The cosmic neutrino background (CνB), the ~1.95 K relic sea of neutrinos left over from the Big Bang, has never been directly detected. If the heaviest neutrino mass eigenstate ν3\nu_3 undergoes radiative decay (ν3→ν1,2+γ\nu_3\to\nu_{1,2}+\gamma) on timescales of 101210^{12}–101710^{17} yr, as allowed in non-standard models of neutrino electromagnetism, the decay photons from all redshifts would form a faint, redshift-smeared spectral edge in the diffuse far-infrared background on top of the cosmic infrared background (CIB). The only existing limit from this channel is τ(ν3)≳3×1012\tau(\nu_3)\gtrsim 3\times 10^{12} yr at 95% confidence from AKARI/Spitzer CIB spectra (Kim et al. 2012), and the proposed next-generation search (e.g. with NASA's PRIMA far-infrared probe) is unrealized. The open problem is to detect or constrain the radiative decay of relic neutrinos through spectral measurements of the diffuse far-infrared background, improving on the existing ∼3×1012\sim 3\times 10^{12} yr limit, with an aspirational reach toward O(1015)O(10^{15}) yr.

Background

About one second after the Big Bang, neutrinos decoupled from the cosmic plasma and have since filled the universe as the cosmic neutrino background (CνB), a thermal relic with temperature 1.95 K and number density about 110 particles per cm3^3 per flavor generation. Its presence is indirectly confirmed by the CMB (e.g. the phase shift in the acoustic peaks measured by Follin et al. 2015), but no direct detection exists. Neutrino oscillation experiments show that neutrinos have mass and that the three mass eigenstates ν1,ν2,ν3\nu_1,\nu_2,\nu_3 have known mass-squared splittings but an unknown absolute scale; the heaviest state ν3\nu_3 has m3≳0.05m_3\gtrsim 0.05 eV in the normal mass ordering (the arrangement in which ν3\nu_3 is the heaviest state). A heavier neutrino can in principle decay radiatively into a lighter one plus a photon, νi→νj+γ\nu_i\to\nu_j+\gamma. In the two-body rest frame the photon is monoenergetic, with wavelength λ0=hc 2mimi2−mj2\lambda_0=\frac{hc\,2m_i}{m_i^2-m_j^2}; for m3≈50m_3\approx 50 meV this lies near 50 μm50\,\mu\mathrm{m}, in the far-infrared. The Standard Model rate for this loop-suppressed process gives a lifetime of order 104310^{43} yr (Pal and Wolfenstein 1982), far beyond observation, but non-standard physics that enhances the neutrino transition magnetic moment (the dipole coupling that mediates the decay) — for instance supersymmetric extensions containing vectorlike leptons (new heavy lepton-like fermions whose left- and right-handed components transform identically under the Standard Model gauge group) — can shorten the lifetime to 101210^{12}–101710^{17} yr (Aboubrahim et al. 2013), making the decay observable in principle. Because the relic neutrinos are non-relativistic today and decays occurred at all redshifts, the accumulated decay photons form a diffuse background: a spectrum with a sharp short-wavelength edge at λ0\lambda_0 (from nearby, low-redshift decays) and a long tail to longer wavelengths from decays at higher redshift. This signal must be sought inside the cosmic infrared background (CIB), the diffuse far-infrared glow from unresolved dusty galaxies measured by COBE, the AKARI infrared satellite (Matsuura et al. 2011) and Spitzer, which itself sits under the zodiacal emission — thermal radiation from interplanetary dust that dominates all far-infrared diffuse measurements by orders of magnitude. Kim, Takemasa, Takeuchi and Matsuura (2012) fitted the AKARI and Spitzer CIB spectra with a decay template plus continuum using a maximum-likelihood method and obtained the only existing far-infrared-background limit, τ(ν3)≥3.1\tau(\nu_3)\ge 3.1–3.8×10123.8\times 10^{12} yr at 95% confidence for m3=50m_3=50–150150 meV. Complementary bounds come from distortions of the cosmic microwave background (CMB) blackbody spectrum measured by COBE-FIRAS (the Far-Infrared Absolute Spectrophotometer aboard COBE): Mirizzi, Montanino and Serpico (2007) found τ≳\tau\gtrsim a few ×1019\times 10^{19}–5×10205\times 10^{20} s depending on ordering and mass, and Aalberts et al. (2018), using exact decay and inverse-absorption formulae, found τ12≳4×1021\tau_{12}\gtrsim 4\times 10^{21} s for the smallest mass splitting but only τ13,τ23≳1019\tau_{13},\tau_{23}\gtrsim 10^{19} s (≈3×1011\approx 3\times 10^{11} yr) for the splittings involving ν3\nu_3 — so for the heaviest eigenstate the CIB limit is the strongest, and the window 101210^{12}–101710^{17} yr remains observationally open. Takeuchi, Matsuura, Kim and Iida (2025) proposed the definitive search: using the FIRESS spectrometer (resolving power R∼100R\sim 100) on PRIMA, NASA's first Probe-class far-infrared mission (selected July 2024, launch no earlier than about 2031), a roughly 1-square-degree spectroscopic survey over 24–240 μ\mum with removal of known galaxies and joint modeling of the CIB and zodiacal foregrounds could reach lifetimes of order 101510^{15} yr in about 100 hours, since the decay signal at 50 μ50\,\mum for τ∼1015\tau\sim 10^{15} yr is more than an order of magnitude fainter than the CIB and over three orders of magnitude fainter than the zodiacal foreground, distinguishable only by its characteristic spectral edge.

Problem Statement

Determine observationally whether relic cosmic neutrinos undergo radiative decay on timescales of 101210^{12}–101710^{17} yr by searching the diffuse far-infrared background spectrum for the accumulated decay photons of the cosmic neutrino background. Specifically: using absolutely calibrated spectral measurements of the diffuse background in the wavelength range spanning the decay edge (approximately 24–240 μ\mum, set by the rest-frame photon wavelength λ0=hc 2m3m32−m1,22\lambda_0=\frac{hc\,2m_3}{m_3^2-m_{1,2}^2} of ν3→ν1,2+γ\nu_3\to\nu_{1,2}+\gamma for m3≳0.05m_3\gtrsim 0.05 eV), with resolved galaxies removed and the astrophysical cosmic-infrared-background continuum and the zodiacal emission foreground jointly modeled, search for the redshift-smeared spectral edge of the decay signal and either (a) detect it — extracting the ν3\nu_3 radiative lifetime and, from the edge wavelength, the absolute neutrino mass — or (b) place a lower limit on the radiative-decay lifetime τ(ν3)\tau(\nu_3) at a stated confidence level that improves on the existing bound of about 3×10123\times 10^{12} yr (Kim et al. 2012). The O(1015)O(10^{15}) yr sensitivity targeted by next-generation far-infrared spectroscopy (Takeuchi et al. 2025) is an aspirational reach, not a required threshold. These are the detection and constraint outcomes of a single search; the problem is not tied to any particular instrument. The claimed signal or limit must not be attributable to foreground modeling, calibration, or point-source-subtraction systematics.

References

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