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REVIEW 3 major objections 4 minor 3 cited by

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.

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2026-08-03 19:29 UTC pith:CQ4WRQZX

load-bearing objection 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. the 3 major comments →

arxiv 2512.00165 v2 pith:CQ4WRQZX submitted 2025-11-28 hep-ph astro-ph.COastro-ph.HEhep-ex

Widen the Resonance at Ultra-High Energies: Novel Probes of Neutrino Self-interactions in the High-Mass Regime

Pedro A. N. Machado , Isaac R. Wang , Xun-Jie Xu , Bei Zhou This is my paper
classification hep-ph astro-ph.COastro-ph.HEhep-ex
keywords neutrino self-interactionsultra-high-energy neutrinoscosmic neutrino backgroundresonant absorptionGRANDcosmogenic neutrino productionrelativistic neutrinosBoltzmann equation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

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.

Core claim

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

What carries the argument

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

Load-bearing premise

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.

What would settle it

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.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • 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.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • 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.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

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.

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 (3)
  1. [Sec. 1 and Eq. (7)] 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.
  2. [Sec. 5, Eq. (28)] 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.
  3. [Sec. 3, Fig. 2] 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.
minor comments (4)
  1. [Fig. 1 caption] The caption contains an apparent artifact '19931126' that should be removed.
  2. [Sec. 5, text after Eq. (28)] 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.
  3. [Sec. 2.1, Eq. (5)] 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.
  4. [General] 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.

Circularity Check

0 steps flagged

No circular reduction: the same-author formula Eq. (7) is parameter-free and the GRAND reach is an output; the m1<T_CNB condition is a physical assumption, not a circular input.

full rationale

No circular step is present. The paper's central sensitivity (Fig. 5) is obtained by solving the Boltzmann equation (Eq. 11) with the absorption rate (Eq. 7) and collision terms (Eqs. 13-16) inherited from Ref. [1], which shares three authors with this work. This is the only prominent self-citation in the derivation chain, but it does not reduce to an input-output identification: Eq. (7) is stated to follow from integrating the narrow-width cross section (Eq. 6) over the thermal CNB distribution, and Ref. [1] is a parameter-free, falsifiable result, not fitted to the present GRAND projections. The source term uses the semi-analytic cosmogenic neutrino framework from the external Ref. [72] and is validated against CRPropa-type simulations [32]; the astrophysical source parameters m, Gamma, and E_max are marginalized as nuisances rather than tuned to the nuSI signal. The projected sensitivity curves are outputs of the pipeline, not fitted to the signal. The paper's reach is conditional on the lightest neutrino mass eigenstate being relativistic today (m1<T_CNB~0.16 meV), which is an unproven physical assumption and a correctness risk, but not a definitional or circular step. The score of 2 reflects only the presence of a load-bearing same-author citation [1], with no circular reduction of the central claim.

Axiom & Free-Parameter Ledger

4 free parameters · 8 axioms · 0 invented entities

The projection rests on the relativistic-CNB premise plus a simplified cosmogenic flux model with three marginalized source parameters. The scalar mediator is not invented here; it is standard νSI model-building. No new particles or forces are introduced by this paper.

free parameters (4)
  • source evolution index m = marginalized over [-3,3] in likelihood
    Controls redshift evolution of cosmogenic sources, Eq. (20); marginalized so sensitivity is not a prediction for a specific source class.
  • UHECR spectral index Γ = marginalized over [2.0,3.0]
    Injected proton spectrum Eq. (22); benchmark 2.5; marginalized to absorb astrophysical uncertainty.
  • UHECR cutoff E_max^p = marginalized over [10^2,10^5] (EeV)
    Exponential cutoff in Eq. (22); benchmark 250 EeV; affects cosmogenic flux normalization and shape.
  • λ (unidentified likelihood nuisance) = marginalized (undefined)
    Mentioned in Sec. 5 as a parameter marginalized with m, but not present in Eq. (28) or defined; if it is a flux normalization it is a free parameter.
axioms (8)
  • domain assumption A neutrino mass eigenstate with m1 < T_CNB ≈ 0.16 meV exists and is thermally distributed today.
    Secs. 1 and 2.2; required for the widened resonance, Eq. (7). Without it the CNB resonance is narrow as in Ref. [32].
  • domain assumption Resonant s-channel scattering νν→φ→νν dominates; non-resonant terms ∝ g^4 are negligible.
    Sec. 2.3; valid for g≲1e-3 but not stated quantitatively.
  • domain assumption Cosmogenic UHE neutrino production is dominated by photopion production on CMB; other processes are negligible.
    Sec. 3; based on Kelner-Aharonian Ψ fits [72] and standard GZK estimates.
  • domain assumption UHECRs are all protons; composition uncertainty is absorbed by source-evolution parameter m.
    Sec. 3; needed to use Eqs. (21)-(22).
  • domain assumption After production, oscillations generate a nearly flavor-independent neutrino flux.
    Sec. 3; required for applying Eq. (24) and the source term in all flavors.
  • domain assumption GRAND's direction-averaged effective area and 10-year exposure from Ref. [83] are accurate.
    Sec. 5 and Fig. 4; drives event rates in Eq. (27).
  • domain assumption ΛCDM expansion with H0=67.36, Ωm=0.315, ΩΛ=0.685.
    Eq. (12); standard PDG values; affects propagation redshift.
  • domain assumption Neutrinos are Majorana and the new mediator is a real scalar coupled as in Eq. (2).
    Defines the νSI model under study; not derived in this paper.

pith-pipeline@v1.3.0-alltime-deepseek · 18678 in / 16501 out tokens · 158676 ms · 2026-08-03T19:29:03.162295+00:00 · methodology

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read the original abstract

Neutrino self-interaction beyond the Standard Model is well motivated by the nonzero masses of neutrinos, which are the only known particles guaranteed to have new physics. Cosmic messengers, especially neutrinos, play a central role in probing new physics, as they provide experimental conditions far beyond the reach of laboratories and serve as the link between laboratory fundamental-physics discoveries and their roles in the Universe, where many new physics motivations originate. In this work, we propose a novel probe of neutrino self-interactions through ultra-high-energy neutrinos scattering off the cosmic neutrino background when the lightest neutrino species remains relativistic today. This allows us to ``Widen the Resonance'' of such scattering. Meanwhile, we also provide a semi-analytic framework for cosmogenic UHE neutrino production, avoiding computationally intensive simulations and yielding results precise enough for BSM studies. The widened resonance enables future ultrahigh-energy neutrino telescopes, in particular GRAND, to probe mediator masses from MeV to GeV, reaching couplings down to $g \sim 10^{-3}$ -- up to two orders of magnitude beyond current bounds. Our results enhance the discovery potential of $\nu$SI in the high-mass regime, potentially offering crucial insights into the connections between the neutrino sector and dark sector.

Figures

Figures reproduced from arXiv: 2512.00165 by Bei Zhou, Isaac R. Wang, Pedro A. N. Machado, Xun-Jie Xu.

Figure 1
Figure 1. Figure 1: Mean-free-path estimate of the νSI strength relevant to UHE neutrino propagation. The black dashed lines are obtained using Eq. (10), and the blue region is obtained by further imposing a finite range of Eν. where fX with X ∈ {ν1, ν2, ν3, ϕ} denotes the phase space distribution of particle X, Γ ± ν and Γ ± ϕ are production and depletion rates of ν and ϕ via scattering or decay processes, and Sν is the astr… view at source ↗
Figure 2
Figure 2. Figure 2: Neutrino energy spectrum without νSI calculated using our semi-analytic framework, which is consistent with the result from computationally intensive simulations [32, 77] within the theoretical uncertainty characterized by the difference between the two solid or dashed lines. We show the results for our benchmark cases, Γ = 2.5, Emax = 250 EeV, with m = 0 and 3 being optimistic and pessimistic scenarios, r… view at source ↗
Figure 3
Figure 3. Figure 3: UHE neutrino fluxes modified by νSI. The left and right panels assume flavor universal and ντ -philic couplings, respectively. The upper panels present the flux spectrum, whereas the lower panels show the ratio of the modified flux to the standard one with free propagation. a perfectly diagonal gij . We then include the effect of neutrino regeneration from ϕ decay. Since the decay rate into each flavor is … view at source ↗
Figure 4
Figure 4. Figure 4: Left: direction-averaged effective area of GRAND for UHE tau neutrino detection. Right: our calculated event rates of UHE neutrinos at GRAND with ten years of exposure. We also use two histograms to show our energy binning. To observe the EAS, GRAND aims to measure their radio emission by deploying a large-scale net￾work of up to 200,000 autonomous radio antennas over an area of about 200,000 km2 , primari… view at source ↗
Figure 5
Figure 5. Figure 5: (Main result of the paper.) Our projected sensitivities on νSI from UHE neutrinos absorbed by relativistic CNB, i.e., under the “widening the resonance” scenario, along with results from previous works. Red solid (dashed) curves: our sensitivities using the GRAND UHE neutrino detector, assuming optimistic (pessimistic) fluxes. Blue curves: previous results from UHE neutrinos absorbed by non-relativistic CN… view at source ↗

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Forward citations

Cited by 3 Pith papers

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Reference graph

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