{"id":"337a0ab6-6402-4287-9c2c-df862109fe25","arxiv_id":"1909.01932","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Current neutrino limits constrain the combination of proton fraction and source evolution in ultra-high-energy cosmic rays, ruling out large proton fractions together with strong source evolution.","lead":"This paper uses the absence of ultra-high-energy neutrinos to limit how many protons can be among the highest-energy cosmic rays reaching Earth. The result favors models where protons make up only a small fraction at the highest energies, unless the cosmic-ray sources evolve weakly with cosmic time.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The quantitative bound f≲0.11 depends on equating current neutrino upper limits to a single flux level of 10^-8 at 1 EeV; actual limits may differ by factors, shifting the bound.","rationale":"Both the reader and I see the quantitative conclusion as the central claim. The reader's weakest assumption focuses on the sweet-spot approximation. That approximation is in part self-calibrated in this paper: Fig. 2's shaded bands show the spread of f(m) across the scanned alpha and Emax ranges, so a conservative reading (upper edge of the lightest band) is reasonably robust to those parameters. The unquantified part is the translation of real detector upper limits into the single flux level 10^-8 GeV cm^-2 s^-1 sr^-1 used to draw the exclusion. Because the neutrino flux is proportional to f in the regime considered, this mapping directly sets the numeric value of the bound. If the actual 1 EeV limit is a factor of two weaker, the bound f<0.11 becomes f<0.22, which would weaken the strongest claim but not overturn the qualitative conclusion. This warrants the CONDITIONAL verdict, not rejection: the method is reasonable and the qualitative statement likely survives, but the numeric headline needs an uncertainty or a direct use of the published limits. My recommendation is therefore to keep the reader's CONDITIONAL verdict.","tokens_in":7995,"tokens_out":10805,"duration_ms":110467,"concrete_test":"Recompute the exclusion using the published 90% C.L. single-flavor differential limits at E_nu = 1 EeV from IceCube (arXiv:1807.01820, Fig. 3) and Auger (arXiv:1906.07422), interpolated at exactly 1 EeV, instead of the assumed 10^-8 GeV cm^-2 s^-1 sr^-1. If the interpolated limit is a factor of 2 above 10^-8, re-evaluate f(m) at m=7.1 and compare with f<0.11. For a stronger check, weight the model spectrum (for each f,m) by the detector's exposure and compute the 90% CL exclusion with a Poisson log-likelihood in the relevant half-decade energy bin, rather than a single-energy comparison.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 4 converts the current Auger/IceCube 90% C.L. differential single-flavor limits into the statement that the top-right of Fig. 2 is excluded, giving f ≲ 0.11 for m ≳ 7.1. This relies on Sec. 3's identification of a neutrino flux level of 10^-8 GeV cm^-2 s^-1 sr^-1 at E_nu = 1 EeV as 'roughly' the current sensitivity. The actual experimental limits are binned, detector-specific upper limits, not a single flux value; the paper does not show the 1 EeV limit values it used or propagate their uncertainty. Since the cosmogenic neutrino flux scales approximately linearly with f at fixed m, a factor-two change in the assumed limit flux level changes the f bound by approximately a factor two (e.g., 2×10^-8 would give f ≲ 0.22). The sweet-spot approximation's dependence on alpha and Emax is partly controlled by the shaded bands in Fig. 2: using the upper edge of the lightest band is conservative over the scanned ranges, so the more direct load-bearing issue is the limit-to-flux-level mapping. The paper itself labels the correspondence 'roughly', so the numeric headline is not supported with a stated accuracy.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper argues that the cosmogenic neutrino flux at a 'sweet spot' energy of Eν ≈ 1 EeV depends primarily on the fraction of protons f in UHECRs at Earth at E0 = 10^1.55 EeV and on the source evolution parameter m. Using CRPropa 3 simulations of an additional proton component, with α ∈ [1, 3] and log(Emax/EeV) ∈ [1.6, 5], the authors compute the (f, m) combinations that give a single-flavor neutrino flux of 10^-8 GeV cm^-2 s^-1 sr^-1 at 1 EeV, which they identify 'roughly' with the current sensitivity of IceCube and Auger. They conclude that the region of large f and large m is already excluded, quoting f ≲ 0.11 for m ≳ 7.1, and that this constraint is independent of hadronic interaction models. The paper is a short proceedings contribution that builds on the companion paper Ref. [1] for the 'sweet spot' property.","tokens_in":8316,"tokens_out":7307,"duration_ms":64798,"significance":"If the 'sweet spot' approximation holds, the paper offers a valuable, hadronic-model-independent way to constrain UHECR composition and source evolution from existing neutrino limits. The use of the public CRPropa 3 code, the explicit enumeration of the parameter ranges scanned, and the candid discussion of neglected EGMF effects are strengths. The qualitative result that a large proton fraction combined with strong source evolution is disfavored by current data is plausible and interesting. The main weakness is that the quantitative bound is tied to an unquantified 'rough' identification of the experimental limits with a single flux level, which is the load-bearing point.","major_comments":[{"comment":"The quoted bound f ≲ 0.11 for m ≳ 7.1 is obtained by equating the current Auger and IceCube upper limits to a single flux level of 10^-8 GeV cm^-2 s^-1 sr^-1 at Eν = 1 EeV. The actual experimental limits are binned, energy-dependent upper limits with different systematics; the paper does not report the limit values at 1 EeV or overlay the differential limit curves on the predicted fluxes. Because the cosmogenic neutrino flux at fixed m scales approximately linearly with f, a factor-of-two difference between the assumed and actual sensitivity would change the f bound by a factor of two (e.g., a 90% C.L. limit of 2×10^-8 GeV cm^-2 s^-1 sr^-1 would loosen the bound to f ≲ 0.22). Since the paper itself labels the correspondence as 'roughly', the numerical headline is not supported with a stated accuracy. The authors should either compute the exclusion directly from the differential limit curves or propagate the uncertainty of the flux-level mapping into the quoted f bound.","section":"Sec. 4, Fig. 2"},{"comment":"The 'sweet spot' approximation from Ref. [1] is load-bearing: it justifies neglecting the dependence on α, Emax and the EBL at Eν ≈ 1 EeV. The shaded bands in Fig. 2 illustrate the spread across the scanned parameter ranges, but the paper does not quantify the width of these bands in terms of f at fixed m, nor does it compare this spread with the experimental uncertainty in the flux level. A quantitative statement (e.g., the range of f spanned by the lightest band at m = 7) is needed to assess whether the f ≲ 0.11 limit is robust against the sweet-spot approximation. In addition, the normalization to the Auger spectrum at E0 = 10^1.55 EeV carries an experimental uncertainty that is not propagated into the (f, m) contours; quoting this uncertainty would help the reader judge the significance of the constraint.","section":"Sec. 3, Fig. 2"}],"minor_comments":[{"comment":"After noting that EGMF effects could enhance the expected flux by up to a factor of a few, the paper states that the predictions 'can be considered as lower bounds' but does not spell out the consequence for the direction of the derived constraint; it would be helpful to state explicitly that the exclusion region in Fig. 2 is therefore conservative.","section":"Sec. 2"},{"comment":"The caption says the TA spectrum is shown 'for comparison' but does not indicate that it appears in the left panel; please make the panel reference explicit.","section":"Fig. 1 caption"},{"comment":"The phrase 'as long as f & 0.01' is imprecise; 'for f ≳ 0.01' or 'if f ≳ 0.01' would be clearer.","section":"Sec. 2"},{"comment":"The paper switches between log(Emax/EeV) in the text and log(Emax/eV) in the Fig. 2 caption; please use one convention consistently.","section":"Sec. 2 / Fig. 2 caption"},{"comment":"The first and second branches of SE(z) both read (1+z)^m; although the conditions m ≤ 0 and m > 0, z < 1.5 are distinct, a brief explanatory note would avoid confusing readers into thinking this is a typo.","section":"Eq. (2.1)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a conference proceedings contribution, so the level of derivation detail is limited compared with a full journal article. My major comments concern the quantitative bound rather than the underlying simulation methodology. If the proceedings venue allows the authors to present the claim as an order-of-magnitude statement, a softening of the language in Sec. 4 might suffice; otherwise, I would ask for a direct comparison with the actual Auger and IceCube limit curves. The work is otherwise sound and builds appropriately on the companion paper."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear X,\n\nThe paper applies the sweet-spot method from the authors' companion PRD paper to current IceCube/Auger limits and derives a constraint on the proton fraction f versus source evolution m. The useful new bit is the parameter-scanned exclusion plot: for strong source evolution (m≳7), f is constrained to ≲0.1 at 10^1.55 EeV. The qualitative conclusion (strong evolution + large proton fraction is disfavored) was already visible in Auger's own reference parameter set, so the novelty is modest, but the systematic scan over alpha and Emax ranges is a legitimate step.\n\nThe calculation is transparent: CRPropa 3, stated parameter ranges, normalization to the Auger spectrum, and a clear discussion of why EBL and EGMF are secondary. The authors are honest that EGMF effects could raise the flux by up to a factor of a few, which would strengthen the constraint (lower the bound on f), so neglecting EGMF is conservative. The central argument holds.\n\nThe soft spot is the translation from experimental limits to a single flux level. The paper says 10^-8 GeV cm^-2 s^-1 sr^-1 at 1 EeV is 'roughly' the current sensitivity, then converts to f≲0.11 for m≳7.1. The actual limits are binned and detector-specific; they are not shown at 1 EeV and no uncertainty is propagated. Since the flux scales approximately linearly with f, a factor-two difference in the assumed limit changes the bound by about a factor two. So the numeric headline is order-of-magnitude, not precise. The paper should have shown the actual limit values and a band on f. Also, the sweet-spot approximation itself is taken from Ref [1]; if that approximation fails, the whole mapping shifts. The shaded bands in Fig. 2 do illustrate the alpha/Emax spread, and using the upper edge is conservative, so the load-bearing issue is really the limit-to-flux-level mapping.\n\nOverall: a clean but small contribution. It does not resolve the composition problem, and the method is from the companion paper. As a conference proceedings, it does what it claims: it shows current limits already exclude a class of source models, independent of hadronic models. I think it deserves normal peer review rather than desk rejection, but the authors should be pushed to state the accuracy of the f bound and to overlay the actual experimental limits.","headline":"Useful parameter-scan application of the authors' own sweet-spot method; the qualitative constraint is solid, but the f<0.11 number is rougher than it looks.","tokens_in":8843,"tokens_out":2165,"would_cite":false,"duration_ms":22303,"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":"Cosmogenic neutrinos at 1 EeV already place an 11% cap on UHECR protons.","keywords":["cosmogenic neutrinos","ultra-high-energy cosmic rays","proton fraction","source evolution parameter","EeV neutrino flux","UHECR composition","neutrino flux upper limits"],"falsifier":"Recompute the constant-flux contours with the two extreme parameter sets (e.g. $\\alpha=1.0,\\ \\log(E_{\\max}/\\mathrm{eV})=19.6$ and $\\alpha=3.0,\\ \\log(E_{\\max}/\\mathrm{eV})=23$) plus an extragalactic magnetic-field model that boosts the 1 EeV flux by the maximal factor; if a non-negligible part of the region $f>0.11,\\ m>7.1$ then falls below the current upper limits, the claimed exclusion is not robust. Conversely, a detected flux above the assumed reference level at 1 EeV for a model with $f\\lesssim 0.11$ and $m\\gtrsim 7.1$ would disprove the mapping.","tokens_in":7818,"feed_emoji":"🌌","tokens_out":10388,"duration_ms":101849,"temperature":0.7,"pith_summary":"This paper tries to establish that cosmogenic neutrinos—the ones produced when ultra-high-energy cosmic rays (UHECRs) pass through extragalactic photon fields—can already be used as an interaction-model-independent probe of UHECR composition. At a neutrino energy near $E_\\nu \\approx 1$ EeV, the expected flux is a 'sweet spot': it depends mainly on two unknowns, the fraction $f$ of protons in UHECRs at Earth at $10^{1.55}$ EeV and the source-evolution parameter $m$, with only mild dependence on spectral index, maximum energy, and extragalactic background light. Given that current neutrino observatory upper limits sit roughly at the flux level this paper uses, the authors conclude that the combination of a large proton fraction and a strong source evolution is already excluded, specifically $f \\lesssim 0.11$ for $m \\gtrsim 7.1$. If correct, this gives an independent, hadronic-model-free way to bound the proton content of UHECRs and to discriminate among source classes.","feed_headline":"Neutrino limits cap proton share of cosmic rays at 11 percent","feed_subtitle":"At ~1 EeV the predicted neutrino flux hinges mostly on proton fraction and source evolution, so current limits prune models.","key_machinery":"The load-bearing object is the 'sweet spot' at $E_\\nu \\approx 1$ EeV: a neutrino energy at which the predicted cosmogenic flux is nearly insensitive to the spectral index $\\alpha$, the maximum source energy $E_{\\max}$, and the extragalactic background light, so the flux level is effectively set by the two parameters $f$ and $m$ alone. The argument is carried by a map of constant neutrino flux contours in the $(f,m)$ plane, generated by propagating simulated proton spectra—with injection spectrum $dN/dE \\propto E^{-\\alpha}\\exp(-E/E_{\\max})$ and a broken power-law source evolution $\\mathrm{SE}(z) = (1+z)^m$ for $z<1.5$, flattening above—and normalizing to the measured UHECR flux at $E_0$. Shifting to smaller $f$ scales both the cosmic-ray and neutrino spectra linearly, so each fixed flux level becomes one curve; the current upper limits then carve out the excluded side of that curve.","core_discovery":"The central claim is that the existing upper limits on the cosmogenic neutrino flux at $E_\\nu \\approx 1$ EeV already constrain the two parameters that jointly control that flux: the fraction $f$ of protons in UHECRs at Earth at $E_0 = 10^{1.55}$ EeV and the redshift evolution $m$ of the sources. Using the sweet-spot approximation from the authors' companion work, the paper computes fixed-flux contours—for example the single-flavor level $E^2_\\nu\\,dN/dE_\\nu = 10^{-8}$ GeV cm$^{-2}$ s$^{-1}$ sr$^{-1}$, which tracks current sensitivity—through the $(f,m)$ plane for realistic ranges of spectral index and maximum energy. Overlaying the current EeV-range neutrino upper limits, the region of strong source evolution combined with a large proton fraction is ruled out; concretely, for $m \\gtrsim 7.1$ the allowed proton fraction must satisfy $f \\lesssim 0.11$. That number corresponds to the source evolution of high-luminosity active galactic nuclei, so the paper reads this as: if such sources dominate UHECRs, at most about 11% of the detected cosmic rays at $E_0$ can be protons.","pith_inferences":["The same two-parameter degeneracy could be tested against independent composition probes at the same energy: if air-shower measurements later put a strict upper bound on protons at $E_0$ tighter than $f \\lesssim 0.11$, the neutrino result would not be needed; if they disagree, it would point to a flaw in the sweet-spot assumption.","The normalization to the measured cosmic-ray flux at one energy ($E_0$) makes the derived $f$ sensitive to the choice of that reference energy and to the assumed proton spectral shape; recomputing the contours at a different reference energy would show how robust the 11% number is.","If a fraction of the highest-energy protons originates from rare sources with very high maximum energies rather than from the dominant source population, the same neutrino limits may effectively become a constraint on the luminosity of that subpopulation, not on the overall UHECR composition.","A null detection at 1 EeV at the next sensitivity level would push the allowed $f$ downward for all $m$, effectively excluding source classes whose evolution is strong even if their proton contribution is small."],"forward_implications":["If a source class has strong evolution $m \\gtrsim 7$, its contribution of protons at $E_0$ must stay below roughly 11%, and this bound tightens if future limits go below the current sensitivity.","A detection of cosmogenic neutrinos near 1 EeV would pin down the combination $(f,m)$, with the degeneracy broken by assuming a source evolution or by combining with proton-fraction estimates from other measurements.","Because the constraining argument does not rely on hadronic interaction models, it can be cross-checked against composition inferred from air-shower depth, where such models are required.","The same contours, evaluated at lower flux levels, become a forecast: next-generation radio-array neutrino detectors with roughly one or two orders of magnitude better sensitivity would constrain the proton fraction for essentially any realistic source evolution.","Current limits are most restrictive for large $m$; for moderate evolution, such as star-formation-like $m\\sim 3$, the same flux level allows larger $f$, so the discriminating power of the sweet spot grows as limits improve."],"supporting_citations":[{"why":"Establishes the sweet-spot behaviour and defines $f$ and $m$ as the two controlling parameters at ~1 EeV.","marker":"[1]"},{"why":"Supplies one of the current differential 90% confidence single-flavor upper limits at EeV energies that define the exclusion level.","marker":"[4]"},{"why":"Supplies the other current EeV-range upper limit used to set the reference flux level.","marker":"[5]"},{"why":"Provides the measured UHECR spectrum at $10^{1.55}$ EeV used to normalize the simulated proton flux.","marker":"[6]"},{"why":"Quantifies how neglected extragalactic magnetic fields could raise the 1 EeV flux by up to a factor of a few, setting the size of that uncertainty.","marker":"[23]"},{"why":"Provides the public simulation code used to propagate protons and compute the expected cosmogenic neutrino flux.","marker":"[25]"},{"why":"Supplies the source-evolution parametrization for high-luminosity AGN used to translate $m\\gtrsim 7.1$ into a concrete source class.","marker":"[31]"}],"fun_headline_variants":["Cosmogenic neutrinos force 11% proton ceiling for strong sources","For strong sources, neutrino limits cap protons at 11%","Strong evolution + neutrinos = 11% proton cap","At ~1 EeV, neutrinos cap protons at 11% for strong evolution"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument assumes that at $E_\\nu \\approx 1$ EeV the spread in predicted cosmogenic flux from the unknown spectral index, maximum energy, and extragalactic background is small compared with the distance between the contours, and that extragalactic magnetic fields change the flux by no more than a factor of a few.","fun_headline_variants_meta":{"raw":{"variants":["Cosmogenic neutrinos force 11% proton ceiling for strong sources","For strong sources, neutrino limits cap protons at 11%","Strong evolution + neutrinos = 11% proton cap","At ~1 EeV, neutrinos cap protons at 11% for strong evolution"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001854,"raw_usage":{"total_tokens":7332,"prompt_tokens":1044,"completion_tokens":6288,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":660,"completion_tokens_details":{"reasoning_tokens":6211}},"tokens_in":660,"tokens_out":6288,"duration_ms":43131,"temperature":1.0,"reasoning_tokens":6211,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T05:04:14.323260+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the constant-flux contours with the two extreme parameter sets (e.g. $\\alpha=1.0,\\ \\log(E_{\\max}/\\mathrm{eV})=19.6$ and $\\alpha=3.0,\\ \\log(E_{\\max}/\\mathrm{eV})=23$) plus an extragalactic magnetic-field model that boosts the 1 EeV flux by the maximal factor; if a non-negligible part of the region $f>0.11,\\ m>7.1$ then falls below the current upper limits, the claimed exclusion is not robust. Conversely, a detected flux above the assumed reference level at 1 EeV for a model with $f\\lesssim 0.11$ and $m\\gtrsim 7.1$ would disprove the mapping.","supporting_citations":[{"cited_title":"Fenu for the Pierre Auger Collaboration, The cosmic ray energy spectrum measured using the Pierre Auger Observatory, PoS(ICRC2017)486 (2018)","cited_arxiv_id":null,"evidence_quote":"Provides the measured UHECR spectrum at $10^{1.55}$ EeV used to normalize the simulated proton flux."},{"cited_title":"Predictions for the flux of high-energy cosmogenic neutrinos and the influence of the extragalactic magnetic field","cited_arxiv_id":"1810.03769","evidence_quote":"Quantifies how neglected extragalactic magnetic fields could raise the 1 EeV flux by up to a factor of a few, setting the size of that uncertainty."}],"review_version":1}