High-energy atmospheric muon flux calculations in comparison with recent measurements

2); (2) Irkutsk State University; (3) Lomonosov Moscow State University; 4); 4) ((1) Institute of Solar-Terrestrial Physics SB RAS; (4) Joint Institute for Nuclear Research; (5) Irkutsk State Transport University); A. A. Kochanov (1; A.D. Morozova (3; S.I. Sinegovsky (2

arxiv: 1907.00640 · v1 · pith:YSI4VD45new · submitted 2019-07-01 · ✦ hep-ph · astro-ph.HE

High-energy atmospheric muon flux calculations in comparison with recent measurements

A. A. Kochanov (1 , 2) , A.D. Morozova (3 , 4) , T.S. Sinegovskaya (5) , S.I. Sinegovsky (2 , 4) ((1) Institute of Solar-Terrestrial Physics SB RAS , (2) Irkutsk State University

show 3 more authors

(3) Lomonosov Moscow State University (4) Joint Institute for Nuclear Research (5) Irkutsk State Transport University)

This is my paper

Pith reviewed 2026-05-25 12:08 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.HE

keywords atmospheric muonsprompt muonsIceCube experimentquark-gluon string modelcharm productionhadronic interaction modelscosmic ray spectrummuon flux calculations

0 comments

The pith

The quark-gluon string model reproduces IceCube high-energy atmospheric muon spectra, while lower charm models require additional contributions from rare meson decays.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper calculates the conventional atmospheric muon flux from 10 GeV to 10 PeV using hadronic models paired with two cosmic ray spectrum parameterizations. It shows that prompt muons computed via the quark-gluon string model match the IceCube measurements indicating a prompt component above 500 TeV. For charm models that give lower prompt fluxes, the data require an extra contribution, apparently from rare decays of short-lived unflavored mesons. A reader would care because these calculations help interpret high-energy muon data from neutrino observatories and test models of particle production in cosmic ray air showers.

Core claim

The calculation of the prompt muons with use of the quark-gluon string model (QGSM) reproduces the muon data of the IceCube experiment. Nevertheless, an additional contribution to the prompt muon component is required to describe the IceCube muon spectra in case if a charm production model predicts the appreciably lower prompt lepton flux as compared with QGSM. This addition, apparently originating from rare decay modes of the short-lived unflavored mesons η, η′, ρ, ω, ϕ, might ensure the competing contribution to the high-energy atmospheric muon flux.

What carries the argument

The quark-gluon string model (QGSM) applied to prompt muon production from charm particle decays, used to compare calculated fluxes with IceCube data.

If this is right

The IceCube data confirm the presence of a prompt muon component above 500 TeV.
QGSM provides a reproduction of the observed muon spectra without additional terms.
Charm production models with lower fluxes need supplementation from rare decays of η, η', ρ, ω, and ϕ mesons.
The conventional flux calculations are consistent with data when using the specified cosmic ray spectra up to 10 PeV.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If correct, this implies that rare decay channels of light mesons may contribute noticeably to high-energy lepton fluxes in the atmosphere.
Similar adjustments might be needed when modeling high-energy atmospheric neutrinos from the same sources.
Precision measurements at PeV energies could test whether QGSM or adjusted models better describe the data.
These results could influence estimates of the atmospheric background for astrophysical neutrino searches.

Load-bearing premise

The hadronic interaction models and the chosen cosmic-ray spectrum parameterizations correctly capture the relevant physics at energies up to 10 PeV.

What would settle it

An experimental measurement of the muon flux at 1 PeV that is inconsistent with the QGSM prediction would show that the model does not reproduce the IceCube data.

Figures

Figures reproduced from arXiv: 1907.00640 by 2), (2) Irkutsk State University, (3) Lomonosov Moscow State University, 4), 4) ((1) Institute of Solar-Terrestrial Physics SB RAS, (4) Joint Institute for Nuclear Research, (5) Irkutsk State Transport University), A. A. Kochanov (1, A.D. Morozova (3, S.I. Sinegovsky (2, T.S. Sinegovskaya (5).

**Figure 1.** Figure 1: Calculated muon flux at θ = 0◦ (curves) vs. the experimental data of last decades measurements (see text) and latest results of the IceCube + IceTop recontruction [2]. 101 102 103 104 105 106 107 108 10-14 10-13 10-12 10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 EPOS-LHC + H3a (cosT!) IceCube fit QGSJET II-03 + H3a SIBYLL 2.1 + H3a KM + H3a cosT (EP / GeV) 2 d)P/dEP (GeV -1 cm -2 s -1 sr… view at source ↗

**Figure 2.** Figure 2: Calculated muon spectrum near the vertical and the best fit [2] for IceCube + IceTop data in the energy range 6 − 400 TeV (red line). Curves: EPOS-LHC, КM, and SIBYLL 2.1 combined with the cosmic-ray spectrum H3a. component with harder spectrum than is expected for the conventional flux. Such behavior is consistent with sizable contribution of prompt muons, and thus the IceCube experiment reveals the hard … view at source ↗

**Figure 3.** Figure 3: IceCube data measurements [1] for zenith angles θ < 60◦ . Curves: calculations for hadronic models QGSJET II-03, SIBYLL 2.1, EPOS-LHC and КM combined with the cosmic-ray spectrum H3a. 104 105 106 Eµ, GeV 100 101 102 (Eµ/GeV) 3.7 · Φµ, (cm2 s sr GeV) −1 IceCube, 60◦ – 84◦ H3a+KM Н3a+КМ+QGSM H3a+EPOS-LHC H3a+SIBYLL 2.1 H3a+QGSJET-II-03 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: IceCube data measurements for θ > 60◦ and calculations. The same notation as in figure 3. angle enhancement of the conventional muon flux. The prompt muon component calculated with QGSM, being added to the conventional flux, agrees well with the IceCube data in both angle intervals. The all-sky reconstruction of the atmospheric muon spectrum in IceCube experiment [1] is [PITH_FULL_IMAGE:figures/full_fig_p… view at source ↗

**Figure 5.** Figure 5: IceCube data (points) and calculations using EPOS-LHC, КM, SIBYLL 2.1, and QGSJET II-03 combined with cosmic-ray spectra models H3a and ZS. Contribution of vector mesons decays (η, η′ , ρ, ω, φ): solid cyan line – [16]; black dash-dotted – this work (EPOS-LHC). shown in figure 5. The set of curves shows the muon spectra calculated using models EPOSLHC, КM, SIBYLL 2.1, and QGSJET II-03 with the CR spectra … view at source ↗

read the original abstract

Recently the atmospheric muon spectra at high energies were reconstructed for two ranges of zenith angles, basing on the events collected with the IceCube detector. These measurements reach high energies at which the contribution to atmospheric muon fluxes from decays of short-lived hadrons is expected. Latest IceCube measurements of the high-energy atmospheric muon spectrum indicate the presence of prompt muon component at energies above 500 TeV. In this work, the atmospheric conventional muon flux in the energy range 10 GeV - 10 PeV is calculated using a set of hadronic models in combination with known parameterizations of the cosmic ray spectrum by Zatsepin $\&$ Sokolskaya and by Hillas $\&$ Gaisser. The calculation of the prompt muons with use of the quark-gluon string model (QGSM) reproduces the muon data of the IceCube experiment. Nevertheless, an additional contribution to the prompt muon component is required to describe the IceCube muon spectra in case if a charm production model predicts the appreciably lower prompt lepton flux as compared with QGSM. This addition, apparently originating from rare decay modes of the short-lived unflavored mesons $\eta, \eta^\prime, \rho, \omega, \phi$, might ensure the competing contribution to the high-energy atmospheric muon flux.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper runs standard hadronic models against IceCube muon data and finds QGSM matches while lower charm models would need an uncalculated extra term from rare meson decays.

read the letter

The main takeaway is that this is an application paper: it combines published cosmic-ray spectra (Zatsepin & Sokolskaya, Hillas & Gaisser) with existing hadronic models to compute conventional and prompt muon fluxes from 10 GeV to 10 PeV, then compares the results to the recent IceCube measurements. The QGSM prompt calculation reproduces the data, while the authors note that appreciably lower charm models would require an additional prompt component, apparently from rare decays of short-lived unflavored mesons like eta, rho, omega and phi. That is the extent of what is new here—no new derivation, no new technique, no new data reduction. The calculation itself follows the usual cascade-equation approach and shows qualitative agreement with the measurements. That is useful for people who need updated background estimates for neutrino astronomy, but it is incremental. The soft spot is exactly where the stress-test note points: the claim that an extra prompt term “is required” and “might ensure the competing contribution” is stated without any production spectra, branching ratios, or flux numbers attached to it. The paper never demonstrates that this term would actually close the gap to the IceCube spectrum. There are also no error budgets, validation plots, or quantitative fit metrics shown, so the agreement remains descriptive rather than measured. The central assumption—that the chosen models correctly capture the relevant physics up to 10 PeV—is invoked directly but not tested with uncertainties. This work is for specialists already working on atmospheric muon and neutrino backgrounds who want to see how current parameterizations perform against the latest IceCube points. It does not contain enough new substance or demonstrated results to justify peer review.

Referee Report

2 major / 0 minor

Summary. The manuscript calculates conventional and prompt atmospheric muon fluxes from 10 GeV to 10 PeV using established hadronic interaction models together with the Zatsepin & Sokolskaya and Hillas & Gaisser cosmic-ray spectrum parameterizations. It reports that the quark-gluon string model (QGSM) prompt-muon component reproduces the IceCube high-energy muon spectra, while any charm-production model yielding appreciably lower prompt fluxes would require an extra prompt-muon contribution from rare decays of short-lived unflavored mesons (η, η′, ρ, ω, φ) to match the data.

Significance. If the central claims were quantitatively demonstrated, the work would usefully constrain the prompt-muon component above ~500 TeV and flag the possible relevance of rare unflavored-meson decays. The reliance on externally published spectra and models without internal tuning to IceCube data is a methodological strength. However, the absence of error budgets, quantitative fit metrics, or validation plots, together with the uncalculated extra component, substantially reduces the immediate impact of the results.

major comments (2)

[Abstract] Abstract: The assertion that an additional prompt-muon contribution 'is required' when charm models predict lower flux rests on an untested statement. No production spectra, branching ratios, or resulting muon flux from the rare decays of η, η′, ρ, ω, φ are computed, so it is not shown that this component would close any gap to the IceCube data.
[Abstract] Abstract and results sections: The claim that the QGSM calculation 'reproduces the muon data of the IceCube experiment' is presented without quantitative support such as χ² values, residual plots, or error budgets on the comparison. This absence makes the reproduction statement difficult to evaluate.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful review and constructive feedback on our manuscript. We address the major comments point by point below, with an emphasis on honest assessment of the current results and planned revisions where appropriate.

read point-by-point responses

Referee: [Abstract] Abstract: The assertion that an additional prompt-muon contribution 'is required' when charm models predict lower flux rests on an untested statement. No production spectra, branching ratios, or resulting muon flux from the rare decays of η, η′, ρ, ω, φ are computed, so it is not shown that this component would close any gap to the IceCube data.

Authors: We acknowledge that the manuscript does not contain explicit calculations of production spectra, branching ratios, or muon fluxes from the rare decays of the listed unflavored mesons. The statement is a qualitative inference drawn from the fact that QGSM matches the IceCube data while lower charm models fall short, together with the known existence of prompt decay channels for these short-lived particles. To address the concern directly, we will revise the abstract and discussion sections to replace the phrasing 'is required' with 'could provide an additional contribution' and explicitly note that a quantitative evaluation of this component lies outside the scope of the present work. revision: yes
Referee: [Abstract] Abstract and results sections: The claim that the QGSM calculation 'reproduces the muon data of the IceCube experiment' is presented without quantitative support such as χ² values, residual plots, or error budgets on the comparison. This absence makes the reproduction statement difficult to evaluate.

Authors: The agreement is shown via direct comparison of the calculated QGSM prompt flux with the IceCube data points in the relevant figures. Because the calculation employs published external models and parameterizations without any tuning to the IceCube measurements, and given the sizable systematic uncertainties in both the hadronic interaction models and the cosmic-ray spectra, we did not compute formal χ² values or residual plots. In the revised manuscript we will expand the discussion of uncertainties and include residual plots to make the level of agreement more transparent. revision: partial

Circularity Check

0 steps flagged

No circularity; external models and spectra used without fitting to IceCube data

full rationale

The derivation uses independent, externally published cosmic-ray spectrum parameterizations (Zatsepin & Sokolskaya; Hillas & Gaisser) and established hadronic interaction models (including QGSM) as inputs. Flux calculations are performed with these and then compared to IceCube measurements; no parameters are adjusted to the target data, and no prediction reduces to a fit or self-definition by construction. The assertion that an uncalculated extra prompt component 'might ensure' the contribution for lower charm models is an untested statement rather than a load-bearing derivation step. This is a standard forward calculation with external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Paper relies on standard hadronic models and two published cosmic-ray spectrum parameterizations without introducing new free parameters or entities in the abstract.

free parameters (1)

hadronic model internal parameters
Each hadronic model (including QGSM) contains parameters tuned to accelerator or lower-energy data.

axioms (1)

domain assumption Zatsepin & Sokolskaya and Hillas & Gaisser cosmic-ray spectra are accurate inputs up to 10 PeV
Invoked when computing the conventional muon flux component.

pith-pipeline@v0.9.0 · 5843 in / 1151 out tokens · 26704 ms · 2026-05-25T12:08:22.990535+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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Aartsen M G et al (IceCube Collaboration) 2016 Astropart. Phys. 78 1-27

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The IceCube Neutrino Observatory - Contributions to ICRC 2017 Part III: Cosmic Rays

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Ostapchenko S 2006 Phys. Rev. D 74 014026

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Ahn E J, Engel R, Gaisser T K, Lipari P, Stanev T 2009 Phys. Rev. D 80 094003

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145 18002

Pierog T 2017 EPJ Web Conf. 145 18002

work page 2017

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Astrophys

Zatsepin V I and Sokolskaya N V 2006 Astron. Astrophys. 458 1-5

work page 2006

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Gaisser T K 2012 Astropart. Phys. 35 801-806

work page 2012

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C 12 41-73

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work page

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Sinegovsky S I and Sorokovikov M N 2017 Rus. Phys. J. 60 1189

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Sinegovsky S I and Sorokovikov M N 2018 Prompt atmospher ic neutrinos in the quark-gluon string model Preprint P2-2018-4 JINR, Dubna

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Volkova L V 2011 Phys. Atom. Nucl. 74 318-323

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Sinegovskaya, Misaki A and Takahashi N 2010 Int

Sinegovsky S I, Kochanov A A, T.S. Sinegovskaya, Misaki A and Takahashi N 2010 Int. J. Mod. Phys. A 25 3733

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Kochanov A A, Sinegovskaya T S and Sinegovsky S I 2013 J. Exp. Theor. Phys. 116 395

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Sinegovskaya T S, Morozova A D and Sinegovsky S I 2015 Phys. Rev. D 91 063011

work page 2015

[22] [22]

Calculation of conventional and prompt lepton fluxes at very high energy

Fedynitch A, Engel R, Gaisser T K, Riehn F and Stanev T 201 5 Calculation of conventional and prompt lepton ﬂuxes at very high energy EPJ Web Conf. 99 08001 ( Preprint 1503.00544)

work page internal anchor Pith review Pith/arXiv arXiv

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Fedynitch A 2017 https://github.com/afedynitch/MCE q

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Morozova A D, Kochanov A A, Sinegovskaya T S and Sinegovs ky S I 2017 J. Phys. Conf. Ser. 934, 012008

work page 2017

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Fedynitch A, Engel R, Gaisser T K, Riehn F and Stanev T 201 8 The hadronic interaction model Sibyll 2.3c and inclusive lepton ﬂuxes Preprint 1806.04140

work page arXiv

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Nikolsky S I, Stamenov J N and Ushev S Z 1984 Sov. Phys. JETP 60 10-21

work page 1984

[29] [29]

Erlykin A D, Krutikova N P and Shabelskii Yu M 1987 Yad. Fiz. 45 1075

work page 1987

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Thunman M, Ingelman G and Gondolo P 1996 Astropart. Phys. 5 309

work page 1996

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Bogdanov A G, Kokoulin R P, Novoseltsev Yu F, Novoseltse va R V, Petkov V B and Petrukhin A A 2009 Energy spectrum of cosmic ray muons in 100 TeV energy region r econstructed from the BUST data Preprint 0911.1692

work page internal anchor Pith review Pith/arXiv arXiv 2009

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Bogdanov A G, Kokoulin R P, Novoseltsev Yu F, Novoseltse va R V, Petkov V B and Petrukhin A A 2012 Astropart. Phys. 36 224

work page 2012