{"id":"562b77d5-c5b7-4840-af7c-e1c7b7513d93","arxiv_id":"2507.22463","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Simulations show that underground muon bundle counts could constrain the inelastic pion-air cross section to roughly 10-15% near 1-2 TeV.","lead":"This paper proposes a way to measure how often high-energy pions collide with air nuclei, using the muon bundles that deep underground detectors like IceCube see. The authors calculate that such measurements could pin down the pion-air cross section to about 10 to 15 percent near 1 to 2 TeV, which would sharpen cosmic-ray air shower simulations and help address the muon puzzle.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The sensitivity forecast in Eqs. 3-7 treats the measured muon multiplicity distribution as a noiseless, one-to-one transform of primary energy, ignoring shower-to-shower fluctuations in N_mu; if those fluctuations are non-negligible, the projected 10-15% pion-air cross-section constraint is…","rationale":"I read the paper as a proof-of-principle sensitivity study, not as a claim of a demonstrated measurement. The internal logic of the Fisher forecast is coherent under its stated assumptions. The reader's weakest assumption is SIBYLL model-dependence; my concern is orthogonal and more fundamental to the observable. The method's Eq. 3 maps the mean multiplicity to a differential flux, but the real data are distributions of individual bundle sizes with fluctuations. I do not claim this kills the method; if the fluctuation width is small (say below 0.1 in log10 N_mu), the forecast stands. The proposed CORSIKA-based test is feasible and would settle whether the noiseless transform is adequate. Because the paper is explicit about being preliminary and the reader's conditional verdict already accounts for idealizations, I keep the verdict unchanged. If the test shows significant degradation, the paper would need to fold a fluctuation kernel into the observable or present the sensitivity as a function of the allowed fluctuation width.","tokens_in":6355,"tokens_out":9680,"duration_ms":121833,"concrete_test":"Use CORSIKA (or another shower Monte Carlo) with SIBYLL 2.3c to simulate many proton-initiated showers at fixed energies spanning roughly 10^5-10^7 GeV, propagate the muons to 1.5 km w.e. (e.g., with MUTE), and histogram N_mu above 100 GeV for each E_CR to estimate P(N_mu | E_CR). Then replace Eq. 3 by M_obs(N_mu) = integral dE_CR Phi(E_CR) P(N_mu | E_CR) and repeat the Fisher calculation of Eq. 7, using the same 0.1 log10(M) per-bin uncertainty. If the recovered uncertainty on sigma_pi+air in the 1-2 TeV region degrades by more than about 30% relative to the noiseless transform, the projection is not robust to shower fluctuations.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing unchecked assumption is not only SIBYLL 2.3c's fidelity, but the statistical model of the observable itself. In Sec. 2, Eq. 3 defines the muon bundle flux as M(N_mu) = Phi_CR(E_CR(N_mu)) dE_CR/dN_mu, with the statement that 'the muon multiplicity is a monotonic function of the cosmic ray energy.' This is a deterministic Jacobian transform of the mean multiplicity <N_mu(E_CR)> computed by MCEq/MUTE. Real underground detectors observe event-by-event muon multiplicities, which fluctuate around <N_mu> because of shower-to-shower variations in the first interaction, inelasticity, and particle production. The observable is therefore a convolution of Phi_CR with the conditional distribution P(N_mu | E_CR), not the right-hand side of Eq. 3. The quoted sensitivity in Sec. 4 (Eqs. 6-7) uses gradients dM/dc_i computed for this noiseless transform and a per-bin log-normal uncertainty of 0.1. That uncertainty may represent reconstruction accuracy, but it does not substitute for the physical smearing of the N_mu-E_CR relation, which changes both the shape of M(N_mu) and its response to cross-section modifications. Even granting SIBYLL 2.3c as truth, the Fisher forecast is for a different observable unless fluctuations are negligible. This is concrete and testable, and it directly affects the headline 10-15% uncertainty estimate.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper proposes a new indirect method to constrain the inelastic pion-air cross section and proton-air cross section at multi-TeV energies using the muon multiplicity distribution of bundles detected in deep underground Cherenkov detectors such as IceCube and KM3NeT. The authors use MCEq and MUTE with the SIBYLL 2.3c hadronic interaction model to compute mean muon multiplicities as a function of primary cosmic-ray energy, replace the nominal cross section with a cubic-spline parametrization, and estimate the sensitivity of the bundle multiplicity distribution to each spline coefficient via a penalized chi-square Fisher forecast. They find that, assuming a per-bin multiplicity uncertainty of log10(Delta M/M) = 0.1, the pion-air cross section can be constrained to roughly 10-15% between about 0.7 and 2 TeV at a depth of 1.5 km w.e., with a second region of 25-30% sensitivity around 200 TeV, while the proton-air cross section can be constrained to about 10% near 100 TeV. The paper concludes that this method could provide the first multi-TeV pion-air cross-section constraints and help address the muon puzzle.","tokens_in":6635,"tokens_out":9587,"duration_ms":114381,"significance":"If the forecast is validated, the method would fill an important experimental gap: accelerator measurements of pion-air interactions currently stop at a few hundred GeV, so a multi-TeV constraint from cosmic-ray data would be genuinely novel and useful for air-shower simulations. The study is computationally concrete: it uses established tools (MCEq, MUTE, SIBYLL 2.3c), parameterizes the cross section with a spline, and propagates gradients and covariances in a standard Fisher framework. The depth-dependent sensitivity map is falsifiable and could guide future analyses with real IceCube or KM3NeT data. However, the numerical claims rest on two unverified statistical assumptions: the muon multiplicity is treated as a deterministic function of primary energy, and the per-bin uncertainty is specified without defining the binning or exposure. These issues make the current 10-15% figure an optimistic estimate rather than a robust projection.","major_comments":[{"comment":"Eq. (3) defines the bundle flux M(N_mu) as a deterministic change of variables from E_CR to N_mu, using the mean multiplicity <N_mu(E_CR)> computed by MCEq/MUTE. Real underground detectors observe event-by-event muon multiplicities, which fluctuate around <N_mu> because of shower-to-shower variations in the first interaction, inelasticity, and particle production. The observable is therefore a convolution of Phi_CR(E_CR) with the conditional distribution P(N_mu | E_CR), not the right-hand side of Eq. (3). Because both the pseudo-data and the model in Secs. 2.2 and 4 are generated from the same deterministic map, the Fisher forecast in Eqs. (6)-(7) is for a different observable unless the fluctuations are negligible. Please quantify the width of P(N_mu | E_CR) at the energies of interest, using e.g. full air-shower simulations, and either show that it is small relative to the assumed log10(Delta M/M)=0.1 per-bin uncertainty or propagate it through Eq. (3). This is a concrete and testable issue that directly affects the headline 10-15% uncertainty.","section":"Sec. 2, Eq. (3)"},{"comment":"The chi-square in Eq. (6) assumes a per-bin uncertainty log10(Delta M/M)=0.1, but the number of multiplicity bins, their widths, and whether they are treated as independent are not specified. For a Fisher forecast, the parameter covariance scales with the number of independent bins and with the bin width, so the absolute uncertainties shown in Fig. 4 and quoted in the text (10-15% for sigma_pi+air) are not well-defined without this information. Please specify the binning scheme used to evaluate Eq. (6), and if the result is intended to be binning-independent, demonstrate that explicitly. If the 0.1 dex uncertainty includes statistical contributions, the assumed exposure and observation time should also be stated. Without these details, the numerical precision claims cannot be reproduced or independently assessed.","section":"Sec. 4, Eqs. (6)-(7)"}],"minor_comments":[{"comment":"The summation symbol in Eq. (2) is not defined; specify whether the sum runs over primary species, nucleons, or perturbed runs, and clarify the resulting units of the 'muon multiplicity flux'.","section":"Sec. 2, Eq. (2)"},{"comment":"The notation M((1+delta)c_i) is ambiguous because c_i are spline coefficients rather than direct cross-section values; clarify how a relative perturbation of a coefficient translates into the modified cross-section table that is inserted into MCEq.","section":"Sec. 2.2, Eq. (4)"},{"comment":"The left panels of Fig. 3 plot the ratio of log10(modified) to log10(nominal), which compresses the visual magnitude of the effect; consider showing the relative difference (modified/nominal - 1) in linear scale for easier interpretation.","section":"Sec. 3, Fig. 3"},{"comment":"The two panels use different x-axis labels (E and E_p), and the 'ratio' subpanels are not defined in the caption; state what quantity is plotted in each subpanel and what the SIBYLL 2.3c curve represents.","section":"Sec. 4, Fig. 4"},{"comment":"After mentioning 10 knots, the text says the spline is 'fully defined by 12 coefficients'; a one-sentence explanation of the two edge-padding coefficients would remove confusion.","section":"Sec. 2.2"},{"comment":"Reference [15] is marked as 'Submitted to Phys. Rev. D (2025)'; if it is not yet published, this should be stated explicitly in the citation or updated once the published version is available.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper is written in a conference-proceedings style, and the central idea is promising. However, the quantitative sensitivity estimate currently depends on two unspecified or idealized ingredients: the treatment of shower-to-shower multiplicity fluctuations and the definition of the multiplicity binning. Both are fixable in a revision. The heavy use of the authors' own simulation tools is not circular for a forecast, but the 'measurement' language in the title and abstract should be tempered unless the model-systematic uncertainties are addressed. The manuscript would be better suited to a revised journal submission after these points are resolved."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The core idea here is genuinely new and worth taking seriously: using the underground muon bundle multiplicity distribution to constrain the inelastic pion-air cross section at multi-TeV energies, where no direct data exist. The authors build the forecast carefully: spline parametrization, numerical gradients through MCEq/MUTE, a penalized chi-square, and linear error propagation. Figure 4 is honest and informative, and the complementary sensitivity windows for pion-air and proton-air are a nice result. The 10-15% number is clearly labeled as an idealized projection, not a measured value.\n\nThe main soft spot is the statistical model of the observable, and it is load-bearing. Equation 3 is a deterministic Jacobian transform of the mean multiplicity <N_mu(E_CR)>, giving a smooth 'multiplicity flux.' Real underground detectors observe event-by-event muon bundles, which fluctuate around that mean because of shower-to-shower variations in the first interaction, inelasticity, and particle production. The actual observable is a convolution of the CR spectrum with P(N_mu | E_CR), not the right-hand side of Eq. 3. Until that smearing is modeled, the quoted sensitivity is for a hypothetical noiseless mean-multiplicity distribution, not for IceCube or KM3NeT data. The 0.1 log10 per-bin uncertainty covers reconstruction accuracy, not physical fluctuations, so it does not substitute for this missing ingredient.\n\nTwo smaller issues: SIBYLL 2.3c serves as both pseudo-truth and model, so the forecast does not include systematic errors from CR flux or particle production. And no code, data, or exact binning/exposure choices are provided, which limits reproducibility. These are common for an ICRC proceedings paper, so I do not treat them as fatal.\n\nThe paper deserves a serious referee: the idea is new, the calculation is transparent, and a referee could push the authors to reformulate the observable with proper fluctuations. It should be read as a proof-of-principle, not as a demonstrated measurement capability. I would not cite it in my own work yet, but I would recommend engaging with it and requesting a revised version that addresses the statistical model.","headline":"A clean, genuinely new sensitivity forecast for pion-air cross sections from underground muon bundles, but the projected 10-15% is for a mean-multiplicity observable that ignores shower-to-shower fluctuations.","tokens_in":7231,"tokens_out":2577,"would_cite":false,"duration_ms":33528,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper argues that underground muon-bundle counts can measure the inelastic pion-air cross section at TeV energies, with sensitivity projected at 10-15% around 1-2 TeV.","keywords":["pion-air cross section","muon bundles","underground detectors","IceCube","KM3NeT","muon puzzle","hadronic interaction models","cosmic-ray air showers"],"falsifier":"Generate mock underground muon multiplicity data from a simulation in which the pion-air cross section is artificially increased by, say, 20%, then run the paper's spline-fitting pipeline on it: if the 20% increase is not recovered within the quoted 10-15% uncertainty, the method's projected sensitivity is overstated.","tokens_in":6082,"feed_emoji":"🧊","tokens_out":8797,"duration_ms":89815,"temperature":0.7,"pith_summary":"The paper proposes that the muon bundles recorded by deep underground detectors such as IceCube carry a measurable imprint of the inelastic pion-air cross section. Because accelerator beams cannot reach multi-TeV pion-air collisions, the authors develop a sensitivity forecast: after replacing the SIBYLL 2.3c cross section with a spline and perturbing it, they compute how the muon multiplicity distribution responds. With a realistic assumption on multiplicity resolution (an uncertainty of log10(ΔM/M)=0.1 per bin), they claim the pion-air inelastic cross section could be constrained to roughly 10-15% between 1 and 2 TeV, and to better than 50% between 200 GeV and 6 TeV at 1.5 km w.e. depth. If real IceCube or KM3NeT data are analyzed this way, it would provide the first multi-TeV constraint on this quantity and reduce the hadronic-model uncertainty behind the muon puzzle.","feed_headline":"Muon bundles could pin pion-air cross section to 10-15%","feed_subtitle":"Using muon bundle sizes in deep detectors, it targets pion interactions no accelerator can reach.","key_machinery":"The central object is the underground muon multiplicity distribution M(N_mu), computed by MCEq and MUTE as a function of cosmic-ray energy and depth. The argument is carried by a cubic-spline parameterization of the inelastic cross section, denoted \\hat{\\$\\sigma$}_{c_i}, with 10 knots spaced logarithmically from 10 GeV to $10^{10}$ GeV; the 12 spline coefficients c_i are the tuning parameters. Finite-difference gradients \\partial M/\\partial \\hat{c}_i (Eq. 4) form a linearized response model (Eq. 5), which is fitted to pseudo-data via a penalized chi-square (Eq. 6) with Gaussian priors; the covariance of the fitted coefficients is propagated through the cross-section Jacobian (Eq. 7). The physics mechanism is the competition between interaction and decay lengths near the critical energy (~100-200 GeV), which makes an increased cross section raise the multiplicity through low-energy muon pile-up.","core_discovery":"The paper establishes, through a numerical sensitivity study, that the inclusive underground muon multiplicity distribution changes in a specific, calculable way when the inelastic pion-air cross section is increased: at energies above the ~100-200 GeV critical energy, a larger cross section suppresses higher-energy muons and boosts lower-energy pile-up, raising the multiplicity. Using MCEq with SIBYLL 2.3c at the South Pole location, the authors replace the nominal cross section with a cubic spline having 10 logarithmic knots, compute the gradient of the flux with respect to each knot (Eq. 4), and build a linearized model (Eq. 5). Pseudo-data generated at the nominal model with log10(ΔM/M)=0.1 per bin, a penalized chi-square fit with Gaussian priors, and covariance propagation yield the projected uncertainties: 10-15% for sigma_{\\pi+air} around 1-2 TeV and below 50% from 200 GeV to 6 TeV at 1.5 km w.e., with a second sensitivity window near 200 TeV; sigma_{p+air} is constrained to ~10% around 80-200 TeV. The energy and depth dependence cleanly separates the pion and proton contributions.","pith_inferences":["If real data return constraints near the projected precision, the same spline-perturbation technique could be applied to kaon-air cross sections or to other hadronic observables such as charm production, extending the method beyond pions.","The depth dependence the authors find (peak sensitivity shifting ~1 TeV per km w.e.) suggests that a single detector measuring bundles at multiple depths, e.g., via different overburdens or zenith angles, could map the cross section as a function of energy with one dataset.","The projection assumes SIBYLL 2.3c is otherwise correct; a comparison against predictions with other hadronic models would reveal how much of the claimed reach is model-dependent rather than physics.","Cross-section constraints from this method could also serve as a prior for atmospheric lepton flux calculations, reducing the systematic error in neutrino-telescope analyses."],"forward_implications":["Real IceCube or KM3NeT bundle counts could yield the first constraints on the multi-TeV inelastic pion-air cross section.","If the quoted sensitivity holds, hadronic interaction models would gain a new anchor point at energies no accelerator can currently reach, directly feeding into air-shower simulations.","The method also constrains the proton-air cross section around 100 TeV, complementing LHC-based measurements.","Extending the analysis to multiple zenith angles could broaden the measurable energy window from a few TeV to several hundred TeV.","A measured cross section that disagrees with SIBYLL 2.3c would give concrete input for resolving the muon puzzle rather than only parameterizing it."],"supporting_citations":[{"why":"Supplies the MCEq cascade-equation solver that computes the ground-level muon yields from primary cosmic rays.","marker":"[10]"},{"why":"Defines the SIBYLL 2.3c hadronic interaction model whose nominal cross section is replaced by the spline.","marker":"[11]"},{"why":"Provides the MUTE v3 code that propagates muon yields to underground depths used for the multiplicity distributions.","marker":"[4]"},{"why":"Gives the Global Spline Fit cosmic-ray flux and composition model used in the convolution to build the muon multiplicity distribution.","marker":"[12]"},{"why":"Motivates the assumed log10(ΔM/M)=0.1 multiplicity uncertainty via measured IceCube bundle reconstruction accuracies.","marker":"[15]"},{"why":"Documents the Sibyll 2.3 series hadronic model and its cross-section parametrization, the baseline that the spline perturbation modifies.","marker":"[14]"}],"fun_headline_variants":["Muon bundle shapes reveal pion-air cross section to 10–15%","Deep detectors size up pion interactions via muon multiplicities","Underground muons target pion-air cross section gap","Pion-air cross section from muon count gradients in ice","Multi-TeV pion cross section via muon bundle depths"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The method assumes that SIBYLL 2.3c's treatment of everything except the pion-air cross section is accurate, so perturbing just that cross section in the simulation reproduces what a real change would do to underground muon bundles.","fun_headline_variants_meta":{"raw":{"variants":["Muon bundle shapes reveal pion-air cross section to 10–15%","Deep detectors size up pion interactions via muon multiplicities","Underground muons target pion-air cross section gap","Pion-air cross section from muon count gradients in ice","Multi-TeV pion cross section via muon bundle depths"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000121,"raw_usage":{"total_tokens":1077,"prompt_tokens":911,"completion_tokens":166,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":527,"completion_tokens_details":{"reasoning_tokens":80}},"tokens_in":527,"tokens_out":166,"duration_ms":2950,"temperature":1.0,"reasoning_tokens":80,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T11:38:42.224515+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Generate mock underground muon multiplicity data from a simulation in which the pion-air cross section is artificially increased by, say, 20%, then run the paper's spline-fitting pipeline on it: if the 20% increase is not recovered within the quoted 10-15% uncertainty, the method's projected sensitivity is overstated.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Motivates the assumed log10(ΔM/M)=0.1 multiplicity uncertainty via measured IceCube bundle reconstruction accuracies."}],"review_version":1}