Testing a low-scale origin of neutrino mass through scalar-mediated neutrino self-interactions in astrophysical neutrino signals

Neutrino oscillations prove that neutrinos have sub-eV masses but not how those masses arise. In the canonical Type-I seesaw, lepton-number violation enters near $10^{14}$ GeV, placing the mass-generation mechanism beyond any direct experimental test. Late-time (low-scale) mass-generation models instead break a lepton-number-like U(1) symmetry at a low scale $f$ through a scalar $\phi$ that couples only to neutrinos, giving $m_\nu = y_\nu f$; the same light scalar — in the Majorana case a majoron-like pseudo-Goldstone boson of the broken lepton number, with a small but non-zero mass $M_\phi$ — unavoidably mediates new neutrino self-interactions (νSI). The parent paper (Baker, Goldberg, Perez, Sarcevic 2007) showed that resonant exchange of this scalar between the diffuse supernova neutrino background (DSNB) and the cosmic neutrino background carves model-specific depletion features into the DSNB spectrum, in principle revealing the Majorana/Dirac nature, the mass hierarchy, and the absolute masses. The problem, at the scope of the parent paper's single-U(1) late-time mass-generation framework, is whether lepton-number violation at an experimentally accessible scale $f$ is realized in Nature, and whether its predicted scalar-mediated νSI can be confirmed or constrained through astrophysical and complementary observations. The 2014–2026 νSI, majoron, and DSNB literature leaves this question open: there is no positive evidence, and existing exclusions cover the target region only under restrictive assumptions — the Planck 2018 CMB analysis of Escudero and Witte (2020) excludes post-BBN-thermalized majorons with flavor-universal couplings down into the sub-keV range, but leaves the flavor-specific and non-thermal motivated parameter space unconstrained (notably mediator masses of order 100–300 eV and below, where DSNB searches at Hyper-K-Gd, JUNO, and DUNE reach projected sensitivities down to $g \sim 10^{-8}$, surpassing all current flavor-blind bounds below about 100 eV), while the DSNB itself has only now reached the threshold of detectability (Super-K-Gd flux limits and a reported 2.6σ indication).

Background

Neutrino oscillation experiments have established that neutrinos have small, non-zero masses, but the mechanism that generates them is unknown. In the minimal Standard Model neutrinos are exactly massless, so masses are evidence of physics beyond the Standard Model. The textbook explanation is the Type-I seesaw: Standard-Model-singlet right-handed neutrinos are given gauge-singlet Majorana masses $M$ — mass terms coupling a neutrino to its own charge conjugate, possible only because neutrinos are electrically neutral — which violate total lepton number $L$ (the charge, +1 per lepton, conserved in the Standard Model) by two units; at lower energies this induces the dimension-five operator $(LH)^2/\Lambda_L$ (with $L$ the lepton doublet and $H$ the Higgs field), so that $m_\nu \sim v^2/\Lambda_L$ where $v \simeq 246$ GeV is the Higgs vacuum expectation value. The observed scale $m_\nu \sim 0.05$ eV then forces $\Lambda_L$ of order $10^{14}$–$10^{15}$ GeV: the lepton-number-violating (LNV) physics behind neutrino mass would sit far beyond any conceivable experiment, so the mechanism's naturalness is bought at the price of untestability.

A complementary class of models generates neutrino masses at low scales by late-time symmetry breaking (often called late-time or low-scale neutrino mass generation). A global U(1) symmetry, acting differently on neutrinos than on charged fermions, is spontaneously broken at a low scale $f$ by the vacuum expectation value of a new light scalar $\phi$. The renormalizable interactions are $y_\nu\,\phi\,\bar\nu N$ (if neutrinos are Dirac particles, with $N$ a new singlet) or $y_\nu\,\phi\,\nu\nu$ (if they are Majorana particles, i.e., their own antiparticles), so that after symmetry breaking $m_\nu = y_\nu f$ with the smallness of $m_\nu$ carried by the small scale $f$ rather than by tiny couplings. Because $\phi$ couples only to neutrinos, laboratory and cosmological constraints on $f$ are weak. Crucially, the same interaction that generates the mass also creates a new neutrino–neutrino force: neutrino self-interactions (νSI) mediated by the light scalar — in the Majorana case a majoron-like pseudo-Goldstone boson: spontaneous breaking of the continuous lepton-number symmetry yields a Goldstone mode which, in the presence of small explicit breaking, acquires a small but non-zero mass $M_\phi$, treated in this problem as a free parameter in the eV–keV range.

The parent paper of this candidate (Baker, Goldberg, Perez, and Sarcevic, Phys. Rev. D 76, 063004 (2007)) identified the sharpest low-energy consequence of this setup. Supernova relic neutrinos — the diffuse supernova neutrino background (DSNB), the integrated neutrino emission of all core-collapse supernovae in cosmic history, observable as an $\mathcal{O}(10)$ MeV $\bar\nu_e$ flux via inverse beta decay ($\bar\nu_e + p \to e^+ + n$) in gadolinium-loaded water Cerenkov detectors — scatter resonantly off the cosmic neutrino background (CνB, the Big-Bang relic neutrinos, about 112 per cm$^3$ per flavor including antineutrinos) through on-shell scalar exchange. The resonance occurs at $E_{\rm res} = M_\phi^2/(2 m_i)$ for scalar mass $M_\phi$ and neutrino mass $m_i$; for sub-eV neutrino masses and eV-to-keV scalar masses this lands exactly in the 10–30 MeV DSNB window. Neutrinos crossing resonance are absorbed and redistributed to lower energies, producing broad depletion (and, for some hierarchies, low-energy enhancement) features whose positions depend only on $M_\phi$ and the neutrino masses — not on the astrophysical emission model — and whose depth is set by the coupling (observable absorption requires roughly $y \gtrsim 4.6\times10^{-8}\,(M_\phi/\mathrm{keV})$). A measured DSNB spectrum would therefore probe the mass-generation sector itself: the Majorana-versus-Dirac nature, the mass hierarchy, and potentially the absolute masses. Complementary constraints on the same coupling exist from cosmology (the effective relativistic species count $N_{\rm eff}$ constrains majoron–neutrino thermalization and decay), from supernova cooling (the neutrino burst observed from supernova SN1987A), and from neutrinoless double beta decay with scalar emission (0νββφ) — the hypothetical nuclear transition converting two neutrons into two protons with emission of the scalar $\phi$ instead of neutrinos, possible only if neutrinos are Majorana particles. Because the scalar–neutrino coupling scales as $g \sim m_\nu/f$, any νSI measurement directly bounds the symmetry-breaking scale $f$, i.e., the scale of lepton-number breaking — which is what gives the astrophysical search a direct bearing on the origin question.

Problem Statement

Determine whether neutrino masses originate from lepton-number violation at an experimentally accessible scale — in particular whether the low-scale symmetry-breaking origin considered by the parent paper, in which a single Abelian U(1) symmetry is broken at a scale $f$ so that $m_\nu = y_\nu f$ arises from neutrino couplings to a light scalar $\phi$ whose vacuum expectation value $f$ is the symmetry-breaking scale, is realized in Nature — and establish whether the scalar-mediated neutrino self-interactions that such an origin unavoidably predicts can be confirmed or constrained through their imprint on astrophysical neutrino signals, principally the resonant exchange between the diffuse supernova neutrino background (DSNB) and the cosmic neutrino background.

The following linked elements serve the single objective of establishing the scale and mechanism of neutrino-mass generation:

1. Theoretical specification: a viable low-scale mass-generation model (or class), its symmetry-breaking pattern, and its predicted νSI signal — the coupling and flavor structure across the three neutrino mass eigenstates (the weak-interaction flavor states being related to the mass eigenstates through the three-flavor Pontecorvo–Maki–Nakagawa–Sakata (PMNS) mixing matrix), the Majorana or Dirac character, the scalar mass $M_\phi$, and the induced DSNB spectral distortions (resonance energies $E_{\rm res} = M_\phi^2/(2 m_i)$ and depletion/enhancement patterns), together with the coupling–mass relation $g \sim m_\nu/f$ that ties any measured coupling to the lepton-number-breaking scale $f$.

2. Observational confrontation: a quantitative comparison with observation — against all currently available data (DSNB spectral measurements, e.g., the gadolinium-loaded Super-Kamiokande (Super-K-Gd) flux limits and spectral fits, and complementary constraints: cosmic microwave background (CMB) limits on the effective relativistic species count $N_{\rm eff}$ and on majoron decay, the SN1987A supernova neutrino burst, neutrinoless double beta decay with scalar emission (0νββφ), and laboratory searches) and, for the sub-keV target region that current data do not yet cover, through rigorous sensitivity forecasts for next-generation channels such as Hyper-Kamiokande-Gd, the Jiangmen Underground Neutrino Observatory (JUNO), and the Deep Underground Neutrino Experiment (DUNE). In that region the comparison is made through a projected discovery/exclusion reach rather than a present-data verdict, while a present-data discovery or exclusion applies wherever the data support it. The astrophysical uncertainties of the DSNB (core-collapse rate, emission spectra, flavor conversion, detector response) must be treated so that new-physics distortions are not confused with, or hidden by, astrophysical variation.

3. Interpretation: if a νSI signal tied to neutrino mass is found, extraction of the scale and flavor pattern of lepton-number breaking (and its implications for the Majorana/Dirac question and the mass hierarchy); if not, a quantitative statement of which low-scale-origin model classes and parameter regions are excluded.

The problem is posed at the scope of the parent paper: the low-scale mass-generation class with a single Abelian U(1) symmetry broken at scale $f$, a light scalar $\phi$ (majoron-like in the Majorana case) of mass $M_\phi$ in the eV–keV range, and neutrino couplings diagonal in the mass basis. The scientific target of the problem is to establish either the resonant DSNB spectral-distortion signature (with extraction of the lepton-number-breaking scale $f$ and the flavor/coupling pattern through $g \sim m_\nu/f$), or a quantitative exclusion of this stated model class over the DSNB-relevant parameter region — sub-keV $M_\phi$ with the resonance $E_{\rm res} = M_\phi^2/(2 m_i)$ inside the 10–30 MeV DSNB window and couplings at or above the absorption threshold $y \gtrsim 4.6\times10^{-8}\,(M_\phi/\mathrm{keV})$ — based on existing data where they apply and on rigorous sensitivity forecasts for next-generation channels. Parameter regions already excluded by other probes — for example 10 MeV–1 GeV mediators from SN1987A and core-collapse physics — lie outside the DSNB-relevant region of interest.

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