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REVIEW 3 major objections 5 minor 106 references

Constraints on Neutrino Secret Interactions from Multi-messenger Neutrinos Scattering on C$\nu$B

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Astrophysical neutrinos traveling through the cosmic neutrino background set new, generally stronger upper bounds on secret neutrino self-interactions, especially for a vector mediator at low mass.

desk verdict A coherent, modest analytical extension of the Kolb–Turner framework to KM3-230213A; the KM3-based 'new region' is real only if the source is extragalactic, which the paper itself concedes but the abstract does not. read the letter →

arxiv 2505.14332 v3 pith:4OSEHHXQ submitted 2025-05-20 hep-ph

Maria Petropavlova This is my paper
classification hep-ph
keywords mediatorneutrinoneutrinosconstraintscouplingmassdiracinteractions
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

Neutrinos barely interact, but some beyond-Standard-Model theories add a new force between neutrinos, carried by a light particle called a mediator. If such a force exists, high-energy neutrinos from distant cosmic sources would scatter on the sea of relic neutrinos left over from the Big Bang, the cosmic neutrino background. The more strongly they scatter, the less likely they are to reach Earth. The paper turns detected neutrinos from SN1987A, the blazars TXS 0506+056 and PKS 0735+178, the galaxy NGC 1068, and the extreme-energy KM3-230213A event into a simple test: if a neutrino arrived, the line of sight must be nearly transparent, which forbids large values of the new coupling g.

For a heavy spin-one mediator coupled to Dirac neutrinos, the authors compute scattering cross sections, mean free paths, and redshift effects, and translate transparency into exclusion curves in the plane of coupling versus mediator mass. They also treat scalar mediators and Majorana neutrinos. They find that a vector mediator gives stronger limits at low mediator mass than a scalar one, and that the KM3 event extends sensitivity to heavier mediators, provided that event came from beyond the local universe. They note the KM3 source is unknown and show results for four assumed distances.

The main caveats are that the constraints are model-dependent, use fixed source energies and distances with no quoted uncertainties, and rely on the simplifying assumption of a flavor-universal coupling. The low-mass vector constraints also depend on how the t-channel singularity is regularized, which the paper explores through a cutoff parameter.

Extended reading notes

Core claim

The central claim is that high-energy astrophysical neutrinos passing through the cosmic neutrino background yield new upper bounds on the neutrino secret interaction coupling g, with "significant constraints on the νSI vector coupling in the low mediator mass region, compared to the scalar coupling scenario," and that "the inclusion of the extreme-energy KM3-230213A event potentially allowed us to probe an entirely new scale of interaction strength." If correct, these curves exclude previously allowed (g, M) values for the vector and scalar mediator models considered.

Load-bearing premise

The claim that KM3-230213A probes a previously unconstrained mediator-mass region rests on the assumed distance to the unidentified source. Section V.E states: "As the origin of the event remains yet unclear, we take four representative light-travel distances" (10 kpc, 10 Mpc, 1 Gpc, 4.12 Gpc). If the true origin is galactic or otherwise local, the headline high-energy constraints weaken dramatically and the new parameter space is no longer covered. Separately, all constraints assume an equal-density, universal-mass CνB and flavor-universal coupling, which set the resonance positions in the NR and UR regimes.

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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper derives upper bounds on the neutrino secret interaction (νSI) coupling g by requiring that the optical depth τ = D/λ for high-energy astrophysical neutrinos propagating through the cosmic neutrino background (CνB) satisfies τ ≲ 1. The analysis treats a massive vector mediator coupled to Dirac neutrinos and a scalar mediator coupled to Dirac and Majorana neutrinos, in both non-relativistic and ultra-relativistic CνB regimes, using sources SN1987A, TXS 0506+056, PKS 0735+178, NGC 1068, and the KM3-230213A event. The central new claim is that the 220 PeV KM3-230213A event can probe a previously unconstrained mediator-mass/coupling region, provided that its unknown source is sufficiently distant.

Significance. If the underlying assumptions hold, the paper provides a useful and mostly analytic set of constraints: it includes full mediator-mass dependence rather than only the light/heavy asymptotic limits, compares vector and scalar mediators and Dirac versus Majorana neutrinos, and reproduces the Kolb-Turner result in Fig. 9 as a cross-check. The bounds are not circular: they follow from computed cross sections and the optical-depth condition without fitting any constant to the data. The main significance is conditional, however, because the headline KM3-based exclusion region depends on an unconfirmed source distance, and the NR constraint curves use a neutrino mass below the oscillation-established floor.

major comments (3)
  1. [Sec. V.E and Abstract/Conclusion] The claim that KM3-230213A probes a previously unconstrained parameter region is conditional on the assumed distance to an unidentified source. Equation (11) gives g ≤ (λ_{g=1}/D)^{1/4}, so moving from the 1 Gpc benchmark to the galactic 10 kpc benchmark weakens the bound by a factor of (10^5)^{1/4} ≈ 18; the 10 kpc curves in Figs. 7 and 8 therefore do not extend the exclusions from TXS 0506+056 or NGC 1068. The text does flag this with 'potentially' in Sec. VI and with the criterion 'beyond the local universe (≳1 Mpc)' in Sec. V.E, but the Abstract states the expansion of limits without that qualification. Please rephrase the Abstract and the 'entirely new scale' discussion so that the strong KM3-based constraints are presented as distance-dependent projections, or redraw the figures to make the galactic benchmark the default reading.
  2. [Sec. IV.B, Eq. (8)] The ultra-relativistic resonance contribution is computed with the narrow-width approximation, but Eq. (8) is introduced without derivation, and the accompanying statement that the Breit-Wigner propagator 'fails to reproduce the correct heavy mediator scaling s/M^4' is not demonstrated. Because the resonance region controls the dips in the UR exclusion curves (Figs. 2–8), this is a load-bearing element of the central constraints. Please provide a derivation of Eq. (8) or a quantitative comparison with the full Breit-Wigner calculation, including an estimate of the error introduced by combining the NWA rate with the off-resonance amplitude.
  3. [Sec. IV assumptions and Fig. 2 caption] The NR constraints are computed with a universal neutrino mass m = 10^{-3} eV. This value is below the mass of the heavier mass eigenstates implied by neutrino oscillations (m_2 ≈ 8.6×10^{-3} eV and m_3 ≈ 5×10^{-2} eV), so a common mass for all CνB species cannot be as small as 10^{-3} eV. Since the NR mean free path and the s-channel resonance position depend on m through s ≈ m^2 + 2mE, the curves in Fig. 2 (left) and similar figures are not the limits for a physically allowed common mass, and Sec. V.B itself states that the results are highly sensitive to m. Please present the NR curves for a realistic mass or as an envelope over the allowed mass range, and state in each figure caption which mass is used.
minor comments (5)
  1. [Table I and Sec. III.d] Table I assigns PKS 0735+178 a redshift z = 0.65, while the text reports z ≈ 0.65 or z = 0.45 ± 0.06 as alternatives; please state which value is adopted in the constraints and, ideally, show the sensitivity to this choice.
  2. [Figures 2–8] The exclusion curves are drawn as single lines without uncertainty bands; the source distances, neutrino energies, and neutrino mass have nontrivial uncertainties, and the KM3 energy in particular is reported as a median value. A band or a short statement quantifying the induced variation in g would make the constraints easier to interpret.
  3. [Sec. V.F.3] The claims about numerical inconsistencies in Tables 1 and 2 of Ref. [12] and about an omitted negative sign in Ref. [25] are made without equations or page references; please provide the specific entries and expressions so that these assertions can be checked.
  4. [Fig. 9 caption] The caption states 'no resonance width is included,' but the main UR calculation uses the narrow-width resonance treatment of Sec. IV.B; please clarify whether Fig. 9 is meant to illustrate only the off-resonance comparison and how it relates to the final UR bounds.
  5. [References] Some reference entries are incomplete or inconsistently formatted, for example Ref. [14] is missing its year and volume/page details; please audit the bibliography against the journal style.
Assumptions & free parameters 5 free parameters · 7 assumptions · 0 invented entities

The mediator particles (massive vector boson and scalar) are borrowed from established BSM frameworks cited in the paper, not introduced by this work, so no new entity is postulated and no independent falsifiable handle is added. The five free parameters above are model inputs or scanned quantities; none is fitted to the neutrino data used for the constraints.

free parameters (5)
  • mediator mass M = scanned over range
    Central model parameter defining the resonance position and t-channel behavior; no fit to data.
  • coupling constant g = excluded above g_bound(M)
    The quantity constrained; upper limits are derived from the optical depth condition, not fitted.
  • common neutrino mass m = 1e-3 eV (NR main plots), 1e-2 eV in comparison
    Sets the NR resonance s ~ m^2 + 2mE; the paper varies it to show sensitivity.
  • t-channel cutoff epsilon = 0 to 0.5 in Figure 10
    Regulates the massless-mediator divergence; strongly affects low-M vector constraints.
  • KM3-230213A source distance = 10 kpc, 10 Mpc, 1 Gpc, 4.12 Gpc
    Source is unidentified; constraints scale with the assumed benchmark distance.
assumptions (7)
  • domain assumption CνB consists of all neutrino and antineutrino species with equal number density 56 cm^-3 and a Fermi-Dirac spectrum with T=1.68e-4 eV.
    Section IV lists this as assumption 1 and Section IV.B defines the distribution.
  • domain assumption All neutrino masses are equal and m < 0.1 eV; the NR regime uses m=1e-3 eV.
    Section IV assumption 2 and Figure 3 left panel.
  • domain assumption The interaction is flavor-diagonal and universal, g_alpha_beta = g delta_alpha_beta.
    Section IV assumption 3; the flavor non-universal case in Section V.C is an explicit variation.
  • domain assumption The mediator couples only to active neutrinos; couplings to charged particles are negligible.
    Section II.B states this assumption explicitly.
  • domain assumption Detection of at least one neutrino from a source implies optical depth tau = D/lambda <= 1.
    Section V, Eq. (11), uses this to set the upper bound on g.
  • standard math The differential cross sections in Tables II, III, V, and VI are correct standard QFT results.
    The tables are not derived in the text; the paper says they can be cross-checked against Bhabha and Møller scattering.
  • domain assumption The narrow-width approximation for the s-channel resonance, Eq. (8), is valid in the UR regime.
    Section IV.B state the NWA is used and combined with the off-resonance bare-propagator result.

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Pith. "Pith review of Constraints on Neutrino Secret Interactions from Multi-messenger Neutrinos Scattering on C$\nu$B." pith.science (2026). https://pith.science/paper/4OSEHHXQ

@misc{pith2026250514332,
  author       = {Pith},
  title        = {Pith review of: Constraints on Neutrino Secret Interactions from Multi-messenger Neutrinos Scattering on C$\nu$B},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4OSEHHXQ}},
  note         = {Machine review of arXiv:2505.14332}
}
abstract

We present new constraints on neutrino secret interactions ($\nu$SI) by studying high-energy neutrinos from well-known astrophysical sources, such as SN1987A, the blazars TXS $0506+056$ and PKS $0735+178$, the active galaxy NGC 1068, and the KM3-230213A neutrino event. We expand existing limits by probing a previously unconstrained region of the mediator mass parameter space. Our study focuses on Dirac neutrinos interacting with a massive spin-one boson as they propagate through the Cosmic Neutrino Background, while also examining Majorana and Dirac neutrinos scattering via a scalar mediator. We consider both ultra-relativistic and non-relativistic regimes, establishing bounds on the $\nu$SI coupling constant across the wide $\nu$SI mediator mass range. Our results, obtained using analytical methods, demonstrate significant constraints on the $\nu$SI vector coupling in the low mediator mass region, compared to the scalar coupling scenario.

Figures

Figures reproduced from arXiv: 2505.14332 by the authors.

Figure 1
Figure 1. The tree-level Feynman diagrams contributing to [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Exclusion plots for the coupling constant [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. Left panel: Illustration of the sensitivity of the coupling constant exclusion to [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: Exclusion plots for the coupling constant [PITH_FULL_IMAGE:figures/full_fig_p017_4.png]
Figure 5
Figure 5. Figure 5: Comparison of exclusion limits on the coupling constant for scalar and vector [PITH_FULL_IMAGE:figures/full_fig_p019_5.png]
Figure 6
Figure 6. Figure 6: Comparison of exclusion limits on the coupling constant for Dirac and Majorana [PITH_FULL_IMAGE:figures/full_fig_p020_6.png]
Figure 7
Figure 7. Figure 7: Exclusion plots for the coupling constant [PITH_FULL_IMAGE:figures/full_fig_p021_7.png]
Figure 8
Figure 8. Figure 8: Exclusion plots for the coupling constant [PITH_FULL_IMAGE:figures/full_fig_p021_8.png]
Figure 9
Figure 9. Figure 9: Comparison of the full mass range analysis (solid curve) with the limiting cases [PITH_FULL_IMAGE:figures/full_fig_p022_9.png]
Figure 10
Figure 10. Figure 10: Exclusion plots illustrating the impact of the cutoff parameter [PITH_FULL_IMAGE:figures/full_fig_p023_10.png]
Figure 11
Figure 11. Figure 11: The figure shows a comparison with the recent work [14] for Majorana [PITH_FULL_IMAGE:figures/full_fig_p024_11.png]

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