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LHAASO protons versus LHAASO diffuse gamma-rays: a consistency check

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read LHAASO's newly measured proton spectrum, converted into a predicted diffuse gamma-ray flux, overshoots the same observatory's diffuse gamma-ray measurements in both the inner and lateral Galactic regions, in normalization and in spectral…

desk verdict Useful first direct LHAASO-vs-LHAASO consistency check, but the 'robust overshoot' claim is overstated once you use the Planck gas map and take the uniform-CR assumption seriously. read the letter →

arxiv 2506.06593 v2 pith:MHKB5MBR submitted 2025-06-06 astro-ph.HE

Luis Enrique Espinosa Castro , Francesco Lorenzo Villante , Vittoria Vecchiotti , Carmelo Evoli , Giulia Pagliaroli This is my paper
classification astro-ph.HE PACS 95.85.Pw96.50.S
keywords cosmic-raykneeLHAASOprotonspectrumGalacticdiffusegamma-rayemissionhadronicproductionpropagationTeV-PeVskyAAFRAGcross-section
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper aims to show that the two flagship measurements of the LHAASO observatory do not agree with each other: the newly measured cosmic-ray proton spectrum at the knee and the same collaboration's maps of diffuse Galactic gamma-ray emission. The authors translate the local proton spectrum, together with rigidity-scaled helium and heavy nuclei, into a predicted hadronic gamma-ray flux using gas templates and the AAFRAG cross-section, and compare it with LHAASO's diffuse gamma-ray data in two sky regions. The predicted flux overshoots the observations in both the inner and the lateral Galaxy, and the mismatch shows up in the overall normalization as well as in the spectral shape. If the result stands, the locally measured cosmic-ray sea cannot straightforwardly account for the TeV-PeV diffuse gamma-ray emission under standard assumptions, and current cosmic-ray models that link local measurements to the Galactic sky need revision.

What carries the argument

The load-bearing device is the factorization $\phi_\gamma(E_\gamma, \hat n) = N(E_\gamma, \hat n)\,Y(E_\gamma)$. The yield $Y(E_\gamma)$ is the gamma-ray emissivity of the local cosmic-ray nucleon flux $\phi_{\mathrm{CR},\odot}(E_n)$, namely protons plus helium and heavy elements shifted in energy by rigidity, convolved with the differential proton-proton production cross-section, for which the AAFRAG parameterization is used because among the tested models it gives the smallest and softest predictions. The factor $N(E_\gamma, \hat n)$ is the integral along the line of sight of the gas density $n_g$ times the cosmic-ray density profile $g(r)$; setting $g(r)=1$ makes the prediction a pure convolution of the locally measured proton spectrum with the target gas templates taken from GALPROP or from Planck dust opacity. The diagnostic that carries the argument is the inner-to-lateral gamma-ray flux ratio, which for a uniform cosmic-ray density and a position-independent cosmic-ray spectrum is an energy-independent constant set only by the gas column densities in the two sky regions. The observed deviation of that ratio from the predicted constant, together with energy-dependent data-to-model ratios, is the evidence that the spectral shape of the cosmic-ray population producing the gamma rays differs from the local one.

What would settle it

Measure the cosmic-ray helium flux in the 100 TeV-PeV band, where no direct data exist, and determine the LHAASO diffuse gamma-ray inner-to-lateral flux ratio with the mask systematics reduced. If helium proves far less abundant at the knee than the rigidity-scaled model assumes, the predicted diffuse flux drops toward the data and the claimed overshoot is refuted; if the nucleon flux is instead confirmed while the inner-region spectrum below about 30 TeV still falls below the prediction, the paper's central claim stands.

Watch

Extended reading notes

Core claim

The paper's central claim is that the diffuse gamma-ray flux predicted from the locally measured LHAASO proton spectrum robustly overshoots the diffuse gamma-ray flux that LHAASO actually observes, in both the inner region ($|b| < 5^\circ$, $15^\circ < l < 125^\circ$) and the lateral region ($|b| < 5^\circ$, $125^\circ < l < 235^\circ$). The prediction is built from a four-break fit to the proton flux from GeV to PeV energies, a helium flux with spectral breaks at twice the proton energies (the same rigidity), a conservative band for heavy nuclei, the AAFRAG hadronic cross-section, and gas templates taken from the GALPROP code or from Planck dust opacity. The data-to-model ratio is not a constant: the mismatch grows toward lower photon energies and is largest in the inner region below roughly 30 TeV. The authors argue that the discrepancy cannot be blamed on the hadronic interaction model, since AAFRAG gives the smallest and softest gamma-ray predictions and every alternative parameterization increases the flux and the tension, nor on gamma-ray absorption, estimated to be small below the PeV range. A cosmic-ray density that is higher toward the inner Galaxy and lower outward would reduce the predicted lateral flux by up to about 20 percent but would increase the inner flux, so it cannot remove the mismatch by itself. The paper concludes that either the cosmic-ray spectrum responsible for the observed gamma-ray emission differs from the local one, for example a Galactic knee near 300 TeV instead of the local value near 3 PeV, or the conventional picture connecting the local cosmic-ray sea to diffuse gamma-ray emission must be revised.

Load-bearing premise

The baseline prediction assumes the cosmic-ray density is uniform across the Galaxy ($g(r)=1$), so the locally measured LHAASO proton spectrum is used unmodified along every line of sight; a position-dependent density or spectrum would change the size of the overshoot and alter the spectral-shape mismatch, and the paper does not replace this simplification with a full propagation model.

Editorial extensions

If this is right

  • Switching to any other hadronic interaction model (Geant4, Pythia8, SIBYLL, QGSJET) makes the predicted gamma-ray flux larger and slightly harder, so the overshoot cannot be cured by the cross-section choice.
  • Allowing the cosmic-ray density to follow the source distribution (higher inward, lower outward) reduces the predicted lateral-region flux by up to about 20 percent in the most optimistic scenario but raises the inner-region prediction, deepening the mismatch there.
  • The spectral-shape discrepancy is compatible with a Galactic cosmic-ray spectrum whose knee sits near 300 TeV rather than the local value around 3 PeV, a hypothesis the authors propose to test with gamma-ray observations of the break energy.
  • A lower helium contribution at the knee, currently unconstrained by direct measurements between 100 TeV and a few PeV, would decrease the predicted diffuse flux and could relieve part of the tension.
  • If the updated KASCADE proton reanalysis is confirmed, all charged cosmic-ray measurements become mutually compatible and the persistent gamma-ray tension becomes a purely astrophysical problem rather than an artifact of conflicting charged-particle data.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: molecular clouds at different Galactocentric radii act as standard cosmic-ray barometers, and their TeV-PeV gamma-ray emission measured with the same LHAASO detector would map the density profile $g(r)$ and the local spectral shape directly, without the line-of-sight averaging that blurs the diffuse maps.
  • Editorial inference: if the Galactic cosmic-ray spectrum truly has a knee near 300 TeV away from the Sun, the diffuse gamma-ray spectrum should show a break at $E_\gamma \simeq 30$ TeV that sharpens toward the inner Galaxy; the paper's inner-region data below about 30 TeV are already suggestive of such a break, and higher-statistics observations could confirm it.
  • Editorial inference: the same convolution applied to neutrinos implies that the predicted Galactic neutrino flux inherits the same overshoot, so TeV-PeV neutrino observations offer an independent, cross-checkable lever on whether the problem lies in the cosmic-ray sea or in the gamma-ray production model.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. This paper performs a consistency check between the LHAASO measurement of the cosmic-ray proton spectrum at the knee and the LHAASO measurement of TeV-PeV Galactic diffuse gamma-ray emission. The authors fit the proton and helium spectra from GeV to PeV energies, add heavy nuclei through a rigidity-scaling assumption, and compute the hadronic gamma-ray flux using two gas templates (GALPROP and Planck) and the AAFRAG cross-section. Under the assumption of a uniform cosmic-ray density in the Galaxy, g(r)=1, they compare the predicted flux with LHAASO data in the inner and lateral regions and report a mismatch in both normalization and spectral shape. They also examine the inner-to-lateral flux ratio and discuss possible explanations, including spatial variation of the CR spectrum, additional gamma-ray absorption, and unresolved sources.

Significance. The paper is a transparent and useful cross-check between two recent LHAASO measurements. Its strengths are the forward nature of the calculation, the explicit comparison of gas templates and cross-section models, and the use of the region-ratio diagnostic. If the claimed tension survives a more complete treatment of CR propagation, it would pose an important challenge to conventional Galactic CR models. However, the current analysis is built on the simplifying assumption g(r)=1, and the paper's own text shows that the lateral overshoot disappears for the Planck gas model; these gaps currently limit the robustness of the central claim.

major comments (4)
  1. [Section 4 / Abstract] The abstract states that the predicted flux 'robustly overshoots the LHAASO data in both inner and lateral Galactic regions', but Section 4 reports that the Planck-based prediction avoids overshooting in the lateral region and the authors adopt the Planck model as the reference for the ratio analysis. For the lateral region, the overshoot therefore depends on the gas template and is not robust to that choice. The central claim needs to be restated with this caveat or supported by a quantitative significance that includes the gas-template systematic.
  2. [Section 3, Eq. (8)] The baseline calculation assumes a uniform CR density, g(r)=1, so the local LHAASO proton spectrum is used for every line of sight. Section 5 concedes that a source-like g(r) reduces the lateral flux by up to 20% in the most optimistic scenario. Since the Planck-based lateral prediction is already consistent with the data, this reduction is sufficient to remove or reverse the lateral tension. In addition, the spectral-shape mismatch, the second pillar of the abstract, could be absorbed by a spatially varying CR spectrum, which the paper lists as a possible explanation but does not model. The paper should either replace g(r)=1 with a self-consistent propagation model or quantify the full range of g(r) and spectral-shape variations that would erase the discrepancy before claiming a robust mismatch.
  3. [Figures 3 and 4] The paper does not provide any statistical measure of the disagreement, such as chi-square, p-value, or a likelihood, and the shaded bands in Fig. 3 appear to represent only the heavy-element composition uncertainty rather than the combined uncertainties from gas templates, cross-sections, and CR flux systematics. Without such quantification, the words 'robust', 'persistent', and 'significant mismatch' are not supported by the presented analysis. A simple goodness-of-fit comparison for the two regions and gas templates would strengthen or qualify the claim.
  4. [Section 2] The proton fit uses only the LHAASO EPOS-LHC data set, while the QGSJet-II-04 variant is shown in Fig. 1 but not used, and GRAPES-3 data are discarded because of disagreement. Because the predicted gamma-ray flux is most sensitive to the proton spectrum in the 10^4 to 10^7 GeV range, the choice among hadronic interaction models used to derive the LHAASO proton flux could shift the predicted normalization and shape. The paper should justify this choice quantitatively, for example by repeating the gamma-ray prediction using the QGSJet-based LHAASO proton spectrum and discussing the resulting change in the discrepancy.
minor comments (5)
  1. [Eq. (12)] The subscripts 'in' and 'lat' in Eq. (12) are not defined in the text; please define them at first use.
  2. [Eqs. (9)-(11)] The symbol N is used for the gas column integral in Eq. (11) while N_n is used earlier for the number of nucleons; this notational overlap is confusing and should be resolved.
  3. [Section 4] The text refers to an Appendix containing the comparison with other cross-section parametrizations, but no appendix appears in the provided manuscript text. If the appendix is missing from the arXiv version, it should be included or the citation should be made specific.
  4. [Section 2] The paper uses both 'AAFRAG' and 'AAFrag' for the same cross-section model; please choose one notation for consistency.
  5. [Data Availability] 'Data available upon reasonable request' is vague; for reproducibility, please consider releasing the fitting code and the derived gamma-ray prediction tables as supplementary material.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the gamma-ray prediction is a forward calculation whose inputs (CR nucleon flux, gas templates, cross-section) are independent of the LHAASO gamma-ray data being compared.

full rationale

The central derivation is Eq. (7): phi_gamma(E_gamma, n_hat) is obtained by convolving the CR nucleon flux phi_CR(E_n, r) with the gas density n_g and the hadronic cross-section dsigma/dE_gamma. The local CR nucleon flux phi_CR,sun is fitted to charged-particle data (PAMELA, AMS-02, DAMPE, CALET, CREAM, ATIC, IceTop, and LHAASO proton and all-particle measurements), not to the LHAASO diffuse gamma-ray data. The comparison in Section 4 is therefore a genuine consistency check between two independent LHAASO data sets, and the gamma-ray flux is not obtained by fitting the gamma-ray observations. The framework expressed in Eqs. (7)-(11) is standard formalism cited to the authors' earlier papers, but the claim does not reduce to those citations, and no uniqueness theorem or ansatz is imported from them. The assumption g(r)=1 in Eq. (8) is explicitly stated as an initial simplification and its consequences are discussed in Section 5; it is a physical modeling assumption, not a circular redefinition. The heavy-element normalization eta is derived from the LHAASO all-particle flux, which is a different observable from the diffuse gamma-ray emission. No fitted parameter is later renamed as a prediction, and no self-citation is load-bearing: the contextual references to Vecchiotti et al. (2024) and Cataldo et al. (2019) support the discussion but are not the basis of the central overshoot claim. The paper is self-contained as a consistency check, so no circularity is found.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The paper rests entirely on inputs from prior literature: the CR spectra (fitted here), gas maps, cross-section models, and the factorization of spatial and energy dependence. No new entities or first-principles derivations are introduced. The most fragile input is the uniform CR density assumption (g=1), which the authors acknowledge and partially address only through cited estimates.

free parameters (3)
  • Proton flux spectral parameters (K_H, alpha_i, E_b,i, omega_i)
    Best-fit values from a 4-break function fitted to PAMELA, AMS-02, DAMPE, CALET, CREAM, ATIC, IceTop and LHAASO proton data; reported in the Supplementary Material. These parameters set the CR nucleon flux that drives the gamma-ray prediction.
  • Helium flux spectral parameters
    Same functional form fitted to helium data; enters the nucleon flux through Eq. (4).
  • Heavy-element normalization factor k = estimated range (carbon-to-iron), based on eta ~ 1.7
    Derived from the all-particle flux (LHAASO Cao et al. 2024) and composition assumptions; the paper uses a conservative range for A=12 to A=56 in Eq. (6).
assumptions (5)
  • domain assumption The CR flux at any point factorizes as phi_CR(En,r) = g(r) phi_CR,odot(En), with g(r)=1 in the baseline.
    Section 3, Eq. (8)-(9). The local CR spectrum is used for the whole Galaxy. This is the load-bearing simplification discussed in the weakest_assumption.
  • domain assumption Gas density traced by GALPROP maps or Planck dust opacity with X_D^-1 = 1.18e-26 cm^2.
    Section 3, around Eq. (11). The two gas models bracket the gas uncertainty but may both be inaccurate.
  • domain assumption Gamma-ray production cross-section from AAFRAG parameterization.
    Section 3 and Appendix. AAFRAG gives the smallest flux among considered models, so the tension would grow with other cross-sections.
  • domain assumption Heavy nuclei follow the helium rigidity spectrum with a fixed normalization eta ~ 1.7.
    Section 2, Eq. (5)-(6). This affects the nucleon flux, though heavy elements are subdominant at PeV energies.
  • ad hoc to paper GRAPES-3 proton data are excluded from the fit.
    Section 2. The paper discards GRAPES-3 because it disagrees with LHAASO; this selection can affect the ~100 TeV break and is not tested for its influence on the final mismatch.

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Cite this review

Pith. "Pith review of LHAASO protons versus LHAASO diffuse gamma-rays: a consistency check." pith.science (2026). https://pith.science/paper/MHKB5MBR

@misc{pith2026250606593,
  author       = {Pith},
  title        = {Pith review of: LHAASO protons versus LHAASO diffuse gamma-rays: a consistency check},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MHKB5MBR}},
  note         = {Machine review of arXiv:2506.06593}
}
read the original abstract

We perform the first direct consistency check between the recently measured proton spectrum at the knee by Large High Altitude Air Shower Observatory (LHAASO) and the collaboration's own high-precision mapping of Galactic diffuse gamma-ray emission. By modeling the hadronic gamma-ray production using the updated cosmic-ray spectra, gas templates and cross-section models, we show that the predicted gamma-ray flux robustly overshoots the LHAASO data in both inner and lateral Galactic regions. This persistent mismatch in both normalization and spectral shape challenges conventional scenarios linking the local cosmic-ray sea to Galactic gamma-ray emission, and calls for a revision of current cosmic ray models in the TeV-PeV sky.

Figures

Figures reproduced from arXiv: 2506.06593 by the authors.

Figure 1
Figure 1. Flux of Galactic cosmic ray protons as a function of energy per nuclei. Observation data by direct detection experiments (PAMELA Adriani et al. (2011), AMS-02 Aguilar et al. (2015a,b), DAMPE An et al. (2019); Alemanno et al. (2021), CALET Adriani et al. (2019, 2023), CREAM Yoon et al. (2017) and ATIC-2 Panov et al. (2009)) as well as ground-based ob￾servatories (GRAPES-3 Varsi et al. (2024), IceTop Aartsen et al. (2… view at source ↗
Figure 2
Figure 2. , where the heavy element contribution is given as a shaded band delimited by the maximum and minimum limits described above. Contrary to what happens for the all-particle CR spectrum, helium and heavy elements are subdominant everywhere and, in particular, have a negligible role at PeV energies. All this shows that 𝛾−ray diffuse emission is essentially probing the CR proton spectrum and in particular the position o… view at source ↗
Figure 3
Figure 3. Diffuse gamma-ray flux in LHAASO inner (|𝑏| < 5 ◦ , 15◦ < 𝑙 < 125◦ , top panel) and lateral (|𝑏| < 5 ◦ , 125◦ < 𝑙 < 235◦ , bottom panel) Galaxy regions. The 𝛾-flux expectations obtained from our model are shown by blue (GALPROP gas model) and green (Planck gas model) shaded bands. Observational data by LHAASO (Cao et al. 2025b) are added with black points. We find this result cannot be attributed to the hadronic int… view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: Ratio of 𝛾-fluxes in inner and lateral Galaxy regions as a function of gamma-ray energy. Ratio obtained from expectations by our model using GALPROP Galactic gas map (Porter et al. 2022) and Planck Galactic dust opacity map (Ade et al. 2011) displayed with blue and gre…
Figure 4
Figure 4. Figure 4: Ratio of measured and expected 𝛾-fluxes (for Planck gas distribution scenario) in LHAASO inner (|𝑏| < 5 ◦ , 15◦ < 𝑙 < 125◦ , top panel) and lateral (|𝑏| < 5 ◦ , 125◦ < 𝑙 < 235◦ , bottom panel) Galaxy regions as a function of gamma-ray energy. Dashed black line represen…

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Forward citations

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