- Open Access
Addressing uncertainties of model predictions for extensive air showers initiated by high energy cosmic rays
Phys. Rev. D 114, 063046 – Published 23 September, 2026
DOI: https://doi.org/10.1103/fz3g-13vy
Abstract
A new Monte Carlo generator of hadronic collisions is applied for studying model uncertainties regarding calculations of the development of extensive air showers (EAS) initiated by interactions of high energy cosmic rays in the atmosphere. More specifically, we investigate possibilities to modify the model predictions for two EAS characteristics mostly used in experimental studies of cosmic ray composition: air shower maximum depth and the muon number at ground level. For all the considered modifications of the model, we discuss in some detail the underlying physics mechanisms and investigate the impact of the changes, regarding a comparison of the model results to relevant accelerator data.
Physics Subject Headings (PhySH)
- Cosmic ray composition & spectra
- Cosmic rays & astroparticles
- Models & methods for nuclear reactions
- Nonperturbative effects in field theory
- Nuclear reactions
- Nucleon induced nuclear reactions
- Particle & resonance production
- Particle interactions
- Particle production
- Phenomenology
- Strong interaction
- Total cross sections
Article Text
References (57)
- M. Nagano and A. A. Watson, Observations and implications of the ultrahigh-energy cosmic rays, Rev. Mod. Phys. 72, 689 (2000).
- J. Blumer, R. Engel, and J. R. Horandel, Cosmic rays from the knee to the highest energies, Prog. Part. Nucl. Phys. 63, 293 (2009).
- D. Heck, J. Knapp, J. N. Capdevielle, G. Schatz, and T. Thouw, corsika: A Monte Carlo code to simulate extensive air showers, Forschungszentrum Karlsruhe Internal Report FZKA-6019 (1998).
- R. Engel, D. Heck, and T. Pierog, Extensive air showers and hadronic interactions at high energy, Annu. Rev. Nucl. Part. Sci. 61, 467 (2011).
- R. Ulrich, R. Engel, and M. Unger, Hadronic multiparticle production at ultra-high energies and extensive air showers, Phys. Rev. D 83, 054026 (2011).
- R. D. Parsons, C. Bleve, S. S. Ostapchenko, and J. Knapp, Systematic uncertainties in air shower measurements from high-energy hadronic interaction models, Astropart. Phys. 34, 832 (2011).
- S. Ostapchenko and G. Sigl, Model uncertainties for the predicted maximum depth of extensive air showers, Phys. Rev. D 110, 063041 (2024).
- S. Ostapchenko and G. Sigl, On the model uncertainties for the predicted muon content of extensive air showers, Astropart. Phys. 163, 103004 (2024).
- S. Ostapchenko, M. Bleicher, T. Pierog, and K. Werner, Constraining high energy interaction mechanisms by studying forward hadron production at the LHC, Phys. Rev. D 94, 114026 (2016).
- S. Ostapchenko, Cosmic ray interactions in the atmosphere: QGSJET-III and other models, SciPost Phys. Proc. 13, 004 (2023).
- S. Ostapchenko, T. Pierog, and G. Sigl, A new approach to modeling cosmic ray interactions, Proc. Sci. ICRC2025 (2025) 351.
- S. Ostapchenko, T. Pierog, and G. Sigl, Basic model for high energy cosmic ray interactions, Phys. Rev. D 113, 074001 (2026).
- A. Abdul Halim et al. (Pierre Auger Collaboration), Testing hadronic-model predictions of depth of maximum of air-shower profiles and ground-particle signals using hybrid data of the Pierre Auger Observatory, Phys. Rev. D 109, 102001 (2024).
- R. J. Glauber, High-energy collision theory, In: Lectures in theoretical physics, edited by W. E. Brittin and L. G. Dunham (Interscience Publishers, New York, 1959), Vol. 1, pp. 315–414.
- V. N. Gribov, Glauber corrections and the interaction between high-energy hadrons and nuclei, Sov. Phys. JETP 29, 483 (1969).
- G. Antchev et al. (TOTEM Collaboration), First measurement of elastic, inelastic and total cross-section at by TOTEM and overview of cross-section data at LHC energies, Eur. Phys. J. C 79, 103 (2019).
- G. Aad et al. (ATLAS Collaboration), Measurement of the total cross section and -parameter from elastic scattering in pp collisions at with the ATLAS detector, Eur. Phys. J. C 83, 441 (2023).
- R. L. Workman et al. (Particle Data Group), Review of particle physics, Prog. Theor. Exp. Phys. 2022, 083C01 (2022).
- S. Chatrchyan et al. (CMS Collaboration and TOTEM Collaboration), Measurement of pseudorapidity distributions of charged particles in proton-proton collisions at by the CMS and TOTEM experiments, Eur. Phys. J. C 74, 3053 (2014).
- S. S. Ostapchenko, Contemporary models of high-energy interactions: Present status and perspectives, J. Phys. G 29, 831 (2003).
- O. Adriani et al. (LHCf Collaboration), Measurement of very forward neutron energy spectra for proton-proton collisions at the Large Hadron Collider, Phys. Lett. B 750, 360 (2015).
- O. Adriani et al. (LHCf Collaboration), Measurement of energy flow, cross section and average inelasticity of forward neutrons produced in proton-proton collisions with the LHCf Arm2 detector, J. High Energy Phys. 07 (2020) 016.
- S. Acharya et al. (ALICE Collaboration), Study of very forward energy and its correlation with particle production at midrapidity in and -Pb collisions at the LHC, J. High Energy Phys. 08 (2022) 086.
- S. Acharya et al. (ALICE Collaboration), First observation of strange baryon enhancement with effective energy in pp collisions at the LHC, J. High Energy Phys. 03 (2025) 029.
- S. Ostapchenko and M. Bleicher, Constraining pion interactions at very high energies by cosmic ray data, Phys. Rev. D 93, 051501(R) (2016).
- A. Aab et al. (Pierre Auger Collaboration), Muons in air showers at the Pierre Auger Observatory: Measurement of atmospheric production depth, Phys. Rev. D 90, 012012 (2014).
- B. Z. Kopeliovich and B. G. Zakharov, Novel mechanisms of baryon number flow over large rapidity gap, Z. Phys. C 43, 241 (1989).
- A. Capella and B. Z. Kopeliovich, Novel mechanism of nucleon stopping in heavy ion collisions, Phys. Lett. B 381, 325 (1996).
- D. Kharzeev, Can gluons trace baryon number?, Phys. Lett. B 378, 238 (1996).
- H. J. Drescher, A. Dumitru, and M. Strikman, High-density QCD and cosmic ray air showers, Phys. Rev. Lett. 94, 231801 (2005).
- A. B. Kaidalov and K. A. Ter-Martirosyan, Pomeron as quark-gluon strings and multiple hadron production at SPS collider energies, Phys. Lett. 117B, 247 (1982).
- A. Capella, U. Sukhatme, C.-I. Tan, and J. Tran Thanh Van, Dual parton model, Phys. Rep. 236, 225 (1994).
- G. C. Rossi and G. Veneziano, A possible description of baryon dynamics in dual and gauge theories, Nucl. Phys. B123, 507 (1977) 507.
- P. D. B. Collins, An Introduction to Regge Theory and High Energy Physics (Cambridge U.P., Cambridge, England, 1977).
- A. Aab et al. (Pierre Auger Collaboration), Muons in air showers at the Pierre Auger Observatory: Mean number in highly inclined events, Phys. Rev. D 91, 032003 (2015).
- A. Aab et al. (Pierre Auger Collaboration), Testing hadronic interactions at ultrahigh energies with air showers measured by the Pierre Auger Observatory, Phys. Rev. Lett. 117, 192001 (2016).
- J. Albrecht, L. Cazon, H. Dembinski, A. Fedynitch, and K.-H. Kampert, The Muon Puzzle in cosmic-ray induced air showers and its connection to the Large Hadron Collider, Astrophys. Space Sci. 367, 27 (2022).
- A. M. Hillas, Shower simulation: Lessons from MOCCA, Nucl. Phys. B, Proc. Suppl. 52, 29 (1997).
- M. Reininghaus, R. Ulrich, and T. Pierog, Air shower genealogy for muon production, Proc. Sci. ICRC2021 (2021) 463.
- S. Ostapchenko, QGSJET-II: Physics, recent improvements, and results for air showers, EPJ Web Conf. 52, 02001 (2013).
- A. Aduszkiewicz et al. (NA61/SHINE Collaboration), Measurement of meson resonance production in -C interactions at SPS energies, Eur. Phys. J. C 77, 626 (2017).
- N. M. Agababyan et al. (EHS-NA22 Collaboration), Inclusive production of vector mesons in interactions at 250 GeV/c, Z. Phys. C 46, 387 (1990).
- R. J. Apsimon et al. (OMEGA Photon Collaboration), Comparison of photon and hadron induced production of mesons in the energy range of 65 GeV to 175 GeV, Z. Phys. C 53, 581 (1992).
- T. Pierog and K. Werner, Muon production in extended air shower simulations, Phys. Rev. Lett. 101, 171101 (2008).
- J. Manshanden, Günter Sigl, and M. V. Garzelli, Modeling strangeness enhancements to resolve the muon excess in cosmic ray extensive air shower data, J. Cosmol. Astropart. Phys. 02 (2023) 017.
- H. Adhikary et al. (NA61/SHINE Collaboration), Measurement of hadron production in -C interactions at 158 and with NA61/SHINE at the CERN SPS, Phys. Rev. D 107, 062004 (2023).
- H. Adhikary et al. (NA61/SHINE Collaboration), Evidence of isospin-symmetry violation in high-energy collisions of atomic nuclei, Nat. Commun. 16, 2849 (2025).
- A. Aduszkiewicz et al. (NA61/SHINE Collaboration), Measurements of hadron production in and interactions at 60 GeV/c, Phys. Rev. D 100, 112004 (2019).
- A. E. Brenner et al., Experimental study of single particle inclusive hadron scattering and associated multiplicities, Phys. Rev. D 26, 1497 (1982).
- D. S. Barton et al., Experimental study of the -dependence of inclusive hadron fragmentation, Phys. Rev. D 27, 2580 (1983).
- M. Apollonio et al. (HARP Collaboration) Measurements of forward proton production with incident protons and charged pions on nuclear targets at the CERN proton synchroton, Phys. Rev. C 82, 045208 (2010).
- M. Aguilar-Benitez et al. (LEBC-EHS Collaboration), Longitudinal distribution of , , protons and anti-protons produced in interactions, Europhys. Lett. 4, 1261 (1987).
- T. Pierog, The EPOS.LHC-R global approach and its latest development (to be published).
- F. Riehn, A. Fedynitch, and R. Engel, Sibyll*, Astropart. Phys. 160, 102964 (2024).
- S. Baur, H. Dembinski, M. Perlin, T. Pierog, R. Ulrich, and K. Werner, Core-corona effect in hadron collisions and muon production in air showers, Phys. Rev. D 107, 094031 (2023).
- T. Pierog, The impact of accelerator data on our understanding of extensive air showers, Proc. Sci. ICRC2025 (2025) 1417.
- D. Soldin, I. Coronado, E. Waters, and F. Kling, Predictions of neutrino fluxes at the Forward Physics Facility at the high-luminosity LHC, Proc. Sci. ICRC2025 (2025) 1182.