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REVIEW 4 major objections 5 minor 79 references

Diffuse Supernova Neutrino Background and Neutrino Non-Radiative Decay: a Bayesian Perspective

T0 review · 4 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper claims that if the neutrino mass ordering is normal and strongly hierarchical, the diffuse supernova neutrino background cannot distinguish non-radiative neutrino decay from no decay in the lifetime-to-mass range…

desk verdict First Bayesian DSNB decay forecast; the NO SH no-go is the headline, but it rests on an unstated helicity-conserving/flipping mix that should be tested before the no-go is taken as general. read the letter →

arxiv 2412.14681 v1 pith:X6YSHEUU submitted 2024-12-19 hep-ph astro-ph.HEastro-ph.SRhep-ex

Noah Roux , M. Cristina Volpe This is my paper · ORCID
classification hep-phastro-ph.HEastro-ph.SRhep-ex
keywords diffusesupernovaneutrinobackgroundnon-radiativedecaylifetime-to-massratioBayesfactorsnormalmassorderinginvertedhierarchydegeneracyrelicneutrinos
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 are known to have mass, so a heavier mass eigenstate could in principle decay into a lighter one plus a massless particle; the relic flux of neutrinos from all past core-collapse supernovae, the diffuse supernova neutrino background (DSNB), is one of the few places this non-radiative decay would show up. This paper asks whether upcoming experiments can actually tell a universe with decay from one without it, and answers with the first Bayesian analysis of the question in a full three-flavour framework. It computes DSNB fluxes and event rates under two independent sets of one-dimensional supernova simulations, with uncertainties from the evolving core-collapse supernova rate and the fraction of failed supernovae, and reports Bayes factors for inverse $\beta$ decay and neutrino-argon events in SK-Gd (Super-Kamiokande with gadolinium), Hyper-Kamiokande, JUNO and DUNE. The central conclusion is that if the neutrino mass ordering is normal and the masses are strongly hierarchical, the decay and no-decay predictions are so degenerate that no combination of these detectors can discriminate $\tau/m \in [10^9, 10^{11}]~\mathrm{s/eV}$; discriminating power appears for quasi-degenerate normal masses and, even more, for inverted ordering.

What carries the argument

The argument is carried by two pieces. First, the decaying DSNB flux is obtained from neutrino kinetic equations with a supernova source term plus decay source and sink terms, solved in closed form along the line of sight; the decay is described by mass-pattern-dependent daughter energy spectra, a delta function in the quasi-degenerate case and two distinct spectra for helicity-conserving and helicity-flipping decays in the strongly hierarchical case. Second, the statistical discriminator is the expected mean logarithmic Bayes factor, the ratio of background-marginalised binned Poisson likelihoods for a decay hypothesis versus the no-decay hypothesis, averaged over Markov-chain Monte Carlo pseudo-data, with thresholds of 3 and 5 marking strong and very strong evidence. The single free decay parameter, one $\tau/m$ for all decaying eigenstates, is what lets the whole comparison be summarised as a Bayes-factor map over $\tau/m$.

What would settle it

Compute the mean logarithmic Bayes factor between no decay and $\tau/m = 10^9~\mathrm{s/eV}$ from the actual binned inverse $\beta$ decay spectra of SK-Gd, HK (or HK-Gd) and JUNO plus the neutrino-argon spectrum of DUNE after 20 years of data, using this paper's background model and assuming normal ordering with strongly hierarchical masses; if the observed $\log B_{10}$ exceeds 3, the paper's no-discriminating-power claim for this mass pattern is falsified.

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Extended reading notes

Core claim

Working in a three-neutrino framework with two-body non-radiative decay $\nu_h \to \nu_l + \phi$ (or $\bar\nu_l + \phi$), and assuming mass-eigenstate decay with democratic branching ratios and one common lifetime-to-mass ratio $\tau/m$, the authors scan $\tau/m = 10^9, 10^{10}, 10^{11}~\mathrm{s/eV}$. For each mass pattern (normal strongly hierarchical, normal quasi-degenerate, inverted), they build binned Poisson likelihoods for the main detection channels, marginalise over Gaussian signal and background nuisance parameters in a conservative and an optimistic scenario, and quote expected mean logarithmic Bayes factors from Markov-chain Monte Carlo pseudo-data. The central finding is that in the normal strongly hierarchical case the Bayes factors essentially vanish in every channel and even in the idealized zero-background, zero-uncertainty limit, so the DSNB has no discriminating power between decay and no decay in the scanned range. In the quasi-degenerate normal case the combined analysis reaches strong evidence for $\tau/m = 10^9~\mathrm{s/eV}$ against stable neutrinos under optimistic uncertainties, while in the inverted case $\tau/m \lesssim 10^9~\mathrm{s/eV}$ can be ruled out with very strong evidence if neutrinos are stable or decay slowly. Neutrino-proton scattering in JUNO, which a previous analysis suggested could break the degeneracies, does not help at expected event rates; only a hypothetical very-low-background version approaches strong evidence.

Load-bearing premise

The whole analysis collapses neutrino decay into a single number, one common lifetime-to-mass ratio for every decaying eigenstate with democratic branching ratios, so if real decay couplings are uneven or eigenstate lifetimes differ, the projected Bayes factors, including the NO SH no-go, could change.

Editorial extensions

If this is right

  • If the true mass pattern is normal and strongly hierarchical, the DSNB will provide no constraint on non-radiative neutrino decay in the $\tau/m \in [10^9, 10^{11}]~\mathrm{s/eV}$ range, regardless of accumulated statistics in SK-Gd, HK, JUNO and DUNE.
  • For normal ordering with quasi-degenerate masses, combining the four experiments can yield strong evidence against stable neutrinos if $\tau/m$ is near $10^9~\mathrm{s/eV}$, assuming optimistic uncertainties on signal and background.
  • For inverted ordering, $\tau/m \lesssim 10^9~\mathrm{s/eV}$ can be rejected with very strong evidence when neutrinos are stable or decay with $\tau/m \gtrsim 10^{10}~\mathrm{s/eV}$, reaching this level in JUNO and the gadolinium-loaded Hyper-Kamiokande even under conservative uncertainties.
  • The neutrino-proton scattering channel in JUNO does not improve discrimination at expected event rates, contrary to an earlier two-flavour study, and would need very low backgrounds to approach strong evidence against $\tau/m = 10^9~\mathrm{s/eV}$.
  • Projected DSNB limits from this analysis could be competitive with cosmological neutrino-lifetime bounds once the heaviest neutrino mass is $m_h \gtrsim 0.05~\mathrm{eV}$.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Extension: because the analysis reduces decay to one common $\tau/m$ with democratic branching ratios, the normal strongly hierarchical (NO SH) no-go is a statement about that single-parameter family; a model with non-democratic couplings or eigenstate-dependent lifetimes could in principle produce distinguishable DSNB spectra and should be tested with the same Bayes-factor machinery.
  • Extension: a practical corollary the authors leave implicit is that a future DSNB detection under normal hierarchical masses would not count as evidence against neutrino decay, and would primarily constrain supernova astrophysics rather than particle physics.
  • Extension: running this Bayesian pipeline on real observed counts rather than Markov-chain Monte Carlo pseudo-data would turn the Bayes-factor maps directly into lower limits on $\tau/m$ for the quasi-degenerate and inverted cases, and would confirm or refute the no-go by whether the observed log Bayes factor stays below 3.
  • Extension: the large simulation-to-simulation spread in event rates suggests treating the supernova simulation choice as a discrete nuisance in a model-averaged Bayes factor; the authors compute per-scenario maps but do not average over the two simulation sets.
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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

4 major / 5 minor

Summary. This paper presents a three-neutrino framework calculation of the diffuse supernova neutrino background (DSNB) both with and without non-radiative two-body neutrino decay, and uses it to perform a Bayesian sensitivity projection for SK-Gd, HK, JUNO, and DUNE. The DSNB flux is built from two sets of one-dimensional supernova simulations (Garching and Nakazato), with progenitor-mass dependence, a range of black-hole fractions, MSW flavor conversion, and uncertainties in the local core-collapse supernova rate. Event rates are computed for inverse beta decay, neutrino-proton, neutrino-electron, oxygen, and argon channels. The statistical analysis uses binned Poisson likelihoods with Gaussian nuisance parameters for signal and background, and reports mean logarithmic Bayes factors for pairwise comparisons of no-decay versus decay with tau/m in [1e9, 1e11] s/eV. The central qualitative results are that normal ordering with a strongly hierarchical mass pattern gives essentially no Bayesian discriminating power for this parameter range, while quasi-degenerate normal ordering and inverted ordering yield strong or very strong evidence in several scenarios, especially when experiments are combined.

Significance. If the results are correct, this is the first Bayesian treatment of DSNB constraints on non-radiative neutrino decay and provides useful sensitivity projections for the next generation of detectors. The paper is transparent about many of its modeling choices: it states the use of MSW only, lists the supernova simulation inputs, and checks the no-background, no-uncertainty limit in Figure 18. The kinetic-equation solution and event-rate integrals are standard and clearly presented. The main significance of the work lies in the claimed no-go result for normal ordering with strongly hierarchical masses, which, if robust, would have a direct impact on how DSNB searches are interpreted. The paper also clearly identifies competing degeneracies in the quasi-degenerate and inverted-ordering cases. However, as detailed below, the no-go statement is currently not fully supported because of an unspecified helicity branching ratio in the visible-decay calculation and because of a conflict between the conclusions and the authors' own idealized neutrino-proton analysis.

major comments (4)
  1. [Section 4.2, Eq. (4.9)] The visible-decay analysis for the strongly hierarchical patterns never specifies the relative weights of the helicity-conserving and helicity-flipping daughter spectra, even though Eq. (4.9) shows that the two spectra are very different: h.c. decays give hard daughters while h.f. decays give soft daughters. The invisible-decay discussion in Section 7.1 explicitly assumes democratic branching between helicity-flipping and helicity-conserving decays, but no analogous statement is made for the visible decays that drive the main results. Since the NO SH no-go conclusion in Section 8 depends on the daughter spectra closely resembling the parent flux at the observed energies, the conclusion is underdetermined unless this ratio is specified. Please state the assumed h.c./h.f. branching ratio for the visible SH case and, ideally, show the sensitivity of the NO SH Bayes factors to this ratio (for example pure h.c., pure h.f., and 50/50). If h.f. decays dominate, the high-energy DSNB flux is suppressed and the degeneracy with no-decay may be broken.
  2. [Section 5, Eq. (5.2)] The marginalization in Eq. (5.2) uses a single background nuisance parameter beta for all experiments and channels, but the backgrounds of SK-Gd, HK, JUNO, and DUNE are physically independent and are described separately in Section 6.2.2. A common fractional background scale allows a fluctuation in one experiment to be partially compensated by the others in the joint likelihood, which can inflate the combined Bayes factors. This is a load-bearing issue for the quantitative 'strong' and 'very strong' claims for NO QD and IO in Figures 13, 15, and 17. Please replace the single beta with per-experiment (or per-channel) nuisance parameters beta_j with their own widths; the signal uncertainty alpha can reasonably remain global because the DSNB flux is common across channels. The idealized no-background test in Figure 18 is unaffected by this issue.
  3. [Section 8 vs. Figure 19] The conclusion in Section 8 states that for normal ordering with a strongly hierarchical pattern, a Bayesian analysis has no discriminating power between no-decay and decay in the range tau/m in [1e9, 1e11] s/eV 'even combining all channels in the four experiments.' This is too strong relative to the paper's own Figure 19, which shows that adding neutrino-proton scattering with optimistic DSNB fluxes and ignoring the neutrino-proton background yields almost strong evidence in the NO SH case. The no-go statement should be restricted to the channels with realistic current-level backgrounds, or it should be explicitly qualified by the idealized assumptions used in Figure 19. As written, the conclusions overstate the reach of the analysis and conflict with the earlier discussion in Section 7.2.
  4. [Section 4.2 and Fig. 4 caption] The entire Bayesian projection assumes democratic branching ratios among the allowed daughter states and a single common lifetime-to-mass ratio for all decaying eigenstates. This reduces the decay parameter space to one number, as the authors state. However, the no-go conclusion in Section 8 is phrased as a statement about neutrino non-radiative decay for the NO SH mass pattern, not about this specific parameterization. If the true decay couplings are non-democratic, or if the eigenstates have different lifetimes, the daughter flux composition and hence the Bayes factors can change. Please add an explicit caveat to the conclusions that the no-go result holds under the democratic, equal-tau/m assumption, or test at least one alternative branching pattern to demonstrate robustness.
minor comments (5)
  1. [Section 3.1] The text says 'from Nazakato's groups' but the group name is spelled 'Nakazato' elsewhere; please correct this typo.
  2. [Section 5] The paragraph after Table 1 ends with the stray word 'two-body' that appears to be a leftover fragment; it should be removed.
  3. [Section 7.2, Figure 18] The ideal no-background test in Figure 18 combines only the IBD channels and the argon channel; it does not include neutrino-proton scattering, neutrino-electron scattering, or the oxygen channels. The caption or text should state this explicitly so that the reader does not interpret the figure as a test of 'all channels'.
  4. [Section 6.2.1, Table 5] The energy range for the HK IBD channel is listed as (16.0, 30.0) MeV while SK-Gd and JUNO use (11.5, 29.5) MeV; the reason for this different lower threshold is not stated in the text and should be clarified.
  5. [Section 3.1] The description of the Nakazato scenarios in the text and in Figure 2 would be easier to follow if the choice of metallicities and shock revival times were summarized in a single sentence in the main text, since the current text refers to the figure for the templates.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Bayesian sensitivity study consumes external supernova yields and scans tau/m without fitting, so the no-go result is a conditional consequence rather than an input.

full rationale

The paper's central claims are sensitivity projections, not data-driven inferences. No parameter is fitted to DSNB data: the neutrino yields come from independent external simulations (Garching and Nakazato), the astrophysical inputs (star-formation rate, failed-supernova fraction) are fixed from the literature with quoted uncertainties, and the decay parameter tau/m is scanned over three fixed values. The pseudo-data Bayes-factor setup generates data from the model being tested, which is the standard way to forecast discriminating power, not a circular prediction. The key no-go conclusion for normal ordering with strongly hierarchical masses is a conditional deduction from the computed flux degeneracies shown in Figure 7 and confirmed under an idealized no-background test in Figure 18; it is not imposed by the statistical framework. The self-citations to ref. [28] provide parameter tables and integral expressions, but the flux results are recomputed here ('the same as those in ref. [28] when we use the same DSNB inputs'), and the kinetic equations and decay spectra are borrowed from the independent ref. [23]. No uniqueness theorem is invoked, and no ansatz is smuggled in through citation. The explicit assumptions of democratic branching ratios and equal lifetime-to-mass ratios are stated limitations that bound the conclusions rather than circularly constructing them; potential sensitivity to the helicity-conserving versus helicity-flipping branching is an assumption-dependence concern, not circularity. Flux predictions are also checked against external experimental upper limits from KamLAND and Super-Kamiokande, providing an independent anchor. Overall, the derivation chain is self-contained for the stated scope, with no fitted input relabeled as a prediction and no load-bearing self-citation.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

No new particles or forces are introduced; the scalar boson phi is the standard Majoron from refs. [29,35,36], and the sterile daughter case is an existing possibility, not a new entity. The free parameters listed are hand-set priors over the decay and nuisance parameter space; they do not come from a fit to data, but the reported Bayes factors depend on them.

free parameters (3)
  • Democratic branching ratios = NO SH: 1/4 (nu3, anti-nu3), 1/2 (nu2, anti-nu2); NO QD: 1/2 (nu3, anti-nu3), 1 (nu2, anti-nu2); IO: 1/3 (nu2…
    Chosen by hand in Sec. 4.2 and Fig. 4 to reduce the decay parameter space; the Bayes factor results depend on these values.
  • Common lifetime-to-mass ratio tau/m = 10^9, 10^10, 10^11 s/eV (scanned)
    Assumed equal for all decaying eigenstates (Sec. 4.2) so that only one decay parameter remains; the projected evidence is quoted for these values.
  • Nuisance uncertainty widths sigma_alpha, sigma_beta = Conservative 40%/20%; optimistic 20%/10%
    Chosen in Sec. 5 to define conservative and optimistic scenarios; they directly set the width of the marginalized likelihood and thus the Bayes factors.
assumptions (6)
  • domain assumption LambdaCDM expansion history with H0=70 km/s/Mpc, Omega_Lambda=0.7, Omega_m=0.3 (Eq. 3.2)
    The DSNB redshift integral assumes this cosmological model; H0 variation is checked only for the no-decay flux in Fig. 6.
  • domain assumption Salpeter IMF and broken power-law star formation history (Eqs. 3.3-3.5)
    These astrophysical inputs set the supernova rate R_SN(z,M) and hence the overall DSNB normalization and redshift evolution.
  • domain assumption Only MSW flavor conversions are included; collective oscillations, turbulence, and shock-wave effects are neglected (Sec. 3.1)
    The mass-eigenstate yields at the star surface (Eqs. 3.11-3.12) assume MSW only; additional flavor mechanisms could change the spectral shapes used in the Bayes factors.
  • domain assumption Neutrino decay occurs in vacuum and the decaying eigenstates coincide with the mass eigenstates (Sec. 2)
    The paper explicitly assumes no mismatch between decay and mass eigenstates, citing refs. [30,31] for the expected complications.
  • domain assumption The daughter neutrinos are active and visible for the main results (Sec. 6.1)
    The main event-rate and Bayes-factor results assume visible daughters; invisible decay is treated separately in Sec. 7.1 and Fig. 16.
  • standard math The analytic solution of the kinetic equations, Eq. (4.5), is taken from ref. [23] with explicit integrals in appendix B of ref. [28]
    The paper does not re-derive this solution; correctness rests on the cited derivation.

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Pith. "Pith review of Diffuse Supernova Neutrino Background and Neutrino Non-Radiative Decay: a Bayesian Perspective." pith.science (2026). https://pith.science/paper/X6YSHEUU

@misc{pith2026241214681,
  author       = {Pith},
  title        = {Pith review of: Diffuse Supernova Neutrino Background and Neutrino Non-Radiative Decay: a Bayesian Perspective},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/X6YSHEUU}},
  note         = {Machine review of arXiv:2412.14681}
}
read the original abstract

Neutrinos being massive could undergo non-radiative decay, a property for which the diffuse supernova neutrino background has a unique sensitivity. We extend previous analyses to explore our ability to disentangle predictions for the diffuse supernova neutrino background in presence or absence of neutrino non-radiative two-body decay. In a three-neutrino framework, we give predictions of the corresponding neutrino fluxes and the expected number of events in the Super-Kamiokande+Gadolinium, the Hyper-Kamiokande, the JUNO and the DUNE experiments. In our analysis, we employ supernova simulations from different groups and include current uncertainties from both the evolving core-collapse supernova rate and the fraction of failed supernovae. We perform the first Bayesian analysis to see our ability to disentangle the cases in presence and absence of neutrino decay. To this aim we combine the expected events in inverse beta-decay and the neutrino-argon detection channels. We also discuss neutrino-electron, neutrino-proton and of neutrino-oxygen scattering. Our investigation covers the different possible decay patterns for normal mass ordering, both strongly-hierarchical and quasi-degenerate as well as the inverted neutrino mass ordering.

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