Fortschritte der Physik / Progress of Physics: Band 24, Heft 3 1976 [Reprint 2021 ed.] 9783112520406, 9783112520390

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HEFT 3 • 1976 • BAND 24

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V E R L A G EVP 10,- M 31728

B E R L I N

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Fortschritte der Physik 28, 127-209 (1976)

Electromagnetic Interactions of High Energy Cosmic Ray Muons*) C. GBUPEN

Gesamthochschule Siegen, Siegen,

BRD**)

Abstract This paper investigates the electromagnetic interactions of muons. The various processes such as kjiock-on electron-, bremsstrahlung-, direct electron pair production, and nuclear interactions are described in detail. The energy range concerned extends from 109 eV up to 1015 eV for primary muons and from 108 eV up to 1014 eV for energy transfers to the secondaries. On the one hand the measurement of muon interactions represents a test of quantum electrodynamics. On the other hand the high energies available in cosmic rays would possibly lead to the measurement of new processes or the detection of new particles. One hopes to find in the high energy domain the answer to the question why the muon exists at all and if there are properties (apart from differences in mass, lifetime, and lepton number) which distinguish it from a mere heavy electron. The different experimental techniques are described and the various experimental results on muon interactions are presented and compared with relevant QED-theories. Observed deviations between theory and experiment and anomalies in muon interactions are critically investigated and discussed in the light of experimental difficulties and interpretation problems. In general, agreement between theory and experiment is found, i.e. QED-theories describe the results adequately. However, some experiments claim to have detected anomalies in muon physics in the cosmic ray beam. But the hypotheses on new processes and new particles in the high energy range do not withstand a critical analysis. It is concluded that the observed deviations can be understood in the framework of conventional theories.

Contents Abstract

127

1. Introduction

128

2. Theories on Muon Interactions 2.1. Preliminary Remarks 2.2. Knock-on Process 2.3. Bremsstrahlung 2.4. Direct Pair Production 2.5. Inelastic Scattering of Muons on Nucléons 2.6. Inelastic Scattering of Muons on Nuclei 2.7. Energy-loss Relation for Muons

132 132 133 134 134 140 144 144

*) This paper represents the 'Habilitationsschrift' which has been submitted to the Faculty of Science, Department of Physics at the Gesamthochschule Siegen. * * ) Author Address: 59 Siegen-Weidenau, Hölderlinstr. 3 Fachbereich 7. 10

Zeitschrift „Fortschritte der Physik", Heft 3

128

C. Grupen

3. Experimental Techniques 3.1. 3.2. 3.3. 3.4. 3.5. 3.6.

145

Preliminary Remarks Underground Measurements Burst- and Burst-Size Measurements Measurements with Spectrographs Measurements with Spectrographs and Calorimeters Measurements of Horizontal Air Showers (HAS)

4. Experiments on Muon Interactions 4.1. 4.2. 4.3. 4.4. 4.5.

154

Preliminary Remarks ! . . . . . Experiments Investigating the Knock-on Process Experiments Investigating the Process of Direct Electron Pair Production Experiments Investigating the Process of Muon Bremsstrahlung Nuclear Interactions of Muons

5. Comparison of Experimental Results with Theories and Discussion 5.1. 5.2. 5.3. 5.4. 5.5.

Preliminary Remarks Knock-on Process Direct Pair-Production Bremsstrahlung Nuclear Interactions

154 155 167 171 178 182 182 183 188 188 190

6. Anomalies in Muon Interactions 6.1. 6.2. 6.3. 6.4. 6.5.

145 145 148 150 151 153

192

Preliminary Remarks Charge Dependence in Electromagnetic Interactions of Cosmic Ray Muons Stopping Muons Underground Horizontal Air Showers Muon-Poor Showers

192 192 196 201 202

7. Concluding Remarks and Outlook

203

8. References

204

1. Introduction Primary cosmic rays mainly consist of protons (85%), a-particles (12.5%), and a smaller fraction of nuclei (1.5%) with charge number > 2. There is a small abundance of electrons (1%) admixed to the otherwise positively charged primary component [1]. The primary cosmic radiation is distributed over a wide spectrum of energies covering the range from a few MeV up to 10 21 eV. On entering the earth's atmosphere protons and heavier nuclei interact with the nuclei of the atmosphere. A substantial fraction of energy of the primaries is liberated in the form of production of new particles in these collisions. The incident hadrons loose roughly 5 0 % of their energy per collision. Pions, kaons, and baryons are mainly produced in these interactions. These particles initiate in subsequent interactions a nuclear cascade. Only a small fraction of the secondary hadrons reach sea-level, the majority being absorbed in the atmosphere. Charged pions and kaons can either interact with nuclei or decay into muons. The decay probability depends on the energy being higher at low energies. The steepness of the pion and kaon spectrum and the enhanced decay probability at low energies results in copious muon production at low energies. These muons undergo electromagnetic and weak interactions only and can therefore penetrate to sea-level depending on their energy. Muons represent the penetrating component of cosmic rays at sea-level.

Electromagnetic Interactions of High Energy Cosmic Ray Muons

129

Neutral pions decay into two photons and initiate the electromagnetic cascades in the atmosphere. The various processes in the atmosphere lead to the observed particle composition at sea-level. We see «¿75% muons, an 25% electrons, «si 1% protons, and a small contamination of other hadrons at sea-level. The ratio of positive to negative muons (charge ratio) exceeds unity. This reflects the positive nature of primary cosmic rays. A comparatively pure cosmic ray muon beam is obtained under a massive absorber (e.g. underground). This muon beam is only accompanied by the secondaries produced by muons via electromagnetic interactions. An absorber of some meter water equivalent (1 m.w.e. = 100 g/cm 2 ) is already sufficient to filter out electrons and hadrons. The interaction of muons with matter is mediated by their Coulomb field. For impact parameters which are large compared to atomic distances excitation and ionisation are observed. If the energy of the incoming muon is sufficiently high the atomic electrons can be considered to be free. In this case the muons are scattered on 'free' electrons. This process in which a certain amount of energy and momentum is transferred to the electron (knock-on electron) dominates at low muon energies some GeV). For highly relativistic particles the maximum energy transfer to the electron can nearly equal the muon energy. Decreasing impact parameters are coupled on the average with increasing energy transfers. For small impact parameters the muon is scattered in the Coulomb field of the nucleus. Deceleration of muons in the Coulomb field of the nucleus is followed by bremsstrahlung. These bremsstrahlung quanta can carry away a considerable amount of the muon energy. A third process is the direct electron pair production in the Coulomb field of the target nucleons via virtual photons coming from the photon field of the muon. The fourth type of interaction is the inelastic scattering of muons on nucleons in the course of which hadrons are generated. These hadrons can either be generated in the interaction (pions, kaons, ...) or evaporated from the target nucleus (neutrons, protons). This process can be understood as photoproduction of hadrons via virtual photons from the photon field of the muon. Table 1 gives a summary on the main Feynman-graphs describing the four types of muon interactions. The energies of cosmic ray muons are distributed over a wide spectral range. A maximum of intensity is observed in the region of 1 GeV and the spectrum extends up to high energies ( > 10 15 eV). The differential and integral muon spectrum in the momentum range from 0.1 to 103 GeV/c is shown in Figure 1. [2]. Of course, muons can be produced at accelerators for laboratory experiments. A direct acceleration of muons is impossible due to their limited lifetime of 2.2 • 10~6 s. However, secondary muon beams can be extracted from proton accelerators. The present energy limit for muons from accelerators is at some hundred GeV laboratory energy ( < 400 GeV) coming from the large operating accelerators (NAL) or accelerators under construction (CERN II). The technique of proton storage rings (ISR) allows higher equivalent laboratory energies to obtain for protons ( ~ 2 0 0 0 GeV), but no secondary beams can be extracted. The obvious advantages of earth bound accelerators are given in intensity-rich and nearly monoenergetic beams at limited energies. Investigations with cosmic ray muons are of interest only at energies in excess of some hundred GeV, an energy range which is not available at present day accelerators. However, some disadvantages in experiments with cosmic ray muons have to be considered: the cosmic ray muon beam is of low intensity and it is not monoenergetic. The absolute intensity of muons with energies > 1 TeV = 10 12 eV in vertical directions is [2] 5.2 • 10~8 cm - 2 s _ 1 sr- 1 ; 10*

130

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Electromagnetic Interactions of High Energy Cosmic Ray Muons

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i.e. a large detector of an acceptance of 1000 cm 2 sr will register 4.5 muons per day beyond this energy. It is of advantage to orientate the detector to large zenith angles. This is so, because the parent particles of muons (n, K, ...) traverse at these zenith angles longer paths in rarer parts of the atmosphere. Hence the decay probability at large zenith angles is enhanced relatively to the interaction probability compared to the vertical direction. This effect leads to an increased muon intensity at high energies at large zenith angles. For a zenith angle of 83° the intensity of muons > 1 TeV is increased by a factor of 10 in comparison to the vertical direction [