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REVIEW 2 major objections 5 minor 72 references

Stopped atmospheric muons inside Earth add a nearly site-independent low-energy neutrino flux below 100 MeV.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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Updated Honda-framework 3D atmospheric neutrino fluxes for seven sites now include Earth-stopped muon decay/capture, yielding a site-independent low-energy increment and reduced hadronic uncertainty.

T0 review reviewed 2026-07-10 challenge →

load-bearing objection Solid, usable extension of Honda: first 3D Earth-stopped-muon fluxes plus modern multi-site tables; capture-spectrum proxy and missing topography are real but already-flagged precision floors, not show-stoppers. the 2 major comments →

arxiv 2607.08310 v1 pith:K3JTLMZN submitted 2026-07-09 hep-ph astro-ph.HEhep-ex

Precision three-Dimensional Atmospheric Neutrino Flux Calculation Based on Honda Flux Model

Jie Cheng , Yu-Feng Li , Liang-Jian Wen This is my paper
classification hep-ph astro-ph.HEhep-ex PACS 14.60.Pq95.55.Vj96.50.S-
keywords atmospheric neutrinosthree-dimensional fluxmuon propagationnuclear captureneutrino fogDSNB backgroundgeomagnetic cutoffhadronic uncertainty
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

Atmospheric neutrinos are the main background for dark-matter and diffuse-supernova searches and a key signal for oscillation physics, yet earlier three-dimensional calculations stopped at the ground surface. This paper recalculates the full flux from 10 MeV to 10 TeV at seven detector sites, adding for the first time the neutrinos produced when atmospheric muons enter the Earth, stop, and then decay or are captured by nuclei. That extra component is globally present and roughly constant in absolute size, so its relative importance is largest where the ordinary atmospheric flux is smallest. Updated cosmic-ray, geomagnetic and hadronic models shift the flux above 100 MeV by only a few percent while tightening the hadronic uncertainty. The new tables therefore supply a consistent, multi-site background model for current and next-generation experiments.

Core claim

When atmospheric muons that penetrate the ground are allowed to stop and decay or undergo nuclear capture, they produce an additional neutrino flux below about 100 MeV whose absolute size is approximately the same at every geographic site; the fractional enhancement is therefore largest at high-cutoff sites and follows the flavor ordering νe ≈ ν̄µ > νµ > ν̄e.

What carries the argument

Three-dimensional Monte Carlo cascade simulation extended by an Earth-propagation module that tracks muons through CRUST1.0 media until they stop, then applies free decay for µ+ and element-dependent atomic capture versus nuclear capture for µ−, generating Michel and capture neutrino spectra.

Load-bearing premise

The energy spectrum of neutrinos from nuclear capture of stopped muons is taken from measured gamma-ray spectra of pion capture on oxygen and silicon, with the silicon spectrum used as a stand-in for all heavier crustal nuclei, and local mountain overburden is still ignored.

What would settle it

A direct measurement or ab-initio calculation of the neutrino energy spectrum from muon nuclear capture on silicon or iron that differs substantially from the adopted pion-capture proxy spectra would change the high-energy tail of the predicted νµ excess above 60 MeV.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • DSNB and low-mass dark-matter analyses at every site must now include an extra absolute neutrino component of comparable size below 100 MeV.
  • Inter-site flux ratios below 1 GeV remain dominated by geomagnetic cutoff differences of up to a factor of four, not by the new muon-propagation term.
  • Hadronic systematic uncertainty in the 1–10 GeV horizontal band drops to a few percent, tightening oscillation-parameter extractions that use atmospheric neutrinos.
  • Nuclear-capture νµ extends to ~95 MeV, overlapping the upper end of the DSNB window and requiring updated background templates.

Where Pith is reading between the lines

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

  • Because the absolute increment is nearly universal, a single low-energy correction table could be shared among experiments once mountain-profile effects are added.
  • Future multi-site dark-matter searches could use the residual site-to-site difference in fractional enhancement as an independent cross-check of the geomagnetic baseline flux.
  • The same stopped-muon source will also generate a small but calculable flux of low-energy electrons and positrons that could appear as a surface or near-surface background in shallow detectors.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The manuscript presents a three-dimensional atmospheric neutrino flux calculation built on the HKKMS15 Monte-Carlo framework, extended for the first time to include atmospheric-muon propagation inside the Earth and the subsequent free decay or nuclear capture of stopped muons. Essential inputs are updated (AMS02-based primary cosmic-ray spectra, IGRF2020 geomagnetic field, muon-recalibrated JAM/DPMJET-III hadronic model, NRLMSISE-00 atmosphere, CRUST1.0 crust). Fluxes are computed for seven detector sites spanning a wide range of geomagnetic cutoffs, from 10 MeV to 10^4 GeV. For E_ν > 100 MeV the authors report 2–10 % shifts relative to HKKMS15 and strong site dependence below ~10 GeV; below 100 MeV they find that Earth-stopped muons supply a globally significant, approximately site-independent absolute flux increment with flavor hierarchy ν_e ≈ ν̄_µ > ν_µ > ν̄_e. Hadronic uncertainties are re-evaluated with the muon-constraint method of Honda et al., yielding a few-percent total uncertainty in the 1–10 GeV horizontal band.

Significance. If the results hold, the work supplies the first multi-site 3D atmospheric-neutrino fluxes that include the Earth-stopped-muon channel below 100 MeV—the energy window that dominates DSNB and low-mass dark-matter backgrounds—and simultaneously reduces the hadronic systematic error that has limited oscillation analyses. The public data release for seven sites (JUNO, SK, CJPL, ORCA, IceCube, DUNE, TRIDENT) and the quantitative comparison with HKKMS15 make the calculation immediately usable by the experimental community. The central technical advance (muon propagation + nuclear capture) is cleanly isolated and its absolute contribution is shown to be roughly site-independent, a non-trivial and falsifiable prediction.

major comments (2)
  1. Appendix A.5 and Fig. 20: the ν_µ spectrum from nuclear capture of stopped µ− is taken from measured γ spectra of π− radiative capture on 16O and 28Si, with the Si spectrum used as a proxy for all heavier crustal nuclei. No direct µ−-capture neutrino data exist. Because the capture channel is the only source of ν_µ above the Michel endpoint (~53 MeV) and produces the high-energy tail visible in the bottom row of Fig. 13, the absolute size of the claimed “globally significant” increment above ~60 MeV rests on this untested proxy. A quantitative sensitivity study (varying the capture spectrum shape within the O–Si difference, or quoting an additional systematic band) is needed before the absolute increment can be treated as precision input for DSNB analyses.
  2. Sec. 3.2 and Sec. 5: local mountain topography is omitted; path lengths and stopping media are taken solely from the CRUST1.0 global crustal model. For mountain sites (CJPL, JUNO) the overburden can change the stopping probability and the rock/water fraction for near-horizontal muons by tens of percent. While the paper correctly notes this as future work, the absolute difference Δϕ_ν shown in Fig. 13 is presented without an associated topography systematic. A simple estimate of the possible bias (e.g., using SRTM/ASTER DEM for one mountain site) would strengthen the claim that the absolute increment is “approximately site-independent.”
minor comments (5)
  1. Abstract and throughout: “develeped” → “developed”; several other minor typos (e.g., “atm µ/2” missing m_µ).
  2. Fig. 13 bottom row: absolute difference curves would be clearer if plotted on a common vertical scale or with an explicit unit label for the peak height.
  3. Table 1: the check-mark for muon propagation is useful; adding a one-line note that mountain profiles are still omitted would avoid over-reading the “✓”.
  4. Sec. 4: the comparison with Sato et al. (accelerator-tuned) is welcome; a short sentence on whether the two uncertainty bands are statistically independent would help readers combine them.
  5. Data-availability statement: the GitHub link is given; confirming that the files include the with/without-muon-propagation pairs for all seven sites would increase usability.

Circularity Check

0 steps flagged

No circularity: 3D Monte Carlo fluxes are forward predictions from independent external inputs (AMS02 primaries, IGRF2020, muon-calibrated hadronics, CRUST1.0) plus standard decay/capture physics; nothing is fitted to the neutrino fluxes themselves.

full rationale

The paper computes atmospheric neutrino fluxes via a 3D Monte Carlo cascade simulation (Honda HKKMS framework) whose inputs are all external and independent of the final neutrino results: AMS02/BESS/PAMELA primary spectra, public IGRF2020 geomagnetic field, NRLMSISE-00 atmosphere, and a hadronic model (JAM+DPMJET-III) recalibrated solely against independent atmospheric-muon data sets (BESS, L3+C, MUTRON). The novel low-energy contribution is obtained by propagating those same muons into the Earth (CRUST1.0 medium), applying free Michel decay for µ+ and literature branching fractions plus π-capture γ-spectrum proxies for µ- nuclear capture; no free parameter is adjusted to any neutrino measurement. Uncertainty bands are likewise derived from the muon-constraint method of Honda et al., not from the neutrino fluxes. Comparison to HKKMS15 simply quantifies the effect of the updated external inputs. There is therefore no self-definitional loop, no fitted-input-called-prediction, and no load-bearing self-citation that forces the central claims. The known limitations (capture-spectrum proxy, omitted local topography) are openly stated as future work and do not create circularity.

Axiom & Free-Parameter Ledger

2 free parameters · 4 axioms · 0 invented entities

The calculation inherits the entire HKKMS Monte-Carlo geometry and the standard cascade physics; the only new physical ingredients are the underground muon stopping and the element-dependent capture branching ratios taken from the literature. Free parameters are limited to the empirical re-tuning of the hadronic generators against muon data and the choice of Si as proxy for heavy nuclei.

free parameters (2)
  • muon-recalibrated JAM/DPMJET-III parameters
    Hadronic generators are adjusted so that calculated sea-level and mountain muon fluxes match BESS/L3+C/MUTRON data within ~5 %; the precise parameter shifts are not tabulated but are inherited from Honda et al. 2019.
  • Si proxy spectrum for nuclei heavier than silicon
    Nuclear-capture νµ spectrum for all crustal elements heavier than Si is taken from the 28Si(π−,γ) data; no free fit is performed, but the choice is an ad-hoc modeling decision.
axioms (4)
  • domain assumption Stopped µ+ decays freely with the standard Michel spectrum; stopped µ− forms a muonic atom and either decays in orbit or undergoes nuclear capture with element-dependent branching ratios Dµ− taken from Guo 2019 / Measday 2001.
    Appendix A.5 and Table 2; standard nuclear-physics input.
  • ad hoc to paper νµ energy spectrum from µ− nuclear capture can be approximated by the measured γ spectrum of π− radiative capture on the same nucleus.
    Explicitly stated in Appendix A.5; no direct experimental νµ capture spectra exist.
  • domain assumption Primary cosmic-ray spectra, geomagnetic field and atmospheric density are given by the AMS-02-based model, IGRF2020 and NRLMSISE-00 respectively.
    Section 2 and Appendix A; standard external data products.
  • domain assumption Muons lose energy only electromagnetically and stop without nuclear interactions before decaying or capturing.
    Flowchart Fig. 21 note; common approximation for low-energy atmospheric muons.

reviewed 2026-07-10 · how reviews work

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Cite this review

Pith. "Pith review of Precision three-Dimensional Atmospheric Neutrino Flux Calculation Based on Honda Flux Model." pith.science (2026). https://pith.science/paper/K3JTLMZN

@misc{pith2026260708310,
  author       = {Pith},
  title        = {Pith review of: Precision three-Dimensional Atmospheric Neutrino Flux Calculation Based on Honda Flux Model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/K3JTLMZN}},
  note         = {Machine review of arXiv:2607.08310}
}
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read the original abstract

We present a comprehensive three-dimensional atmospheric neutrino flux calculation based on the well-recognized simulation framework develeped by Honda and his collaborators, incorporating for the first time the muon propagation inside the Earth and its subsequent decay or nuclear capture. Other updates of essential input models include: the AMS02-based primary cosmic ray model, IGRF2020 geomagnetic field, and muon-recalibrated hadronic interaction model. The calculation covers seven detector sites across diverse geomagnetic environments, spanning 10~MeV to $10^4$~GeV. Significant site-dependent differences appear at $E_\nu < 10$~GeV, with $\nu_\mu$ flux at IceCube approximately twice that at JUNO below 1~GeV. Compared to HKKMS15, deviations of 2\%--10\% are attributed to the updated input models. Below 100~MeV, we present precise flux results, revealing that muon propagation contributes a globally significant component to the low-energy neutrino flux at all sites, with an approximately site-independent absolute increment. The hadronic uncertainty is re-estimated across the energy range using the updated hadronic interaction model, with significant reduction of the systematic error compared to previous calculations. These results provide essential inputs for neutrino oscillation and rare-event search experiments including JUNO, Super-Kamiokande/Hyper-Kamiokande, DUNE, KM3NeT/ORCA, and IceCube, as well as direct dark matter detection experiments facing the neutrino fog.

Figures

Figures reproduced from arXiv: 2607.08310 by Jie Cheng, Liang-jian Wen, Yu-Feng Li.

Figure 1
Figure 1. Figure 1: (a) Schematic illustration of the atmospheric neutrino flux calculation scheme (not to [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Yearly averaged, all-direction averaged atmospheric neutrino fluxes predicted for seven [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Neutrino flavor ratios for seven detector sites (JUNO, SK, CJPL, TRIDENT, IceCube, [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Yearly averaged atmospheric neutrino fluxes predicted for seven distinct detector sites [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Ratios of yearly averaged atmospheric neutrino fluxes at seven distinct detector sites [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Flux-weighted production locations of 1 GeV atmospheric [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Zenith-angle flux ratios of atmospheric neutrinos for seven detector sites. The top row [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Fractional contribution of primary cosmic ray energy bins to the atmospheric neutrino [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Normalized atmospheric neutrino flux at the JUNO site as a function of zenith angle [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Flux-weighted production locations of 0.1 GeV atmospheric [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Azimuthal distribution of the atmospheric neutrino flux at 1 GeV for the horizontal [PITH_FULL_IMAGE:figures/full_fig_p019_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Ratio of the atmospheric neutrino flux calculated in the current work to that of the [PITH_FULL_IMAGE:figures/full_fig_p020_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: All-direction-averaged atmospheric neutrino fluxes for seven experiment sites in the [PITH_FULL_IMAGE:figures/full_fig_p023_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Comparison of the all-direction-averaged atmospheric neutrino fluxes across six experi [PITH_FULL_IMAGE:figures/full_fig_p024_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Breakdown of the hadronic uncertainty component ( [PITH_FULL_IMAGE:figures/full_fig_p028_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Total relative uncertainty (δtot) of the atmospheric neutrino flux. The layout fol￾lows [PITH_FULL_IMAGE:figures/full_fig_p029_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Primary cosmic ray data and spectra models. Left panel: Available data for cosmic [PITH_FULL_IMAGE:figures/full_fig_p039_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: The geomagnetic horizontal field strength obtained from IGRF2020, along with data [PITH_FULL_IMAGE:figures/full_fig_p040_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Schematic diagram of muon decay and capture processes inside the Earth. A stopped [PITH_FULL_IMAGE:figures/full_fig_p044_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Energy spectra (dN/d log10 E) of neutrinos from µ − absorbed in 16O atom (left panel) and 28Si atom (right panel). Three components are shown: ¯νe from muon decay (blue), νµ from muon decay (red), and νµ from nuclear capture (green). The gray dashed line marks the Michel endpoint mµ/2 ≈ 52.8 MeV, which limits the decay spectra; in contrast, the nuclear capture spectrum extends to ∼95 MeV. The integral of … view at source ↗
Figure 21
Figure 21. Figure 21: Flowchart of the muon propagation calculation. The surrounding medium (rock, [PITH_FULL_IMAGE:figures/full_fig_p046_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Global map of crustal thickness based on the CRUST1.0 model [44]. The map distin [PITH_FULL_IMAGE:figures/full_fig_p047_22.png] view at source ↗

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This paper was first reviewed by grok-4.5 on July 10, 2026.