Modified Hadronic Interactions and the future of UHECR observations

Eva Santos; Jakub V\'icha; Jan Ebr; Ji\v{r}\'i Bla\v{z}ek; Nikolas Denner; Petr Tr\'avn\'i\v{c}ek; Ralf Ulrich; Tanguy Pierog

REVIEW 4 major objections 5 minor 14 references

Modified Hadronic Interactions and the future of UHECR observations

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

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A retuned hadronic model can match Auger's muon and Xmax data, but only with simultaneous changes to cross-section, multiplicity, and elasticity, and those changes strain against other measurements.

desk verdict Useful 3D simulation library with honest caveats; the iron-mediated conclusions rest on a flagged but untested superposition assumption. read the letter →

arxiv 2502.08798 v2 pith:V74O7M5N submitted 2025-02-12 astro-ph.HE

Jan Ebr , Jiří Blažek , Jakub Vícha , Tanguy Pierog , Eva Santos , Petr Trávníček , Nikolas Denner , Ralf Ulrich This is my paper · ORCID

classification astro-ph.HE

keywords ultra-high-energycosmicraysairshowershadronicinteractionmodelsmuoncontentdepthofshowermaximumPierreAugerObservatoryCORSIKAsimulationsSibyll2.3d

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

The paper asks whether the discrepancies between current hadronic interaction models and ultra-high-energy cosmic-ray observations can be removed by modest, energy-dependent retuning of ordinary hadronic physics. Using a library of 750,000 simulated showers built from 75 combinations of changes to cross-section, multiplicity, and elasticity applied to the Sibyll 2.3d model, the authors find that the Pierre Auger Observatory's hybrid data can indeed be reproduced, but only by decreasing the cross-section and increasing both multiplicity and elasticity. That specific combination already conflicts with Auger's own proton-air cross-section measurement and with measured fluctuations in shower maximum, so a fully consistent description of all observations remains out of reach. The library itself is the lasting product: it offers a realistic spread of hadronic-model freedom for quantifying systematic uncertainties and for testing the design of future observatories.

What carries the argument

The central object is a parameterized modification scheme applied inside the CORSIKA simulation code to the hadronic model Sibyll 2.3d. Modifications to elasticity, multiplicity, and cross-section take effect above an energy threshold and grow logarithmically with energy, reaching a chosen value at $10^{19}$ eV; 75 combinations of these settings were simulated for proton and iron primaries at $10^{18.7}$ eV across five zenith angles, giving 750,000 showers. For nuclear projectiles, the scheme assumes superposition: an iron nucleus is treated as independent nucleons, each modified at $1/56$ of the primary energy, which automatically makes modification effects smaller for iron than for proton primaries. This machinery lets the authors compare modified predictions directly with Auger observations and drives their distance-dependent, detector-geometry-dependent conclusions about muon counts and proton-iron separation power.

What would settle it

A direct test is to compare the best-fit modified model's predictions for the energy dependence of the muon signal and for the slope and fluctuations of the $X_{\rm max}$ distribution against Auger's full energy scan: if no single set of the three parameters reproduces all of these simultaneously, the claimed simultaneous description fails. A future measurement of the proton-air cross-section at around $10^{18.7}$ eV that rules out the fitted value would also falsify the central finding.

Watch

Extended reading notes

Core claim

The authors discover that, within their predefined parameter space, the hadronic model Sibyll 2.3d can be modified to describe Auger's simultaneous measurements of the muon content at ground and the depth of shower maximum, but only if all three interaction parameters are changed together: cross-section down, multiplicity up, and elasticity up. The increase in elasticity is the hardest to reconcile with other data: Auger's proton-air cross-section measurement constrains the cross-section-elasticity plane such that a lower cross-section should be accompanied by a lower elasticity, and a higher elasticity enlarges the shower-to-shower fluctuations of $X_{\rm max}$ for protons beyond what Auger's profile measurements appear to allow. The paper therefore concludes that no combination in the library gives a fully consistent description of all UHECR observations, while the library itself provides a realistic representation of the freedom in modeling hadronic interactions at ultra-high energies.

Load-bearing premise

The calculation assumes that an iron nucleus hitting air behaves exactly as a superposition of independent modified nucleon-air interactions, with each nucleon carrying one fifty-sixth of the primary energy; if collective nuclear effects break this picture, the iron-related conclusions and merit-factor results would change, while the proton-only conclusions would remain intact.

Editorial extensions

If this is right

If the combined modification is correct, the long-standing muon deficit and the $X_{\rm max}$ discrepancy can be produced by ordinary hadronic physics retuned within accelerator bounds, without invoking dramatically new physics at ultra-high energies.
The three standard models (Sibyll 2.3d, EPOS-LHC, QGSJET-II-04) may all lie on the same side of the data, so using their spread as the modeling uncertainty could underestimate the true range of possibilities.
For a future observatory, proton-iron separation power depends on the detector type and on its distance from the shower axis; quantities such as muon-to-electromagnetic ratios behave differently at 500 m and 1000 m, so design choices can be tested quantitatively with this library.
A consistent description of UHECR showers remains elusive: the modifications that fit the hybrid Auger data are already in tension with the proton-air cross-section and $X_{\rm max}$ fluctuation measurements.
The strong correlations between the iron-proton merit factor and the change in muon number for protons mean that composition measurements and hadronic-model uncertainties cannot be treated independently in future analyses.

Reading between the lines

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

One extension the authors do not pursue is to use the library to build a model-independent mapping from measured ground-signal ratios to primary mass; the strong correlations they report at 1000 m suggest such a mapping could be more robust to hadronic uncertainty than absolute muon counts.
The finding that muon counts can shift by up to 10% at fixed $DX = X - X_{\rm max}$ while the electromagnetic energy density stays nearly fixed implies that future arrays with different detector spacing may infer different compositions from the same cosmic-ray flux, providing a cross-check of the library's assumptions.
If the superposition assumption for nuclei is relaxed in later work, the proton-only results would survive but the iron-based conclusions and merit factors would need to be recomputed; a full treatment of nuclear effects is the natural next test.
Because the parameter space explored here is deliberately mechanism-agnostic, the best-fit region can serve as a target for more specific physical models that aim to explain the same Auger data through collective effects or modified hadronization.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Jan, here's my read. The genuinely useful part of this paper is the 3D simulation library: 75 modified hadronic settings, proton and iron, five zenith angles, 750k CORSIKA showers, with the modifications tied to accelerator constraints. The authors show that 3D geometry matters for detector response—the sensitivity to cross-section versus multiplicity changes with core distance and zenith—and that the usual three-model spread (Sibyll/EPOS/QGSJET) may not bracket the truth. That is a real contribution for anyone estimating model uncertainty in future observatory design.

The paper is also honest. It flags the superposition assumption for nuclear primaries, and it does not pretend the modifications are unique. The main physical claim—that a retuned Sibyll 2.3d can describe the Auger hybrid data [8] only by decreasing cross-section and increasing both multiplicity and elasticity, and that this retuning conflicts with the proton-air cross-section [10] and Xmax fluctuations [11]—is plausible and consistent with the cited prior papers.

The soft spots are real but proportionate. First, this proceedings text does not show the actual comparison to the Auger data or any statistical uncertainties; the 'only with changes to all three' statement is asserted rather than demonstrated here. Second, the iron-shower conclusions rest on the superposition ansatz, each nucleon at E/A. The stress-test note is correct that this is load-bearing for the merit-factor correlations and for the composition-mixed fit; the authors flag it but do not quantify how the conclusions shift under alternatives like Glauber shadowing or energy sharing. Third, the library covers a single primary energy (10^18.7 eV) and one baseline model, so extrapolating to other energies is an assumption.

None of this sinks the paper. The 'consistent description remains elusive' message survives even if the iron-mediated claims are wrong, because the proton-only tensions with [10] and [11] are independent of the superposition ansatz. For a proceedings contribution, the scope is right and the claims are modest. What is missing is that the library itself is not public and the parameters are only summarized by reference to earlier papers; that limits reproducibility.

Who should read it: people designing the next-generation UHECR observatory and anyone who wants a practical alternative to the three-model uncertainty bracket. I'd send it to peer review—it deserves referee time—but as a journal article it would need the actual data comparison and error bars, not as a proceedings note. My recommendation: engage with the library, cite it for the merit-factor analysis, and treat the superposition caveat as an explicit limitation rather than a hidden flaw.

Referee Report

4 major / 5 minor

Summary. This conference paper describes a large CORSIKA simulation library in which the high-energy hadronic interaction parameters (cross-section, multiplicity, and elasticity) of Sibyll 2.3d are modified in an energy-dependent, accelerator-consistent way. For proton and iron primaries at a single primary energy of 10^18.7 eV and several zenith angles, the authors study how ground-level observables, Xmax, and proton/iron separation merit factors respond to the modifications. Their main physics claim is that the Pierre Auger Observatory data of Ref. [8] can be reproduced by a modification of Sibyll 2.3d only if all three parameters are changed together (decreased cross-section, increased multiplicity, increased elasticity), and that this required combination is already in tension with other Auger measurements. The remaining paper is devoted to illustrating how the library can quantify modeling uncertainties for future observatory designs, focusing on distance-dependent effects and proton/iron discrimination.

Significance. If the main claim is substantiated, the paper provides a useful demonstration that the UHECR muon and Xmax tensions can be simultaneously accommodated by a retuned hadronic model, but only at the price of new tensions, reinforcing the conclusion that a fully consistent description remains elusive. The simulation library itself is a potentially valuable community resource: it systematically spans 75 modified interaction scenarios with a fully three-dimensional treatment, and the authors are explicit that their parameter choices respect accelerator constraints and avoid abrupt energy dependence. The paper also honestly flags its main modeling assumption about nuclear projectiles. However, the paper does not actually show the comparison to the Auger data that supports its central claim, reports no statistical uncertainties, and presents only a single primary energy and a single baseline model. These omissions make the significance conditional on the availability of the underlying comparison, which would need to be documented for the claims to be independently assessable.

major comments (4)

[§1] The central claim that "the hadronic model Sibyll 2.3d can indeed be modified to describe this particular Auger data well within our set parameter space, but only with changes to all three parameters" is not supported by any displayed comparison. No figure or table shows the Auger data of Ref. [8] together with the modified simulations, no goodness-of-fit statistic is given, and the reader is not told which observables, zenith angles, or composition assumptions enter the comparison. This statement drives the abstract and the conclusions, so it must be documented quantitatively, for example with a plot of the allowed/excluded parameter combinations in the (σ, N, η) space.
[§3] The iron/proton merit-factor results and the statement that "the effects of modifications for iron primaries are always smaller than for proton primaries" rest on the pure-superposition assumption, with each nucleon treated at 1/A of the primary energy. The paper explicitly acknowledges this assumption, but it does not test or bound its impact. If nuclear effects such as Glauber shadowing, leading-nucleon energy sharing, or collective behavior make the iron response nonlinear in the modification parameters, the correlations in Figs. 2 and 3 could change, and the conclusion that only a triple modification fits the Auger data would need re-evaluation. The proton-only conclusions would survive, but the composition-related claims require either a test against an alternative nuclear treatment or a stronger caveat stating which conclusions are robust.
[§1 and Figs. 1–3] All quantitative statements are made at a single primary energy (10^18.7 eV) with 1000 showers per setting, and no statistical uncertainties are reported on mean profiles, merit factors, or relative changes. Since the text itself notes that shower-to-shower fluctuations are generally larger than differences between modifications, the reader cannot judge whether the reported trends, such as the 10% muon increase or the tight correlations in Fig. 2, are significant. Error bars or confidence intervals should be added at least for the quantities that support the main claims.
[§1] The parameter space is not defined in this paper: the threshold energy, the f19 values for cross-section, multiplicity, and elasticity, and the exact 75 combinations are deferred to previous works. Without a table or appendix listing these values, the phrases "well within our set parameter space" and "reasonable limits" cannot be checked, and the claim that the modifications stay within accelerator constraints is not self-contained in this manuscript.

minor comments (5)

[§1] Typographical errors should be corrected, including "the none of current hadronic interaction models" and "for for D_X > 200 g/cm2."
[Figs. 2 and 3] The figures are dense: in Fig. 2 the color coding for zenith angles and parameter values is difficult to separate, and the baseline (unmodified) point is not marked. Please mark the unmodified model explicitly and consider enlarging the legend or using a separate panel for the baseline.
[§2] The sentence stating that the EM energy density and charged-particle number density are conserved "within a few percent" at fixed D_X is only supported by visual inspection of Fig. 1; the relevant numerical values should be given, including the range of D_X over which this statement holds.
[§3] Equation (1) defines the merit factor, but the text should clarify whether the quoted merit factors use the mean and standard deviation over simulated showers only, or also include systematic spreads due to the different modifications themselves.
[§4] The conclusion would benefit from explicitly separating the results that are robust (proton-only muon and Xmax tensions) from those that depend on the superposition assumption for iron, since the text currently mixes the two levels of robustness.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the modified-interaction scan is compared against external Auger data, and no claimed prediction reduces to a fitted input.

full rationale

The paper's central empirical claim is that, within its pre-defined grid of modified Sibyll 2.3d parameters, agreement with the Pierre Auger data [8] requires a decrease in sigma and increases in both N and eta. This is a search result against external hybrid data, not a quantity obtained by substituting those data into the definitions of the model. The modification parameters are inputs chosen from accelerator constraints, and no equation in the paper equals an observable to a fitted constant. Eq. (1) defines a merit factor from simulated distributions but is not used to fit the parameters. The Section 3 superposition ansatz for nuclear projectiles is a modeling assumption that the authors explicitly flag, writing 'we certainly do not claim that other possibilities should not be considered'; even if it is load-bearing for the proton/iron merit factors, it is a stated premise whose failure would shift conclusions, not a circular reduction. Citations [1-5] include prior work by overlapping authors, but the present CORSIKA library and its comparisons are new, and the cited [5] parameterization is an openly adopted ad-hoc scheme rather than an external 'uniqueness theorem' invoked to force the result. Therefore no circular step meets the quoted-equation standard.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The catalog of modifications is described by a set of hand-chosen amplitudes and thresholds; the paper is transparent that these are not derived from first principles. The most fragile modeling assumption is the superposition treatment of nuclear projectiles, explicitly acknowledged in Section 3. No new particles, forces, or conserved quantities are introduced.

free parameters (4)

Cross-section modification amplitude f19(sigma) = scanned grid: 0.8, 1.0, 1.2 (relative to Sibyll 2.3d)
Chosen by hand to stay within accelerator-data constraints. It tunes the shower depth and muon number and is one of the three parameters needed to match the Auger data.
Multiplicity modification amplitude f19(N) = scanned grid: 0.6, 0.8, 1.0, 1.3, 1.7
Selected by hand from the range of accelerator-compatible values. Increasing it raises muon production and is part of the Auger-matching combination.
Elasticity modification amplitude f19(eta) = scanned grid: 0.6, 0.8, 1.0, 1.2, 1.5
Chosen by hand. Higher elasticity moves Xmax deeper and increases fluctuations, which creates the tension with the proton-air cross-section measurement.
Energy threshold for the start of modifications = not stated numerically in this paper
The threshold is a modeling choice that keeps accelerator-energy predictions within measurement uncertainties, but the exact value is not given here and affects the gradual rise of modifications with energy.

assumptions (4)

ad hoc to paper The energy-dependent modification scheme (threshold then logarithmic rise to f19 at 10^19 eV) is a valid representation of unknown high-energy hadronic physics.
Defined in Section 1 to generate the library; it is an ad-hoc ansatz that is only loosely constrained by accelerator data.
domain assumption Nucleus-air interactions can be modeled as a pure superposition of modified nucleon-air interactions at 1/A of the primary energy.
Explicitly assumed in Section 3 and flagged by the authors as an implicit assumption that affects all iron-primary results.
domain assumption Sibyll 2.3d is an adequate baseline hadronic model for unmodified reference showers.
The library uses Sibyll 2.3d as its reference; the paper does not test whether the conclusions are robust to a different baseline model.
standard math Gaisser-Hillas form with an additional constant term adequately describes ground-signal profiles as a function of DX.
Used in Section 2 for fitting profiles; this is a standard empirical form in air-shower physics, referenced to [14].

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Cite this review

Pith. "Pith review of Modified Hadronic Interactions and the future of UHECR observations." pith.science (2026). https://pith.science/paper/V74O7M5N

@misc{pith2026250208798,
  author       = {Pith},
  title        = {Pith review of: Modified Hadronic Interactions and the future of UHECR observations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/V74O7M5N}},
  note         = {Machine review of arXiv:2502.08798}
}

read the original abstract

Data from multiple experiments suggest that the current interaction models used in Monte Carlo simulations do not correctly reproduce the hadronic interactions in air showers produced by ultra-high-energy cosmic rays (UHECR). We have created a large library of UHECR simulations where the interactions at the highest energies are slightly modified in various ways - but always within the constraints of the accelerator data, without any abrupt changes with energy and without assuming any specific mechanism or dramatically new physics at the ultra-high energies. Recent results of the Pierre Auger Observatory indicate a need for a change in the prediction of the models for both the muon content at ground and the depth of the maximum of longitudinal development of the shower. In our parameter space, we find combinations of modifications that are in agreement with this analysis, however a consistent description of UHECR showers remains elusive. Our library however provides a realistic representation of the freedom in the modeling of the hadronic interactions and offers an opportunity to quantify uncertainties of various predictions. This can be particularly valuable for the design of future observatories where hadronic models are often used as input for the prediction of the performance. We demonstrate this powerful capability on several selected examples.

Figures

Figures reproduced from arXiv: 2502.08798 by the authors.

**Figure 1.** D𝑋 profiles for the muon number density, electromagnetic energy density and charged-particle number density for proton primaries at 1000 meters from the shower axis (top left), iron at 1000 meters (top right) and proton at 500 meters (bottom left). For each quantity, 75 mean profiles are plotted, each corresponding to a different combination of modifications. Bottom right: relative changes in the profiles with respe… view at source ↗

**Figure 2.** Top left: Correlation between the merit factor for iron-proton separation with muons at 1000 meters from the shower axis and the change in the number of muons for proton primaries at different zenith angles (color coded). Top right: points for vertical showers colored by changes in 𝜂 and 𝑁. Bottom left: Correlation between merit factors for iron-proton separations with muons at 500 and 1500 meters from the shower ax… view at source ↗

**Figure 3.** Left column: comparison between merit factors for iron-proton separation using the ratio of number density of muons to energy density of electromagnetic particles and using the ratio of number density of all charged particles to energy density of electromagnetic particles. Right column: comparison between merit factors for iron-proton separation using the ratio of number density of muons to energy density of electro… view at source ↗

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Reference graph

Works this paper leans on

14 extracted references · 8 canonical work pages

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [8]

Abdul Halim et al.,Testing hadronic-model predictions of depth of maximum of air-shower profiles and ground-particle signals using hybrid data of the Pierre Auger Observatory, Phys

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arXiv 2024

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Abreu et al.,Measurement of the proton-air cross-section at√𝑠 = 57 TeV with the Pierre Auger Observatory,Phys

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arXiv 2014

[4] [1]

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work page Pith review arXiv 2023

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J. Ebr, J. Blazek, J. Vicha, T. Pierog, E. Santos, P. Travnicek et al.,Modified Characteristics of Hadronic Interactions in Ultra-High-Energy Cosmic-Ray Showers, Ukr. J. Phys.69 (2024) 786 [2410.15699]

work page Pith review arXiv 2024

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Ulrich, R

R. Ulrich, R. Engel and M. Unger,Hadronic Multiparticle Production at Ultra-High Energies and Extensive Air Showers, Phys. Rev. D83(2011) 054026 [1010.4310]

arXiv 2011