The diffuse supernova neutrino background (DSNB) — the cumulative neutrino glow of all past core collapses — has a unique sensitivity to nonradiative (invisible) two-body neutrino decay for lifetime-to-mass ratios τ/m\tau/m between 10910^9 and 101110^{11} s/eV, because DSNB neutrinos travel cosmological distances at MeV energies. The first three-neutrino analysis of decay in DSNB predictions (Iváñez-Ballesteros and Volpe, 2023) showed that decay signatures are largely degenerate with astrophysical uncertainties (the redshift-evolving core-collapse rate and the black-hole-forming collapse fraction), that several decay scenarios are nearly indistinguishable from the no-decay case within current detector thresholds, and that the unknown neutrino mass ordering is the principal degeneracy. That analysis, however, included only the MSW flavor-conversion effect and assumed democratic decay branching ratios with equal τ/m\tau/m for all mass eigenstates. The open problem is to determine, with realistic flavor conversion beyond MSW, generalized decay hypotheses, quantified astrophysical systematics, and realistic detector response, under what conditions DSNB observations at SK-Gd, Hyper-Kamiokande, JUNO, and DUNE can distinguish neutrino decay from standard physics or set robust lifetime bounds, and what external information would be needed to break the remaining degeneracies. Follow-up work through 2026 (Bayesian multi-channel analyses, improved astrophysical modeling, first SK-Gd and KamLAND search results) has sharpened but not removed these degeneracies, so the problem remains open.

Background

The diffuse supernova neutrino background (DSNB) is the faint, nearly isotropic flux of neutrinos and antineutrinos accumulated from all core-collapse supernovae in the observable Universe. It has not yet been discovered: dedicated searches in Super-Kamiokande (including its gadolinium-loaded phase, SK-Gd, which tags neutrons from inverse beta decay, νˉe+p→e++n\bar{\nu}_e + p \rightarrow e^+ + n, to reject backgrounds) and in KamLAND have set upper limits within a factor of a few of theoretical predictions, and detection is expected at SK-Gd, Hyper-Kamiokande (HK, a next-generation water-Cherenkov detector), JUNO (Jiangmen Underground Neutrino Observatory, a large liquid-scintillator detector), and DUNE (Deep Underground Neutrino Experiment, a liquid-argon detector) in the coming decade.

Neutrinos are massive and may undergo nonradiative (invisible) two-body decay, νi→νj+ϕ\nu_i \rightarrow \nu_j + \phi, in which a heavier mass eigenstate νi\nu_i decays into a lighter one and a light or massless scalar (for example a Majoron, the Goldstone boson of lepton-number symmetry breaking); only the lifetime-to-mass ratio τ/m\tau/m is observable. Existing bounds come from solar, atmospheric, SN1987A, and cosmological data; for instance, a likelihood analysis of the 24 SN1987A events gives τ/m≥1.2×105\tau/m \geq 1.2 \times 10^5 s/eV (for the inverted ordering). Because DSNB neutrinos travel gigaparsec distances, the DSNB probes a unique window, τ/m∈[109,1011]\tau/m \in [10^9, 10^{11}] s/eV, unreachable by other sources.

Inside a supernova, neutrinos are produced as flavor eigenstates and propagate as mass eigenstates. The Mikheev–Smirnov–Wolfenstein (MSW) effect — resonant flavor conversion induced by the matter potential of the stellar envelope — is routinely included in DSNB predictions. Additional established mechanisms — collective flavor conversion driven by neutrino–neutrino forward scattering, shock-wave propagation through the MSW resonances, and turbulence — were deliberately omitted in the decay-DSNB analyses; earlier studies in the "bulb" model - a simplified spherical treatment of neutrino emission from the proto-neutron-star surface - found they can modify DSNB rates by 10–20%.

The parent analysis (Iváñez-Ballesteros and Volpe, Phys. Rev. D 107, 023017 (2023); summarized in their TAUP2023 proceedings) was the first to combine a three-neutrino decay treatment with the main astrophysical uncertainties: the redshift-evolving core-collapse rate and the fraction fBHf_{\rm BH} of failed, black-hole-forming ("dark") collapses, explored in three scenarios (fBH=0.09,0.21,0.41f_{\rm BH} = 0.09, 0.21, 0.41). It assumed democratic branching ratios (each heavier eigenstate decays into each lighter one with equal weight) and equal τ/m\tau/m for all decaying eigenstates, and considered the quasi-degenerate (QD) and strongly hierarchical (SH) mass patterns in the normal ordering (NO), plus the inverted ordering (IO). Its central findings define the problem: for NO and SH masses with τ/m=109\tau/m = 10^9 s/eV the predicted event rates are essentially degenerate with the no-decay case; for NO and QD masses the flux is enhanced (assuming stable neutrinos underestimates events by up to a factor of about 2); for IO the flux is suppressed and clearly distinguishable at short τ/m\tau/m; astrophysical uncertainty bands overlap decay signatures in several scenarios; and the unknown mass ordering is the principal degeneracy — if the ordering is inverted, a non-observation of the DSNB could be attributed to decay rather than to conservative standard inputs, while if it is normal, decay and no-decay predictions largely overlap. In the SH+NO case the decay-induced spectral distortions appear only at low energies, below current detector thresholds.

Problem Statement

Determine, in a three-neutrino framework, whether observations of the diffuse supernova neutrino background at SK-Gd, Hyper-Kamiokande, JUNO, and DUNE can distinguish the presence of neutrino nonradiative two-body decay from its absence — or set robust bounds on the lifetime-to-mass ratio τ/m\tau/m in the window 10910^9–101110^{11} s/eV — when the prediction and inference incorporate: (i) supernova flavor conversion beyond the MSW effect, including collective neutrino–neutrino interactions, shock-wave propagation, and turbulence, which modify the flavor content before decay; (ii) generalized decay hypotheses, i.e. non-democratic branching ratios and unequal τ/m\tau/m among the mass eigenstates; (iii) quantified astrophysical uncertainties, namely the redshift-evolving core-collapse rate and the fraction fBHf_{\rm BH} of black-hole-forming collapses; and (iv) realistic detector thresholds and backgrounds. For each mass ordering (normal and inverted) and decay pattern (strongly hierarchical and quasi-degenerate in the normal ordering; the inverted-ordering case), the determination is of which lifetime ranges remain degenerate with standard-physics variance after marginalizing the stated systematics, which ranges are testable at which exposures and channel combinations, what threshold and background performance is required to access the low-energy decay-induced spectral features (decisive in the strongly hierarchical, normal-ordering case), and what external information — an independent mass-ordering determination, improved core-collapse-rate and failed-supernova measurements, or multi-messenger constraints on fBHf_{\rm BH} — would break the remaining degeneracies. A lifetime range counts as testable, and the decay hypothesis as distinguishable from no-decay, when the decay hypothesis is preferred over the no-decay hypothesis at 3σ3\sigma (equivalently Δχ2≥9\Delta\chi^2 \ge 9 for nested fits); lifetime bounds are quoted at a stated confidence level, and the quantitative results are given at a common reference exposure and channel combination together with how they scale with exposure; the residual uncertainty of the beyond-MSW flavor-conversion effects of (i) is propagated into the prediction.

References

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