Skip to main content
Log in

Cosmic Ray Muons of High and Ultrahigh Energies

  • Published:
Physics of Particles and Nuclei Aims and scope Submit manuscript

Abstract

Muons are the main component of cosmic rays on the Earth’s surface and underground. The energy spectrum and angular distribution of muons in the atmosphere are related both to the mechanisms of their generation and to the basic characteristics of the primary cosmic rays—their energy spectrum and mass composition. Changes in the muon flux underground are determined by muon energy losses, and its measurements allow muon interaction processes to be studied. The history of extensive cosmic-ray muon investigations covers many decades. A retrospective overview of important directions of cosmic ray muon studies is presented, and analysis of the main experiments and results is given. Special attention is paid to the “muon puzzle”, that is, the muon excess increasing with the energy of primary particles, and to possible ways of solving it.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.

Similar content being viewed by others

REFERENCES

  1. A. A. Petrukhin, “Muon puzzle in cosmic ray experiments and its possible solution,” Nucl. Instrum. Methods Phys. Res., Sect. A 742, 228–231 (2014).

    Google Scholar 

  2. S. Matsuno, F. Kajino, Y. Kawashima, T. Kitamura, K. Mitsui, Y. Muraki, Y. Ohashi, A. Okada, T. Suda, Y. Minorikawa, K. Kobayakawa, Y. Kamiya, I. Nakamura, and T. Takahashi, “Cosmic-ray muon spectrum up to 20 TeV at 89° zenith angle,” Phys. Rev. D: Part. Fields 29, 1–23 (1984).

    Article  ADS  Google Scholar 

  3. O. C. Allkofer, G. Bella, W. D. Dau, H. Jokisch, G. Klemke, Y. Oren, and R. Uhr, “Cosmic ray muon spectra at sea-level up to 10 TeV,” Nucl. Phys. B 259, 1–18 (1985).

    Article  ADS  Google Scholar 

  4. M. G. Thompson, R. Thornley, M. R. Whalley, and A. W. Wolfendale, “The momentum spectrum and charge ratio of muons to 3 TeV/c,” In Proceedings of the 15th International Cosmic Ray Conference, Plovdiv, Bulgaria, 1977, vol. 6, pp. 21–25.

  5. B. C. Nandi and M. S. Sinha, “The momentum spectrum of muons at sea level in the range 5–1200 GeV/c,” J. Phys. A: Gen. Phys. 5, 1384–1394 (1972).

    Article  ADS  Google Scholar 

  6. B. C. Rastin, “An accurate measurement of the sea-level muon spectrum within the range 4 to 3000 GeV/c,” J. Phys. G: Nucl. Phys. 10, 1609–1628 (1984).

    ADS  Google Scholar 

  7. P. Achard et al. (L3 Collab.), “Measurement of the atmospheric muon spectrum from 20 to 3000 GeV,” Phys. Lett. B 598, 15–32 (2004).

    Article  Google Scholar 

  8. M. R. Krishnaswamy, M. G. K. Menon, N. K. Mondal, V. S. Narasimham, B. V. Sreekantan, Y. Hayashi, N. Ito, S. Kawakami, and S. Miyake, “Results from the KGF proton decay experiment,” Nuovo Cimento C 9, 167–181.

  9. W. Rhode, “Measurements of the muon-flux with the Frejus-detector,” Nucl. Phys. B (Proc. Suppl.) 35, 250–253 (1994).

    Article  ADS  Google Scholar 

  10. M. Yu. Andreyev, E. A. Chudakov, I. V. Gurentsov, and M. I. Kogai, “Muon intensity at great depth in zenith angle intervals 50°–70° and 70°–85° obtained by Baksan Underground Scintillation Telescope,” In Proceedings of the 21st International Cosmic Ray Conference, Adelaide, Australia, 1990, vol. 9, pp. 301–304.

  11. M. Ambrosio et al. (MACRO Collab.), “Vertical muon intensity measured with MACRO at the Gran Sasso Laboratory,” Phys. Rev. D: Part. Fields 52, 3793–3802 (1995).

    Article  ADS  Google Scholar 

  12. M. Aglietta et al., (LVD Collab.), “Muon “depth-intensity” relation measured by the LVD underground experiment and cosmic-ray muon spectrum at sea level,” Phys. Rev. D: Part. Fields 58, 092005 (1998).

    Article  ADS  Google Scholar 

  13. V. D. Ashitkov, T. M. Kirina, A. P. Klimakov, R. P. Kokoulin, A. A. Petrukhin, and V. I. Yumatov, “Energy spectrum of cascade showers induced by cosmic ray muons in the range from 50 GeV to 5 TeV,” In Proceedings of 19th International Cosmic Ray Conference, La Jolla, USA, 1985, vol, 8, pp. 77-80.

  14. R. I. Enikeev, G. T. Zatsepin, E. V. Korol’kova, V. A. Kudryavtsev, A. S. Mal’gin, O. G. Ryazhskaya, and F. F. Khal’chukov, “Study of the muon spectrum at a depth 570 m.w.e. underground by means of the 100-t scintillation detector,” Sov. J. Nucl. Phys. 47, 1044–1053 (1988).

    Google Scholar 

  15. V. I. Bakatanov, Yu. F. Novosel’tsev, R. V. Novosel’tseva, A. M. Semenov, and A. E. Chudakov, “Intensity of cosmic-ray muons and nucleons of primary cosmic radiation according to the Baksan Underground Scintillation Telescope,” Yad. Fiz. 55, 2107–2116 (1992).

    Google Scholar 

  16. G. T. Zatsepin, N. P. Il’ina, N. N. Kalmykov, L. A. Kuz’michev, E. A. Osipova, I. V. Rakobol’skaya, and V. S. Khlytchieva, “Energy spectrum of PCR nucleons in the region of 20–400 TeV and charm generation according to the results of the MSU muon experiment,” Izv. Ross. Akad. Nauk, Ser. Fiz. 58, 119–122 (1994).

    Google Scholar 

  17. V. M. Aynutdinov et al. (Baikal Collab.), “Limit on the high-energy muon flux according to the data from the NT–200 Baikal Neutrino Telescope,” Izv. Ross. Akad. Nauk, Ser. Fiz. 69, 406–409 (2005).

    Google Scholar 

  18. A. A. Petrukhin, “Cherenkov water detector NEVOD,” Phys.-Usp. 58, 486–494 (2015).

    Article  Google Scholar 

  19. M. Nagano, H. Yoshii, T. Hara, N. Hayashida, M. Honda, K. Kamata, S. Kawaguchi, T. Kifune, Y. Matsubara, G. Tanahashi, and M. Teshima, “An upper limit on the muon flux at energies above 100 TeV determined from horizontal air showers observed at Akeno,” J. Phys. G: Nucl. Part. Phys. 12, 69–84 (1986).

    Article  ADS  Google Scholar 

  20. G. Navarra et al. (EAS-TOP Collab.) “Study of horizontal air showers from EAS-TOP: A possible tool for UHE neutrino detection?” Nucl. Phys. B (Proc. Suppl.) 70, 509–511 (1999).

    Article  ADS  Google Scholar 

  21. I. S. Alekseev and G. T. Zatsepin, “High-energy µ‑mesons,” In Proceedings of the 6th International Conference on Cosmic Rays, Moscow, USSR, 1959, vol. 1, pp. 326–329 [in Russian].

  22. R. P. Kokoulin and A. A. Petrukhin, “Theory of the pair meter for high energy muon measurements,” Nucl. Instrum. Methods Phys. Res., Sect. A 263, 468–479 (1988).

    Google Scholar 

  23. R. P. Kokoulin and A. A. Petrukhin, “Pair meter—a new type of muon spectrometer,” Fiz. Elem. Chastits At. Yadra 21, 774–811 (1990).

    Google Scholar 

  24. I. Nakamura, T. Kitamura, K. Mitsui, Y. Muraki, Y. Ohashi, A. Okada, and T. Takahashi, “A measurement of the high energy muon spectrum by pair meter,” in Proceedings of the 16th International Cosmic Ray Conference, Kyoto, Japan, 1979, vol. 10, pp. 19–23.

  25. A. P. Chikkatur et al. (Nu TeV/CCFR Collab.), “Tests of a calorimetric technique for measuring the energy of cosmic ray muons in the TeV energy range,” Z. Phys. C 74, 279–289 (1997).

    Article  Google Scholar 

  26. C. Castagnoli, A. Castellina, O. Saavedra, T. M. Kirina, R. P. Kokoulin, and A. A. Petrukhin, “Multiple interactions of muons in the NUSEX detector and muon energy spectrum deep underground,” Astropart. Phys. 6, 187–195 (1997).

    Article  ADS  Google Scholar 

  27. V. B. Anikeev, S. P. Denisov, G. Gennaro, S. N. Gurzhiev, T. M. Kirina, R. P. Kokoulin, V. M. Korablev, V. V. Lipaev, A. A. Petrukhin, A. M. Rybin, F. Sergiampietri, G. Spandre, and E. E. Yanson, “Pair meter technique measurements of horizontal muon energy spectrum,” In Proceedings of the 27th International Cosmic Ray Conference, Hamburg, Germany, 2001, vol. 3, pp. 958–961.

  28. A. G. Bogdanov, R. P. Kokoulin, Yu. F. Novoseltsev, R. V. Novoseltseva, V. B. Petkov, and A. A. Petrukhin, “Energy spectrum of cosmic ray muons in ~100 TeV energy region reconstructed from the BUST data,” Astropart. Phys. 36, 224–236 (2012).

    Article  ADS  Google Scholar 

  29. M. G. Aartsen et al. (IceCube Collab.), “Characterization of the atmospheric muon flux in IceCube,” Astropart. Phys. 78, 1–27 (2016).

    Article  ADS  Google Scholar 

  30. C. Patrignani et al. (Particle Data Group) “Review of Particle Physics (Cosmic Rays),” Chin. Phys. C 40, 100001–421 (2016).

    Article  ADS  Google Scholar 

  31. E. V. Bugaev, A. Misaki, V. A. Naumov, T. S. Sinegovskaya, S. I. Sinegovsky, and N. Takahashi, “Atmospheric muon flux at sea level, underground, and underwater,” Phys. Rev. D: Part. Fields 58, 05401 (1998).

    Google Scholar 

  32. P. K. F. Grieder, Extensive Air Showers. High Energy Phenomena and Astrophysical Aspects. A Tutorial, Reference Manual and Data Book. (Springer, 2010).

    MATH  Google Scholar 

  33. V. N. Bakatanov, Yu. F. Novoseltsev, and R. V. Novoseltseva, “Observation of the "knee” in cosmic ray energy spectrum with underground muons and primary mass composition in the range 1015-1017 eV," Astropart. Phys. 12, 19–24 (1999).

    Article  ADS  Google Scholar 

  34. A. E. Chudakov, A. S. Lidvansky, A. L. Tsyabuk, A. V. Voevodsky, and J. Szabelski, “Multiplicity spectra of muon bundles deep underground,” Nucl. Phys. B (Proc. Suppl.) 97, 243–246 (2001).

    Article  ADS  Google Scholar 

  35. V. B. Petkov and J. Szabelski, “Study of the primary spectrum and composition around the knee at the Andyrchy-BUST experiment,” Astrophys. Space Sci. Trans. 7, 111–114 (2011).

    Article  ADS  Google Scholar 

  36. M. Aglietta et al. (EAS-TOP Collab., LVD Collab.), “The high energy muon spectrum in extensive air showers: First data from LVD and EAS-TOP at Gran Sasso,” Astropart. Phys. 9, 185–192 (1998).

    Article  ADS  Google Scholar 

  37. M. Aglietta et al. (EAS-TOP Collab.), “The cosmic ray primary composition in the “knee” region through the EAS electromagnetic and muon measurements at EAS-TOP,” Astropart. Phys. 21, 583–596 (2004).

    Article  ADS  Google Scholar 

  38. M. Aglietta et al. (EAS-TOP Collab., MACRO Collab.), “The cosmic ray primary composition between 1015 and 1016 eV from extensive air showers electromagnetic and TeV muon data,” Astropart. Phys. 20, 641–652 (2004).

    Article  ADS  Google Scholar 

  39. A. G. Bogdanov, D. M. Gromushkin, R. P. Kokoulin, G. Mannocchi, A. A. Petrukhin, O. Saavedra, G. Trinkero, D. V. Chernov, V. V. Shutenko, and I. I. Yashin, “Investigation of the properties of the flux and interaction of ultrahigh-energy cosmic rays by the method of local-muon-density spectra,” Phys. At. Nucl. 73, 1852 (2010).

    Article  Google Scholar 

  40. H. Tanaka, S. R. Dugad, S. K. Gupta, A. Jain, P. K. Mohanty, B. S. Rao, K. C. Ravindran, K. Siva-prasad, S. C. Tonwar, Y. Hayashi, N. Ito, S. Kawakami, M. Minamino, T. Nonaka, and A. Oshima, “Studies of the energy spectrum and composition of the primary cosmic rays at 100-1000 TeV from the GRAPES-3 experiment,” J. Phys. G: Nucl. Part. Phys. 39, 026201 (2012).

    Article  Google Scholar 

  41. V. Avati, L. Dick, K. Eggert, J. Strom, H. Wachsmuth, S. Schmeling, T. Ziegler, A. Bruhl, and C. Grupen, “Cosmic multi-muon events observed in the Underground CERN-LEP tunnel with the ALEPH experiment,” Astropart. Phys. 19, 513–523 (2003).

    Article  ADS  Google Scholar 

  42. J. Abdallah (DELPHI Collab.), “Study of multi-muon bundles in cosmic ray showers detected with the DELPHI detector at LEP,” Astropart. Phys. 28, 273–286 (2007).

    Article  Google Scholar 

  43. Y. Ma and C. Zhang, “A measurement of high multiplicity muon events with the L3+C detector,” In Proceedings of the 30th International Cosmic Ray Conference, Merida, Mexico, 2008, vol. 5, pp. 1213–1216.

  44. J. Adam et al. (ALICE Collab.), “Study of cosmic ray events with high muon multiplicity using the ALICE detector at the CERN Large Hadron Collider,” J. Cosm. Astropart. Phys. 2016, 032 (2016).

  45. T. Abu-Zayyad et al. (HiRes/MIA Collab.), “Evidence for changing of cosmic ray composition between 1017 and 1018 eV from multicomponent measurements,” Phys. Rev. Lett. 84, 4276–4279 (2000).

    Article  ADS  Google Scholar 

  46. D. Heck, J. Knapp, J. N. Capdevielle, G. Schatz, and T. Thouw, “CORSIKA: A Monte Carlo code to simulate extensive air showers,” Forschungszentrum Report: FZKA 6019, Karlsruhe, 1998.

  47. A. Aab (Pierre Auger Collab.), “Muons in air showers at the Pierre Auger Observatory: Mean number in highly inclined events,” Phys. Rev. D 91, 032003 (2015).

    Article  ADS  Google Scholar 

  48. P. Sokolsky, “Final results from the high solution Fly’S Eye (HiRes) experiment,” Nucl. Phys. B (Proc. Suppl.) 212–213, 74–78 (2011).

    Article  Google Scholar 

  49. A. Aab et al. (Pierre Auger Collab.), “Depth of maximum of air-shower profiles at the Pierre Auger Observatory. I. Measurements at energies above 1017.8 eV,” Phys. Rev. D: Part. Fields, Gravitation, Cosmol. 90, 122005 (2014).

    Article  Google Scholar 

  50. A. G. Bogdanov, N. S. Barbashina, D. V. Chernov, L. I. Dushkin, S. S. Khokhlov, V. A. Khomyakov, V. V. Kindin, R. P. Kokoulin, K. G. Kompaniets, G. Mannocchi, A. A. Petrukhin, O. Saavedra, G. Trinchero, V. V. Shutenko, I. I. Yashin, and E. A. Yurina, “Energy characteristics of multi-muon events in a wide range of zenith angles,” J. Phys.: Conf. Series 798, 012049 (2017).

    Google Scholar 

Download references

ACKNOWLEDGMENTS

The work was supported by the Ministry of Education and Science of the Russian Federation (State Assignment and MEPhI Academic Excellence Project 02.a03.21.0005).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. A. Petrukhin.

Additional information

Translated by M. Potapov

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Petrukhin, A.A., Bogdanov, A.G. & Kokoulin, R.P. Cosmic Ray Muons of High and Ultrahigh Energies. Phys. Part. Nuclei 49, 639–651 (2018). https://doi.org/10.1134/S1063779618040469

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063779618040469

Keywords

Navigation