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Charmed hadron production in the QGSJET-III model: Relevance to calculations of the prompt atmospheric neutrino background

Sergey Ostapchenko and Günter Sigl

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Phys. Rev. D 112, 054017 – Published 11 September, 2025

DOI: https://doi.org/10.1103/88lj-2w9x

Abstract

The treatment of charmed hadron production in the framework of the QGSJET-III Monte Carlo generator is developed, including both perturbative and nonperturbative contributions. For the former, a leading order (LO) perturbative formalism is employed. The so-called K factor designed to take effectively into account higher-order corrections, which controls the magnitude of the LO perturbative contribution, is fixed based on a comparison with experimental data on D meson production at the Large Hadron Collider. For the nonperturbative intrinsic charm, a phenomenological Regge-based treatment is developed, with the corresponding normalization being chosen based on measurements of the spectra of Λc baryons at large values of Feynman x. The model is applied for a calculation of the prompt atmospheric muon neutrino flux in the 10–100 TeV and 1–10 PeV energy intervals.

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References (68)

  1. T. K. Gaisser, F. Halzen, and T. Stanev, Particle astrophysics with high-energy neutrinos, Phys. Rep. 258, 173 (1995).
  2. P. Nason, S. Dawson, and R. K. Ellis, The one particle inclusive differential cross section for heavy quark production in hadronic collisions, Nucl. Phys. B327, 49 (1989).
  3. W. Beenakker, W. L. van Neerven, R. Meng, G. A. Schuler, and J. Smith, QCD corrections to heavy quark production in hadron hadron collisions, Nucl. Phys. B351, 507 (1991).
  4. R. Aaij et al. (LHCb Collaboration), Prompt charm production in pp collisions at s=7  TeV, Nucl. Phys. B871, 1 (2013).
  5. R. Aaij et al. (LHCb Collaboration), Measurements of prompt charm production cross-sections in pp collisions at s=13  TeV, J. High Energy Phys. 03 (2016) 159.
  6. R. Aaij et al. (LHCb Collaboration), Measurements of prompt charm production cross-sections in pp collisions at s=5  TeV, J. High Energy Phys. 06 (2017) 147.
  7. R. Gauld, J. Rojo, L. Rottoli, and J. Talbert, Charm production in the forward region: constraints on the small-x gluon and backgrounds for neutrino astronomy, J. High Energy Phys. 11 (2015) 009.
  8. O. Zenaiev et al. (PROSA Collaboration), Impact of heavy-flavour production cross sections measured by the LHCb experiment on parton distribution functions at low x, Eur. Phys. J. C 75, 396 (2015).
  9. R. Gauld and J. Rojo, Precision determination of the small-x gluon from charm production at LHCb, Phys. Rev. Lett. 118, 072001 (2017).
  10. O. Zenaiev, M. V. Garzelli, K. Lipka, S.-O. Moch, A. Cooper-Sarkar, F. Olness, A. Geiser, and G. Sigl (PROSA Collaboration), Improved constraints on parton distributions using LHCb, ALICE and HERA heavy-flavour measurements and implications for the predictions for prompt atmospheric-neutrino fluxes, J. High Energy Phys. 04 (2020) 118.
  11. R. E. Nelson, R. Vogt, and A. D. Frawley, Narrowing the uncertainty on the total charm cross section and its effect on the J/ψ cross section, Phys. Rev. C 87, 014908 (2013).
  12. S. J. Brodsky, P. Hoyer, C. Peterson, and N. Sakai, The intrinsic charm of the proton, Phys. Lett. 93B, 451 (1980).
  13. S. J. Brodsky, C. Peterson, and N. Sakai, Intrinsic heavy-quark states, Phys. Rev. D 23, 2745 (1981).
  14. T. J. Hobbs, J. T. Londergan, and W. Melnitchouk, Phenomenology of nonperturbative charm in the nucleon, Phys. Rev. D 89, 074008 (2014).
  15. P. Jimenez-Delgado, T. J. Hobbs, J. T. Londergan, and W. Melnitchouk, New limits on intrinsic charm in the nucleon from global analysis of parton distributions, Phys. Rev. Lett. 114, 082002 (2015).
  16. V. A. Bednyakov, S. J. Brodsky, A. V. Lipatov, G. I. Lykasov, M. A. Malyshev, J. Smiesko, and S. Tokar, Constraints on the intrinsic charm content of the proton from recent ATLAS data, Eur. Phys. J. C 79, 92 (2019).
  17. S. Ostapchenko, QGSJET-III model of high energy hadronic interactions: The formalism, Phys. Rev. D 109, 034002 (2024).
  18. S. Ostapchenko, QGSJET-III model of high energy hadronic interactions: II. Particle production and extensive air shower characteristics, Phys. Rev. D 109, 094019 (2024).
  19. G. Bari et al., A Measurement of Λc+ baryon production in proton proton interactions at s= 62  GeV, Nuovo Cimento A 104, 571 (1991).
  20. M. G. Aartsen et al. (IceCube Collaboration), Observation and characterization of a cosmic muon neutrino flux from the northern hemisphere using six years of IceCube data, Astrophys. J. 833, 3 (2016).
  21. V. N. Gribov, A reggeon diagram technique, Sov. Phys. JETP 26, 414 (1968).
  22. V. N. Gribov, Glauber corrections and the interaction between high-energy hadrons and nuclei, Sov. Phys. JETP 29, 483 (1969).
  23. V. N. Gribov and L. N. Lipatov, Deep inelastic e p scattering in perturbation theory, Sov. J. Nucl. Phys. 15, 438 (1972).
  24. G. Altarelli and G. Parisi, Asymptotic freedom in parton language, Nucl. Phys. B126, 298 (1977).
  25. Yu. L. Dokshitzer, Calculation of the structure functions for deep inelastic scattering and e+e− annihilation by perturbation theory in quantum chromodynamics, Sov. Phys. JETP 46, 641 (1977).
  26. H. J. Drescher, M. Hladik, S. Ostapchenko, and K. Werner, A Unified treatment of high-energy interactions, J. Phys. G 25, L91 (1999).
  27. H. J. Drescher, M. Hladik, S. Ostapchenko, T. Pierog, and K. Werner, Parton based Gribov-Regge theory, Phys. Rep. 350, 93 (2001).
  28. S. Ostapchenko, H. J. Drescher, F. M. Liu, T. Pierog, and K. Werner, Consistent treatment of soft and hard processes in hadronic interactions, J. Phys. G 28, 2597 (2002).
  29. S. Ostapchenko, On the re-summation of enhanced Pomeron diagrams, Phys. Lett. B 636, 40 (2006).
  30. S. Ostapchenko, Enhanced Pomeron diagrams: Re-summation of unitarity cuts, Phys. Rev. D 77, 034009 (2008).
  31. S. Ostapchenko, Total and diffractive cross sections in enhanced Pomeron scheme, Phys. Rev. D 81, 114028 (2010).
  32. V. A. Abramovsky, V. N. Gribov, and O. V. Kancheli, Character of inclusive spectra and fluctuations produced in inelastic processes by multi-pomeron exchange, Sov. J. Nucl. Phys. 18, 308 (1974).
  33. S. Ostapchenko, Monte Carlo treatment of hadronic interactions in enhanced Pomeron scheme: QGSJET-II model, Phys. Rev. D 83, 014018 (2011).
  34. J. C. Collins, D. E. Soper, and G. F. Sterman, Factorization of hard processes in QCD, Adv. Ser. Dir. High Energy Phys. 5, 1 (1989).
  35. S. Ostapchenko, Nonlinear screening effects in high energy hadronic interactions, Phys. Rev. D 74, 014026 (2006).
  36. S. Ostapchenko and M. Bleicher, Double parton scattering: Impact of nonperturbative parton correlations, Phys. Rev. D 93, 034015 (2016).
  37. R. K. Ellis, W. J. Stirling, and B. R. Webber, QCD and collider physics, Cambridge Monogr. Part. Phys., Nucl. Phys., Cosmol. 78, 1 (1996).
  38. A. B. Kaidalov, J/ψcc¯ production in e+e− and hadronic interactions, JETP Lett. 77, 349 (2003).
  39. A. B. Kaidalov and O. I. Piskunova, Inclusive spectra of baryons in the Quark-Gluon String model, Z. Phys. C 30, 145 (1986).
  40. A. B. Kaidalov, Quark and diquark fragmentation functions in the model of quark gluon strings, Sov. J. Nucl. Phys. 45, 902 (1987).
  41. S. J. Brodsky and P. Hoyer, Nucleus as a color filter in QCD: Hadron production in nuclei, Phys. Rev. Lett. 63, 1566 (1989).
  42. S. J. Brodsky, P. Hoyer, A. H. Mueller, and W.-K. Tang, New QCD production mechanisms for hard processes at large x, Nucl. Phys. B369, 519 (1992).
  43. S. Ostapchenko, M. V. Garzelli, and G. Sigl, On the prompt contribution to the atmospheric neutrino flux, Phys. Rev. D 107, 023014 (2023).
  44. M. L. Good and W. D. Walker, Diffraction disssociation of beam particles, Phys. Rev. 120, 1857 (1960).
  45. L. Frankfurt, M. Strikman, D. Treleani, and C. Weiss, Evidence for color fluctuations in the nucleon in high-energy scattering, Phys. Rev. Lett. 101, 202003 (2008).
  46. P. Chauvat et al. (R608 Collaboration), Production of Λc with large xF at the ISR, Phys. Lett. B 199, 304 (1987).
  47. F. G. Garcia et al. (SELEX Collaboration), Hadronic production of Λc from 600  GeV/c π−, Σ− and p beams, Phys. Lett. B 528, 49 (2002).
  48. A. Bhattacharya, R. Enberg, M. H. Reno, I. Sarcevic, and A. Stasto, Prompt atmospheric neutrino fluxes: Perturbative QCD models and nuclear effects, J. High Energy Phys. 11 (2016) 167.
  49. R. Ammar et al. (LEBC-MPS Collaboration) D-Meson production in 800− GeV/c pp interactions, Phys. Rev. Lett. 61, 2185 (1988).
  50. S. Dulat, T.-J. Hou, J. Gao, M. Guzzi, J. Huston, P. Nadolsky, J. Pumplin, C. Schmidt, D. Stump, and C.-P. Yuan, New parton distribution functions from a global analysis of quantum chromodynamics, Phys. Rev. D 93, 033006 (2016).
  51. R. D. Ball et al. (NNPDF Collaboration), Parton distributions from high-precision collider data, Eur. Phys. J. C 77, 663 (2017).
  52. G. V. Kulikov and G. B. Khristiansen, On the size spectrum of extensive air showers, Sov. Phys. JETP 8, 441 (1959).
  53. T. Antoni et al. (KASCADE Collaboration), KASCADE measurements of energy spectra for elemental groups of cosmic rays: Results and open problems, Astropart. Phys. 24, 1 (2005).
  54. W. D. Apel et al. (KASCADE-Grande Collaboration), Knee-like structure in the spectrum of the heavy component of cosmic rays observed with KASCADE-Grande, Phys. Rev. Lett. 107, 171104 (2011).
  55. W. D. Apel et al. (KASCADE-Grande Collaboration), KASCADE-Grande measurements of energy spectra for elemental groups of cosmic rays, Astropart. Phys. 47, 54 (2013).
  56. W. D. Apel et al. (KASCADE-Grande Collaboration), Ankle-like feature in the energy spectrum of light elements of cosmic rays observed with KASCADE-Grande, Phys. Rev. D 87, 081101 (2013).
  57. M. G. Aartsen et al. (IceCube Collaboration), Cosmic ray spectrum and composition from PeV to EeV using 3 years of data from IceTop and IceCube, Phys. Rev. D 100, 082002 (2019).
  58. M. Thunman, G. Ingelman, and P. Gondolo, Charm production and high energy atmospheric muon and neutrino fluxes, Astropart. Phys. 5, 309 (1996).
  59. J. Boettcher et al. (IceCube Collaboration), Search for the prompt atmospheric neutrino flux in IceCube, Proc. Sci. ICRC2023 (2023) 1068 [arXiv:2309.07560].
  60. R. Laha and S. J. Brodsky, IceCube can constrain the intrinsic charm of the proton, Phys. Rev. D 96, 123002 (2017).
  61. Z. Cao et al. (LHAASO Collaboration), First identification and precise spectral measurement of the proton component in the cosmic-ray ‘Knee’, arXiv:2505.14447.
  62. E. Norrbin and T. Sjostrand, Production and hadronization of heavy quarks, Eur. Phys. J. C 17, 137 (2000).
  63. A. V. Giannini, V. P. Goncalves, and F. S. Navarra, Intrinsic charm contribution to the prompt atmospheric neutrino flux, Phys. Rev. D 98, 014012 (2018).
  64. R. Maciuła and A. Szczurek, Intrinsic charm in the nucleon and charm production at large rapidities in collinear, hybrid and kT-factorization approaches, J. High Energy Phys. 10 (2020) 135.
  65. J. J. Aubert et al. (EMC Collaboration), A study of dimuon events in 280 GeV muon interactions, Phys. Lett. 94B, 96 (1980).
  66. J. J. Aubert et al. (EMC Collaboration), An experimental limit on the intrinsic charm component of the nucleon, Phys. Lett. 110B, 73 (1982).
  67. J. J. Aubert et al. (EMC Collaboration), Production of charmed particles in 250 GeV μ+-iron interactions, Nucl. Phys. B213, 31 (1983).
  68. J. Blümlein, A kinematic condition on intrinsic charm, Phys. Lett. B 753, 619 (2016).

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Phys. Rev. D 112, 054017– Published 11 September, 2025
  • Received 11 June 2025
  • Accepted 20 August 2025
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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. Funded by SCOAP3.

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