Cite Us!#

If you use MCEq in your scientific publication, please cite the code AND the physical models.

The current citation for the MCEq is:

Calculation of conventional and prompt lepton fluxes at very high energy
A. Fedynitch, R. Engel, T. K. Gaisser, F. Riehn, T. Stanev,
EPJ Web Conf. 99 (2015) 08001
arXiv:1503.00544

The citation for specific lepton flux calcations can be found here:

Hadronic interaction model sibyll 2.3c and inclusive lepton fluxes
A. Fedynitch, F. Riehn, R. Engel, T. K. Gaisser, T. Stanev
Phys.Rev.D 100 (2019) 10, 103018
arXiv:1806.04140

Cite Others!#

Cosmic-ray flux parameterizations#

The parameterizations of the flux of cosmic rays are provided via the module crflux. The references are given in the module’s documentation.

Atmosphere#

  • CORSIKA parametrizations
    CORSIKA: A Monte Carlo Code to Simulate Extensive Air Showers
    D. Heck, J. Knapp, J. Capdevielle, G. Schatz, T. Thouw
    Tech. Rep. FZKA 6019, Karsruhe (1998)
  • NRLMSISE-00
    NRLMSISE-00 empirical model of the atmosphere: Statistical comparisons and scientific issues
    J.M. Picone, A.E. Hedin, D.P. Drob, and A.C. Aikin
    J. Geophys. Res., 107(A12), 1468, doi:10.1029/2002JA009430, (2002)
  • NRLMSIS 2.1 (model description of NRLMSIS 2.0, on which 2.1 builds)
    NRLMSIS 2.0: A whole-atmosphere empirical model of temperature and neutral species densities
    J. T. Emmert et al.
    Earth and Space Science 8 (2021) e2020EA001321, doi:10.1029/2020EA001321

Geomagnetic cutoff#

  • gtracr (rigidity cutoffs from cosmic-ray trajectory tracing)
    K. Watanabe, gtracr, kwat0308/gtracr
  • IGRF-13
    International Geomagnetic Reference Field: the thirteenth generation
    P. Alken et al.
    Earth Planets Space 73 (2021) 49, doi:10.1186/s40623-020-01288-x

Hadronic interaction models#

  • SIBYLL★:
    Sibyll★
    F. Riehn, A. Fedynitch, R. Engel
    Astropart.Phys. 160 (2024) 102964
    arXiv:2404.02636
  • SIBYLL-2.3d & c:
    Hadronic interaction model sibyll 2.3d and extensive air showers
    F. Riehn, R. Engel, A. Fedynitch, T. K. Gaisser, T. Stanev
    Phys.Rev.D 102 (2020) 6, 063002
    arXiv:1912.03300

    Hadronic interaction model sibyll 2.3c and inclusive lepton fluxes
    A. Fedynitch, F. Riehn, R. Engel, T. K. Gaisser, T. Stanev
    Phys.Rev.D 100 (2019) 10, 103018
    arXiv:1806.04140
  • SIBYLL-2.1:
    Cosmic ray interaction event generator SIBYLL 2.1
    E.-J. Ahn, R. Engel, T. K. Gaisser, P. Lipari, T.Stanev
    Phys.Rev. D80 (2009) 094003
  • EPOS-LHC-R:
    EPOS LHC-R : a global approach to solve the muon puzzle
    T. Pierog and K. Werner
    PoS ICRC2025 (2025) 358
    PoS
  • EPOS-LHC:
    EPOS LHC : test of collective hadronization with LHC data
    T. Pierog, I. Karpenko, J. M. Katzy, E. Yatsenko, and K. Werner
    Phys. Rev. C92 (2015) 034906
    arXiv:1306.0121
  • QGSJET-III Particle Production and Extensive Air Showers:
    QGSJET-III model of high energy hadronic interactions: II. Particle production and extensive air shower characteristics
    Sergey Ostapchenko
    Phys.Rev.D 109 (2024) 9, 094019,
  • QGSJET-III Formalism:
    QGSJET-III model of high energy hadronic interactions: The formalism
    Sergey Ostapchenko
    Phys.Rev.D 109 (2024) 3, 034002,
  • QGSJET-II-04:
    Monte Carlo treatment of hadronic interactions in enhanced Pomeron scheme: I. QGSJET-II model
    Sergey Ostapchenko
    Phys.Rev. D83 (2011) 014018,
  • DPMJET-III:
    The Monte Carlo event generator DPMJET-III
    S. Roesler, R. Engel, J. Ranft
    Advanced Monte Carlo for radiation physics, particle transport simulation and applications. Proceedings, Conference, MC2000, Lisbon, Portugal, October 23-26, 2000
  • DPMJET-III-19.3:
    Cascade equations and hadronic interactions at very high energies
    A. Fedynitch
    CERN-THESIS-2015-371
  • FLUKA:
    The FLUKA code: Overview and new developments
    F. Ballarini et al.
    EPJ Nucl. Sci. Technol. 10 (2024) 16, doi:10.1051/epjn/2024015
  • PYTHIA 8:
    A comprehensive guide to the physics and usage of PYTHIA 8.3
    C. Bierlich et al.
    SciPost Phys. Codeb. 2022 (2022) 8
    arXiv:2203.11601

    Hadron interactions for arbitrary energies and species, with applications to cosmic rays
    T. Sjöstrand, M. Utheim
    Eur.Phys.J.C 82 (2022) 1, 21
    arXiv:2108.03481
  • PYTHIA 8 Angantyr:
    The Angantyr model for Heavy-Ion Collisions in PYTHIA8
    C. Bierlich, G. Gustafson, L. Lönnblad, H. Shah
    JHEP 10 (2018) 134
    arXiv:1806.10820