University of Oulu

Koldobskiy, S., Kachelrieß, M., Lskavyan, A., Neronov, A., Ostapchenko, S., & Semikoz, D. V. (2021). Energy spectra of secondaries in proton-proton interactions. Physical Review D, 104, 123027.

Energy spectra of secondaries in proton-proton interactions

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Author: Koldobskiy, S.1,2; Kachelrieß, M.3; Lskavyan, A.1;
Organizations: 1National Research Nuclear University MEPHI, 115409 Moscow, Russia
2Space Physics and Astronomy Research Unit and Sodankylä Geophysical Observatory, University of Oulu, 90014 Oulu, Finland
3Institutt for fysikk, NTNU, Trondheim N-7491, Norway
4APC, Université Paris Diderot, CNRS/IN2P3, CEA/IRFU, Observatoire de Paris, Sorbonne Paris Cité, 119 75205 Paris, France
5Astronomy Department, University of Geneva, Chemin d’Ecogia 16, 1290 Versoix, Switzerland
6II. Institute for Theoretical Physics, Hamburg University, Hamburg 22761, Germany
7D.V. Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow 119992, Russia
8INR RAS, 60th October Anniversary prospect 7a, Moscow 117312, Russia
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 1 MB)
Persistent link:
Language: English
Published: American Physical Society, 2021
Publish Date: 2022-01-04


We compare the predictions of AAfrag for the spectra of secondary photons, neutrinos, electrons, and positrons produced in proton-proton collisions to those of the parametrizations of Kamae et al., Kelner et al. and Kafexhiu et al. We find that the differences in the normalization of the photon energy spectra reach 20%–50% at intermediate values of the transferred energy fraction x, growing up to a factor of two for x →1, while the differences in the neutrino spectra are even larger. We argue that LHCf results on the forward production of photons and neutral pions favor the use of the QGSJET-II-04m model on which AAfrag is based. The differences in the normalization have important implications in the context of multimessenger astronomy, in particular, for the prediction of neutrino fluxes, based on gamma-ray flux measurements, or regarding the inference of the cosmic ray spectrum, based on gamma-ray data. We note also that the positron-electron ratio from hadronic interactions increases with energy toward the cutoff, an effect which is missed using the average electron-positron spectrum from Kelner et al. Finally, we describe the publicly available PYTHON package aafragpy, which provides the secondary spectra of photons, neutrinos, electrons, and positrons. This package complements the AAfrag results for protons with energies above 4 GeV with previous analytical parameterizations of particle spectra for lower energy protons.

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Series: Physical review. D
ISSN: 2470-0010
ISSN-E: 2470-0029
ISSN-L: 2470-0010
Volume: 104
Article number: 123027
DOI: 10.1103/PhysRevD.104.123027
Type of Publication: A1 Journal article – refereed
Field of Science: 115 Astronomy and space science
Funding: S. O. acknowledges support from the Deutsche Forschungsgemeinschaft (Project No. 465275045). S. K. acknowledges support from the Ministry of Science and Higher Education of the Russian Federation under project “Fundamental problems of cosmic rays and dark matter” No. 0723-2020-0040.
Copyright information: © 2021 American Physical Society.