{"id":"ff4051f0-98cd-4aa4-a8c6-e1d11d353281","arxiv_id":"2512.00165","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"If one neutrino species in the cosmic neutrino background is still relativistic today, UHE neutrinos scattering off it can resonantly disappear over a broad energy range, and GRAND could detect that dip to probe neutrino self-interactions down to g ~ 10^-3.","lead":"Ultra-high-energy neutrinos hitting the relic neutrino sea could be absorbed through new neutrino self-interactions, creating a broad dip in the spectrum. This paper shows that the planned GRAND radio telescope could see that dip, probing mediator masses from MeV to GeV at couplings down to about 10^-3.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Reach depends on unestablished m1 < T_CNB; internal derivation sound, conditional verdict matches.","rationale":"The stress-test confirms the reader's weakest-assumption identification: the relativistic CNB condition is the load-bearing element of the central claim. We examined the derivation of Eq. (7) from the resonant cross section and thermal distribution; the numerical coefficient and exponential factor are consistent with a standard Boltzmann integration, and the Boltzmann-equation treatment (including regeneration) is internally coherent. The semi-analytic cosmogenic flux model is validated against CRPropa within the stated uncertainties, and the detector assumptions are clearly stated. No fatal internal inconsistency was found. The only substantive concern is external: the viability of m1 < T_CNB is not established, and the paper's projected improvement over non-relativistic CNB studies is exactly the widened resonance made possible by that condition. Since the paper itself acknowledges this limitation and frames the results conditionally, a CONDITIONAL verdict is appropriate. The concrete test proposed would quantify the fragility of the reach to the neutrino-mass assumption, directly testing whether this concern lands.","tokens_in":18932,"tokens_out":21718,"duration_ms":188523,"concrete_test":"Recompute the GRAND sensitivity curves in Fig. 5 for a lightest mass eigenstate m1 = 0.12 meV (semi-relativistic, close to T_CNB) instead of m1 ≈ 0, using the full massive Fermi-Dirac distribution in the absorption-rate integral. If the red contours shift by more than a factor of 2 in g or compress significantly in m_φ range, the central claim is critically sensitive to the unestablished neutrino-mass condition. Also, report the posterior probability of m1 < T_CNB from DESI+Planck+BAO Σm constraints to gauge how likely the scenario actually is.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that GRAND can probe νSI up to m_φ ~ 1 GeV and g ~ 10^-3 rests entirely on the lightest neutrino mass eigenstate being relativistic today (m1 < T_CNB ≈ 0.16 meV). This condition is not established by current data; oscillation bounds allow it, and DESI hints at low Σm, but the posterior probability is not quantified. If m1 > T_CNB, the CNB is non-relativistic and the resonance is narrow (as in Ref. [32]), eliminating the 'widening' effect and invalidating the improved sensitivity. The paper explicitly frames this as a condition, and we found no internal error in the derivation of Eq. (7) or the Boltzmann treatment. However, the entire projected discovery reach is contingent on a scenario whose real-world probability remains unknown, which warrants a conditional rather than unconditional acceptance.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper proposes that ultra-high-energy (UHE) cosmogenic neutrinos propagating through a relativistic cosmic neutrino background (CNB) can be resonantly absorbed by neutrino self-interactions (νSI) via s-channel mediator production (νν→φ→νν), and that the thermal spread of the CNB broadens the absorption feature in Eν ('widened resonance'). The authors derive the resonant absorption rate, build a Boltzmann transport code with resonant collision terms, introduce a semi-analytic framework for cosmogenic UHE neutrino production, and perform a binned Poisson likelihood forecast for GRAND with ten years of exposure. Their central result (Fig. 5) is that GRAND can probe scalar mediators of mass ~MeV–GeV with couplings g down to ~1e-3, which for ντ-philic couplings improves on current Z-invisible/BBN/IceCube bounds by up to two orders of magnitude, and for universal couplings is competitive with rare-meson-decay bounds. The entire projection is explicitly conditional on the lightest neutrino mass eigenstate remaining relativistic today, m1 < T_CNB ≈ 0.16 meV.","tokens_in":19204,"tokens_out":8855,"duration_ms":88925,"significance":"The calculation is coherent and the result, if the conditional scenario is realized, is significant: it opens a high-mass νSI parameter region (mφ up to ~1 GeV) that existing UHE-neutrino studies with a non-relativistic CNB do not reach, and it provides a useful semi-analytic cosmogenic-flux framework that can simplify future phenomenological studies. The sensitivity curves in Fig. 5 are outputs of a forward calculation, not fitted to the signal, and the derivation of Eq. (7) from the thermal CNB distribution is internally reasonable. The main caveat is external: the reach relies on m1 < T_CNB, a condition that is allowed by oscillation data and hinted at by DESI but not established. The paper should therefore be judged as a conditional sensitivity forecast rather than an unconditional discovery claim.","major_comments":[{"comment":"The entire widened-resonance absorption rate assumes the lightest neutrino mass eigenstate is relativistic today, m1 < T_CNB ≈ 0.16 meV. The paper states this as a condition and cites DESI, but it does not quantify the current status. If m1 > T_CNB, the CNB target is effectively monochromatic, the resonance is narrow (as in Ref. [32]), and the red sensitivity curves in Fig. 5 do not follow. Since this is the load-bearing physical assumption, please (i) quantify the current constraint/allowed range of m1 from oscillation data and cosmology (e.g., Σm from DESI+Planck), (ii) discuss how plausible m1 < T_CNB is in concrete neutrino-mass models, and (iii) ideally show how the projected sensitivity degrades as m1/T_CNB increases. This is not an internal derivation error, but it is essential for assessing the reach claim in the abstract.","section":"Sec. 1 and Eq. (7)"},{"comment":"The likelihood is written as χ²(m, Γ, Emax | g, mφ), but the text says 'We include the parameters λ and m to account for astrophysical uncertainties in N_st,k and marginalize them.' The parameter λ is never defined in or near Eq. (28), and m is used both as the source-evolution index in Eq. (20) and as a nuisance in this sentence. This makes the statistical procedure unreproducible and directly affects the reported red contours. Please define the full likelihood with all nuisance parameters, specify their ranges and priors, and explain exactly how they enter N_st,k.","section":"Sec. 5, Eq. (28)"},{"comment":"The validation of the semi-analytic cosmogenic flux is only qualitative: the text states consistency with simulations 'within the theoretical uncertainty,' but no numerical residual or error metric is given. Since Eq. (28) uses absolute event counts N_st,k derived from this flux, a systematic mismatch could bias the sensitivity projection. Please provide a quantitative comparison (e.g., per-bin ratio or χ² between the semi-analytic flux and the CRPropa/Ref. [32] benchmark) and state whether this uncertainty is included in the marginalized astrophysical nuisance parameters.","section":"Sec. 3, Fig. 2"}],"minor_comments":[{"comment":"The caption contains an apparent artifact '19931126' that should be removed.","section":"Fig. 1 caption"},{"comment":"The sentence 'marginalize over m∈[-3,3], Γ∈[2.0,3.0], and Emax∈[10^2,10^5] around two benchmark points' is confusing: is the full range scanned, or are m fixed to 0/3 for the pessimistic/optimistic curves while Γ and Emax are marginalized? Please clarify the exact scanning procedure.","section":"Sec. 5, text after Eq. (28)"},{"comment":"The CP-violating phase δ_CP is used in Eq. (5) before its values are introduced at the end of the subsection. Define δ_CP and the mixing parameters before Eq. (5) for readability.","section":"Sec. 2.1, Eq. (5)"},{"comment":"The paper would benefit from releasing the Boltzmann-solver code or providing a brief reproducibility note, since the numerical solution of 800 coupled ODEs is central to the results but not documented in detail.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a legitimate conditional forecast and the self-citation to Ref. [1] is appropriate: Eq. (7) is a parameter-free prediction from the same widening mechanism, and the new UHE application is not a trivial repetition. The main risk is external: if cosmological data ultimately rule out m1 < T_CNB, the advertised GRAND reach disappears. I recommend major revision to quantify this condition and to repair the undefined λ nuisance and the qualitative flux validation; after that, the paper could be acceptable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here’s my take on arXiv:2512.00165. The paper is a solid, clearly-scoped phenomenological projection. It extends the “widened resonance” idea from the authors’ earlier DSNB work to UHE neutrinos scattering off the cosmic neutrino background, and shows that GRAND could probe scalar mediators in the MeV–GeV range with couplings down to ~1e-3 — two orders of magnitude beyond current Z-invisible bounds in the tau-philic case. The three-flavor Boltzmann treatment with the flavor-dependent spectral distortions (Fig. 3) is a real step beyond the single-flavor treatments in earlier work, and the semi-analytic cosmogenic flux framework (Fig. 2) is useful, even if it is a simplification of existing simulations rather than a totally new derivation.\n\nThe central caveat is exactly what the authors flag: the whole projection assumes the lightest neutrino mass eigenstate is relativistic today (m1 < T_CNB ~ 0.16 meV). That is allowed by oscillation data and hinted at by DESI, but it is not established. If m1 > T_CNB, the resonance is narrow and the sensitivity reverts to the earlier non-relativistic results. So this is a conditional forecast, not a discovery claim. I don’t consider that a flaw in the derivation — Eq. (7) is inherited from their own parameter-free derivation in Ref. [1], and the self-citation is legitimate — but it should be stated prominently in the abstract and conclusion, and the paper should quantify how the posterior probability of this scenario is currently unknown. The stress-test note is correct on this point.\n\nMinor issues: λ in Eq. (28) is not defined; the figure caption inconsistency for Fig. 1 (blue region uses Eν in [0.1, 20] EeV while text says [0.1,100] EeV) is cosmetic; no code is provided, which would help reproducibility given the Boltzmann solver is central. None of these are load-bearing. The likelihood analysis marginalizes over astrophysical uncertainties, and the red sensitivity curves are outputs, not fits to the signal, so no circularity.\n\nWho is this for? Anyone working on νSI phenomenology, UHE neutrino telescopes, or cosmogenic flux modeling. It will be a useful reference for GRAND projections. It deserves a serious referee — the core physics is sound, the conditionality is explicit, and the new elements are worth publishing. I’d send it to peer review with a request to clarify the λ definition, add a quantitative note on the m1 < T_CNB prior, and consider releasing the code.","headline":"Conditional but well-executed: the GRAND sensitivity reach for MeV–GeV νSI mediators follows from a widening-resonance mechanism that depends on the lightest neutrino mass eigenstate being relativistic today.","tokens_in":19662,"tokens_out":2337,"would_cite":true,"duration_ms":21555,"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":"If the lightest neutrino is still relativistic today, the cosmic neutrino background can turn ultra-high-energy neutrinos into a probe of new neutrino self-interactions down to coupling g ≈ 10^-3.","keywords":["neutrino self-interactions","ultra-high-energy neutrinos","cosmic neutrino background","resonant absorption","GRAND","cosmogenic neutrino production","relativistic neutrinos","Boltzmann equation"],"falsifier":"A cosmological measurement that forces the sum of neutrino masses well above the minimum oscillation value—so no mass eigenstate is relativistic today—would remove the thermal spread of the cosmic neutrino background and suppress the widened absorption, invalidating the projected sensitivity. More directly, if GRAND's measured ultra-high-energy neutrino spectrum shows no broad absorption dip at the predicted energies for parameters within the claimed reach, the widened-resonance mechanism would be falsified.","tokens_in":18884,"feed_emoji":"🔭","tokens_out":5070,"duration_ms":48087,"temperature":0.7,"pith_summary":"The paper argues that a relativistic component of the cosmic neutrino background—allowed by oscillation data and hinted by recent cosmological measurements—would broaden the resonant absorption of ultra-high-energy neutrinos by over an order of magnitude in energy. This 'widened resonance' makes the cosmic neutrino background partially opaque to ultra-high-energy neutrinos, creating a smooth spectral dip rather than a narrow line. By solving the Boltzmann equation with a new semi-analytic model of cosmogenic neutrino production, the authors project that the future GRAND radio detector could see this dip and thereby probe neutrino self-interactions with mediator masses from MeV to about 1 GeV and couplings down to g ~ 10^-3, improving on current bounds by up to two orders of magnitude in the tau-philic case.","feed_headline":"Cosmic neutrino sea widens resonance, letting GRAND reach g~10^-3","feed_subtitle":"If the lightest neutrino stays relativistic, thermal spread turns UHE absorption into a broad dip that exposes MeV-GeV mediators.","key_machinery":"The key object is the widened-resonance absorption rate for a relativistic cosmic neutrino background, Γ_abs,i ≈ g² m_φ² T / (16π E²) exp(−m_φ²/4TE), which replaces the delta-function resonance of the non-relativistic case with a Gaussian-like dependence on incoming neutrino energy. This rate, together with the resonant collision terms of the Boltzmann equation (Γ⁻_ν, Γ⁺_ν, Γ⁺_φ, Γ⁻_φ), determines the spectral dip and regeneration features. A second piece of machinery is the semi-analytic framework for cosmogenic ultra-high-energy neutrino production based on a parameterization of the neutrino spectrum per proton-photon interaction, which produces fluxes consistent with full simulations with","core_discovery":"The central discovery claim is that the thermal momentum spread of a relativistic cosmic-neutrino-background species changes the s-channel resonant scattering νν → φ → νν from a narrow absorption feature into a wide one, with an absorption rate Γ_abs ∝ (g² m_φ² T / E²) exp(−m_φ²/4TE). This broadens the accessible ultra-high-energy neutrino energy range around E_peak ≈ m_φ²/(8T), so that absorption affects a large portion of the observable spectrum. The authors show, with a full Boltzmann treatment and a likelihood analysis for GRAND, that this widened absorption yields projected sensitivities to neutrino self-interaction mediator masses up to 1 GeV and couplings down to g ~ 10^-3, exceeding","pith_inferences":["If recent baryon-acoustic-oscillation measurements confirm that the neutrino mass sum is near the minimum allowed by oscillations, the relativistic-cosmic-neutrino-background assumption becomes the default, making the widened resonance the standard expectation for ultra-high-energy neutrino propagation rather than a special scenario.","The same mechanism should widen the resonance for TeV–PeV neutrinos scattering on a relativistic cosmic neutrino background, so high-statistics TeV–PeV neutrino telescopes may reach smaller couplings than estimates that assume a non-relativistic background.","The semi-analytic production framework could be used to reinterpret the recent KM3NeT ultra-high-energy event: if a large ultra-high-energy flux is confirmed, the absorption dip would be even more pronounced than under the cosmogenic-only assumption, strengthening the discovery potential of neutrino self-interactions."],"forward_implications":["GRAND, with ten years of exposure, could detect the widened spectral dip and probe neutrino self-interactions with mediator masses up to about 1 GeV and couplings down to g ~ 10^-3 in the tau-philic scenario, two orders of magnitude beyond the current Z-invisible bound.","In the flavor-universal coupling case, the projected sensitivity beats rare-meson-decay bounds by a few-fold for mediator masses above about 10 MeV.","The absorption appears as a smooth, broad dip rather than a narrow line, making the probe robust to energy-resolution limitations and giving it statistical power from the wide affected energy range.","The semi-analytic cosmogenic production framework reproduces full simulation results within theoretical uncertainties, making BSM studies of ultra-high-energy neutrinos computationally cheaper.","The widened-resonance mechanism is general: it applies whenever both initial-state neutrinos have continuum energy distributions (e.g., the diffuse supernova neutrino background), extending the reach beyond ultra-high-energy neutrinos."],"fun_headline_variants":["Relativistic CνB widens resonance, GRAND reaches g~10^-3","Widened resonance lets GRAND probe neutrino self-interactions to g~10^-3","Thermal spread of CνB widens resonance, making GRAND sensitive to g~10^-3","New probe: UHE neutrinos widen resonance, GRAND sees g~10^-3"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The lightest neutrino mass eigenstate is relativistic today, with mass below the cosmic neutrino background temperature of about 0.16 meV, so that a thermal, relativistic cosmic neutrino background actually exists to scatter off.","fun_headline_variants_meta":{"raw":{"variants":["Relativistic CνB widens resonance, GRAND reaches g~10^-3","Widened resonance lets GRAND probe neutrino self-interactions to g~10^-3","Thermal spread of CνB widens resonance, making GRAND sensitive to g~10^-3","New probe: UHE neutrinos widen resonance, GRAND sees g~10^-3"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001357,"raw_usage":{"total_tokens":5365,"prompt_tokens":786,"completion_tokens":4579,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":530,"completion_tokens_details":{"reasoning_tokens":4481}},"tokens_in":530,"tokens_out":4579,"duration_ms":30872,"temperature":1.0,"reasoning_tokens":4481,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T19:29:03.162295+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A cosmological measurement that forces the sum of neutrino masses well above the minimum oscillation value—so no mass eigenstate is relativistic today—would remove the thermal spread of the cosmic neutrino background and suppress the widened absorption, invalidating the projected sensitivity. More directly, if GRAND's measured ultra-high-energy neutrino spectrum shows no broad absorption dip at the predicted energies for parameters within the claimed reach, the widened-resonance mechanism would be falsified.","supporting_citations":[],"review_version":1}