintillator for detection. The way the low energy neutrino detection confirms the solar fusion model is as follows: in the hydrogen fusion reaction, there are two neutrinos emitted, together with 26 MeV of energy as photons for each two neutrino. The energy emitted comes out as solar luminosity, which has been measured fairly accurately. Thus if the emitted number of neutrinos is measured also accurately, that will confirm the solar fusion model. The Gallex, SAGE, and Borexino experiments have done this measurement and have confirmed the solar fusion model. This provides a complete understanding of the longstanding problem of energy generation by the Sun (Fig. 13.6). Another important aspect of understanding the Sun involves knowledge of what elements are in it and how much of each element is there. We know

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Fig. 13.6 Nuclear fusion processes that are at the heart of energy generation in the Sun. Source: Wikipedia.org

that the main constituents of the Sun are hydrogen and helium atoms. The conversion of the former to the latter via nuclear fusion being its main energy source, that causes the Sun to shine, sustaining life on Earth. What else is there in the Sun? This question is phrased in astronomy as “how metallic is the Sun?” Astronomers define a metal as any element heavier than helium. Clearly, common sense tells us that the more metallic the Sun is, the more opaque to light the Sun will be. The more opaque the Sun is to light, the hotter it will be since energy in light cannot escape due to the opaque nature. Nuclear physics calculations of solar fusion of hydrogen to helium show that these nuclear reaction rates depend very sensitively on the solar core temperature, affecting the neutrino production rates. Thus, the rate of neutrino production indirectly can provide information about the core temperature of the Sun. This is a very valuable piece of information and could apply to all stars. It will also affect the longevity of the Sun and stars with high metalicity. The detailed understanding of this aspect of the Sun is still evolving.

14 What Have We Learned about Neutrinos from Neutrino Oscillation Experiments?

The discovery of neutrino oscillations was a ground breaking discovery, and the first thing we learned from this discovery is that the neutrinos have mass, unlike what we were led to believe by the standard model. This is already a profound new lesson, which says that the standard model needs modification. What else have we learned? The next thing we learnt is that the three neutrinos have different masses. This is because the neutrino oscillation requires that the mass difference between the neutrinos that oscillate into each other cannot be zero. The frequency of neutrino oscillations depends on the mass difference square divided by the neutrino energy and does not say what the individual masses are.

14.1 Who Is Heavy and Who Is Light: Mass Ordering of Neutrinos To see what we actually learned, note that there are two classes of oscillations: one, where the neutrinos from the atmosphere oscillate, and another where the neutrinos from the sun oscillate. In the first case, it is primarily the muon type neutrinos that oscillate. They outnumber the electron type neutrinos by a factor of two. In the solar case, it is the electron type neutrinos that oscillate, since no other types of neutrinos can be produced in the sun due to lepton number conservation. Thus there are two separate mass differences involved. With three neutrinos, one can only have two differences. In fact, what we have learned from the atmospheric oscillation observations is that there is a mass © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2_14

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Fig. 14.1 The two possible mass orderings allowed by current oscillation observations. Colors represent the kind of neutrino and different colors in each bar tells how much the neutrinos mix with each other

difference between νμ − ντ which is of order m2μτ ∼ 2.5 × 10−3 eV2 . This is called the atmospheric mass difference. Similarly from the solar oscillation, we find the corresponding νe −νμ mass difference square to be smaller and of order

m2e−μ ∼ 7.4 × 10−5 eV2 . This is called the solar mass difference [27].1 Thus, while the mass differences are determined very precisely by the oscillation observations, the individual masses are left undetermined by them. It turns out therefore that the mass arrangements of the neutrinos (called mass ordering) are not known, even after so many oscillation observations have been carried out. The two mass orderings allowed by current observations are given in Fig. 14.1 and are called normal and inverted mass orderings. Normal refers to the case where the tau neutrino which is the counterpart lepton of the third family is heaviest, like the top and bottom quarks and the τ lepton. Then comes the muon neutrino as the next heaviest (like muon, charm and strange quarks), and the electron type neutrino as the lightest. For the inverted case, this arrangement is opposite as shown in Fig. 14.1 i.e. the muon and the electron type neutrinos are the heaviest and are separated by the solar mass difference and the tau neutrino is the lightest. We also now know most of the mixing matrix for the neutrinos, thanks to many beautiful experiments. The mixing matrix is an arrangement of the elements which represents the strength of the various mixings between neutrinos. This mixing matrix is called the Pontecorvo–Maki–Nakagawa–Sakata matrix, after the scientists who first 1 An

eV is a unit of mass commonly used in particle physics and one eV is equivalent to 10−33 g.

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Fig. 14.2 Mixings between neutrinos that followed from the observation of neutrino oscillations

proposed that neutrinos can oscillate. It is given symbolically in Fig. 14.2. The idea of neutrino oscillations started with Bruno Pontecorvo as noted before [21, 31]. The mixing between the second and third generation neutrinos (νμ and ντ ) (for normal hierarchy) was derived mostly from the measurement of atmospheric neutrino deficit. The mixing between the first and second generation neutrinos (i.e. between νe and νμ ) was derived mostly from the solar neutrino deficit observations and was confirmed by the KamLand experiment. Then there is the remaining angle that mixes the first and third generation (νe and ντ ). Most people thought that this angle must be vanishingly small in analogy with the quark sector, and some theoretical symmetry arguments suggested that. This however, was shown by experiments not to be true. The point about this angle is that it accompanies the CP violating force in the neutrino mixing matrix. If this mixing was vanishingly small, there would have been no chance to see the CP violating effects in the neutrino oscillation experiments. That would have been a pity! However, in 2012, several experiments that used reactor neutrinos observed that this mixing angle is indeed quite large [40]. That was an important discovery, which made it plausible that the neutrino oscillation experiments can also tell whether there is CP violating interactions in neutrino oscillation. We still have not discovered the CP violation in neutrino oscillations. These angles are all given in the cartoon Fig. 14.2, where the size of a square indicates roughly how big that mixing is. From the Fig. 14.2, we see that the mixing pattern among neutrinos, which does not depend on whether the mass ordering is normal or inverted, is a new clue to a possible future complete theory of neutrino. This has been a fertile ground for research in the past two decades. The point is that the mixing pattern among quarks is very different and is mostly of nearest neighbor type, which means that as two families become farther apart, their mixing weakens (see Fig. 11.3). This is in some sense intuitively understandable. However, for leptons, it is very

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different. The first and second families mix almost as strongly as the second and third family. Why is this so? If quarks and leptons are to be part of the same kind of matter as grand unified theories would want them to be, how do we understand such a diverse pattern in their mixing? This has remained a challenge to theorists working on building unified models for neutrinos with quarks. There are speculations that they may owe their origin to new symmetries of nature or some particular kind of grand unified theory [66].

14.2 Refraction of Neutrinos in Matter The phenomenon of light refraction is well known from high school physics. When light passes through a transparent medium such as glass or water, the ray of light gets bent. The reason for this is, as light travels from one medium to another, its speed becomes less if the second medium is denser. Since according to quantum mechanics, all matter also behave like waves, could it be that neutrinos passing through matter undergo refraction, just like light? The fact that this indeed happens to neutrinos was first suggested by Lincoln Wolfenstein in 1978 [104]. As the neutrinos pass from a less dense to a more dense medium, their speed goes down. How much the speed goes down also depends on their original speed. And if the neutrinos mix, the oscillation from one to the other neutrino takes place at a different rate in a medium than in an empty space. This has significant implications for neutrinos traveling through the sun or the Earth, or other dense environments, like supernovae. After this suggestion was made by Wolfenstein, it was applied to neutrinos coming from the core of the sun to the Earth by Stanislaw Mikheyev and Alexei Smirnov [74], to see how it manifests in the solar neutrino signal on Earth. Since the sun has a lot of matter and neutrinos produced in the sun’s core have to travel through it, there has to be some effect on them. Mikheyev and Smirnov studied this in detail and showed how it affects the oscillation pattern of the neutrinos of different energies. This effect is called the MSW effect after them. Since the various solar neutrino experiments explore different energy neutrinos from the sun (and the MSW effect depends on the neutrino energy), this kind of effect should be observable by a different final energy distribution of neutrinos on Earth compared to what was expected from the core. It indeed appears that solar neutrinos exhibit matter-induced refractive effects due to the core of the sun. A confirmation of this effect is expected to come from the observation of other solar neutrino effects. For instance, when the solar neutrinos come to the Earth during the day time, they do not go through the Earth matter,

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whereas, when they reach the detector at night, they do. If the neutrinos indeed undergo matter refraction, there should be a difference between the day and night amounts of solar neutrinos at the Earth based detector. That is called the day–night effect. Experiments like Super-Kamiokande and SNO have looked for it. At the moment, there is only some weak evidence for it from the Super-K observations.

14.3 Do Neutrinos Decay? Since the neutrino puzzles discovered in the solar and atmospheric neutrino searches involved missing neutrinos, a logical possibility is that the neutrinos on their way could be decaying to some other particles. This possibility has been extensively studied [48]. The first question that arises in the discussion is how the neutrinos which are such tiny, ultra-light particles could decay. The heavier neutrinos could decay to a lighter one together with a photon or three light neutrinos. For a review of the current knowledge about these decays, see [48]. An interesting situation arises when the decay to final states are invisible. A possible theory for such an invisible decay was discussed in 1980 by Yuichi Chikashige, Rabindra Mohapatra (the author), and Roberto Peccei [29]. It was suggested in [29] that if the neutrinos are their own anti-particles, there could exist a massless particle called the Majoron to which the neutrinos connect. Therefore a heavier neutrino could decay into lighter ones by emitting a Majoron. If we denote the Majoron particle by the symbol J , then decay could be something like νi → νj + J . Since we do not know which neutrino is heavier among the three, we could have either the solar or the atmospheric muon neutrino or both involve in this decay. That could explain the observed deficits since a decay makes the particle disappear. Such decays however have other manifestations which constrain their strength to such an extent that they are not able to explain the solar [5] and atmospheric neutrino deficits fully. They could be contributing to the fluxes partially, though. There are however ongoing experiments to search for such invisible decays, as well as the presence of the Majoron particle in the universe, using the same neutrinoless double beta decay experiments mentioned earlier (see Chap. 11). Majoron decays have other implications for cosmology as well [30].

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14.4 Long Distance Communication Using Neutrinos Our civilization relies very heavily on effective forms of communication (e.g. emails, GPS systems, etc.). Currently, most communications are done using radio waves. But they have a lot of limitations. For example, seawater can stop or affect the propagation of radio waves. Similarly, in space travel, if we are on the other side of the moon, communication using radio waves is not possible. On the other hand, neutrinos pass through almost all matter without getting deflected or stopped. A neutrino can pass through 1000 light years of lead without its beam getting distorted. As a result, messages sent with neutrino beams can travel very far without distortion. Is the idea feasible? Communication needs a sender of the beam and a receiver of the beam and a message carrier which remains undistorted over long distances. For radio waves, there are many effective ways to do both the sending and receiving. Neutrinos are not yet emitted in large enough numbers to make communication feasible with the current state of technology. Attempts on the small scale have however been successful as shown in an experiment done at Fermi National Lab. A message using the neutrino beam was sent using the NuMI experimental beam as the source and was detected one kilometer away in a detector called MINERVA. The message sent was the word “neutrino” using a modulation of the neutrino beam. It is interesting that the attempt was successful when the detector was in close proximity. Possibly, at some stage the technology will improve to the extent of making such communication feasible as well as practical at longer distances. The message rate in the MINERVA was of course slow, only 0.1 bits/s. But things can improve with time. All science starts slow!

14.5 Using Neutrinos for National Security Purpose One of the things we learn from nuclear physics is that in a nuclear explosion, a lot of neutrinos are produced and since they interact very weakly, they can go for long distances without any interruptions and convey the message that there was a nuclear explosion. If there is a rogue nation which does a clandestine nuclear explosion, its location can be pinpointed by putting three detectors in different countries surrounding the rogue country. Down the line, this can be a potentially important application of neutrino physics.

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14.6 Worldwide Effort to a Fuller Understanding of Neutrino Mass Currently, there are many efforts in various parts of the world to understand the neutrino masses better, and to the fullest extent possible. In the USA, major funding to Fermilab is given for the neutrino project, called DUNE (Deep Underground Neutrino Experiment), which will direct a neutrino beam from Fermilab to Lead, South Dakota to study the neutrino oscillations. As already mentioned, the primary aim of this experiment is to discover the CP violating forces among neutrinos, as well as to provide evidence for either of the two mass orderings described above. Another experiment in Japan which is called T2K (short form for Tokai to Kamiokande) is also attempting to establish the mass ordering and CP violation in the neutrino sector, the same goal as DUNE. Then there is another reactor experiments in China, called JUNO (Jiangmen Underground Neutrino Observatory), and a planned experiment in India to study atmospheric neutrinos, called INO (Indian Neutrino Observatory) [9]. JUNO’s goal is to use reactor neutrinos to study the mass ordering problem among other things. INO will study the atmospheric neutrino oscillation in finer detail using iron as the detector (iron calorimeter). The latter project at the moment has been plagued by local political problems, which presumably will be resolved and the experiment can go on. Then, there are many experiments all over the world to search for what are called sterile neutrinos, discussed in a subsequent chapters. These experiments put neutrino detectors from the reactor sources at shorter distances so that they are sensitive to higher mass differences.

14.7 Can Neutrino Be Sensitive to Magnetic Forces: The Neutrino Magnetic Moment Being deflected in a magnetic field is a property of charged fermions. A charged fermion moving in space creates a magnetic field. These are all well known properties. But we saw earlier in the book that neutrons which are electrically neutral also have a magnetic moment, i.e. they behave like tiny magnets in a magnetic field. That is already understood to be due to the quarks inside the neutron, which have electric charge and are constantly moving around. How about the neutrino? Could it have a magnetic property i.e. magnetic moment due to something going on inside it? As far as we know, it has no

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electrically charged constituent (in fact, most likely no constituent at all). It turns out that in the Quantum Field Theory framework, a neutrino can break up to a “virtual electron” and a virtual W boson and recombine. These are virtual processes but are constantly occurring according to Quantum Field Theory. Since both the W and the electron have electric charge and are also moving around, they create a magnetic moment for the neutrino, making it behave like a very tiny magnet. Estimates show that this induced magnetic moment is likely about 10−19 − 10−11 times the magnetic moment of the electron, depending on different theoretical possibilities [51]. It also depends on the mass of the neutrino. If the neutrino was massless like in the standard model, it would have no magnetic moment. So, observation of a magnetic moment would be a new way to search for neutrino related physics beyond the standard model. Discovery of a neutrino magnetic moment will therefore be revolutionary with all kinds of implications for new forces and matter beyond the standard model. If the magnetic moment of the electron neutrino was large, it would create an 11-year modulation of the solar neutrino signal, since the large magnetic field inside the sun changes every 11 years. The solar magnetic field can flip the electron neutrino into a sterile neutrino, which will give no signal in the solar neutrino detector on Earth. The 11-year cycle has to do with the appearance of the sunspots every 11 years, which is when the magnetic field in the Sun becomes larger. In the beginning of the Ray Davis observation of solar neutrinos, there appeared to be some variation of the solar neutrino signal correlated with the sunspots, but that evidence seems to have gone away. There are however several laboratory experiments searching for the magnetic moment of the electron neutrino, using scattering of reactor neutrinos off electrons and nucleons. The magnetic moment increases the scattering rate of the neutrinos. So far, no evidence for neutrino magnetic moment has been found.

14.8 What Oscillation Experiments Do Not Tell Us While the oscillation experiments have provided a wealth of information about the neutrinos, there is one important piece of information it cannot give us. That is the absolute mass of the neutrinos. As emphasized earlier, the oscillation frequency of neutrinos from the sun, atmosphere, or any other source is always a measure of the difference in their masses. It cannot therefore tell us what the absolute mass of the neutrinos is. There are however ways to find the absolute mass, and experiments are under way to do that. For example, if the neutrinos are Majorana fermions, then the neutrinoless double

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beta decay (see below) measures their absolute mass scale. If however they are Dirac fermions, neutrinoless double beta decay is forbidden, in which case other ways must be sought. There is a way to measure the mass of the electron neutrino since it is emitted in beta decay. How the decay proceeds depends on how massive the electron neutrino (as well as other neutrinos) is. There is an experiment known as KATRIN experiment in Karlsruhe, Germany, where experimentalists are trying to look for how the electrons from the decay of a tritium nucleus behave at different energies. This property depends on how big the neutrino mass is. At the moment, they can tell if the electron neutrino mass is larger than 0.2 eV. That will provide a way, using the oscillation measurements to find the absolute mass values of the various neutrino species. There are also ways to tell what the absolute mass of neutrinos are from looking at cosmological observations. Any value of neutrino mass will affect how the various galaxies formed and how densely they are distributed. These kind of detailed considerations can give mass limits of order of 0.1 eV or less. Such cosmological observations are under way both in Europe and USA. They are both ground based missions, such as the Large Synoptic Survey Telescope (LSST,) and space missions, like the EUCLID mission by European Space Agency and the WFIRST (Wide Field Infrared Survey Telescope) mission by NASA in the USA [55]. There should be interesting results from these searches in the next decade.

Part III

15 Mendeleev’s Periodic Table

Dmitri Ivanovich Mendeleev was born in a small village near Tobolsk, Siberia, in 1834, and grew up as an orthodox Christian. He was one of 17 siblings, 14 of whom survived. He had a very difficult childhood. When he was little, his father who was a teacher went blind, so his mother had to go to work in a local glass factory. The factory burnt down when Dimitri was only fourteen, whereafter they went into poverty. His mother was however determined to get him an education and sent him to St. Petersburg, but 10 days after he was admitted to the school, his mother died. So Dimitri had to make it on his own through sheer hard work. He later trained in Europe as a chemist and returned to Moscow at the age of twenty seven to teach. He was determined to teach the modern ideas that he learned while in Europe to students in Russia. He also kept doing research in chemistry. His work in chemistry led to the famous periodic table that adorns every chemistry classroom today, from high schools to colleges. The periodic table arranged all the various elements in a systematic way that reflected their atomic property. At the time he invented the periodic table in 1869, only sixty three elements were known. Mendeleev arranged the known elements in groups of eight each; he put elements with similar properties in a vertical column. For example, sodium and potassium have similar properties and are vertically one below the other in the periodic table. So are fluorine and chlorine as well as inert gases e.g. helium and neon, etc. It was 5 years after John Newland put forward a theory of octaves, which was similar to Mendeleev’s table but had some defects, such as putting hydrogen and fluorine in the same column, etc. For this and other defects in the arrangement, Newland’s © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2_15

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Fig. 15.1

Periodic table of elements. Source: Wikipedia.org

octave arrangement was not accepted by the chemists whereas Mendeleev’s table fitted all expectations with predictions for missing elements, which were later discovered. Mendeleev’s table was accepted by the chemistry community. The table he created describes the nature of atoms and nuclei around us and is a fundamental contribution to science. He arranged the atoms in increasing order of their atomic number (the value of the Z or the number of protons in a nucleus) along the horizontal part of the table. A new row begins every eight elements except for the “green” middle elements in the fourth through seventh row which are transition metals (Fig. 15.1). The elements along a vertical line have similar chemical property; for example, the extreme right vertical column contains inert gases and the extreme left column contains the alkali metals. Because of this periodic property (i.e. properties repeat every eight atoms), this is called a periodic table. This table has been an extremely useful one in many ways. When Mendeleev set up the periodic table, there were several elements in the table that were not discovered. Mendeleev left gaps in those places and predicted that those elements should be discovered. One such element was gallium, which fell below aluminum, and it was discovered in 1875 with the properties that Mendeleev predicted it should have. This made Mendeleev famous and his periodic table became the standard table of elements for chemists. Other gaps corresponded to germanium and scandium, which were also discovered later. Mendeleev however did not receive the Nobel Prize for this fundamental discovery and lost by one vote in 1906 to French chemist Henri Moissan who received the prize for his work on isolating fluorine from compounds. When Bohr’s model of atoms was generalized using

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quantum mechanics and other aspects of atomic theories, such as electron spin, exclusion principle, etc., this periodicity of the periodic table resulted as a simple consequence of quantum theory. A key feature of the periodic table as we go horizontally is, each element has one more proton in the nucleus than the previous element. We will denote the number of protons in a nucleus by Z (atomic number) and number of neutrons by the letter N—so as we go higher, the elements go from Z → Z + 1 → Z + 2 . . .. There can be many different nuclei with a single Znumber but different neutron numbers N—they are called isotopes of each other and are “lumped” in at one spot in the periodic table. To understand the origin of the periodic table, we have to understand how in the evolution of the universe, the nuclei with one value of Z generated the next nuclei with a value of Z + 1, and so on. This is called heavy element nucleosynthesis. Currently there are 118 elements in the periodic table, out of which 92 occur naturally and the rest were created in accelerators. Little did Mendeleev know (or could have known) that what he created is intimately related to a tiny elusive particle called the neutrino. But that is what it was. The cosmic soup of quarks and leptons got turned into the elements in the periodic table due to neutrinos constantly bombarding against quarks in the first few minutes of the early universe. Neutrinos converted the protons and neutrons to helium, lithium, and beryllium, which are the ancestors of all the elements we know today and owe our existence to. There are two clues to understanding the heavy element nucleosynthesis; one is that it is easier for nuclei to absorb a neutron than a proton, since the proton is repelled by the electric repulsion from other protons in the nuclei, thus the proton has difficulty getting inside the nucleus. Second is that in beta decay reaction, a neutron emits a neutrino and an electron and converts the neutron to a proton i.e. n → p +e− + ν¯ e and thereby it changes the nucleus with Z → Z +1. But how did it all start at the beginning of time, since in those early moments the universe was so hot that all protons and neutrons “melted” to three quarks? Somehow the quarks must have united form protons and neutrons as the universe expanded and the protons and neutrons must have united to form various nuclei. Finally, the nuclei had to combine with the electrons to form an atom. This is a complex and long drawn process that has lasted from the time when the universe was a minute old to “almost now” when the stars formed and evolved. This is a fascinating story. To get to this discussion, we need to establish some background about the role of neutrinos, creating even the first few elements of the periodic table, such as helium, lithium, etc. from which things eventually grow to more complex nuclei. The neutrons and neutrinos hold the key to this story, for at least the 92 known elements that occur naturally. We describe this process in the next chapter.

16 A Brief Overview of the Big Bang Theory of the Universe

To see the role of neutrinos in the universe in the past, present, and future, we need to have an overview of the basic features in the evolution of the universe. The universe is now about 13 billion years old, starting from the moment of the “Big Bang.” It went through many stages in its evolution that eventually created all the known features that we see today, such as galaxies, stars, and various elements in different abundances. So how did it all happen? There have been many people thinking about these issues for the past century, starting with Einstein, De Sitter, Lemaitre, Hubble, Friedmann, Robertson, and Walker, just to name a few. The universe provides a setting that is unlikely to be achievable in the laboratory, but the ideas that went into our understanding of the universe have been inspired by many phenomena that have been observed in the laboratory. For example, the change of water to steam or ice to water is a common phenomenon known as phase transition in physics, and similar phenomena are expected to have occurred in the early stages of the universe.

16.1 Big Bang Theory vs. Steady State Theory The first part of the struggle to understand the details of the universe started with uncovering the overall nature of its evolution. There have been several theories regarding the evolution of the universe, but two most popular rival theories until few decades ago were: (1) the Big Bang theory and (2) steady state theory. The first one was proposed by Belgian priest and physicist George © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2_16

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Lemaitre in 1927, to explain the observed redshirts of the spiral nebulae. He also derived the law of expansion, which was later given by Edwin Hubble and goes by the name Hubble expansion. The second is the steady state theory, which was proposed by Herman Bondi, Thomas Gold, and Fred Hoyle in 1948. In fact, it is ironic that the proponent of the steady state theory, Fred Hoyle, in a tone of sarcasm, gave the name “Big Bang theory” to the rival theory proposed by Lemaitre. In the Big Bang theory, the universe started from an extremely hot beginning (we will call that the beginning of time, although we do not know for sure if that really is) and then kept expanding, as it is doing now, with the rate of expansion steadily slowing down. The rate is determined by the energy density, and energy density in the universe is steadily going down. In the steady state theory, on the other hand, the universe is in a steady state of expansion (hence the name) and supposed to look the same at all times. Both time and space played a symmetric role in this theory. The constancy of the density of energy responsible for the steady expansion of the universe was understood by postulating that matter was being constantly created. This was called the perfect cosmological principle since space and time played a symmetrical role. The perfect cosmological principle was indeed a beautiful concept. In fact, in the beginning, the steady state theory was a very popular theory, widely believed to be the correct theory among cosmologists in England and America. Estimates of the age of the universe in the early days using the Big Bang theory predicted an age of about few billion years, which was far too short, compared to what people believed to be the age then. It was indeed found to be shorter than the age of the sun, which was an argument against the Big Bang theory. This, no doubt, helped the popularity of the steady state theory. In fact, Hoyle was so confident that the steady state theory was correct that he made statements like: “The Big Bang is an irrational process that cannot be described in scientific terms [nor] challenged by an appeal to observation.” Even the Church got into the debate between the Big Bang and steady state theory and came out in favor of the Big Bang theory. Pope Pious XII announced in 1952 that Big Bang cosmology affirmed the notion of a transcendental creator and was in harmony with Christian dogma, rather than the steady state theory, which denies any special place for a moment in time when creation began. The fact that all moments of the universe and all points in space are similar seemed atheistic to the Pope. Gradually, the tide of scientific evidence started turning in favor of the Big Bang theory. The steady state theory predicted that the old and new stars would be equally distributed throughout the universe, whereas the Big Bang

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theory predicted that distant galaxies are older, a claim which was supported by astronomical discoveries in 1948. Also, steady state theory predicted that there should be equal number of radio sources both far as well as close to our own galaxy. This prediction disagreed with observations by Martin Ryle in 1954, who concluded this using of radio telescopes after the World War II. In fact Ryle’s observations were bitterly criticized by Fred Hoyle, saying that Martin Ryle was more interested in destroying the steady state theory than discovering facts. In fact, Barbara Gamow, wife of George Gamow, a believer in the Big Bang theory, wrote a poem to reflect this dispute, a part of which goes as follows: “Your years of toil,” Said Ryle to Hoyle, “Are wasted years, believe me. The steady state Is out of date. Unless my eyes deceive me.”

16.2 Big Bang Theory Wins Then came the discovery of the cosmic microwave background radiation (explained later) by Arno Penzias and Robert Wilson in 1964, which agreed with the predictions of the Big Bang theory and required the steady state model to make further assumptions to explain that observation. A big boost in favor of the Big Bang theory came when Ralph Alpher, a student at George Washington University, Robert Herman, an employee at the Johns Hopkins Applied Laboratory, and George Gamow, a Professor at George Washington University, calculated the relative abundance of helium to hydrogen in the universe using the Big Bang expansion model and laws of nuclear physics, and got a result in rough agreement with observations. The battle between the steady state and Big Bang theory is not a matter of dispute anymore, and after many observations involving the cosmos, the winner has turned out to be the Big Bang theory. This theory is now widely accepted by the cosmology community as the theory of the universe. According to the Big Bang theory, the universe started expanding and cooling at a rate depending on the particles it contains [67]. The expansion rate is slowing down. Expansion is characterized by the property of a mathematical quantity, known as the scale factor (a(t)). The scale factor roughly measures the size of the universe. As the universe expands, the scale factor increases

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and the energy of the relativistic particles becomes smaller and smaller. For example, the energy of a photon at the epoch when the scale factor is a(t) becomes half as the scale factor becomes 2a(t). This is called redshift of particle energy with expansion. All particles in the beginning were hot and moving extremely rapidly, and were relativistic, i.e. moving at or close to the speed of light, which is 186,000 miles per second. Most of those particles behaved like massless particles (similar to the photon). As the universe expanded, the density of energy in it and the density of particles in it started becoming less and less. Since the expansion rate is governed by the energy density according to Einstein’s theory of general relativity, the rate of expansion slows down. The expansion obeys the Hubble law which says that the speed of a particle (star, galaxy) is proportional to its distance from the observer, i.e. the further an object is from a given point in the universe, the faster its speed as observed from that point. This law of expansion holds even today, except that in recent years, a new accelerating phase of the universe has been discovered which we discuss later. At a certain point in its expansion, the particles, which in the beginning were massless, get their mass, and if the temperature of the universe is less than the mass, they start moving slower. If they are unstable, they decay away to lighter particles. During this expansion, several major events happened to the universe that led to what the present universe looks like. One of the major ones is the inflationary phase, which we discuss in the next chapter.

16.3 Major Events in the Universe’s Past The major events from the universe’s past can be summarized as follows: (For a detailed history of the various stages, see [67, 100].) 1. Inflation begins and ends. Inflation refers to sudden rapid expansion of the universe at the beginning, soon after the Big Bang. 2. Matter–anti-matter asymmetry is created. The exact moment when this happened is not known. 3. Quarks turned to protons and neutrons when the universe was about 10−4 s old. 4. Protons and neutrons turned to helium, lithium, and beryllium when the universe was about a minute old. This is known as Big Bang nucleosynthesis. 5. Atoms formed when the universe was about 400,000 years old.

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6. Small and large structures formed in the universe, which grew to be galaxies and stars, etc. about when the universe was 700 million years old. 7. The epoch when the cosmological constant started to dominate and created the second phase of slow accelerated expansion started when the universe was 11 billion years old. We discuss two of these events: inflation and Big Bang nucleosynthesis, since they are relevant to the role of the neutrino.

17 The Inflationary Universe

According to the Big Bang theory, the universe is undergoing continuous expansion from its early moments until today. This is evident from the observation of the cosmic background radiation by Arno Penzias and Wilson, as well as observation of distant galaxies. Penzias and Wilson got the Nobel Prize for this discovery in 1978. The rate of expansion is given by Hubble’s law. The Hubble rate of expansion increases as the square of the temperature if all the particles are relativistic, and slightly slower if they are non-relativistic. As the universe is cooling down, this expansion rate is slowing down with time. It has been realized for almost 40 years that, if this Hubble rate represented the expansion rate from the beginning of Big Bang until now, there would be some difficulty with our understanding of the universe’s history. This led to the suggestion that there is a different expansion phase of the universe before the Hubble rate of expansion began. This is a phase of extremely rapid expansion and is called the “inflationary” expansion phase.

17.1 Inflation: One Beginning Before Another Beginning Why is inflationary expansion needed? There are several reasons for this. If the expansion of the universe was given by the Hubble rate all the way from the beginning of the universe, we would encounter some problems. The first is a causal connection problem among different parts of the universe today. Observations say that the universe is almost isotropic in the temperature of © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2_17

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the cosmic microwave background, i.e. temperature is almost the same in every direction. This means that all parts of the universe must have been in contact for a long time since the beginning. This is necessary to make the temperature the same in all directions. This is hard to understand, except as an accident, in the Hubble expansion picture. Given information about the size of the universe now, we can extrapolate it to the earlier epochs of the universe, by using the Hubble rate of expansion to get the size at an earlier age. If Hubble expansion were the only type of expansion of the universe, the universe at an earlier time (such as the time of Big Bang nucleosynthesis) would have a much smaller size than the expected extrapolation of the current size and thus would only occupy a small fraction of this extrapolated size. There would then have to be many different pieces to the universe in the beginning. This make it hard to understand how the whole universe could have the same temperature since there would have been no “overlap” between different disconnected parts. To resolve this problem, Alan Guth [58] suggested that there was a period of extremely rapid expansion in the beginning stage of the universe, which increased the size of the universe so rapidly that all parts of the universe overlapped and got causally connected. Things happening in one part of the universe influenced those in other parts, as we observe today from the isotropy of the microwave background. If one segment of the universe is isotropic, all other parts would also be isotropic.1 This paper was followed up by Andre Linde, Andreas Albrecht, and Paul Steinhardt [72], who proposed a newer and more refined version of the model, explicitly discussing how inflation would end. A poor analogy to causal connection through inflation can be seen from the following example. Imagine living in a small cubicle with walls all around it in a big hall full of walled cubicles. In such a setting you do not know what is going on in the other corner of the big hall if you are far away from it. On the other hand if there is no wall around the cubicles, you can see everything and know everything and react to everything. Inflation is like removing all the walls and making a whole big hall (the universe) into one large open area. Another major puzzle of the Big Bang theory is that the universe in the beginning was extremely smooth and right now it is extremely non-smooth. There are stars, galaxies and clusters with voids in between, making the universe anything but smooth. How did that happen? The inflation theory seems to provide a solution to this problem. During the period of inflation,

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The Guth paper came in July, 1980. The basic idea of inflation was there in several earlier papers as well, see [64] for a history.

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some small fluctuations in density naturally developed, as would be the case in any fluid. They eventually grew to become galaxies and clusters, etc. at a later stage of the universe. There are also other conceptual problems with the standard Big Bang expansion, i.e. the universe appears to be nearly flat now (not like the surface of a globe but rather like the surface of a dining table), as opposed to Hubble’s expansion theory, which would make it look like a globe. For the universe to appear flat, one has to adjust the curvature very precisely. Inflation solves this problem by making the universe flat, due to its rapid expansion right from the beginning. The inflation ends at a very early moment of the universe—nobody knows when though. Different theories say it ends at different stages and it is a very active area of research right now. After inflation ends, familiar and new kinds of matter start to appear in the universe in a process called reheating in cosmology jargon, and the universe resumes Hubble expansion. Thus, one beginning of the universe is a very rapid expansion via inflation, and as inflation ends, there is another beginning, the beginning of Hubble expansion, which continues until now. Another new accelerated expansion has been discovered during the past two decades, which started in recent times due to the existence of a small cosmological constant. This expansion is not related to the early universe expansion via inflation. Thus the universe has undergone multiple phases in its evolution before it reached today’s state. This will continue as the universe ages further (Fig. 17.1). Inflation is considered a very successful theory and is now a part of many physics textbooks. There are however many objections to the way inflation is supposed to occur. For example, there are many possible ways to get inflation from a starting theory, but only a small number of those theories are observationally consistent. Furthermore, it has been shown that inflation once started does not end everywhere, but only in a small patch of the universe. Also, it is not clear that there is any way to definitively test inflation, but nonetheless, it is an interesting and useful paradigm which has cleared up many unpleasant issues with the Big Bang theory. For a popular exposition of the inflation idea, see [59]. A key question still remains unanswered about inflation—what is the true mechanism behind it? Is there another object like the Higgs boson that is driving inflation, or is it something else? Could it even be that inflation is not the right theory for the beginning of our universe? We have to wait for the answer to these questions. Thus, the jury may still be out on inflation as a theory of the beginning of the universe. At the moment, however, inflation

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Fig. 17.1 A pictorial depiction of inflation. The first jump in the picture is the beginning and end of inflation and the rest of the picture is Hubble expansion until today. Source: Wikipedia.org

may be the best theory we have to understand the beginning of Hubble expansion of the universe.

17.2 Beginning of the Hubble Era after Inflation The next important milestone in the history of the universe is the time when asymmetry between matter and anti-matter was created. There is a lot of evidence in favor of the fact that the universe consists of only matter (protons, electrons, neutrons) and no anti-matter (no anti-protons, positrons, etc.). Cosmic rays contain a small amount of anti-matter that can be explained by production from energetic proton–proton collisions in the space. There is no other known place in the universe which contains anti-matter. In fact, if there were anti-matter in as much abundance as matter (a symmetric universe) close to each other, there would be annihilation and explosion, making the universe completely empty of matter and full of radiation. If there was antimatter isolated in one area of the universe and matter in the other, then there would be an asymmetry in the universe that should be reflected in the cosmic microwave background observations. But no such asymmetry has been found. The amount of matter in proportion to radiation is very small indeed—about one part in a billion parts of radiation is matter.

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Could one argue that the matter was put there by some unknown hand in the beginning and we see it today? That idea would also be untenable if the inflationary picture is correct. The point is that at the beginning of the Hubble expansion after inflation ended, there was hardly any matter or anti-matter in the universe (or at least whatever there was too highly diluted to be of any consequence). Inflation essentially “vacuum cleans” the universe of all matter due to its huge sudden expansion. So where did matter really come from, and at what point in the evolution of the universe was this matter created? Some believe that the neutrino story may also have something to do with that, although it is far from clear that this is the real theory, since there are many plausible ways to generate matter–anti-matter asymmetry. We discuss this in Chap. 23.

18 From Quarks to Protons and Neutrons and Then to Helium and Beryllium and the Dance of Atoms

The period from inflation to the beginning of the Hubble phase of expansion takes only a minute fraction of the age of the universe—about 10−45 s to somewhere around 10−30 s or so. After the Hubble expansion begins, again the universe rushes through various events where it starts from one phase and enters another, depending on the kind of symmetries at play in the early universe. Each kind of symmetry represents a point where the so-called phase transition takes place. A simple and familiar example of phase transition is something we see every morning at breakfast time when we boil water to make tea. When water boils, it goes from liquid to vapor phase. A similar thing happened at least twice or could have happened more often during the Hubble expansion phase of the universe. In one of those phases, the weak bosons W and Z get their mass since they are massless prior to that time. This happens when the universe is about 10−10 s old. This is followed by another phase transition around 10−4 s when the quarks lose their separate identity and bind together to form protons and neutrons, pions, K-mesons, etc. Then when the universe is about a minute old, something very important happens: what physicists call Big Bang Nucleosynthesis.

18.1 Big Bang Nucleosynthesis Before the universe is one minute old, the number of neutrons and protons remains almost same, due to back and forth reactions involving the weak force that changes a proton to neutron and vice versa. Due to the weakness of the © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2_18

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weak force, somewhere near the time when the age of the universe is a minute, the Hubble expansion rate overtakes the the rate at which weak forces can change the neutron to protons by reactions like νe +n → e− +p, etc. After that time, weak interactions cannot change the protons to neutrons and vice versa since weak interactions become too slow compared to the expansion rate of the universe. The number of neutrons and protons at that point remains frozen and as the universe cools a bit more, these neutrons and protons undergo nuclear attraction and combine two protons to two neutrons to form the helium nucleus. Calculation shows that there are more protons than neutrons at the time when neutron and proton numbers freeze. Since it takes an equal number of protons and neutrons to make a helium nucleus, some protons are left over together with the helium nuclei. The leftover protons would form hydrogen atom later on in the history of the universe and the helium nucleus would form a helium atom. The formation of atoms happens much later. This leads to roughly 75% of the mass of the matter as hydrogen and 25% of mass as helium nuclei and a little bit of other nuclei, which are created from further nuclear reactions. The latter reactions form smaller amount of lithium and beryllium, and also some small amount of deuterium whose nucleus has one neutron and one proton. That is all the nuclei that form at the time of Big Bang Nucleosynthesis (BBN), as this epoch is called. They continue that way until later stage in the evolution of the universe. The basic theory of BBN was proposed by Ralph Alpher, Hans Bethe, and George Gamow (the famous Alpha Beta gamma paper). BBN is one of the major triumphs of particle physics and cosmology. It predicts the abundance of deuterium and helium quite accurately and is in remarkable agreement with observations. This is especially notable since the abundance of deuterium is about 10,000 times smaller than that of helium. The BBN model also predicts the lithium-7 abundance (Fig. 18.1). This prediction however disagrees with observations by a factor of four. That is considered one of the puzzles that may be a hint of new physics beyond the standard model (at least some people think so). Thus the neutrino is the key particle in the formation of hydrogen and helium, the two starting members of the periodic table. As noted, at the epoch of BBN, no atoms can form since the temperature of the universe is about ten thousand million degrees and at that temperature, the electrons are free and much too energetic to bind with nuclei to form atoms. They get ionized as soon as they bind to form an atom. But as the universe cools to about 100,000◦ C, the electrons are moving slowly enough not to be able to get away from the attractive force of the proton and would then form atoms (hydrogen atoms, helium atoms, etc.). The age of the universe at that time is about 100,000 years, still pretty young compared to

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Fig. 18.1 This table gives a summary of some nuclear reactions during the BBN epoch and how elements helium-4, deuterium, lithium, and beryllium are formed starting with neutrons and protons: Note how both weak interaction (e.g. reaction1) and nuclear reactions (reactions 2–12) are involved together in this process. The arrows denote the change from one nucleus to another by the reaction whose number is given above the arrow. For example, to go from deuterium (D) to 3 He, the reactions involved are nuclear reactions 3 and 4

its age now (the universe is 13 billion years old today). Things happened very rapidly (almost instantaneously) until BBN and a little slower after that. Then things move much slower once the formation of stars and galaxies starts. Pretty much the entire periodic table remains unexplained at this stage and has to be understood from subsequent developments in the universe. The important lesson, however, is that we are getting a glimpse of how important neutrinos are in starting the building up of the periodic table beginning with BBN. Also it is important to emphasize that if the weak force had a different strength, the ratio of helium to hydrogen would be different and the universe would look a whole lot different. For instance, if weak forces had ten times less strength, the number of neutrons would be closer to the number of protons and therefore the universe afterwards would be more helium than hydrogen. This would mean the Sun would probably have burned out by now–much quicker than is currently expected (which is a few billion years) and there would then be no life on the Earth. Thus what happens at the sub-atomic level is enormously important to the Earth and the universe today.

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18.2 Formation of Galaxies There are four types of galaxies in the universe: spiral, barred spiral, elliptical, and irregular. How did they all form? The details are still in the research stage but there is a broad picture. When the universe was about 5000 years old, there was more energy in matter (like protons, helium, dark matter, etc.) than radiation (light) and as the universe cooled, some of this matter collapsed under gravity to form larger objects. The dark matter of the universe (about which we talk later) had so much gravitational attraction that it attracted baryons, hydrogen, and helium and started the formation of stars and galaxies when the universe was about 700 million years old. Star formation started soon after and peaked when the universe was about 3 billion years. The solar system formed in a few billion years and it is now four and half billion years old. There are two competing theories for how galaxies formed: one says that galaxies were born when large masses of dust and gas collapsed under their own weight and a second one says that small clumps of matter first formed and then merged with each other to form galaxies. The Hubble Telescope has found several such small clumps, providing evidence in favor of a merger of small clumps to form galaxies. Probably, the truth is a combination of both theories. It is known from observations that the overcrowded galaxies in the universe often merge and form larger galaxies. For instance, the Andromeda Galaxy is so close to the Milky Way Galaxy that in four to six billion years, it will collide with our galaxy and the most likely outcome is a larger galaxy, which is likely to be an elliptical galaxy. The process of galaxy formation goes on.

18.3 Cosmic Microwave and Neutrino Backgrounds The early universe was full of very hot (high energy) photons, which were constantly creating particle and anti-particle pairs. The process of photons changing to particle–anti-particle pairs went back and forth. Slowly the heavier particles and anti-particles became rare as the temperature of the universe fell below their mass and became a negligible fraction of the universe. The back and forth process then stopped. The lightest charged particles in the universe are the electron and positron and their mass is half a million electron volt (i.e. one two thousandth of proton mass). This is less than the temperature of the universe when Big Bang Nucleosynthesis took place. The back and

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forth between two photons to electron–positron production therefore went on until the universe’s temperature fell below the mass of electron and the age of the universe was a few hundred thousand seconds. After that particular period of the universe, electrons and positrons became scarcer and the photons floated freely as the universe cooled. When the universe was about 40 years old, electron–photon collision became too weak to change the energy of the photons. The light wavelength after that got stretched out with the universe’s expansion. Light got less and less energetic until the present time when the temperature is about 2.7 K. This process led to about 400 photons per cubic centimeter of the present universe. Such low energy (or microwave energy) photons are present everywhere in the universe today and were detected by the famous Penzias–Wilson Bell lab experiment in 1964. They used a horn antenna in Holmsdale, New Jersey, to detect radiation from between galaxies. They detected a persistent noise, which turned out to be a remnant of the red shifted radiation from the early stage of the universe. In recent years, this experiment has been improved further, leading to finer details in the radiation patterns. More precise studies by the recent WMAP and Planck experiments of the cosmic radiation show that it is now highly isotropic. There is however an anisotropy (or direction dependence) of radiation, about one part in 100,000. The later anisotropy is linked to the formation of structure, which induces non-uniformities to the radiation. Does one expect a cosmic neutrino background similar to the cosmic microwave background (CMB)? The answer is yes. In many ways, the evolution of neutrinos and photons is similar, except for the timing of when they became “decoupled” from the cosmic soup and started their free expansion. The neutrinos “fell behind” the cosmic expansion when the age of the universe was one second. Ever since, they have been freely and slowly expanding, being less and less energetic as their wavelength stretches with the expansion of the universe. They also became less abundant as the universe got older. At the time when the photons decoupled from the cosmic soup, the temperature of the neutrinos went down a bit, and the current temperature of the neutrino background is about 2 K compared to the photon temperature, which is about 3 K now. Just like the microwave background, there is a neutrino background now pervading the entire universe. In principle, they could be detectable, but due to their low energy and very weak interaction, they rarely scatter against matter, making their detection much harder.

19 Stars as the Cooking Pots for Heavy Nuclei

The universe is full of many elements heavier than hydrogen, helium, lithium, and beryllium, which were produced at the time of Big Bang Nucleosynthesis, a major milestone in the history of evolution of the universe. Where did the heavier elements come from, if the Big Bang cosmic evolution only produced the lightest three or four elements given above? This question has occupied the minds of physicists for many decades. Indeed, as we will see, there is a lot of truth to this statement. A lot about how elements are made of stardust has been understood but a lot remains to be resolved. In fact, late astronomer Carl Sagan once said, “The nitrogen in our DNA, the calcium in our teeth, the iron in our blood, the carbon in our apple pies were made in the interiors of collapsing stars. We are made of “star-stuff.” To discuss this, we first note that Fig. 19.1 shows the abundance of some low atomic number heavier elements in the solar system. We then come to the discussion of the remaining heavy elements.

19.1 Stellar Nucleosynthesis After the Big Bang Nucleosynthesis, the next stage in the synthesis of nuclei takes place in stars like the sun and others. The formation of stars takes place when giant clouds of hydrogen get pulled together by gravity. Slowly, the resulting cloud starts to spin, as a result of the strong pull of gravity and other forces. This increases the temperature of the gas to about thirteen million degrees, when hydrogen fusion to helium occurs. The cloud glows, and thus © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2_19

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Fig. 19.1 Abundance of elements in our solar system. The peaks in the figure are elements with even atomic numbers such as carbon, oxygen, neon, sulfur, etc. The lowest points are those with an odd number of protons, such as nitrogen, fluorine, sodium, aluminum, etc. These elements are formed because there are neutrinos. The helium that is formed is not a new element since it was already created at the time of the Big Bang Nucleosynthesis. It not only adds to the existing helium in the universe but more importantly, it starts a process that leads to elements that are newer and heavier. Source: Wikipedia.org

is born a star, called the main sequence star. This is where the first large-scale formation of heavier nuclei starts. To understand how stars “cook” hydrogen to heavier elements, one has to understand how the stars maintain their stable shape for such a long time (millions and billions of years). The gravity would tend to pull together the stellar matter and make the star collapse to the center if nothing else was happening in the star. This is because of the intrinsic property of gravity, which is always an attractive force and increases in strength as the mass increases. What keeps the star from falling under its own weight is that at the center of the sun or a star, hydrogen is constantly fusing to form helium, because of the high temperature and high density. In that process it gives out light and heat. In every weak nuclear reaction we have 4p + 2e− → H e4 + 2νe +heat. The amount of heat generated in this reaction is nearly equivalent to two hundred sixty billion degrees Celsius. The light and heat then push the matter of the star away from the center and keep it from falling under its own weight. Thus, there is a constant tug of war between gravity and nuclear push from the center. Most of the light and heat get out, but more of it is produced as the fusion process continues (Fig. 19.2). The heat and light slowly diffuse through the solar matter and come to the surface, traveling to us as starlight (sunlight). The bottom line is that the fusion process continues until all the nuclear fuel at the core is exhausted. How the new and heavier elements form is the next part of the story. To understand what comes next, we need to understand what happens to a star after all the hydrogen fuel has been used up. How long it takes depends on the mass of the star. For our sun, it will take about 5 billion years. After

19 Stars as the Cooking Pots for Heavy Nuclei

Fig. 19.2

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Nuclear processes during stellar burning

that, there will not be enough radiation coming out of the core of the star to hold the matter from falling under gravity to the center. The stellar core is not hot enough to start the process of helium fusion reaction, which could provide extra energy to prevent gravitational collapse of the core. In the absence of any pushing from heat and light, the core with helium contracts under gravity whereas the hydrogen on the surface, without any boundary to hold it, expands, cools, and becomes red. The mantle can expand quite far. This is called a red giant star. When the sun becomes a red giant, its mantle is expected to expand so much that it will likely engulf the nearby planets like Mercury, Venus and reach the Earth with intense heat. The surface temperature of the mantle will be nearly 2200◦ C. Clearly, humankind would have to migrate to other planets, which might have become warmer by then. At the next stage, the core of a red giant star, which has helium, has fusion reactions due to contraction under gravity whereby three helium nuclei fuse to form a carbon nucleus. Thus carbon, which is most of our body and a lot of our food, is formed from the star. This again releases heat and light, which balance the pull of gravity and keep the red giant in shape until all helium has been used up. That takes a shorter time (a few million years) than it takes to burn out the fuel in the sun and other main sequence stars. After all the helium has finished fusing to carbon, the same process that happened to a star repeats for the red giant. In this case, if the star originally was more massive than the sun, say five times or more, the carbon atoms fuse with helium to give oxygen. After that, other fusion processes produce nitrogen, sodium, and

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neon and finally silicon and then more silicon and sulfur. Finally, silicon fuses with helium to give argon, calcium, titanium, chromium, iron, and nickel. In we give the required conditions for various stages of stellar nucleosynthesis to proceed. With iron, the fusion process stops because unlike the other less heavy elements, when iron fuses, it does not generate extra heat; rather, it requires heat to fuse (such processes are called endothermic) Fig. 19.3. Thus production of heavier elements requires a different site in the universe to be produced. If a star is more than eight times more massive than the sun, after it reaches the stage of iron in the core, no further fusion can generate radiation and the star will undergo a big explosion. At that stage, its core will collapse, giving out more than 90% of its energy in the form of neutrinos and a flare-up of its outer layers producing a big light show called Supernova. It will distribute the new elements and whatever other heavy elements formed prior to that, into the environment around it. The core, on the other hand collapses to form either a neutron star or a black hole depending again what the original mass of the star was prior to explosion. The first supernova was observed by Chinese observers in 185 AD and may also have been observed by Italian astronomers. Then in 393 AD, Chinese astronomers may have seen another supernova in the constellation Scorpius. Another widely observed supernova was in 1054 AD in the constellation Taurus. Supernovae tend to occur every half-century in a galaxy of the size of our own Milky Way Galaxy. In the whole universe, pretty much every second, there is a supernova explosion. It is just that they are not always close to us to be observable. So far, we have covered up to iron in the periodic table, whose mass number (i.e. the number of protons and neutrons together) is near 56 and which has 26 protons in the nucleus, much less than half the proton number and mass number of the last element known to date. How the remaining elements formed is a matter of great debate right now, although there are some ideas and possibly some clues to what really happened. Just to close the section, another type of supernova occurs if a white dwarf star whose mass is less than 1.4 solar masses (the Chandrasekhar limit) pairs up with a red giant. In this case, the white dwarf will suck in mass from the red giant until its mass exceeds 1.4 solar masses or the Chandrasekhar limit, in which case it will go unstable and explode, leaving interstellar dust that contains carbon, oxygen, and nickel. Thus, again some new elements have been formed in the process. All these are collectively called stellar nucleosynthesis that follows the primordial BBN process (Fig. 19.3).

19 Stars as the Cooking Pots for Heavy Nuclei

Fig. 19.3 org

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Why stellar burning stops when an iron nucleus is reached. Source: Wikipedia.

19.2 Still Heavier Elements Where did the elements heavier than iron come from? Where did the jewelstore elements like gold and platinum come from? How about copper in the electrical wiring? How about mercury? Attempts to answer these question are still ongoing, with many astronomical observations of the abundance of different elements in different stars and galaxies. We will give a summary of current understanding in this chapter [74]. One of the basic mechanisms for growing heavier elements is as follows: in some stellar sites, if there is a huge excess of neutrons surrounding the iron nucleus and other elements with a comparable atomic number to iron, then some neutrons can fuse with existing nuclei in the compact high temperature environment to form an isotope with one extra neutron. If the resulting isotope is stable, it absorbs one more neutron, forming a neutron rich isotope that eventually becomes radioactive and unstable. This unstable nucleus then decays weakly with the emission of electron and anti-neutrino, changing in the process one neutron inside the nucleus to a proton. This leads to the formation of the next element in the periodic table since its proton number (atomic number) increases; (N + Z) + n → (N + 1, Z) → (N, Z + 1) + e− + νe . This process repeats itself as many times as allowed by the laws of nuclear forces to generate heavier elements until the final nucleus is unstable.

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Clearly, for this process to occur, one just cannot have one extra neutron around a nucleus. The fusion process will then take too long. The key question then is how many neutrons must be there per cubic centimeter surrounding a nucleus (N, Z) for this neutron absorption process to occur in a short time? It turns out that if the number of neutrons per cubic centimeter is in excess of millions to billions, with a temperature of 100 million degrees Celsius, then the process of generating the heavier nucleus is possible in a short time span. If the neutron capture process is slow compared to the beta decay process, only certain nuclei are produced and this process is called an s-process (slow process) for short. This generates only about half the elements beyond iron. This can happen in the later stages in the evolution of stars with a mass up to 10 solar masses. The s-process is successful because there is enough time for the isotope formed from the capture of a single neutron to decay before another neutron is captured, altering the radioactive property of the isotope. To remind the reader, an isotope of an element has more neutrons in the nucleus of that element than the usually more abundant nucleus with the same number of protons. Iron, for example, has four naturally occurring isotopes and several unstable ones. If the building up process reaches a stage such that the nucleus undergoes alpha decay, then we come back to a lighter element and the s-process stops. Typically an s-process stops with elements lead, bismuth, and polonium. Lead has Z = 82, bismuth has Z = 83 and polonium has Z = 84. Recall that iron has Z = 26. That is quite a progress though still not a complete understanding of the element formation, since it does not explain many familiar heavier nuclei seen in nature such as radium (Z = 88), thorium (Z = 90), uranium (Z = 92), plutonium (Z = 94), etc (Fig. 19.4). When in an astrophysical environment, the number of neutrons per cubic centimeters is a lot higher than a million, say about 1020 neutrons (i.e. 100 million trillion) per cubic centimeter; there, the neutron absorption process occurs more rapidly. This is called r-process (r-for rapid) and this environment generates the remaining half of the nuclei. Such environments are possible only inside supernovae or inside binary neutron star mergers. For a long time it was believed that supernovae were the main sites for r-process nucleosynthesis since calculations showed that there were a huge number of neutrons in them. However, supernovae have a lot of neutrinos as well in their mantle. These neutrinos convert most of these neutrons to protons, which then fuse with two more neutrons to make an alpha particle. This so-called alpha effect depletes the number of neutrons that could have helped the r-process. This makes the buildup of heavier elements difficult in a supernova. There are suggestions that if there is a sterile neutrino (dark neutrino, see below), then many of the active neutrinos could oscillate to the sterile neutrino, reducing the number of neutrinos and thence preventing the so-called alpha effect. Lately, evidence

19 Stars as the Cooking Pots for Heavy Nuclei

Fig. 19.4

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Illustration of a binary neutron star merger. Source: Wikipedia.org

has been emerging in favor of another scenario where a rich neutron source is a binary neutron star merger. Such events are more likely sites for generating such a huge number of neutrons that will speed up the r-process (Fig. 19.4). There is a great deal of attention on these processes now. The neutron stars were predicted to exist very early on, soon after the discovery of the neutron. Baade and Zwicky predicted that the neutron stars might be the end product of solar evolution. Their existence was proven in the 1960s, with the discovery of pulsars by Jocelyn Bell Burnell in 1967. Since then, many such pulsars have been discovered, including some which appear as binary pulsars with another neutron star as a companion. A famous example is the binary pulsar discovered by Hulse and Taylor, for which they were awarded the Nobel Prize. In the neutron star merger situation, the problem coming from the neutrinos present in supernova mantle is not a major obstacle to element formation. The evidence in favor of a binary neutron star merger playing a role in heavy element formation came from observations in an ultra faint dwarf galaxy called reticulum II. More precisely, it seems to have provided evidence against supernova explosions being the site of the r-process for the formation of heavier elements. Reticulum II is a small dwarf galaxy, discovered in 2015 during the dark energy survey. It is part of the local group of galaxies about 98,000 light years away from us (about 30 kps). It is loaded with heavy elements of the kind which are hard to produce in the laboratory and also which cannot be explained by the s-process nucleosynthesis. The way it gave a clue to the heavy element nucleosynthesis is as follows: in this faint galaxy, there are not that many stars but there have been observations of very heavy element emitted light (such as from europium, gold, and barium) as

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was just noted. This then points to the fact that there must have been an r-process in this galaxy. However, if the r-process took place in supernovae in this galaxy, that would require too many supernovae to produce the amount of these heavy elements observed and there are not enough stars in them to meet the requirement. So the r-process most likely took place in a binary neutron star merger, and one such merger is enough to produce the amount of heavy element abundance observed. The fact that neutron stars merge is also now observationally established by the gravitational wave signal from a kilonova event by LIGO and Virgo (GW170817) observatories in 2017. This makes the case stronger for neutron star mergers as the source of the r-process. The figure below illustrates a binary neutron star merger (Fig. 19.4). The scientists are working on how the details of r-process actually take place in a binary neutron star merger. To quote the authors Frebel and Beers “Nuclear physicists are still working to model the r-process, and astrophysicists need to estimate the frequency of neutron-star mergers to assess whether r-process heavy-element production solely or at least significantly takes place in the merger environment.” To be sure, there are also several other sites which are under active consideration as active r-process sites for heavy nucleus formation [48]—for instance, binary black hole-neutron star mergers. Another possibility is the so-called magneto-hydrodynamic jet model where magnetic turbulence in a supernova leads to an ejection of neutron rich material in a jet. This does not have the complication of excessive neutrino density of the conventional supernova r-process and can therefore facilitate heavy nucleosynthesis. Other possibilities include carbon-enhanced metal-poor (CEMP) stars in the Galactic Halo (the environment inside a galaxy) or collapsars (collapsers are failed supernovae with a black hole at the center). Uncovering the sites of the r-process is an extremely active area of research and will go on for a while before we know the final answer to this.1 Also, some elements are formed by cosmic ray collision with light nuclei in the stars, although, this is only a small contribution to the abundance of elements like lithium, beryllium, and boron. The cosmic rays come mostly from extra-galactic space and are quite energetic. So they tend to break up nuclei. Astronomy research that goes on in this field requires meticulous detective work. It involves searching around our galaxy to locate stars with a high abundance of certain heavy elements and looking at the history of the star to determine what could have happened to create this environment. It must be stated though that despite all the active heavy element formation in various sites in the universe, most of the universe is still only hydrogen and helium, with only 2% being heavier elements. 1 A parsec is about 3.2 light years or 3 × 1018 cm—i.e. light takes 3.2 years to travel the distance of 1 parsec.

20 Neutrino Mass Hints at Mirror Symmetry in Nature

The first thing the discovery of neutrino mass says is that the standard model which is so successful in describing so many phenomena is an incomplete theory. There must be new physics in order to give the neutrinos a nonzero mass. What is the nature of this new physics? In previous instances of understanding new physics, the symmetries have played a role. We saw from the history of the standard model that the V − A theory suggested a new kind of local symmetry as early as the 1960s, and eventually that got confirmed, leading to a new successful theory of the universe. Could there be something similar happening now? Is the neutrino mass also hinting at a new symmetry of the universe? If so what is it? Let us explore this possibility. We summarize the speculations in this chapter.

20.1 Back to Symmetries For a discussion of symmetries and symmetry breaking, see Sects. 11.3 and 11.4 where some examples of symmetries and their breaking were given. One can give other examples of symmetric situations: for instance, an empty circle has a continuous rotation symmetry, which is a larger symmetry than the “empty” stop sign of Chap. 11, the latter having only an eightfold rotation symmetry. A spherical soccer ball has a spherical symmetry. The above symmetries, as well as different ones like them, have played a fundamental role in understanding the basic laws of nature, as we already saw from the discussion of the standard model. The reason symmetries are important is that if the basic force laws © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2_20

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have a symmetry, then practical systems which are based on those force laws will have that symmetry reflected in their properties. For instance, laws of electricity are symmetric under reflection in a mirror, as well as rotation around an electric charge. This is reflected in the value of the electric field which is same on both sides of a charge (mirror symmetry) and all around the charge (rotation symmetry). Similar rules apply to gravitational force. By the same token, if we do not know the basic nature of a force, its symmetries can be guessed from the way the processes governed by the force behave. When not much is known about the force, symmetries provide a clue to determine the exact nature of the force.

20.2 Mirror Symmetry and Weak Force Let us delve a bit into mirror symmetry which is connected to neutrino mass. It is a symmetry like one of the above symmetries, which had always been thought to be a fundamental symmetry of nature before the 1956 Lee–Yang revolution. The meaning of mirror symmetry is that all physical processes look the same when reflected in a mirror. This is obeyed by electric forces, which look the same in a mirror, as just stated. The atomic light emission lines obey that symmetry, a fact which was known since Otto Laporte enunciated it in 1925. As noted in Sect. 5.5, it was also known to be valid in nuclear forces and the force of gravity and thus it was thought that every kind of force in nature would have mirror symmetry; but as we now know, the weak force is the odd one out and does not obey the mirror symmetry.

20.3 Mirror Symmetry and Neutrinos How is the mirror symmetry breakdown (parity violation) connected to neutrinos? Again, it all comes from experiment. To repeat some of the earlier discussion, parity violation was confirmed by Wu et al, in the decay of cobalt to nickel, an electron, and an anti-neutrino. From this experiment, one could not tell if mirror symmetry breaking had anything specific to do with neutrinos. But a major understanding came the following year when Goldhaber, Grodzins, and Sunyar carried out an experiment involving the europium atom. This atom decays by capturing one of its own electrons and emitting a neutrino and a photon. This is also a weak force mediated processes. Since total spin in this situation must remain same, both in the beginning and at the end, and the initial total spin is zero, the measurement of the

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photon spin would be just right to compensate for the spin of the neutrino (or the helicity which is spin alignment of the neutrino with its direction of motion). They found that in this decay, only one kind of neutrino, called a left-handed neutrino, emerged (as already explained, left-handed means the spin of the neutrino is opposite to the direction in which it is moving). If mirror symmetry was a good symmetry, an equal number of neutrinos with both left- and right-handed helicity should have been seen, but they were not. This proved that the weak interactions do not respect mirror symmetry and it must have some connection to neutrino helicity. Also it was found that in all beta decay type processes, only the same left-handed helicity neutrino was emitted. If a beta decay emitted an electron, the corresponding neutrino would be an anti-neutrino and its helicity is opposite to that of the the neutrino; thus, the anti-neutrino would be right-handed. This suggests that the universe only has left-handed helicity states of neutrino and right-handed helicity states of anti-neutrino, but not right-handed neutrinos and left-handed anti-neutrinos. This is a profound discovery, since all other matter particles that we know, like electrons, protons, etc. have both left- and right-handed helicities. They are all known to be massive, whereas the neutrinos in the universe have only one kind of helicity. Why is the neutrino so special?

20.4 Mass and Helicity Recall our discussion of helicity in Chap. 2. This is a concept which says how the spin is aligned with respect to its velocity (speed and spin direction together), and it is a very important concept in theoretical physics. As we will see, this will help us understand and appreciate the role of neutrino mass in determining the direction of physics that goes beyond the standard model. The mass of a fermion i.e. a spin one half particle is intimately connected to its helicity. This is explained in Fig. 20.1. Let us analyze Fig. 20.1 where the twirling lines represent the spin direction and the straight line represents the direction of velocity. The principle of relativity says that if a particle has mass, it can move at any speed below the speed of light, whereas if a particle has no mass, it can move only at the speed of light. No less or no more. Now, coming to the Fig. 20.1, it shows a massive particle moving from left to right at some speed, with its spin twirling to the left, and this is a particle with left-handed helicity. But since it has mass, one can look at the same particle from a rapidly moving train, speeding to the right faster than the particle. From the train, the particle will look like it is moving to the left, but its twirling direction is still the same as before. This means that from the moving train, the particle looks right-

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Fig. 20.1

A particle with mass can flip its relative speed direction with respect to spin

handed. Thus a left-handed particle became a right-handed particle. Since the theory of relativity says that physics does not change from one moving frame to another, both helicity states must be realized in nature. The cartoon shows both the states below the picture, to indicate that a massive spin half state must have both left- and right-handed helicity states. We will call the right-handed helicity and left-handed helicity states mass partners. There can be another way two opposite helicity fermions can come about: recall the discussion of anti-matter which said that matter and anti-matter have opposite attributes. In other words, if a matter fermion has left-handed helicity, the anti-matter fermion will have right-handed helicity. So in principle, a matter fermion and anti-matter fermion can together form a mass, even if the right-handed fermion does not exist as a separate state in the universe. In this case the particle and its anti-particle will be mass partners. The problem however is that, if a particle has electric charge, then the anti-matter has opposite charge and therefore they cannot be mass partners, because by going to a rapidly moving frame, one can break electric charge conservation, contrary to all observations. However for neutrinos which do not have electric charge, no such problem arises. Such masses are called Majorana masses and are discussed in a few subsections later in this chapter. Now look at Fig. 20.2 where a spin half particle without mass has its spin and velocity shown. This particle is moving at the speed of light and is a left-handed fermion (or neutrino). Since no train can travel faster than light, the left-handed helicity particle will always remain left-handed in any frame, no matter how fast it moves. That means that to describe the physics of such a particle, one needs to have only one state in the universe. This is the story of a massless neutrino i.e. it exists only as a left-handed state without

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Fig. 20.2 A particle without mass always travels with the speed of light, the highest speed possible in the universe, and therefore does not have a state with opposite spinspeed relation (chirality)

contradicting the theory of relativity, whereas all other particles in the standard model which have mass appear have to have both left and right helicity states, to be in agreement with the theory of relativity. The discovery of neutrino mass therefore means that at least some right-handed neutrino helicity states must be present in nature. This is a major change to our thinking about the neutrino, caused by the discovery of neutrino oscillation.

20.5 Mirror Reflection and Neutrino States and Nature of Weak Force Under mirror reflection (also known as parity), the left-handed helicity state of a fermion goes to the right helicity state. The left-handed helicity neutrino participates in weak forces as described by the standard model, whereas the right-handed helicity neutrino does not since it never appears in any weak decay. For example, if somehow a left helicity neutrino produced in beta decay is “rotated” into a right helicity neutrino (also called right-handed neutrino), the later suddenly will not have any weak force and will move around freely. This is a peculiarity of the weak force. A curious thing about forces is that the ones that respect mirror reflection symmetry (as do the strong force, electric force, etc.) are the ones coupled to particles with mass which have both the left and right helicity states present in the universe. And also, they couple to both helicity states of these particles with equal strength. These forces (strong, electromagnetic) do not affect the neutrinos which come only in the left-handed helicity. On the other hand, the weak force which breaks mirror reflection symmetry couples not only to all other fermions just mentioned which have mass, but also to the neutrino which in the standard model has only left-handed helicity. The weak force law states that it couples asymmetrically to all the particles. Thus it is plausible to assume that since neutrinos have mass, there is a right-handed neutrino, and therefore at some higher energy scale not yet explored, the weak force behaves more like the other forces and becomes mirror

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symmetric. In other words, it couples with equal strength to both the lefthanded neutrino as well as the right-handed neutrino. This is the point of view that was advocated in the so-called left–right symmetric models [81] around 1974–1975, which will be discussed in the next chapter.

21 Mirror Symmetric Weak Force and Neutrino Mass

The mirror symmetric theory of neutrino mass (or left–right symmetric theories as they are called in the literature) was proposed in 1974 and 1975 to understand the origin of mirror symmetry breaking by the weak force. Its connection to neutrino mass came later in 1979. Why was it necessary to think along these lines when the standard model is so successful? Sometimes, speculations about the next level of physics are not determined by experimental facts, but rather by expectations based on aesthetic considerations and conceptual shortcomings. For example, a huge amount of activity right now focuses on the attempts to understand why the mass of the Higgs boson does not become arbitrarily large due to quantum corrections, although from a strictly experimental point of view, there is no need for such thinking. The discovery of the weak force carriers, the W and Z bosons, at collider facilities at CERN, as well as other evidence in the domain of low energy weak force physics has provided spectacular confirmation of the standard model. The 2012 discovery of the Higgs boson was the crowning success of the model. There are, however, conceptual problems with it—one is the aforementioned gauge hierarchy problem or the Higgs mass problem. But more to our concern is that the weak forces were known since 1956 to break mirror symmetry, and since 1957, to involve the V − A type of interaction as suggested by Marshak, Sudarshan, Feynman, and Gell-Mann. How is this fact handled in the standard model? The answer is that it was put into the theory by hand by simply choosing the gauge forces that were induced by the charged W bosons. They were chosen to act on the quarks and leptons having left-handed helicity. As far as the neutrinos go, only the left-handed helicity neutrino was included in © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2_21

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the theory and no right-handed neutrino was included to fit weak interaction observations. As a result, parity symmetry was intrinsically broken by choice. The model reproduced the known V −A charged weak interaction observed in beta decay. As already emphasized, the absence of the right-handed neutrino of course implied that neutrino is massless which we now know not to be correct. We did not know that in 1967, when the standard model was proposed. The left-right symmetric models were proposed to resolve this unsatisfactory feature of the standard model. Since the standard model is so successful, whatever is done to extend it must give back the same observed consequences as the standard model. This is quite a challenge. How was this achieved in the left–right model? The left–right model postulated that there are new kinds of weak forces generated by new W-like bosons. In other words, the familiar W bosons of the standard model are accompanied by new W -like bosons called WR bosons which couple to the right-handed helicity quarks and leptons, exactly like the standard model W couples to left helicity fermions. Clearly this required that there be right-handed neutrinos. The theory is therefore mirror symmetric since, corresponding to any kind of weak process that has been observed to emit the left-handed neutrinos, there is a mirror counterpart weak force which emits right-handed neutrinos, making the theory respect mirror symmetry. The other main point is that in the language of gauge theories which is the framework for the standard model, this is done in a simple manner without breaking any of the rules of the game. The question then arises: why do not we see the mirror counterpart reactions in the laboratory? These are the weak interactions that are of V + A type as opposed to what is observed, i.e. the V − A type. The answer to this is in the left–right models, the mass of the right-handed weak boson WR is much heavier than that of the standard model W boson, so the weak forces that involve the right-handed helicity neutrinos are much weaker and harder to detect. But eventually they should be observed as the energy of colliders increases. Figure 21.1 pictorial view of left–right symmetry compared to the standard model.

21.1 Neutrino Mass-Mirror Symmetry Breaking Connection An immediate question that arises in the left–right symmetric models is the following: the model puts neutrinos in the same footing as the quarks and

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Fig. 21.1

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Left-handed standard model and left–right symmetric model in pictures

charged leptons. So why is the neutrino mass observed to be so small? Just to remind the reader, the lightest quark mass is about 10 MeV (i.e. one hundred times lighter than the proton) and the heaviest quark is known as the top quark whose mass is about 175 times the mass of proton. The heaviest charged lepton is the τ lepton whose mass is about 1.8 times the proton mass, whereas the lightest charged lepton, the electron, has a mass of half an MeV. However, the neutrino oscillation experiments combined with cosmology have conclusively established that the heaviest left-handed neutrino mass is less than an electron volt, so about a million times smaller than the electron. On the other hand, the left-right symmetric theories naively would suggest that the neutrino masses also must be of similar order to the electron mass. So how do we understand the extreme smallness of neutrino masses? The nature of the neutrino itself provides some clues (Fig. 21.2).

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Fig. 21.2

Masses of charged matter versus those of the neutrinos

21.2 Majorana Neutrinos In the left–right symmetric models, the neutrinos and charged fermions are on the same footing. So to start with, the properties of the neutrinos should be very similar to that of the charged fermions, as just noted. In particular, we should not expect the masses of the neutrinos to be that much different from the electrons or muons. However, there is a fundamental difference between the charged fermions (e.g., electron, muon, quarks, etc.) and the neutrino. For example, the charged fermions have electric charge (as the name implies) whereas the neutrinos are electrically neutral particles. This difference is fundamental because the neutrinos (both the left- and the right-handed ones), having no charge, can be their own anti-particles, whereas the charged fermions cannot be their own anti-particles, since an anti-particle will have opposite electric charge and must therefore be different particles. For a charged fermion, the mass is called a Dirac mass after Paul Dirac, who first discussed this, as we noted earlier in connection with the anti-particle. The choices for neutrino mass are wider, i.e. it could either be a Dirac mass where its mass partner will be the right-handed neutrino or it can have its mass partner be its own anti-particle, in which case it is called a Majorana mass, or both. In the first case, the neutrino is more like the electron, whereas in the second case it is very different. The idea of Majorana mass for a neutrino was first proposed by the Italian physicist Ettore Majorana [44, 61]. Majorana was born in the village of Catania, Sicily, on August 5, 1906. His father was an engineer who founded the first telephone company in Sicily and went on to become the chief inspector

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Fig. 21.3 Ettore Majorana, who first proposed the idea of the Majorana neutrino (left panel). Majorana with his mother, sisters, grandmother, and a friend (right panel)

of the ministry of communications. His mother was a home maker. He had a rich scientific pedigree: three of his uncles were chancellors at the University of Catania and another uncle was an experimental physicist. Ettore got his first degree in engineering at the University of Rome, but was persuaded to join the school of physics, where he worked with Enrico Fermi’s group. There he did a number of very interesting works in theoretical physics, until the night of March 26, 1938. At that point, he suddenly disappeared at the young age of thirty one off the coast of Palermo. He boarded a ship with cash and a passport in hand and vanished. Nobody knows what happened to him. The day before he left, he sent a letter to his colleague at the University of Naples, saying that he will be coming back soon. There are many theories about what happened to him, including the possibility of suicide, being kidnapped, joining a monastery or having left Italy for good to live in South America. But despite serious enquiries, nobody seems to know the answer to the question “what happened to Majorana?” Majorana published his most famous paper that started the idea of a neutrino being its own anti-particle (called the Majorana neutrino) in 1937. The paper is: E. Majorana, Symmetrical theory of the electron and the positron, Nuovo Cim. 5, 171–184 (1937). This paper put the idea of a neutrino being its own anti-particle on firm mathematical footing. Most people now think the neutrino may indeed be a Majorana type neutrino (Fig. 21.3). Majorana was one of the most brilliant Italian physicists of all times. To quote the famed Italian physicist, Nobel laureate Enrico Fermi, Because, you see, in the world there are various categories of scientists; people of a secondary or tertiary standing, who do their best but do not go very far. There are also those of high standing, who come to discoveries of great importance, fundamental

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for the development of science. But, then there are geniuses like Galileo and Newton. Well, Ettore was one of them. Majorana had what no one else in the world had.

21.3 Seesaw and Majorana Neutrino Mass Every child has played with a seesaw with their elder siblings. When the elder sibling sits down on one side, the child goes up because he or she is lighter and comes down as the heavier sibling lets the seesaw up. The seesaw has a fulcrum which stays fixed in the middle. The important thing is that seesaw needs two people. The way small neutrino mass is understood, it precisely involves a “heavier sibling” and a “fulcrum.” If the neutrino is a Majorana particle, i.e. it is its own anti-particle, it can form a mass by itself by taking the left-handed helicity particle and paring it with a right-handed anti-particle (recall that for a fermon to get mass, it needs a left-handed helicity to pair up with a righthanded helicity particle). It would not have been possible if the mirror partner of the neutrino was not its own anti-particle. The fulcrum in this case is the mass that combines the left-handed neutrino with the right-handed mirror partner. The technical name for the fulcrum is the Dirac mass of the neutrino. The result is that the light partner gets a small mass which gets smaller as the mass of the right helicity neutrino gets bigger, just like in a seesaw. The heavier the heavy sibling, the higher goes the lighter sibling on the other side. See the figure below for a picturesque description of this. This mechanism was discovered independently by several groups in 1977 and 1979 [75]. From the picture, one can imagine that if the fulcrum is higher, the right-handed heavy neutrino goes deeper which could be thought of as having a higher mass. This is precisely what happens mathematically, i.e. if the Dirac mass is bigger, the right-handed neutrino mass which is called the seesaw mass has to be larger. There are four types of seesaw models: they are called Type I, II, III seesaw and inverse seesaw.1 A conceptual beauty of the seesaw mechanism in the left-right symmetric models is that it explains why we see only left-handed V − A currents in low energy weak processes, being linked to the small mass of the neutrino. In the seesaw mechanism, the heavier the mass of the right-handed neutrino, the more mirror symmetry is broken and the more dominant weak process is the V − A current process. It is quite elegant that the small neutrino mass explains why we do not see right-handed weak force at low energy processes,

1 This

author started calling the first two seesaw types already being discussed in the 1990s as type I and II seesaw, following the nomenclature in superconductivity and supernovae, and the names seem to have stuck.

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Fig. 21.4 Breaking of exact mirror symmetry and small neutrino mass via seesaw. Source: University of Maryland, College Park

such as beta decay. By the same token, one should see the V + A currents in high energy scattering. Eventually, at very high energies, weak interactions will become mirror symmetric like all other forces of nature (Fig. 21.4). There are arguments that while the Majorana mass idea may be correct, it may have nothing to do with the seesaw picture or mirror symmetry. For example, Weinberg has argued that it is some unknown physics, which leads to the Majorana nature of the neutrino [101]. There are also high scale theories (higher mass particles) that do not invoke a right-handed neutrino, called a type II seesaw [73], or a lower scale ones [15]. There are, however, cosmological reasons to believe that the seesaw is more practical than using unknown physics to parameterize the Majorana nature of the neutrino. Of course, ultimately experiments will tell which is the right way. There is also another kind of seesaw to understand the light neutrino mass, called the “inverse seesaw” [76]. Note that in the case of the usual seesaw mechanism, the Majorana mass of the right-handed helicity partner breaks the lepton number by a large amount since it is a heavy mass. The thought then arises: could the lepton number violation be small like the small neutrino mass, and if so, can one still have a small Majorana mass for the neutrino? The answer turns out to be yes, and the resulting mechanism is the so-called inverse seesaw. In this case, one also needs new physics and the new physics scale has to be in the TeV range, which could be probed by the existing and planned future colliders. These class of models are naturally realized with warped extra dimensions [7] or using quantum corrections. One can also test the broad features of these models using the searches for neutrinoless double beta decay [14]. Among other models for neutrino masses is an intriguing possibility that the tiny neutrino mass may have its origin in gravitational interactions [41], since both are super-weak effects. There are also speculations that the cosmological constant responsible for the accelerated expansion of the universe [88] seems

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to have very similar values to the mass of the neutrino, observed in oscillation experiments. Therefore, there may be a connection between the two. The current size of the cosmological constant deduced from cosmological expansion is ∼(10−3 )4 eV4 and the value of the heaviest neutrino that is oscillating is ∼10−2 eV, leading to such speculations. There is yet no theoretical basis for such speculation. We will of course not know for a while whether any of these or even the other theories about the origin of neutrino masses are right. The first requirement for this is to establish whether the neutrino is indeed its own anti-particle.

21.4 Testing Majorana Nature of Neutrinos in Experiments Physics is an experimental science. In particular, experiments need to establish whether the neutrinos are Dirac or Majorana particles. Each possibility has its distinct implications: for example, the idea of understanding the origin using the seesaw mechanism discussed above depends very much on the assumption that neutrinos are Majorana type. So how do we really test this idea? It is clear that if neutrinos are Majorana fermions, the lepton number marker that was discussed above is broken by two units. This breaking is weak. So for most purposes, it will appear as if the lepton number is not broken, but there will be situations where such a small effect can possibly show up and we need to look for such places. One of the ways the weak force manifests itself is via the decay of nuclei to another nuclei with one higher atomic number (i.e., Z → Z + 1), and the fundamental process is n → p +e− + ν¯ e where the neutron that decays resides inside the nucleus. An example of such a decay is: Co60 → Ni60 + e− + ν¯ e and there are many other examples in nature. (Co60 decay is nowadays used in cancer therapy). These processes are called single beta decays, denoting the fact that there is only a single electron emitted per decay. Such decays cannot tell whether the neutrino is a Dirac or Majorana fermion. In these processes, the decaying nucleus is called the mother nucleus and the final nucleus is called is the daughter nucleus. However, there can be processes where there can be the emission of two neutrinos if the single beta decay happens twice inside a nucleus. These processes are called double beta decays. In such a decay, two neutrons inside the nucleus decay simultaneously, instead of just one. There are examples of nuclei where the single beta decay is forbidden by energy considerations, i.e.

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Fig. 21.5

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Neutrinoless double beta decay as a test of the Majorana neutrino

the daughter nucleus for single beta decay has higher mass. Examples of such nuclei are: Ca48 , Ge78 , Mo100 , etc. [93]. One can look for double beta decay in such nuclei. Such processes have been looked for and established for many nuclei, like germanium and molybdenum, etc. When two neutrons decay, they give two neutrinos in the final state. If the neutrino is a Majorana fermion, the final states can be both n + n → p + p + 2e− + 2ν¯ e and a new process where there are no neutrinos in the final state, i.e. n + n → p + p + 2e− . The second case, which is known as neutrinoless double beta decay, can happen if the neutrinos are Majorana fermions. One can think of this as the two Majorana neutrinos “eating” themselves, being their own anti-particles (see Fig. Fig. 21.5) and not appearing in the final state. In the case of Dirac neutrinos on the other hand, the neutrinoless process does not occur since there is no way the neutrinos can disappear, due to the conservation of the lepton number. If we count the lepton number, we see that in the first case, the lepton number is zero in the initial and final state since the anti-neutrinos have lepton number −1 and electrons have L = +1. This implies that Lf inal = 2 − 2 = 0. In the second process, however, the final state has lepton number L = 2 so that the process violates the lepton number by two units. Observation of processes such as n + n → p + p + 2e− will therefore be a confirmation that neutrinos are indeed Majorana fermions [89]. This will be major breakthrough, since it will signal for the first time that a conserved quantum number such as the lepton number is broken. There are now many attempts to discover neutrinoless double beta decay using different nuclei, such as Ge78 , Xe136 , Mo100 , etc. [91], where single neutrino beta decay (conventional one) is forbidden. The results so far are negative. The progress in the field has, however, been enormous, as is clear from Fig. 21.6. In any case, this need not be discouraging, since these are extremely rare processes with lifetimes in the range of 1027 years or more (compare this with the age of the universe which is around 13.7 billion years). Also, at the end, how fast the nucleus decays depends on the Majorana mass of the lightest neutrino, and we do not yet know what the mass of the lightest

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Fig. 21.6 Progress in the search for neutrinoless double beta decay. The y-axis gives the mass of the lightest Majorana neutrino mass in electron volts which a given experiment is sensitive to. The names of the different nuclei used in the search for the process are given next to the red line. Source: Peter Vogel’s review, delivered at the Amherst Center workshop on the subject in 2018

neutrino is since oscillation experiments are only sensitive to the difference in the masses and not their absolute value. Therefore the neutrino could still be a Majorana fermion but neutrinoless double beta decay may never be found. There are of course other proposals to establish the Majorana nature of the neutrino without the assistance of neutrinoless double beta decay searches. Other processes exist which can violate the lepton number and have a better chance of being observed if the theory of neutrino mass is a left–right symmetric theory with WR mass in the TeV range. Examples of those processes in hadron colliders are p + p → e+ e+ jj or p + p → μ+ μ+ jj [65]. The LHC experiments have been searching for the WR boson and have put limits on the mass from their data [94]. In low energy processes involving the decay of heavy quark containing mesons, one can also have two same sign leptons as decay products, e.g. B + → K − e+ e+ , etc. There are intense ongoing efforts to search for such processes, so that the possibility of Majorana neutrino can be established or refuted. Either way, it will be a groundbreaking discovery. For theoretical discussion of general collider searches of TeV mass right-handed neutrinos predicted by seesaw models, see [36] and for lower mass ones, see [13]. The search goes on.

22 Hints of Other New Physics from Neutrino Mass

As already emphasized, neutrino mass is a clue to new physics beyond the standard model. One scenario of new physics described above uses the left– right symmetry of nature at very short distances. There are many other scenarios for neutrino masses. They are too numerous to discuss here. But in this chapter, we focus on one other widely discussed scenario, which is also motivated by attempts at understanding the role of mirror symmetry in nature.

22.1 Mirror Universe Versus Left–Right Symmetry: Two Paths to Parity When Lee and Yang proposed that weak forces break mirror symmetry, they were so uncomfortable with the concept of mirror symmetry violation that they proposed a way to rescue this symmetry in nature while having it remain compatible with its violation in weak forces. They suggested that there might be a mirror universe, a separate set of particles and forces from ours, to which mirror symmetry takes all our particles and forces. The mirror symmetry would therefore be preserved when both universes are taken together. On the other hand, since we are making observations only with particles in our universe, the weak force would violate mirror symmetry as observed. In such a combined scenario of the universe, the number of fundamental constituents of matter will be doubled. In this picture, there will be twice the number of quarks and leptons that exist in the standard model. For example, there will be a mirror proton which is the mirror partner of our proton, a mirror photon © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2_22

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which is the mirror partner of the familiar photon, etc. One word of caution: the mirror universe is part of our universe and is not necessarily related to the multiverse picture of string theory, where presumably the universes are disconnected from one another. There exist different variations of the mirror universe scenario where the two sets of particles “communicate” with each other via different kinds of “portals.” The left–right symmetric theories provide a different way to maintain parity symmetry without doubling the quarks and leptons and without postulating another universe of forces. They keep the same number of quarks and leptons as in the standard model, but only add the right-handed neutrino (three of them) to the standard model fermions. In such models, the neutrino automatically has mass by pairing up with the right-handed neutrino via the seesaw-like mechanism as described. As we saw before, the neutrino mass requires a right-handed neutrino. Thus this is a picture that fits right into the modern discussion of neutrino mass and maintains mirror symmetry in nature. The left–right symmetric theories for neutrino mass are more economical compared to the mirror universe model. However, the mirror universe models do provide an automatic dark matter candidate, which is the lightest baryon of the mirror sector. It also provides extra sterile neutrino states [56] (or mirror neutrino states) in the universe. These would be good candidates to fit some experiments that seem to indicate possible anomalies. The dark or sterile neutrinos interact only with the mirror W , Z and are thus hidden from our view, except for their mixing with ordinary neutrinos, which would then explain the sterile neutrino anomalies. How can we test for the existence of the mirror universe? Various suggestions have been made in the literature about it. In the minimal version of the model where the only force connecting the two universes is gravity (a connection, which is always there), there can be mirror stars, mirror planets, etc. Since these objects are transparent to our photon, light from stars behind a mirror star will pass through it. The rays of light passing on both sides of the mirror star would get bent due to gravitational force and all light beams can meet and brighten up the original star. This is called micro-lensing. In 1998, some micro-lensing events were reported, and they led to speculation that they may be detecting mirror matter objects in the sky. But those observations soon found conventional astrophysical explanations. Still, there is no evidence for mirror universe yet. But astronomers should be alert to these kinds of new possibilities. Micro-lensing is one of the techniques generally used to search for extrasolar planets and has been successfully used. This can also be used for detecting mirror stars and planets. For a picture of how micro-lensing will work for a mirror star, see Fig. 22.1.

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Fig. 22.1 A possible way to search for mirror stars in the sky. Note that there are three rays here from the source to the observer instead of two for a conventional planet or star because light ray passes unhindered through the mirror star

22.2 Grand Unification of Forces and Matter Searching for unified approach to forces and matter has been an eternal goal of physicists. It may have started with Newton, who unified an apple falling from the tree with the motion of planets around the Sun through a common understanding of the laws of gravitation. Apparently unrelated phenomena having the same explanation is after all the goal of unification. Then came Maxwell’s unified approach to electricity and magnetism, which are two manifestations of electric charge. When an electric charge is in motion, it gives rise to magnetic forces. Einstein spent most of his life trying to unify gravity with other forces. Kaluza and Klein provided one early example of such unification using the five-dimensional extension of Einstein’s general theory of relativity. The same dream of finding the ultimate unification of matter and forces has lived on to the present day. After the standard model of forces and matter was proposed, it was suggested [80] that all matter and forces may be unified within certain large symmetry groups called SU (5) and SO(10). In this approach, the observed force strengths unify into one value at a very short distance of order of 10−29 centimeters (see Fig. 22.2). The different force strengths we observe today are a result of simply being at a larger distance, but there is only one force as we go to really short distances. How small that distance is can be deduced by using the rules of Quantum Field Theory. A larger symmetry group dictates how matter and forces behave at these short distances. The choice of the symmetry groups puts quarks and leptons into one group representation, which means

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1/a1 MSSM

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Fig. 22.2 Unification of three force strengths of the standard model at very high energies or very short distances. In this figure the inverse force strengths are plotted against energy denoted by Q

that they are like the three axes in a coordinate system, which can be “rotated” from one to the other by the action of the symmetry group. This makes the theory quite predictive. In fact, one of the successes of this approach is that, with a simple set of assumptions, one can predict the value of a weak mixing angle, called the Weinberg angle, which is a key parameter of the standard model. One implication of this simple hypothesis is that the proton, which consists of three quarks, may have its constituent quarks rotated in a physical process to a lepton (say a positron). This happens because new forces that arise at the GUT scale can allow this possibility. This, for example, can allow a proton to decay to a neutral pion and positron. The lifetime of the proton is then related to the mass of the new force mediator, and that mass is related to the scale at which the forces unify. This makes the idea of grand unification of forces and matter testable in experiments on Earth. In fact, searches for proton decay at the Super-Kamiokande experiment have made tremendous progress and have already disproved a simple theory based on the group SU (5). There are, however, many other grand unified theories which are still viable. One example is a theory based on the SO(10) group [54], which also predicts small neutrino masses via the seesaw mechanism and is therefore more appealing as a theory of forces and matter. For detailed analysis in a simple picture where unification of couplings predicts neutrino masses via the seesaw mechanism in the right range, see [78]. In this case, unification of forces predicts the scale at which seesaw heavy neutrino mass occurs. There are many other possibilities and this is an active field of research now.

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22.3 What if Neutrinos Are not Majorana Fermions? What if the neutrino mass battle between Dirac and Majorana is lost by Majorana and the neutrino is not its own anti-particle, i.e., it is a Dirac fermion? That would be a major change in theoretical research, and the change has already started in the last few years as the evidence for the Majorana nature of the neutrino keeps getting farther and farther away from being established. The Dirac neutrino will have similar characteristics as all the other fermions of the standard model—the electron, the muon, the quarks, etc. In some sense, we might think that it is a natural possibility, except that the neutrino mass is so much smaller than the masses of other fermions, a fact which is hard to understand if it is a Dirac fermion. Of course, it has zero electric charge, unlike the other fermions of the standard model, making it unique among all the standard model fermions. As we saw earlier, this property was one of the main motivations for the seesaw picture of the neutrino that explained naturally why the neutrinos are ultralight. One way that the small Dirac neutrino masses can arise naturally is when there are large extra dimensions. In this case, the smallness of the Dirac neutrino mass is due to the existence of the large extra dimension [38]. Because of the uncertainty principle which specifies that large lengths are associated with small masses, the small neutrino mass is a consequence of the length of extra dimensions being large. These models however lead to cosmological difficulties. One unpleasant implication is that the ultimate temperature of the universe in these models is only a few MeV, which is a drastically new kind of universe. In this case, it is hard to understand many aspects of the early universe, such as, inflation, the origin of matter, etc. At the laboratory level, such models also lead to sizable corrections to the inverse square law of gravity, which has been searched for, and no evidence has emerged yet [98]. How do we experimentally establish that neutrinos are Dirac rather than Majorana fermions? If the neutrinoless double beta decay keeps getting farther and farther from the reach of experimentalists, the interest in neutrinos possibly being Dirac will attract more attention. However, as already stated, for the case of the normal hierarchy of neutrino mass ordering, double beta decay is suppressed anyway. As a result, it cannot be taken as an evidence for Dirac neutrino. Most other experiments do not care if the neutrino is a Dirac or Majorana particle. One possible way to tell that the neutrino is a Dirac particle is as follows: If the neutrino mass ordering is established from long baseline oscillation

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experiments to be inverted, then it follows that there must be an upper limit on the lifetime of the neutrinoless double beta decay. The actual number depends on nuclei. So, if the searches for the neutrinoless double beta decay continue and one violates this upper bound, then understand both long baseline evidence for an inverted hierarchy and the neutrinoless double beta decay results together would require that the neutrino is a Dirac fermion. So far, neither of these conclusions are at hand and therefore we still do not know conclusively whether the neutrino is a Dirac or Majorana type fermion. In fact, the experimental indications now are in favor of the mass ordering being normal which, as remarked, would make it extremely difficult to establish that neutrinos are Majorana fermions, until the neutrinoless double beta decay process is discovered. In the next chapter, we discuss how the seesaw picture can provide a way to understand the origin of matter–anti-matter asymmetry in nature.

23 The Origin of Matter and Neutrinos

Where did matter in the universe come from? We know that the universe is full of matter. There is no evidence that there is any anti-matter in the universe. If there was an equal amount of anti-matter mingled together with familiar matter, they would quickly annihilate, and the universe would be full of “photon smoke” out of that explosion. If matter and anti-matter were segregated in their distribution and present in the universe in separate parts, that would cause a directional asymmetry, which would manifest itself in the cosmic background radiation as being direction dependent. There is no evidence for that. Thus all evidence points to the fact that there is no antimatter in the universe. However, in the Big Bang model, at some point in its evolution, there were an equal number of baryons (matter) and anti-baryons (anti-matter). The number of baryons at the current epoch of the universe have been calculated in various ways and it is found to be about 6 × 10−10 per photon. At the early stage of the evolution of the universe, the baryons and antibaryons would be there in equal numbers and they would continuously annihilate each other and get created back at a rapid rate. Thus their relative number would not change and would remain equal. Then down the line, as the universe kept expanding, the volume became so large that the number of baryons and anti-baryons per unit volume became small. When that happened, they would not have been able to find each other to annihilate and their number would not change after that. One can estimate at what temperature this happened and one can calculate how many baryons and antibaryons per photon were there at that time. The number turns out to be about © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2_23

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10−16 per photon. The temperature of the universe at that time was about 1013 degree Celsius. This number remained frozen until now, but it is tiny compared to the 6 × 10−10 observed for protons and neutrons right now. Also this number contains an equal number of baryons and anti-baryons but since 10−16 is a much smaller number than 6×10−10 , we do not need to worry about why we do not see anti-matter. We still have to explain how 6 × 10−10 baryons per photon appeared in the first place. Note that, for the universe to be electrically neutral, as we believe it is, there must be the same number of electrons as protons. However, since the electrons and positrons hung around together much longer and annihilated each other until the universe was about a 1000 years old, there must have been an asymmetry between the number of positrons and electrons from the beginning as well, when the baryon asymmetry was first created. Thus, accompanying the baryon asymmetry, there must have been a lepton asymmetry, although there is no accurate information regarding the excess of leptons over anti-leptons.

23.1 Enter Sakharov Andrei Sakharov was a Russian nuclear physicist who was known for his activism for peace, disarmament, and human rights. He later became an advocate for civil liberties and civil reforms in the Soviet Union, for which he faced state persecution. He was awarded the Nobel Peace Prize for these sacrifices. He was also an outstanding physicist who in 1967 wrote a profound three page paper (Fig. 23.1). In it, he outlined how matter–anti-matter asymmetry could be created in a universe, which started out being matter–anti-matter symmetric. In an inflation picture, no matter what, at the end of inflation, the universe has no or very little matter and anti-matter. The Hubble expansion does produce an equal number of baryons and anti-baryons, which reduce to a very small amount by the argument given above. So the question remained as to how the observed asymmetry between matter and anti-matter arose. Sakharov laid out three conditions for the origin of matter–anti-matter asymmetry in a symmetric Big Bang model: (i)

There must be baryon number violating forces in the universe. This means that the sacred marker we had for protons and neutrons called the baryon number must be a weakly broken marker. In other words, this means that there must be processes where a proton, instead of always changing to a neutron under the weak force, can change in a very rare

23 The Origin of Matter and Neutrinos

Fig. 23.1

(ii)

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Andrei Sakharov. Source: Wikipedia.org

way to objects that do not carry a baryon number. An example of such ¯ a process is p → e+ + π 0 as well as other processes such as n → n. The first class of processes occur in the SU (5) grand unified theory of Georgi and Glashow [80] and the second kind of process appears in the left–right symmetric theories of neutrino masses described above [77] once the quarks and leptons are unified in that theory. There could be other less known processes that also violate the baryon number. The breakdown of the baryon number has not yet been discovered. There must be forces that are asymmetric between matter and antimatter (also known as CP violation). Such a force was already discovered to exist in 1964, in the decay of K mesons to two pions. What was found is that a particle and its anti-particle known as K 0 and K¯ 0 combine to give one state which is odd under CP and another which is even. The even (symmetric) one is allowed by CP to go into two pions but the odd one is not. So the discovery by the team of Christenson, Turlay, Fitch, and Cronin found that very rarely but surely the CP odd combination leads also to two pions. That proved the existence of CP asymmetric forces in the universe for the first time in 1964. The last is a more technical condition that the baryon number violating processes must not be too rapid or go out of thermal equilibrium for baryogenesis to start to occur. In plain language what it means is that the reverse process to baryon violation (i.e. if the original process is p → e+ π 0 , the reverse process is e+ + π 0 → p ) must be slow enough so

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that any baryon asymmetry generated by the above two conditions must not be undone by the reverse process. In the early universe, if the baryon asymmetry is being produced by the decay of a heavy particle, then when the temperature of the universe is below the mass of the heavy particle, the inverse reaction cannot happen since the final particles just do not have enough energy to produce the particle that is decaying. This will satisfy Sakharov’s third condition. Since the SU (5) grand unified theory of Georgi and Glashow apparently satisfied all these conditions, using Sakharov’s conditions, Japanese physicist M. Yoshimura [106] wrote a paper showing how the Sakharov conditions can generate the desired matter–anti-matter excess in the universe. It was however later discovered that this model does not work due to symmetries of the standard model that erase any baryon asymmetry produced in the SU(5) model at very high temperature of the universe. However, soon many other models which do not share the problem of the SU (5) model and produce baryon asymmetry were discovered. A key element of all these models is that the sacred principle baryon number must be broken.

23.2 The Search for Baryon Number Violation As we just saw, baryon number violation is one of the key ingredients for understanding why the universe has only matter and no anti-matter. How can we experimentally test this idea? Since the lightest baryons are protons and neutrons, there must be processes in nature where a proton disappears into lighter particles or a neutron transmutes into an anti-neutron. Both these processes would break baryon number conservation and would provide key support for Sakharov’s idea. Of course, as we have been discussing, a free neutron is unstable and undergoes beta decay with a lifetime of under about 15 min, without breaking baryon number. The process of neutron–antineutron oscillation therefore must occur before the neutron has had a chance to beta decay. So how do we know what a proton decays to and how long is its lifetime? Energy conservation dictates that a proton can decay to particles whose total mass is less than its own mass. The particles of lower mass than the proton, which do not have a baryon number, are K ±,0 , π ± , π 0 , ρ ±,0 , e± , neutrinos. Also the spin of the original particle must be conserved in the baryon number violating process by the principle of angular momentum

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conservation (it is a sacred principle, like conservation of energy). Similarly, since the proton has one unit of electric charge, when it decays, the electric charge must also be carried by one of the decay products or a combination of them. This leads to the following typical possibilities for proton decay: p → e+ π 0 , e− π + π + , K + ν, K + ν¯ , ρ + ν, ρ + ν¯ , e+ ν¯ ν, etc. There are a few other decay modes as well that satisfy same conditions. Since the world around us is pretty stable, and the universe has been around for 13.8 billion years, it implies that proton lifetime is longer than 13 billion years. Since there are a lot of protons, and as far as we know all protons are intact, that actually means that protons are stable with a lot longer of a lifetime than 13 billion years. In fact, Maurice Goldhaber gave an argument to have a lower bound on the proton lifetime without doing any experiment. He argued that the human body has about 1027 protons. If a proton inside a human body decayed, that would lead to radioactive products, which would emit intense gamma rays and cause cancer. The fact that humans (and animals) are surviving without getting sick implies that the lifetime of the proton must be at least 10,000 trillion years. Goldhaber called it “feeling in the bone” bound. There are many other sophisticated methods that have been used in dedicated facilities to search for proton decay during the last 40 years. All the models of proton decay listed above have been searched for by various experiments. The most extensive of them is the Super-Kamiokande experiment that discovered neutrino oscillation. Another experiments is located in a salt mine near Cleveland (called IMB, short form for Irvine–Michigan– Brookhaven experiment) and the Frejus experiment in the Frejus tunnel in the Alps, Europe. The Super-Kamiokande experiment started out as Kamiokande (where the last three letters NDE stand for nucleon decay experiment). The efforts started in 1980s, with these experiments deep underground, using a large body of water. The idea was to look for decaying protons in the water, so that if it decays as p → e+ +π 0 , both the final state positron and neutral pion would leave a spectacular light signal in water. They used photomultipliers, which are devices that magnify this signal to make observations possible. Locating the experiment underground was important since that helps to shield spurious events looking like proton decay but actually coming from atmospheric neutrinos. The current best limit on the proton lifetime is bigger than 3 × 1034 years from the Super-Kamiokande experiment [3]. Right now, there are two searches which are being planned—one in a gold mine in Lead, South Dakota, where Ray Davis did his solar neutrino experiment, and another in Japan. At the end of these experiments, the current limits are expected to be surpassed by at least a factor of ten. The first experiment is

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called DUNE, which will use 40 kilotons of liquid argon as the detector fluid and the second experiment is called Hyper-Kamiokande, which will use almost 500 kilotons of water. The second kind of baryon number violation process mentioned above is the neutron–anti-neutron oscillation. In this experiment, a free neutron in flight transforms into its own anti-particle, as is predicted by certain theories [77]. This process probes physics near the energies where the present colliders are searching for new physics. If this process is discovered, there is a possibility that the related physics can also be searched for in new higher energy colliders that are being planned. This is an exciting possibility. Neutron–anti-neutron oscillation can be searched for in reactors where many neutrons are emitted. Typically, about ten billion or more neutrons are emitted per cm2 per second. These neutrons in flight can convert to anti-neutrons, and when the anti-neutron hits the detector, it will give a spectacular annihilation signal that can be detected without any trouble (with no background to confuse). There has been one experiment to search for the oscillation of free neutrons in a reactor, at the Institute Laue-Langevin (ILL) in Grenoble, France. In these experiments, one must suppress the Earth’s magnetic field which has the effect of suppressing the n → n¯ transition. This is because how strongly the n and n¯ mix depends on how little the magnetic field is. This kind of technology, which can be used to shield magnetic fields in a region of space, already exists and has been used in the ILL search for neutron–anti-neutron oscillation. The technique uses a nickel–iron alloy, called mu-metal. A more sensitive experiment to search for this oscillation will require a longer baseline to allow more chances for the oscillation to happen. One such experiment is being planned at the European Spallation Facility (ESS) at Lund, Sweden, where a very high intensity neutron source will be available soon. Neutron oscillation can also occur inside a nucleus, though suppressed by the nuclear energy difference between a neutron and anti-neutron, as they “swim” inside it. This can give signals in a proton decay search experiment. Instead of a positron, as in the case of proton decay, in this case, one gets a burst of about four to five pions in the final state after the anti-neutron produced in the oscillation annihilates with another proton or neutron in the nucleus. The limits on this decay are similar to that for proton decay [2], leading to a lower limit on the neutron–anti-neutron transition time of about a few years. This limit is of the same order as was obtained in the ILL experiment.

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23.3 Neutrino Seesaw and Baryon Asymmetry Is there a connection between neutrinos and the matter–anti-matter asymmetry? It was pointed out in 1986 [52] that proton decay may not be a key ingredient in the generation of this asymmetry. Instead, the seesaw picture of neutrino masses discussed above may present a simple way to produce matter–anti-matter asymmetry. It arises from the decay of the heavy righthanded neutrinos. Since the heavy right-handed neutrinos are their own anti-particles (or are Majorana fermions), the lightest of them can decay to produce both leptons with Higgs bosons and anti-leptons with the anti-Higgs boson. In combination with matter–anti-matter asymmetric (CP violating) forces present in the right-handed neutrino decay, leptons and anti-leptons will appear in different numbers i.e. there will be a lepton asymmetry. The conversion of the lepton excess to baryon excess comes from a different source. Fortunately, it comes from a theoretical possibility that exists in the standard model. The standard model which is confirmed by experiments has a property that it can convert leptons to baryons. It happens because the standard model has many vacuum states (or lowest energy states) and processes that can take from one vacuum state to another can change leptons to baryons. The process has the technical name of “sphalerons (Fig. 23.2).” This property of standard model is very hard to test experimentally since the processes that change leptons to baryons are so weak (i.e. they occur so infrequently). According to this theory, even at the highest energy collider LHC, the sphaleron process cannot be observed. Nevertheless, since the standard model is so extremely successful, this property is believed to hold without doubt. Furthermore, even though this lepton to baryon changing property is very weak in the laboratory,

E

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Fig. 23.2 The standard model sphaleron processes in the early universe (T ∼ E) versus in the laboratory where the temperature is the CMB value T0

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in the hot environment of the early universe, the process is expected to be quite rapid. This so-called sphaleron process which is effective in the early universe helps to convert the lepton asymmetry produced in the decay of right-handed neutrino to baryon asymmetry in an instant [70]. This provides a different way of using Sakharov conditions to understand the matter–antimatter asymmetry of the universe, and the route goes via the neutrino seesaw. This particular scenario is of special interest for neutrinos, since the same seesaw mechanism that is supposed to explain the small neutrino masses is also responsible for understanding matter–anti-matter asymmetry. It provides a single unified approach to two different problems—small neutrino mass and asymmetry between matter and anti-matter. In fact, if the seesaw scenario is confirmed, neutrinos might have pulled another miracle in the universe: they create matter, in addition to making matter grow to nuclei, and produce life in the end. What a role for a tiny particle that no one can see and that passes through us in huge numbers every second, without us ever noticing anything. Can we ever test this hypothesis? This scenario known as leptogenesis could happen at a very early moment of the universe e.g. when the universe was only 10−28 s old [26] or when it was somewhat older at 10−12 s old [84]. The latter scenario raises the possibility that the idea of leptogenesis can be tested in the colliders which can attain higher energies than the Large Hadron Collider. There are also scenarios where leptogenesis is connected to the CP violating phase in the neutrino oscillations [25], which can be tested in current experiments. If there is CP violation in the neutrino sector, the neutrinos would oscillate at a different rate than neutrinos. This is what the experimentalists at T2K and NoVA are trying to find out. Both these experiments send muon neutrino and muon anti-neutrino beams over long distances to see if there is difference in the oscillation rate between them. There are some indications that there may be, although the jury is still out on this question. The Fermilab experiment DUNE, already mentioned, will also search for this asymmetry. There are of course several other ways to understand baryon asymmetry. Nobody yet knows which mechanism was operating in the early universe. For instance, it is also possible to understand the origin of matter with Dirac neutrinos [37], although it is little less straightforward than the case of seesaw models for Majorana neutrinos. It is interesting that particle physics ideas associated with the neutrino have the potential to solve such a major cosmic mystery. Detailed discussion of leptogenesis within the seesaw picture, see [25].

24 Dark Universe

That there could be something that we cannot see and yet affects our universe in a profound way is a revolutionary concept. Physics for centuries had been based on experiments that are done on things that we see, either directly or indirectly. In the beginning of twentieth century, something drastic happened where we could not see the objects we were dealing with, i.e. electrons and protons, and started using them to build the laws of physics. We did not see them, but we did see their effect indirectly in many different ways, and are sure that they are there affecting life. When particle detectors such as cloud chambers and bubble chambers were invented, we could see these particles moving through them and leaving a track. We could tell whether they have positive or negative charge using magnetic fields. Similarly, quarks, which cannot exist as free particles, have also been indirectly seen via the tracks, called jets. Thus seeing has, in some sense, been believing in physics. The topic of this chapter is however not the electrons or protons or quarks but rather a new kind of matter that we genuinely do not see and yet we know exist. That matter is called “dark matter.” So how do we then know this exists? This is more like a professional detective story, where circumstantial evidence builds up to such an extent that the guilt of the suspect becomes obvious without a shred of doubt. The main tool that led scientists to first suspect this is through gravitational force, which affects everything. This allows us to detect matter whether it reflects light or not. The first person to suspect this was an astronomer in the early part of the twentieth century, named Fritz Zwicky. Zwicky was a Swiss astronomer born in Bulgaria who migrated to the USA in 1925 to work © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2_24

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with Nobel Prize winning physicist Robert Millikan. He spent his professional life at the California Institute of Technology. He had an eccentric personality and many people thought of him as a curmudgeon who used the choicest words for people he did not like. He had many accomplishments in astronomy. For example, he proposed the existence of neutron stars, as already noted. He also proposed that galaxies can form clusters, but his most profound proposal was that there may be dark matter in the galaxies. He analyzed the redshifts of galaxies inside the Coma Cluster and found that their velocities were much larger than what would be expected if gravitational attraction of only visible matter in the cluster was the cause. He needed to have more matter to understand the observed speeds. He ascribed this discrepancy between observed matter motion (familiar matter) and the one inferred using the gravitational effect of visible matter to be due to something he called “Dunkel materi” (or dark matter). This was in 1933, and those were the early days of cosmology. So this did not become a subject of great importance then as it is now. The next big step came with the thorough and meticulous research by Vera Rubin who studied the rotation curves of hundreds of spiral galaxies. A rotation curve is the speed of stars and gas at different distances from the center of the galaxy, measured using the redshift of light from them.1 She found that the velocities of stars or gas farther out from the center of the galaxy did not go down as expected on the basis of gravitational force. For example, this is clearly established for planets. But speed remained constant even as the distance was further (Fig. 24.1). One way to understand this is to assume that there is dark matter in every galaxy. This confirmed Zwicky’s suspicion that there was indeed hidden matter in galaxies which did not emit or reflect light, but was still there, exerting gravitational force on objects farther away from the center of the galaxy so as to make their speeds remain constant instead of going down. The question is how does one understand the constancy of the rotation speeds observed (Fig. 24.1)? The existence of dark matter is one way to understand it. But another way is to postulate that laws of gravity change at large distances. The latter theory is called Modified Newtonian Dynamics 1 Redshift is the analogous phenomenon to Doppler shift of sound which you experience every day. When

you are standing still on a road side and a police car with siren on passes by you, first as the policeman approaches you, the sound frequency is higher (more shrill) and when the car is going away, the sound frequency is lower. This is a phenomenon which happens with all waves and since light is a wave, it happens to it too. When a star is moving towards Earth, its light frequency will increase. The frequency will be shifted towards blue (called blue shift) and when it is moving away from you, the frequency goes the opposite way i.e. the light will be redshifted.

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Fig. 24.1 Speed of stars in a galaxy at various distances from the center. Line B stands for the observed speed of stars and line A for what is expected if there is no dark matter, providing one piece of evidence for dark matter. Source: Wikipedia.org

(or MOND), and was suggested by Mordehai Milgrom in 1983. This theory could explain the rotation curves, but during the past two decades, evidence for dark matter has appeared from other observations. For example, finer measurements of cosmic microwave background and observation of gravitational lensing2 from two colliding galaxies passing through each other in the Bullet Cluster support the DM hypothesis. These observations cannot be explained by the MOND theory [45]. It is therefore generally assumed that there is dark matter in the universe, contributing about 20% of the mass budget of the universe. The question then is: what is the dark matter?

24.1 Dark Matter and Galaxies The amount of dark matter in the very early stage of the universe is only a small fraction of the energy, with radiation and other relativistic particles containing the bulk of the energy density. As the universe cools, and when it is about 50,000 years old, the dark matter mass starts to dominate over the rest of the energy in the universe. After this time, small ripples in the dark matter density could grow and form attractive regions, where the protons and neutrons fall to form galaxies. This starts to happen after the universe is about 400,000 years old. That is when the electrons and protons combine to form hydrogen atoms, and light just passes through them without scattering. This

2 Gravitational

lensing is like the familiar lensing effect of light except in the case of gravitational lensing, the light is bent not by a lens but by the gravitational field of a massive object.

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happens since hydrogen atoms are neutral. We see this light as the cosmic background radiation. It tells us about the epoch of the universe when atoms formed. Details of how different structures in the universe are distributed are a matter of intense debate and research right now. The nature of the dark matter plays a very critical role in the formation of structure in different regions of the universe.

24.2 What is the Dark Matter? Clearly, dark matter is a new kind of particle which is not present in the standard model. The particle has no electric charge, otherwise it would not be dark. It most likely has no nuclear interactions. We do not know whether it has half integral spin (i.e. a fermion) or integral spin (boson). Whether it has some kind of very weak interaction with normal visible matter (protons, neutrons, electrons, etc.) is a subject of research right now. There are many experiments searching for dark matter and so far there is no positive indication of its detection from any experiment.3 Most stringent constraints on possible dark matter properties are from a recent experiment called Xenon1T experiment [10] that uses liquid xenon as the detector of dark matter. It is also set up inside the same Gran Sasso laboratory in Italy where other experiments are carried out. The precision of dark matter particle research has reached such a stage that it will soon become impossible to distinguish it from the neutrino related background from solar, atmospheric neutrinos, which will produce similar kind of signal to dark matter being. This is called the “neutrino floor” [22]. There have been many dark matter candidates discussed in the literature. They cover physics ideas, all the way from supersymmetric dark matter where the dark matter is heavy to the case of axion dark matter which is light. These ideas were proposed independently of their connection to dark matter. For example, the supersymmetry was proposed to solve the gauge hierarchy

3 There

is an experiment in the underground laboratory in Gran Sasso, Italy, where a collaboration called DAMA and DAMA-LIBRA [20] claimed to have found a signal of dark matter. They found a signal that varies with an annual periodicity as the Earth goes around the Sun. Since this is what one would expect a dark matter signal to do, there has been claim that this is a discovery of dark matter. The reason such annual periodicity is expected to happen is that the dark matter moves with a speed of roughly 300 km per second in one direction. As the Earth goes around the Sun, on one side it faces the moving dark matter as head wind, and 6 months later, as tail wind. The signal in the experiment depends on the speed of the detector on Earth with respect to dark matter. This result has not been confirmed by any independent experiment and therefore remains controversial.

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problem, whereas the axion particle was postulated to solve the so-called strong CP problem of the Quantum Chromodynamic theory of strong interactions. The strong CP problem uses a symmetry, first invented by Roberto Peccei and Helen Quinn. Then there are particles from models with extra dimensions, which also qualify as dark matter. The dark matter particles are the lightest particles of the corresponding theories. The particles heavier than the lightest particle in these theories will eventually decay to the lightest particle and cannot therefore be dark matter. The masses of the dark matter particle are often not given by the theory and they can have masses ranging from thousands of times the proton mass to an extremely tiny mass which is 10−32 times the proton mass, depending on the theory. Most of these particles have properties that make them observable in experiments using familiar matter. So far however, they all have evaded detection. This lack of dark matter signal in currently running experiments has encouraged speculation that, possibly, dark matter has no or very little interaction with matter, as would be the case if dark matter came from a mirror sector of the universe. In most versions of the mirror universe, dark matter typically has very little to no interaction with known matter. This will be discussed in a subsequent subsection. There is also the strong possibility that dark matter interacts with itself. This property is not shared by many of the above dark matter candidates [97]. One reason to suspect self-interaction is that the density profile of dark matter in galaxies such as ours has been calculated using computer models for the evolution of the universe [79]. It is found that if the dark matter has no selfinteraction, the density will peak sharply at the center of a galaxy, unlike what is observed. What is observed is that the density of matter flattens out at the center. If the dark matter particles interact with themselves, they will push each other away due to self-interaction if they get too close. That way, the galactic center will not be sharply peaked in density (or cuspy) [95]. The possibility of self-interaction and lack of signal in underground searches together make a strong case for a model based on the mirror universe idea, with the lightest mirror baryon being the dark matter candidate. It is not only invisible to our light, but it also has self-interaction arising from the mirror strong force to satisfy other properties. As we will see below, such candidates will have very feeble to no non-gravitational interaction with familiar matter, so they cannot be detected using normal detectors. An interesting possibility arises if the dark matter has only strong interaction but no electromagnetic interaction. In that case, the dark particles will form large globs floating in the sky and depending on the strength of the dark

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nuclear force, they could be as large as two meters in diameter. Clearly this would require a new strategy for searching for them [57].

24.3 Is There a Parallel Universe? The idea that there may be parallel universes as part of our existence has been considered for decades and centuries in mythological as well as religious discussions. For example, the concept of heaven, Earth, and hell as three sectors to human existence has been discussed in many places. But as a scientific possibility, the idea of parallel universes first appeared in the celebrated parity violation paper of Lee and Yang, as already stated. They envisioned only two sectors as a way to maintain parity conservation in the whole universe. In this subsection, we discuss whether the same parallel (or mirror) sector of the universe could be the site of dark matter. A cartoon picture of the mirror model particles is seen in Fig. 24.2. To elaborate, just like in the visible world, we expect the mirror sector quarks to form a mirror proton, which does not have our electric charge but the corresponding electric charge from the mirror sector. The mirror sector will also have its own photon, called the mirror photon [92]. Similarly, corresponding to each particle of the visible sector, there is a mirror counterpart. The particles of the mirror sector communicate with our familiar particles (the proton, neutron, and electron) only via gravitational force. Therefore, it is a very weak force and

Fig. 24.2 The duplicate standard model as the mirror universe. The red particles are particles that we are familiar with and the blue ones are the mirror particles

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will only be significant on the cosmological scale with large masses for mirror stars. Because of this, if the dark matter particle comes from this sector, it will not be detectible by conventional dark matter search experiments. As far as self-interaction of dark matter is concerned, this property is now obvious if a mirror hydrogen atom or mirror neutron and proton is the dark matter. This is because the same particles of our sector have self-interaction. Thus self-interaction is an automatic property of mirror dark matter.

24.4 Are There Sterile Neutrinos? We have been discussing so far three kinds of neutrinos (νe , νμ , ντ ) in previous chapters, all of which have been discovered and studied in great detail. As these experiments were going on, an experiment was carried out in Los Alamos National Laboratory in the early 1990s, where a new kind of oscillation of muon neutrinos to electron neutrinos was discovered. This was different from the corresponding oscillations discovered for solar and atmospheric neutrinos. What was found in the Los Alamos experiment (called LSND) was that the mass difference square of the two neutrinos was of the order of one eV2 . This is very different from the solar and atmospheric observations where the mass differences confirmed were much smaller (of order ∼10−5 eV2 . So what is going on? There were many different theoretical models proposed to explain this observation, but the only model that fits all other oscillation observations along with this new one is that there is one or several new kinds of neutrinos which have masses of about one eV. The above process occurs when νμ oscillates to the new state and then the new state (call it νs ) oscillates back to a νe [56]. The mixing angles which determine the strength of this oscillation is much smaller than those controlling solar and atmospheric neutrino oscillations. As a result, the presence of this new oscillation adds very little to the solar and atmospheric results, which are well understood without this new particle. This new neutrino state is called a sterile neutrino, which means it does not have interactions with W and Z bosons. Because if it did, it should have been seen in the decay of the Z boson, which is well studied and understood and has no room for decay to this new neutrino. There are also other observations which have been pointing towards such an oscillation: they are from the anti-neutrinos emitted from a reactor. In a reactor, different radioactive nuclei such as 235 U, 238 U, 239 Pu, 241 Pu (U = uranium and Pu = plutonium) decay, giving rise to electron anti-neutrinos and an electron. Electron energies from these decays are carefully measured, and from

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that the anti-neutrino number (flux) emitted is calculated. Then scientists put neutrino detectors at a short distance from the reactor to measure the antineutrino flux, and found a shortage of the anti-neutrinos compared to the calculated fluxes. A plausible explanation for this is that some of the antineutrinos are oscillating to a muon anti-neutrino, which cannot be detected. This is because it can only produce an anti-muon which is however much heavier than an electron (200 times), so the reactor anti-neutrino does not have enough energy to produce them. But the distance which tells the frequency of oscillation leads to the conclusion that the neutrino to which the electron antineutrino is oscillating has to have a mass near an eV, like in the case of LSND. So if this conclusion is firmly established, that will support the LSND results. There has been a serious and dedicated experiment to check the LSND results at Fermi National Laboratory, called Mini-BooNe, which has also provided some supporting evidence for a sterile neutrino. We must however caution that there are some other oscillation experiments which seem to go against this conclusion [35].Thus the jury is still out on this possibility. The dark neutrino possibility suggests that it could be one of the new neutrinos from the mirror sector. Of the three new neutrinos in the dark (mirror) sector, the LSND neutrino could be one, since it meets all the requirements for a sterile neutrino. This possibility is however not completely free of difficulties, because this would contribute to the total energy of the universe at the time of Big Bang Nucleosynthesis and alter the successes of the standard three neutrino BBN (see Chap. 18.1). There are also arguments to suggest that the dark matter of the universe may be a sterile neutrino but with a mass in the keV range [39]. The known neutrinos cannot be dark matter since they are so light, and if they were, they would move so fast at the epoch of galaxy formation that they would wipe out all structure. So the minimum mass they should have is about a few kilo electron volts. This class of dark matter even without self-interaction can explain why the galaxy centers do not have cusps and also several other problems with the cold dark matter picture. The theoretical implications of the existence of the sterile neutrino are so profound [1] that there are currently many experiments trying to confirm or refute this possibility. The jury is however still out on their possible existence [24].

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24.5 Can We Communicate with the Mirror World? The existence of a mirror universe always raises the possibility of whether we can communicate with it. So far, the mirror universe is only a theoretical construct. Therefore, there has to be a theoretical framework which will allow this communication. There are several possibilities. In the most minimal class of models, only gravity is the communicator. But there could be various other portals, such as light of the two different sectors converting to each other or even neutrinos doing the same. If the sterile neutrinos are confirmed experimentally, it may make the second neutrino mode of communication feasible. That will be a very interesting future possibility. Meanwhile, we may observe mirror stars and gain some information about the parallel universe. Is it possible that one may have already seen the imprint of the mirror world in the periodic extinction of species? The periodic mass extinction of species is believed to have occurred every 25–30 million years in the past. The dinosaurs were extinguished about 65 million years ago. If these extinctions were caused by asteroid collisions, it has been speculated that it could have been caused by a mirror star with an orbital period of 25–30 million years. Communicating with the mirror sector may then provide a way to test this idea. Such communication may also be important in future space travel if a spaceship is close to one such mirror planet or star.

25 Neutrinos from Heavenly Sources

There are two kinds of natural neutrino sources in the universe: one coming from the cosmic neutrinos, which were created during the early moments of the universe from various collisions, such as e+ e− and μ+ μ− , and decays, such as of the weak bosons and the Z bosons, etc. Those neutrinos have become very cold and have very low energy due to the expansion of the universe. They were discussed in Chap. 17. Their energies now are less than an eV. There is another source where the neutrinos are produced at the current era of the universe from violent collisions of energetic protons with protons via the process pp → pn + (π + , K + ), followed by the decays of pion and kaon e.g. (π + , K + ) → (μ+ + νμ , e+ + νe ) or via proton–proton fusion as in the stellar cores. Those neutrinos produced in violent collisions of protons typically have higher energy since they are not affected by the Hubble expansion. For the stellar core emitted neutrinos, the energies are of the order of one to 10 MeVs and for more energetic proton–proton collisions, they can be of order GeVs. In the course of our discussion of neutrino oscillation, we have considered two such heavenly sources of neutrinos: solar neutrinos with MeV range energies emitted from the core of the Sun, and atmospheric sources with GeV range energies originating from energetic protons in cosmic rays, colliding with hydrogen and other atoms in the atmosphere. These are all in some sense “natural–born” neutrinos, like the cosmic neutrinos. The question then is, are there more sources of neutrinos from the sky, like the solar and atmospheric neutrinos, and if so, what are their energies, and is it useful to look for them? The answers to all these questions is “yes” and we will delve into them briefly below. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2_25

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25.1 Why Look for Neutrinos from Extra-Solar Sources and Extra-Galactic Sources There is a lot to be learned about the various stars and galaxies in the universe. That includes their evolution, the nature of stellar collapse, the mechanism of supernova explosion, and more. The more we learn, the more we expand the frontier of knowledge and the better off we are as a society. Deeper knowledge helps us in making useful decisions. The only tool we had before for probing the universe was looking at electromagnetic waves (such as light) from the various distant sources in the sky, using Earth-based telescopes. We had and still have telescopes of different strengths, the famous Hubble Space Telescope being a shining example. We had infrared telescopes and radio telescopes in the past. Major discoveries were made using these devices e.g. the first binary pulsars were discovered by Hulse and Taylor using 1000 ft. diameter radio telescopes. Quasars and exoplanets are other examples of discoveries made using radio telescopes. Also recently, a new class of mysterious cosmic objects known as “fast radio bursts” have been discovered using radio telescopes. All these have inspired a great deal of theoretical activity regarding the nature of different astrophysical objects. The infrared telescopes, such as SPITZER and IRAS telescopes, made their mark with important discoveries like previously unknown rings of Saturn (discovered by Spitzer). Then there is the James Webb Space Telescope, (JWST) being made ready by NASA, which is going to be launched soon. Using both optical and infrared frequencies, JWST will look further back into the universe to see the first galaxies that formed in the universe. This will throw light on the origin of galaxies and how they originally formed from the almost uniform cosmic soup. However, these devices involving electromagnetic radiation of different wavelengths have limitations: they get light that is scattered and absorbed in its path from the source to the Earth where the telescopes are. Similarly, these light beams only provide information about the surface of the source and not the interior, since the light from the interior gets distorted in its path through the outer layers of the emitting object. While they are useful and have provided invaluable information about galaxies, stars, and planets, better devices are called for to learn more. For example, what is going on in the solar core cannot be fully understood using light. The neutrinos on the other hand have very little interaction with the medium they travel through in their journey from the source to the Earth, and therefore preserve the information more accurately. Thus, if we want to understand in great detail the stars and galaxies, neutrinos provide a more

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useful means. By the same token, we need more mammoth detectors to capture the neutrinos. For instance, the 25 to 30 neutrino events from SN 1987A have confirmed our broad understanding of how solar collapse takes place. But we need to know more details about what causes the explosion in a supernova, what is happening in neutron stars that form after the collapse, etc. They can be accurately learned by studying the supernova neutrinos. By the same token, we can also learn more about the properties of the neutrinos from such studies. For example, their mass ordering can leave an imprint on the supernova neutrino energy spectrum. They can also explore events like exploding stars, gamma-ray bursts, and cataclysmic phenomena involving black holes and neutron stars. The gravitational wave observatories LIGO and VIRGO have recently observed gravity waves from a binary neutron star merger. To know the full details of how this merger happened and its consequences, it will be important to know as many other signals as possible from them. The neutrino signal is one important signal since in the neutron star merger, there is likely to be a lot of neutrino emission. This provides another reason why observing neutrino signals from outer space is so important for our understanding of the universe.

25.2 Supernova Neutrinos In 1987, several detectors had been set up mainly to search for proton decay. They were the Kamiokande (pre-cursor to the Super-Kamiokande detector that made the neutrino oscillation discovery) detector in Japan, the IMB detector in the USA, and the Baksan detector in the mountains of Russia. On February 24, 1987, a sudden brightening of a star, named Sanduleak, was observed in the Large Magellanic Cloud. That was light from a supernova explosion. What took place was a supernova that exploded 168,000 years ago, and whose light just reached the Earth on Feb. 24, 1987. It is called SN1987A. Within the same 24 h of light observation, the neutrino detectors mentioned above saw several energetic neutrino events, all clustered within less than 13 s. They were the neutrinos from the supernova explosion, which was the end point of stellar evolution. For the first time, supernova neutrinos were observed on Earth. Their energies were in the few MeV range and they could be understood using the stellar collapse theories known. These few observed events confirmed the broad picture of how supernova explosion generally takes place. To know all the intricacies of a cataclysmic event like this, we need to observe more such supernova neutrinos. There are now many more sensitive water Cherenkov detectors set up around the world for detecting supernova neutrinos, both from our own galaxy as well as galaxies outside the Milky Way.

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25.3 Neutrinos Observed in the IceCube Experiment in the South Pole A major effort to look for more energetic neutrinos has been launched with an experimental setup, called IceCube, in the South Pole. Located at the Amundsen–Scott South Pole station in Antarctica, the setup has thousands of sensors under the ice. The sensors, digital optical modules which have photo multipliers inside them, are buried deep under clear ice to detect light emitted from passing electrons and muons, etc. They are attached to strings, with each string containing about 60 photo-multipliers. They go down to a depth of one and a half to two and a half kilometers. The construction began in 2005 during the Antarctica summer, from November to February when there is 24 h sunlight. The IceCube is essentially a kilometer cube huge water detector for neutrino interactions, and in some sense is the largest detector on Earth for neutrinos. If an energetic neutrino comes by, it will create a corresponding charged leptons (e, μ) by the inverse beta decay process. The (e, μ) traveling fast through the ice will create Cherenkov light that can be detected by the photomultipliers in the strings. IceCube has detected more than 50,000 neutrinos per year and observed 60 extremely high energy neutrino events with energy larger than 60 TeV (60,000 times the proton mass), some with energies of about a million GeV (called a PeV). The origin of PeV neutrinos is still theoretically unclear and it has inspired a lot of research in the theoretical area to find out where they came from. The IceCube experiment has also detected neutrinos from a class of massive astronomical objects called blazars. The blazars are active galactic nuclei, powered by supermassive black holes at the center of galaxies like ours, which are spewing jets of material towards us. They emit extremely energetic radiation, which was detected by the Fermi Large Area telescope (FermiLat) orbiting the Earth, at the same time that the neutrinos were detected. They were coming from the blazar TXS 0506+056 which is 3.7 light years away. Every time a black hole gobbles up a star, it emits both energetic radiation as well as energetic neutrinos. Many thousand blazars have been detected, but neutrinos from one of them were first detected in 2017. After the sun and supernova 1987A, the blazars are the third kind of astronomical objects that we have seen neutrinos from. These are much more energetic neutrinos than the solar or supernova neutrinos. Their energies are roughly 40 times that of the LHC energies at about 500 Terra electron volt.

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The era of neutrino astronomy has arrived and is here to stay. It is likely to thrive with every new discovery in the field. Combined with familiar electromagnetic astronomy and gravity wave astronomy, this adds another tool for exploring the universe. Thus neutrinos have not only helped building the universe but are now poised help explore it.

Part IV

26 Anthropic Principle

We know that the laws of physics have been determined by the meticulous work of many scientific geniuses down through the centuries. They have determined the nature of forces and matter in great detail. A philosophical question that one can ask is: do the observers play a role in determining the laws of nature, including all their features, such as the strength of forces, how matter reacts to forces, or they are all determined in a completely objective manner with the observer having nothing to do with it? This discussion led to the enunciation of a principle called the “anthropic principle” in physics. This phrase was coined by Brandon Carter in 1974 [28], although the basic idea goes back to Herman Weyl [103]. This was elaborated in a book by John Barrow and Frank Tipler [19]. There were also several discussions of this idea before 1974. For example, “Dirac’s large number hypothesis” in 1937 and Arthur Eddington’s “large number coincidences” were also examples of the anthropic principle in different names. Also, in 1954, Fred Hoyle observed that there must exist a state of the carbon-12 nucleus if the universe as we know it could exist at all, a state which was discovered in the next 4 years (see later for a discussion of this).

26.1 Why Go Anthropic? The basic idea behind the anthropic principle can be stated as follows: the laws of physics and some of the parameters of physics are the way they are because humankind can exist to study them today. In other words, the universe © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2_26

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as it exists today must have influenced those laws and parameters of nature. One can argue that a physical law is a law of nature and humankind should have nothing to do with it. Therefore, is the anthropic principle really a necessary principle in science or just a desperate move to postpone theoretical understanding of the universe as we see it? If it is the latter, this almost makes the anthropic principle sound unscientific since that would leave nothing for physicists to explore and understand. In that case, everything becomes a postulate of convenience for humans with the sole goal of making themselves exist. No objective reasoning or basis behind the physical laws and parameters needs to be sought. This raises the question, are all laws anthropic in nature or simply the ones that we do not understand? If that was the case, it would make it even more artificial as a part of human reasoning. Extending this line of reasoning a bit further, one could even ask, does the anthropic principle imply the existence of God, with God deciding what the laws of nature should be and what the field strengths should be, what kind of matter should exist, and even how the universe began? As Stephen Hawking in his book “Brief answers to big questions” put it “If you like, you can always say that the laws are the work of God but that is more definition of God rather than a proof of his existence”. So why and how did the anthropic principle gain so much traction in science? Is there really a need for this in current scientific discourse? To see this, let us examine what the physical laws really involve. Take the case of the standard model, which involves the weak, nuclear, and electromagnetic force. The basic nature of the forces is determined by a principle, called the gauge invariance, that leads to particles that generate the force and then there is a parameter that determines the strength of the force. The question one can ask is how matter (quarks and leptons, which are the fundamental constituents of matter) couples to this force. How all this happened involves legitimate scientific questions that we need to answer before we can claim a fuller understanding of the standard model. The properties of the forces are determined by the scientific principle, but what about the coupling strength? Where did that number come from and is there a scientific way to determine it from the first principles? One reasoning track that scientists have used is to reduce the number of gauge couplings to one value, so that what we have to explain is not three couplings values but just one (not including gravity). The principle used is called the grand unification of forces, postulated in the early 1970s [80] and briefly alluded to in Chap. 22.

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26.2 Many Universes and the Anthropic Principle Of course one could always ask who determined the principles, such as the gauge symmetry, that we use to derive the standard model. Questions like these have led to the idea of extra dimensions where the gauge forces are related to the hidden dimensions. This was first noted by T. Kaluza and Oscar Klein in the early part of the last century. In 1919, Theodor Kaluza extended Einstein’s theory of general relativity to five dimensions—four space and one time—instead of three space plus one time. The space-time metric, which was the fundamental entity in Einstein’s theory and has ten components in four dimensions, now has fifteen components. Kaluza identified the ten of them with Einstein’s gravity, but of the remaining five, he could show that four of them are like the photon field, which is a gauge field, whose generalization is embodied in the standard model. The idea that the fifth dimension should be small and invisible (called compactification) was suggested by Oscar Klein in 1926. Thus, it is plausible to ask whether the gauge symmetry of the standard model, which gives rise to forces, can be derived from a theory with more than the three familiar space dimensions. The question then gets transformed to “where did the extra dimensions come from?” String theory tries to answer this by using a set of theoretical principles, which says that there have to be extra space dimensions with the total number of space-time dimensions being either twenty six or ten. The question becomes: what principle determined how we got to the visible 3 + 1 dimensional space-time? This is where the anthropic principle seems to come in. One looks at the possible lowest energy states where the four dimensional universe can exist in the string theory. String theorists have argued that there are a huge number of such ground states (∼10500 by some count) and our universe is but one of them [96]. Since all these ideas are string theory motivated, presumably the principles remain like before, i.e. extra dimensions leading to gauge principle on compactification. The next question that arises is what are the values of the force strength parameters in all these universes? This is where one may invoke the anthropic principle and claim that the distribution of strength parameters is random, and life and the universe as we see developed only in the one we live in. It almost makes sense and may even prove compelling. That would mean we need not strive hard to understand the force strengths and other properties of the standard model. Science could then come to a halt beyond making “grungy” calculations using these parameters.

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26.3 Other Examples There are other examples where the anthropic principle seemed to provide useful insight into the ways of nature (for a description of some examples see [8, 19, 28]). An early and famous one, already mentioned, is the Hoyle state in a carbon nucleus. Its presence is essential for three alpha particles to fuse and form carbon in the stellar core and go beyond the carbon nucleus to other heavier nuclei of the periodic table. If this state did not exist, the universe as we know it would be impossible, since three helium nuclei cannot fuse in the stellar core and there would be no heavier element than beryllium in the universe. The state was not known when Hoyle postulated it from what we could call the anthropic arguments in 1954. It was experimentally discovered 4 years later by a group of scientists at Cal. Tech., Pasadena, in the beta decay of boron-12. Scientists, since that time are still trying to understand this state from the underlying principle of nuclear physics and may finally have succeeded [43]. There are many other cases where the anthropic principle has been invoked. A well known one is the value of the cosmological constant. What is a cosmological constant? In the past two decades, it has been found from astrophysical observations involving a class of supernovae, known as type Ia supernovae, that the universe is now accelerating at a small rate, instead of slowing down as the Hubble expansion would have predicted. This could have been caused by the cosmological constant. It has been estimated that the cosmological constant amounts to dark energy, which accounts for about 70% of the total energy budget of the universe. It started dominating the universe’s energy density since the time when the universe was about 11 billion years old (Fig. 26.1). The origin of this cosmological acceleration and the amount of dark energy associated with it that dominates the energy budget of the universe are not understood yet. One explanation is that there is a constant called the cosmological constant present in Einstein’s equation for the behavior of matter in general relativity, which has led to the accelerated expansion of the universe. When scientists fit the observations with Einstein’s equation, they find that the value of the cosmological constant required is (2 × 10−4 eV)4 . This is a very small number indeed, although its role in the universe is huge. In an attempt to understand this small number, Steven Weinberg showed that there may be an anthropic reason for this value. He showed that if the value of cosmological constant was more than 200 times larger, the universe as we know it would not exist; the galaxies would not form, and as a result, life would not exist.

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Fig. 26.1 Artist’s conception of the Big Bang model with the cosmological constant. Source: Wikipedia.org

Of course, while there is an anthropic reason for the fact that cosmological constant in our universe must be small, why it is small has not been understood from a basic physical principle in spite of many attempts. Another example where the anthropic principle has been invoked is the value of the weak force strength, denoted by the symbol GF where F stands for Fermi. This coupling strength has a value roughly 10−5 in units of inverse proton mass square. If this value had been slightly weaker, as mentioned earlier, the universe would have had no hydrogen but all helium. So stellar fusion would never have occurred and hence no planetary life would have been possible. Because this value is what it is compared to the strength of gravitational force, the stars burn slow enough so that they can last billions of years, making it possible for life to grow. If its value had been larger, solar burning would have been faster and the Sun would have exhausted its fusion energy sooner. Similarly, in our universe, the proton is lighter than the neutron. If it had been the other way, then at the BBN epoch there would have been less protons than neutrons, and therefore, again the BBN would have made helium and have leftover neutrons. That would lead to a whole different universe than we see today. So why is the value of GF what it is, or why is the neutron heavier than the proton? One may invoke the anthropic principle to explain this, although it would be more satisfying if there was a physical and objective explanation. Once again, it has been shown that if the proton and neutron were heavier, then the luminosity of the stars would increase, and as a result, the sun would burn out more quickly and life would be extinct sooner than what we expect now. So one could ask why the masses of the proton and neutron are what they

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are. Perhaps one day, detailed calculations using Quantum Chromodynamics (QCD) would explain this. In that case, one could ask why the mass scale of QCD which goes into this calculation is what it is, and on and on. There are many free parameters in the standard model, which do not have much to do with the structure of the universe or the existence of life. Examples are the masses of the charm, top or bottom quarks, the QCD CP violating parameter known as θ parameter, and the mixing of different quarks among themselves. If their values were very different, it would not affect the growth of the universe or the existence of life. So those parameters cannot rely on the anthropic principle for their understanding, and must be understood using objective reasoning from physical principles. There are therefore many challenges for theoretical physicists even if the anthropic principle is used to explain some of them. Thus anthropic principle does not completely bypass the need for active research into understanding the basic forces and matter. In some interpretations of the anthropic principle, it can appear as if the existence of human life is a prerequisite for physical laws, since every aspect of a physical law would appear (according to this) to be designed to make life possible. This would be something difficult to accept. Whether the anthropic principle finally remains as part of scientific discourse or not, the anthropic arguments could be around for a long time (maybe forever) in some form, until all the physically important parameters necessary for life and the universe are fully understood, starting with a basic set of physical laws (it is unlikely to be soon or even ever). Perhaps the examples given here, such as Hoyle state, proton mass, etc. can one day be fully understood from basic principles of forces and matter. Can the anthropic arguments be completely discarded? It would appear not, if string theory is established as the ultimate theory of the universe. That is because the multiple ground state (or lowest energy state) problem of string theories may always require some sort of anthropic argument to justify the universe we live in, as well as the success of the standard model. But then maybe string theory does not have much to do with physics, or it may happen that there will be so much progress in string theory that one day, it will determine which one out of the 10500 universes (or ground states) we live in. Only time will tell.

27 What Lies Ahead?

The future is always hard to predict. So how can we contemplate what will happen to such a large system as the universe, with all its galaxies, planets, stars, and gas? Yet, given what we know about the laws of physics and the state of our universe now, a rough future path for the universe can be charted. It is of course always possible that new things and new phenomena will be discovered and the path will change. But in this chapter, we will push ahead with the knowledge we have to predict what can happen. There are several serious discussions of this in the literature [6]. Since this kind of discussion deals with the “end” of the universe, it is often called an “eschatological” study of the universe. Here, we give a brief glimpse of some of the main events at specific future times, like ten billion, 100 billion billion, and 1000 billion billion billion years. One can of course go beyond that time scale, but this book does not.

27.1 “Near” Future: The First Ten Billion (∼1010 ) Years Things that likely will happen to our universe in the billion year time scale are as follows: The Sun and all the stars shining every day, as already alluded, will become red giants in a few billion years. As soon as that happens, the outer region of the Sun starts engulfing the Earth. The detailed studies estimate that Earth will have about 50 years to be totally destroyed [6] once the engulfing starts in a few billion years. There is the possibility that as the sun expands, it may © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2_27

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experience mass loss, implying that its gravitational force on the planets will become weaker and that will push the planets like the Earth, Venus, and Mercury farther from the sun. That way, we on Earth may be spared from the heat death due to the red giant expansion of the Sun. However, we do not know for sure how much mass loss the sun will have, if any. After the stars become red giants, they burn helium to carbon, followed by carbon to oxygen, then neon, silicon, magnesium, and sulfur, until finally they reach a stage where the stellar core is filled with iron. Further compression after that will not generate any radiation energy from nuclear reactions. As a result, the star, if it is massive enough, will explode as a supernova. The star will thus melt and die. Some will become neutron stars and some will end up as black holes floating in the sky, which would move around like an endless parade of zombies. They would whistle occasionally when they fall into each other, giving out gravity waves and possibly some flashes of light, and maybe even neutrinos. Such gravity waves from black hole pairs and neutron star pairs have indeed been seen at the LIGO and VIRGO observatories, and no doubt more will be seen in the future, confirming the general outline (not details) of this picture. If the star has a smaller mass, after the red giant phase it will become a white dwarf and then cool down to become a black dwarf. Stars which have masses of about a few percents of the solar mass cannot sustain nuclear reactions and remain as what is known as brown dwarfs. The galaxies are part of clusters which have many galaxies. As a result, they can collide with each other as they move through the sky. So would the stars in a galaxy, which we discuss next. For example, our galaxy is known to be on a collision course with the closest galaxy to us, the Andromeda Galaxy, and the encounter is likely to occur in some four to six billion years from now. This was first suspected by Vesto Slipher in 1913. When that happens, the two galaxies may merge and the solar system will have different “zip code.” Some astronomers have called the new galaxy resulting from this merger as “Milkomeda,” which will most likely be an elliptical galaxy, unlike the Milky Way, which is a spiral galaxy. In fact, it is now established that our own galaxy has merged with several dwarf galaxies over the course of time. So a galaxy merger is not an uncommon feature. The Hubble Telescope has found evidence for many other galaxy mergers, which have been analyzed by NASA teams and provided a clearer picture of merger rates, say one to a few in ten billion years. Of course contrary to what we may expect, in galactic collision, there is hardly any collision between the stars in the galaxy since the density of stars in a galaxy is very low. However, the interstellar gases will collide and that can

27 What Lies Ahead?

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trigger new star formation in each galaxy. The galaxies may also pass through each other without any spectacular effect.

27.2 One Hundred Billion Billion (∼1020 ) Years At the level of galaxies, the stars collide with each other with a low probability as just noted. That makes the stars evaporate on average in a time scale of 1019 years. The stars may also leave a galaxy as a result of collisions so the galaxies may start to lose stars. There are two ways this can be halted. The presence of the dark matter may delay this process somewhat. It may also happen that brown dwarfs, which do not shine like our sun, have all their nuclear energy unspent, and when two brown dwarfs collide, they may merge and form a new sun-like star. This may replenish some of the star content of the galaxies.

27.3 Far Future: Beyond the Next Million Trillion Trillion Years ∼1030 Years As the universe expands under the influence of the cosmological constant and the resulting accelerated expansion, all galaxies fly farther apart, and in each galaxy stars vanish. Most become black holes, making the universe cold, dark, and depressing. There can also be interesting wrinkles in what happens in the far future, if for example the baryon number is not conserved. The fact that it is not conserved is something that seems guaranteed by Sakharov’s argument about the origin of matter in the universe. As a typical example, we may assume that the proton is unstable and it decays to positron and a π 0 . The π 0 decays in an instant to two photons. The proton may also decay part of the time to neutrinos and a π + . The lower bounds on the lifetimes for these processes is of the order of 1033 years. Similarly, neutron–anti-neutron oscillation inside a nucleus has a lifetime of the same order. This means that eventually when the universe is 1033 years old, these decay processes leading to the disappearance of the proton and a bound neutron start to be effective. Note that in our universe there are about 1078 total of protons and neutrons right now. At that time, all the baryons that made the stars and planets will start to evaporate to electrons, positrons, photons, and some neutrinos. That will leave a dust of these particles as the end product in the universe. If the electric charge conservation was not an exact law, then an electron or positron could decay to a neutrino and a photon or a majoron, in which case, the end product will all be photons with

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or without a mixture of majorons (assuming the majorons exist). Otherwise, the electron and positron are so far apart from each other at the time that they can hardly meet and annihilate. Instead, they will form an analog of the hydrogen atom, called the positronium, and then slowly spiral towards each other to annihilate [34]. All these will lead to what is generally called the “heat death” of the universe, where there is no transfer of energy from one system to another. This idea was initiated by Lord Kelvin in 1851. Kelvin wrote: The result would inevitably be a state of universal rest and death, if the universe were finite and left to obey existing laws. But it is impossible to conceive a limit to the extent of matter in the universe; and therefore science points rather to an endless progress, through an endless space, of action involving the transformation of potential energy into palpable motion and hence into heat, than to a single finite mechanism, running down like a clock, and stopping for ever.

28 Epilogue

This book is supposed to give an abbreviated impression [50] of how important an elusive, ultra weakly interacting, super light, fully invisible particle called the neutrino can be to the evolution of the universe. It takes a homogenous hot soup, repulsive to the existence of any ordered structure, to the present day—one which is a full, ordered, and hospitable universe. The neutrinos had a role in building the elements of the periodic table little by little, slowly but steadily. Sometimes it helped this by being there as at the time of Big Bang Nucleosynthesis and sometimes by not being there. In the latter case, it would hinder element formation by being nearby such as in binary neutron star merger. It is playing a key role in our daily existence since it makes the sun shine every moment of the day. It also provides important clues to the nature of new forces and new matter beyond the standard model [49]. So how well do we understand a particle that has been so vital to the universe as we see it today? There have certainly been major developments in our understanding of the neutrino in the past nine decades, since the time it was first imagined by Pauli. We understand many things starting from what kind of force it participates in to what its properties are. Yet a lot remains to be understood. Scientists are working hard to figure the rest of the properties out using different experiments like neutrinoless double beta decay, long baseline oscillation experiments, searches for sterile neutrinos using the reactors, etc. That various governments the world over have invested in major experiments to unravel the remaining unknown properties of neutrinos is very encouraging. We need to build major observatories to unravel the rest of the mysteries of the neutrino and possibly use them for practical purposes such as © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2_28

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exploring the Earth’s crust, exploring long distance communication as well as monitoring rogue countries before they build up destructive nuclear arsenals. Some basic properties of the neutrino are completely unknown—for example, is the neutrino its own antiparticle (a Majorana neutrino)? This is a property not only vital for uncovering new forces but also for possible future use of the neutrino for practical applications. Are there CP violating forces in the neutrino sector that distinguish between neutrinos and anti-neutrinos? If so, do they solve the major cosmological puzzle of the smooth Big Bang universe, i.e. generating the matter–anti-matter asymmetry that is observed today? If it does, can we test this particular aspect of the leptonic sector explicitly? This physics can have important practical applications. Are there new kinds of dark (or sterile) neutrinos? Many experiments are trying to establish their existence. If they are confirmed to exist, the field of neutrino physics will undergo a transformational change, which mostly has been considering three known “active” neutrinos for understanding their properties. Do they imply the existence of a parallel universe and do they provide a motivation for the dark matter being from the parallel universe? That will be exciting knowledge if confirmed. The fact that we may be living right next to another invisible world gives the word “invisible” a new meaning—invisible stars, invisible planets passing through us every moment is an Earth-shaking concept—literally. With observations of neutrinos from the different astrophysical objects in the sky, a new branch of astronomy has sprung up and is going to thrive: neutrino astronomy. It will add to the conventional astronomy knowledge that used telescopes invented in 1608 and used extensively by Galileo. Add to this the recent arrival of gravity wave astronomy, which observes gravity waves from massive distant objects. They will help scientists in deciphering the inner workings of the objects in the sky, which could not have been studied using conventional optical, infrared, and radio telescopes. Does the anthropic principle play a role in our understanding of physical phenomena? Does string theory require the anthropic principle? What does the future of the universe look like from today’s vantage point with currently available knowledge? Apparently, Enrico Fermi once said, commenting on somebody’s seminar that “Before I came here, I was confused about the subject; after listening to your lecture, I am still confused but at a higher level.” If this book gives the same sense of a higher level confusion and some enlightenment to the reader about the world of the neutrino, I will consider my efforts worth it!

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Index

A

Alpher, R., 125, 136 Angular momentum, 11, 174 Anthropic principle, 6, 33, 47, 197–202 Anti-matter, 16–20, 25, 34, 73, 103, 126, 132, 133, 152, 171, 172, 174, 178 Anti-proton, 20, 132 Atmospheric neutrino, 64, 69, 99–103, 109, 111, 113, 175, 182, 185, 189 Atomic nucleus, 9, 12, 13, 16, 38, 53, 103 B

Bahcall, J., 70, 94–97 Baryon, 27–32, 74, 102, 138, 166, 171–183, 205 Baryon asymmetry, 172–178 Bekenstein, J., 36 Beta decay, 18, 39, 53, 57–59, 61, 63–69, 89, 95, 115, 121, 146, 151, 153, 156, 161–164, 169, 170, 174, 192, 200, 207 Bethe, H., 59, 60, 63, 96, 136

Big Bang, 123–127, 129–131, 135–138, 141, 142, 171, 172, 186, 201, 207 Black holes, 36, 191, 192, 204, 205 Bohr, N., 10–13, 19, 53, 58 Born, M., 58 Bose, S.N., 14, 45 Bosons, 14, 44, 80, 82, 88, 89, 135, 153, 154, 177, 185, 189 Brout, R., 83 Bubble chamber, 179 C

Cabibbo, N., 74 CERN, 24, 44, 70, 83 Chadwick, J., 12, 13, 16, 53, 58, 60, 61 Chandrasekhar, S., 144 Chirality, 153 Clinton, W.J., 99 CMS detector, 220 Cobalt, 67, 150 Compactification, 199 Conservation, 31, 32, 43, 52, 53, 55, 57, 89, 107, 152, 163, 174, 184, 206 Cosmic microwave background, 125, 132, 139, 181

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 R. N. Mohapatra, The Neutrino Story: One Tiny Particle’s Grand Role in the Cosmos, https://doi.org/10.1007/978-3-030-51846-2

219

220

Index

Cosmic neutrino background, 139 Cosmic rays, 15, 19, 21, 24–25, 40, 43, 64, 65, 98, 100, 101, 132, 149, 189 Cosmological constant, 88, 127, 131, 161, 200, 201, 205 Cowan, C., 64–66, 69 CP symmetry, 73 CP violation, 73, 109, 113, 173, 178 Critchfield, 103 Cyclotron, 22, 23, 25 D

Dark energy, 7, 148, 200 Dark matter, 7, 47, 68, 88, 138, 166, 181–186, 205, 208 Davis, R., 64, 70, 95–98, 102, 104, 114, 175 Daya bay experiment, 103 Democritus, 3, 8 Dimensions, Extra, 88, 161, 169, 183, 199 Dirac leptogenesis, 178 Dirac neutrinos, 163 Dirac, P., 18, 19, 25, 56, 58, 115, 158, 160, 162, 163, 169, 170, 178 Discrete symmetries, 77, 93 Double beta decay, Neutrinoless, 115, 161–164, 169, 170, 207 E

Eddington, A., 17, 35, 95, 197 Einstein, A., 11, 16–18, 34, 35, 43, 45, 47, 52, 77, 93, 95, 123, 126, 167, 199, 200 Electromagnetic fields, 37, 51, 57 Electrons, 8–16, 18, 19, 22–25, 32, 37–41, 52, 63, 64, 69, 88, 93–95, 97, 98, 100–103, 114, 115, 121, 132, 136, 139, 145, 150, 151, 157, 162, 172, 181, 186, 192, 205 Energy conservation, 52, 53, 57, 174

Englert, F., 83 Ether, 17 F

Fermi, E., 57–60, 63, 156, 208 Fermilab, 24, 76, 103, 113, 178 Fermions, 14, 45, 77, 79, 82, 88, 113, 153, 154, 156, 162, 163, 169–170, 177 Feynman, R., 64, 79, 153 Forces, 7, 15, 26, 33–41, 43–47, 65, 71–85, 88, 89, 100, 102, 110, 113, 114, 136, 137, 141, 145, 150, 153, 154, 160, 165, 167, 168, 177, 179, 197–199, 201, 202, 208 Fowler, W., 94, 96 Fundamental particles, 28, 52 G

Galileo, G., 4 Gallex experiment, 97 Gamma rays, 12, 63, 65, 175 Gamow, G., 96, 125, 136 Gell-Mann, M., 27, 28, 68, 79, 153 General relativity, 17, 126, 199 Germanium, 97, 120, 163 Glashow, S., 70–73, 173 Grand unified theories, 110, 168 Gran Sasso laboratory, 182 Graviton, 77 Greek philosophers, 3 Guralnik, G., 83 Guth, A., 130 H

Hadron, 24, 29, 46, 71–74, 83, 84, 88, 164, 178 Hagen, C., 83 Handedness, 67 Hawking, S., 36, 87, 198 Heisenberg, 22, 58, 92 Helicity, 14–15, 151–153, 160 Higgs mechanism, 82–83 Higgs, P., 82–83

Index

‘t Hooft, G., 83 Hubble, E., 124 I

Ice Cube, 192–193 IMB experiment, 101, 175, 191 Inflation, 126, 127, 129–133, 169, 172 Inverse seesaw, 160, 161 Inverted mass hierarchy, 108 J

Jung, C., 55 K

Kajita, T., 101 Kaluza, T., 199 KamLand experiment, 103, 109 Kibble, T., 83 K2 K experiment, 103 Klein, O., 199 Koshiba, M., 98 L

Large Hadron Collider, 24, 46, 83 Large Magellanic Cloud, 191 Lee, T.D., 51, 67 Lemaitre, G., 123, 124 Lepton number, 31–32, 161–164 Leptons, 6, 31, 32, 64, 73–77, 88, 110, 153–155, 166, 167, 172, 177 LSND experiment, 185 M

Magnetism, 5, 37, 72, 93, 167 Majorana, E., 158–161 Majorana neutrino, 158–162, 164 Majoron, 111, 206 Maki, Z., 69 Marshak, R., 71, 73, 79, 153 Mass, 6, 9, 10, 14, 15, 17, 18, 20, 27, 32, 34, 36, 53, 72, 79, 80, 87, 88, 92, 94, 95, 102, 109, 113, 114, 136, 138, 144, 149–161, 164, 166, 169, 174, 183, 186, 204 Massless, 6, 15, 82, 84, 102, 111, 114, 126, 152, 154

221

McDonald, A., 101 Mesons, 26–31, 43–46, 68, 71, 74, 84, 101–103, 135, 164, 173 Mikheyev, S., 110 Mirror universe, 68, 165–167, 183, 185, 187 Multiverse, 47, 166 N

Nakagawa, M., 69, 108 Nambu, Y., 26, 82, 84 Negative energy, 18, 19 Neutrino mass decay, 15 magnetic moment, 13, 28 mixings, 74, 108 refraction in matter, 110 Neutron, 8, 12–13, 15, 16, 19, 27, 28, 31, 35, 37, 38, 40, 43, 52, 55, 58–60, 65, 89, 121, 135, 145–148, 174, 176, 184, 185, 191, 201, 204 Newton, I., 4, 5, 33, 34, 36, 93, 167 Nobel Prize, 10, 14, 19, 43, 45, 53, 58, 68, 77, 83, 96–98, 100, 101, 120, 147, 180 Normal hierarchy, 109, 169 NOVA experiment, 103, 178 Nucleosynthesis, 121, 127, 135–138, 141–144, 148, 186, 207 O

Okubo, S., 27, 71 Oscillation, neutrino kaons, 189 neutron-anti-neutron, 89, 176, 205 P

Parallel universe, 68, 187, 208 Particles, 6–31, 33–35, 37–39, 43–47, 52–55, 57, 60, 65, 71, 75, 77–80, 84–87, 89, 91–93, 111, 121, 125, 126, 129, 136, 138, 146, 151–153, 158–163, 181–185, 198, 200, 207

222

Index

Pion, 28, 43, 74, 168, 175, 189 Pontecorvo, B., 63, 64, 69, 108, 109 Positron, 19, 20, 24, 25, 63–65, 72, 89, 132, 138, 168, 172, 175, 176, 205, 206 Proton decay, 89, 98, 174–176, 191 Q

Quantum Field Theory, 58, 72, 82, 114, 167 Quarks, 6, 8, 13, 23, 27–31, 71–76, 83–85, 88, 103, 108–110, 121, 126, 135–139, 153–158, 165–169, 173, 179, 184, 198, 202 R

Radioactivity, 53 Redshift, 124, 126, 180 Reines, F., 64–66, 69, 75 RENO experiment, 103 Right handed neutrinos, 154, 166, 177 Right handed W boson, 114 S

Sakharov, A., 172–174 Salam, A., 70, 71 Scattering, 39, 70, 94, 114, 161, 181 Seesaw, 160–162, 164, 166, 168–170, 177–178

Smirnov, A., 110 Sterile neutrino, 113, 146, 166, 185–186, 207, 208 Sudarshan, E.C.G., 79, 153 Supersymmetry, 45, 88 Symmetry breaking, 80–82, 149, 153, 155–158 T

Tau neutrino, 75, 76, 94, 108 T2 K experiment, 113, 178 Tritium, 115 W

Waves, 35, 36, 51, 77, 92, 93, 110, 112, 148, 180, 190, 191, 193, 204, 208 W-boson, 45 Weinberg, S., 70, 71, 161, 200 Wolfenstein, L., 110 X

X-rays, 9, 52 Y

Yang, C.N., 51, 58, 67, 79, 165, 184 Z

Z-boson, 45, 82, 185 Zweig, G., 28 Zwicky, F., 147, 179, 180