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Modified hadronic interactions in three-dimensional simulations

Jiří Blažek, Jan Ebr*, Jakub Vícha, and Eva dos Santos

Tanguy Pierog and Ralf Ulrich

  • *Contact author: ebr@fzu.cz
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Phys. Rev. D 113, 123066 – Published 25 June, 2026

DOI: https://doi.org/10.1103/s5p3-gq7d

Abstract

We present a method to test the impact of ad hoc modifications of some of the generic parameters of hadronic interactions—cross section, elasticity, and multiplicity—on any observable quantity using full three-dimensional simulations of extensive air showers induced by ultrahigh-energy cosmic rays. Our approach not only extends the existing one-dimensional tools to three dimensions, but also introduces more flexible features to better respond to the needs of both theory and experiment. We first thoroughly validate the conex 3d framework for the simulation of both longitudinal and lateral features of air showers, in particular, for a nonstandard configuration of the framework in which different energy thresholds for modifications are applied. Moreover, we show that the implementations of the ad hoc modifications in this configuration are consistent with the previous one-dimensional simulations. Finally, we discuss the importance of studying the interaction modifications in three dimensions and the effects of parallel modifications of multiple parameters.

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References (32)

  1. D. Soldin (EAS-MSU, IceCube, KASCADE-Grande, NEVOD-DECOR, Pierre Auger, SUGAR, Telescope Array, and Yakutsk EAS Array Collaborations), Update on the combined analysis of muon measurements from nine air shower experiments, Proc. Sci. ICRC2021 (2021) 349 [arXiv:2108.08341].
  2. J. C. Arteaga Velazquez, A report by the WHISP working group on the combined analysis of muon data at cosmic-ray energies above 1 PeV, in Proceedings of 38th International Cosmic Ray Conference—PoS(ICRC2023) (2023), Vol. 444, p. 466, 10.22323/1.444.0466.
  3. 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).
  4. J. Vícha, A. Bakalová, A. L. Müller, O. Tkachenko, and M. K. Stadelmaier, A heavy-metal scenario of ultra-high-energy cosmic rays, Astrophys. J. Lett. 986, L34 (2025).
  5. J. Blazek, J. Vicha, J. Ebr, R. Ulrich, T. Pierog, and P. Travnicek, Modified characteristics of hadronic interactions, Proc. Sci. ICRC2021 (2021) 441.
  6. J. Blazek, J. Ebr, J. Vicha, T. Pierog, and P. Travnicek, A study of modified characteristics of hadronic interactions, EPJ Web Conf. 283, 05005 (2023).
  7. J. Ebr, J. Blažek, J. Vícha, T. Pierog, E. Santos, P. Trávnícek, and N. Denner, Impact of modified characteristics of hadronic interactions on cosmic-ray observables for proton and nuclear primaries, Proc. Sci. ICRC2023 (2023) 245.
  8. J. Ebr, J. Blazek, J. Vicha, T. Pierog, E. Santos, P. Travnicek, N. Denner, and R. Ulrich, Modified characteristics of hadronic interactions in ultra-high-energy cosmic-ray showers, Ukr. J. Phys. 69, 786 (2024).
  9. R. Ulrich, R. Engel, and M. Unger, Hadronic multiparticle production at ultra-high energies and extensive air showers, Phys. Rev. D 83, 054026 (2011).
  10. T. Bergmann, R. Engel, D. Heck, N. N. Kalmykov, S. Ostapchenko, T. Pierog, T. Thouw, and K. Werner, One-dimensional hybrid approach to extensive air shower simulation, Astropart. Phys. 26, 420 (2007).
  11. D. Heck, J. Knapp, J. N. Capdevielle, G. Schatz, and T. Thouw, corsika: A Monte Carlo code to simulate extensive air showers, FZKA Report No. 6019, 1998.
  12. T. Pierog, R. Engel, and D. Heck, 3D air shower simulations using conex in corsika, in 31st International Cosmic Ray Conference, ICRC 2009 (University of Lodz, Lodz, 2009).
  13. J. Albrecht et al., The muon puzzle in cosmic-ray induced air showers and its connection to the large hadron collider, Astrophys. Space Sci. 367, 27 (2022).
  14. F. Riehn, A. Fedynitch, and R. Engel, sibyll*, Astropart. Phys. 160, 102964 (2024).
  15. S. Acharya et al. (ALICE Collaboration), Production of π0 and η mesons up to high transverse momentum in pp collisions at 2.76 TeV, Eur. Phys. J. C 77, 339 (2017).
  16. H. Adhikary et al. (NA61/SHINE Collaboration), Evidence of isospin-symmetry violation in high-energy collisions of atomic nuclei, Nat. Commun. 16, 2849 (2025).
  17. F. Riehn, R. Engel, A. Fedynitch, T. K. Gaisser, and T. Stanev, Hadronic interaction model Sibyll 2.3d and extensive air showers, Phys. Rev. D 102, 063002 (2020).
  18. S. Ostapchenko, Monte Carlo treatment of hadronic interactions in enhanced Pomeron scheme: I. qgsjet-II model, Phys. Rev. D 83, 014018 (2011).
  19. T. Pierog, I. Karpenko, J. M. Katzy, E. Yatsenko, and K. Werner, EPOS LHC: Test of collective hadronization with data measured at the CERN large hadron collider, Phys. Rev. C 92, 034906 (2015).
  20. T. Sjöstrand, The PYTHIA event generator: Past, present and future, Comput. Phys. Commun. 246, 106910 (2020).
  21. A. Fedynitch, H. Dembinski, A. Prosekin, S. El Hadri, and K. Watanabe, chromo: Cosmic ray and hadronic interaction monte- carlo frontend, 10.5281/zenodo.17660458 (2025).
  22. S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  23. G. Antchev et al., First measurement of elastic, inelastic and total cross-section at s=13 tev by totem and overview of cross-section data at LHC energies, Eur. Phys. J. C 79, 103 (2019).
  24. G. Aad et al. (ATLAS Collaboration), Measurement of the total cross section and ρ-parameter from elastic scattering in pp collisions at s=13  TeV with the ATLAS detector, Eur. Phys. J. C 83, 441 (2023).
  25. P. Abreu et al. (Pierre Auger Collaboration), Measurement of the proton-air cross-section at s=57  TeV with the Pierre Auger Observatory, Phys. Rev. Lett. 109, 062002 (2012).
  26. R. Abbasi et al., Measurement of the proton-air cross section with telescope array’s middle drum detector and surface array in hybrid mode, Phys. Rev. D 92, 032007 (2015).
  27. M. Aaboud et al., Measurement of the total cross section from elastic scattering in pp collisions at s=8  TeV with the ATLAS detector, Phys. Lett. B 761, 158 (2016).
  28. A. M. Botti, I. A. Goos, M. Perlin, and T. Pierog, Study of the muon component in the core-corona model using conex 3d, J. Cosmol. Astropart. Phys. 01 (2025) 119.
  29. M. Bleicher, E. Zabrodin, C. Spieles, S. A. Bass, C. Ernst, S. Soff, L. Bravina, M. Belkacem, H. Weber, H. Stöcker, and W. Greiner, Relativistic hadron-hadron collisions in the ultra-relativistic quantum molecular dynamics model, J. Phys. G 25, 1859 (1999).
  30. J. Montanus, An extended Heitler–Matthews model for the full hadronic cascade in cosmic air showers, Astropart. Phys. 59, 4 (2014).
  31. A. Aab et al. (Pierre Auger Collaboration), The Pierre Auger Cosmic ray observatory, Nucl. Instrum. Methods Phys. Res., Sect. A 798, 172 (2015).
  32. J. Ebr, J. Blažek, and J. Vicha, Data for modified hadronic interactions in three-dimensional simulations, Version 2, Zenodo, 10.5281/zenodo.18282785 (2026).

Outline

Information

Phys. Rev. D 113, 123066– Published 25 June, 2026
  • Received 18 January 2026
  • Revised 5 May 2026
  • Accepted 2 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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