Are Neutrinos Stable? Lifetime Bounds From SN1987A to IceCube

In its strictest reading the Standard Model says neutrinos are stable. There is nothing for them to decay into: the lightest fermion in each species column is forbidden from converting to anything by lepton-number conservation, and even if neutrinos have masses the available decay channels are vanishingly weak.

That is a slight overstatement. Once neutrino masses are introduced — which we know must happen, because they oscillate — the heaviest mass eigenstate can in principle decay into a lighter one plus a photon, with a rate predicted at one loop by the Standard Model. The calculation gives a lifetime of roughly $10^{43}$ years for the radiative channel, longer than the age of the universe by some thirty-three orders of magnitude. That is the sense in which Standard-Model neutrinos are essentially eternal: stable for all practical purposes, in defiance of any conceivable experimental probe.

Yet decay rates this small are precisely the regime in which beyond-Standard-Model physics can produce dramatic enhancements. New light scalar particles — generically called Majorons when they arise from spontaneous breaking of lepton number — open up invisible decay channels where a heavier mass eigenstate emits a Majoron and becomes a lighter mass eigenstate, producing no detectable particles in the final state. Even modest couplings give lifetimes much shorter than the Standard-Model expectation, and in the cosmologically relevant regime where γ-factor-boosted lifetimes compete with propagation distances, the effect would be observable.

Constraining how stable neutrinos are is therefore a probe of new light degrees of freedom that no other experimental setup can match. The bounds come from a striking diversity of sources — SN1987A’s twenty detected events, solar-neutrino flavor evolution, atmospheric muon-neutrino disappearance, and IceCube’s TeV-to-PeV astrophysical flux. This post is about how each of those sets a lifetime bound, what kind of decay each is sensitive to, and where the current limits stand.

Visible and invisible decay

Two broad categories of neutrino decay are usually considered.

Radiative decay is a heavier mass eigenstate ${\nu }_i$ converting to a lighter ${\nu }_j$ with the emission of a photon:

${\nu }_i\to {\nu }_j+\gamma$

The Standard Model rate proceeds through a one-loop diagram in which a virtual W and a charged lepton run around the loop. The result, for $m_i\gg m_j$, is

${\Gamma }_{\mathrm{rad}}^{\mathrm{SM}}\approx \frac{9\alpha G_F^2{m}_i^5}{2048{\pi }^4}{\left|{\sum }_l{U}_{li}^{\ast }{U}_{lj}\frac{m_l^2}{m_W^2}\right|}^2\approx 10^{-58}{\mathrm{s}}^{-1}{\left(\frac{m_i}{0.05\mathrm{eV}}\right)}^5$

The branching ratio scales as $m_i^5$, so heavier mass eigenstates decay faster. For the realistic neutrino mass scale around $0.05$ eV the Standard-Model lifetime is about $10^{50}$ seconds. The photon’s energy in the rest frame is $m_i/2$ — sub-eV scale — so a hypothetical Standard-Model radiative decay would produce infrared photons that no observational facility could resolve.

Invisible decay, by contrast, involves a hypothetical new light particle in the final state:

${\nu }_i\to {\nu }_j+J$

where $J$ is a Majoron or similar scalar. The rate depends on the new coupling $g$ and the mass splitting, schematically $\Gamma \sim g^2{m}_i^2/(16\pi m_J^2)$ for various model assumptions. No photons are emitted, no charged particles produced — the only signature is the disappearance of the parent state, replaced by the daughter neutrino with a different energy spectrum. Detecting invisible decay therefore requires looking for a missing-flux signature rather than a positive detection of decay products.

The SN1987A bound

The cleanest and one of the most famous bounds comes from the SN1987A neutrino burst on 23 February 1987. Roughly twenty neutrino events were recorded across Kamiokande, IMB and Baksan within a few seconds of each other and of the optical transient from the Large Magellanic Cloud, 168,000 light-years away. The events were consistent with the predicted spectrum of inverse-beta-decay positrons from the supernova’s neutrinosphere.

If the heavier neutrino mass eigenstates had radiatively decayed during their journey, two effects would have followed. First, some of the expected neutrino flux would have been lost to decays before reaching Earth, reducing the observed event count. Second, the decay photons themselves would have produced a measurable gamma-ray flux from the LMC at the time of the burst. The Solar Maximum Mission, in orbit at the time, set tight limits on any anomalous gamma-ray flux from the Large Magellanic Cloud coincident with the neutrino arrival.

The two constraints together translate into a lower bound on the lifetime over mass:

$\frac{{\tau }_i}{m_i}>10^{5}s/eV$

for the radiative channel. This corresponds to a rest-frame lifetime longer than $10^4$ seconds for a neutrino with mass around $0.1$ eV. Compared to the Standard-Model prediction of $10^{43}$ years, this bound is many orders of magnitude weaker — but it absolutely rules out any beyond-Standard-Model scenario in which the radiative decay is enhanced to a level visible at SN1987A’s distance.

For invisible decay the SN1987A constraint is weaker because the daughter particles do not announce themselves with a photon flux. The bound from missing-flux arguments is still meaningful but is closer to $\tau /m>10^3$ s/eV — restrictive on Majoron-like models but leaving more parameter space open.

Solar neutrinos and the heaviest eigenstates

The Sun emits electron-neutrinos that propagate over 150 million kilometres and arrive at detectors after substantial flavor evolution. The MSW-driven matter effect inside the Sun converts the high-energy ${}^8$B flux into a state dominated by the heavier mass eigenstate ${\nu }_2$ at the surface. Whether this ${\nu }_2$ component arrives intact at Earth depends on whether it has had time to decay.

For solar neutrinos with $E\sim 10$ MeV propagating 1 AU, the lab-frame propagation time is $\sim 500$ seconds. The rest-frame propagation time is shorter by the Lorentz factor $\gamma =E/m\sim 10^8$. So solar neutrinos are sensitive to rest-frame lifetimes around $\sim 5\times 10^{-6}$ seconds per electron-volt of mass. The non-observation of any anomalous distortion of the solar neutrino spectrum, in particular by Borexino, Super-Kamiokande and SNO, sets a bound

$\frac{{\tau }_2}{m_2}>10^{-4}s/eV$

on invisible decay of the ${\nu }_2$ mass eigenstate. This is much weaker than the SN1987A radiative bound but constrains a different decay channel — invisible decay rather than radiative decay — and sets the strongest existing limit on ${\nu }_2$ specifically.

Atmospheric and accelerator-based bounds

Atmospheric muon-neutrinos travel up to the Earth’s diameter at GeV energies. Their oscillation pattern measured by Super-Kamiokande would be modified if any of the mass eigenstates decayed during the journey, producing an additional energy-dependent attenuation on top of the standard oscillation. The analyses constrain the lifetime over mass for ${\nu }_3$ to

$\frac{{\tau }_3}{m_3}>10^{-10}s/eV$

Long-baseline accelerator experiments, with their cleaner beams and better-understood spectra, set similar bounds. None has seen any departure from standard three-flavor oscillation that would point to decay.

IceCube and astrophysical neutrinos

At the highest energies, IceCube’s astrophysical neutrino flux probes lifetimes through both energy spectrum and flavor composition. Astrophysical neutrinos from sources at hundreds of megaparsecs or more travel for hundreds of millions of years. Even with the enormous Lorentz boost from PeV energies, this propagation time is enough to test rest-frame lifetimes that would be inaccessible to any closer probe.

Two effects appear in the data. First, if the heavier mass eigenstates decay before reaching Earth, the arriving flavor composition shifts: the standard 1:1:1 ratio expected from oscillation averaging gets modified, typically depleting ${\nu }_{\tau }$ first because ${\nu }_3$ is most likely the heaviest mass eigenstate. IceCube’s tau-neutrino detection, consistent with the standard ratio, places a bound

$\frac{{\tau }_3}{m_3}>10s/eV$

from the flavor ratio of the astrophysical flux. This is the strongest existing bound on ${\nu }_3$.

Second, decay of the heavier eigenstates would distort the energy spectrum — daughter neutrinos carry only a fraction of the parent energy, producing a softening of the high-energy tail. The observed spectrum is consistent with an unbroken power law, again constraining the parameters of any decay channel that would produce a visible spectral break.

What the limits already tell us

The combination of these bounds has substantially constrained beyond-Standard-Model decay scenarios. The strongest radiative-channel limit, $\tau /m>10^5$ s/eV from SN1987A, rules out any model in which the radiative branching ratio is significantly enhanced over the Standard-Model expectation — many extensions with new charged scalars or vector-like leptons are excluded in their most natural form. The strongest invisible-channel limits, on the heaviest mass eigenstate from IceCube’s flavor composition, rule out Majoron-like couplings stronger than about $g\sim 10^{-7}$ for natural Majoron masses.

Some of the remaining unconstrained parameter space is intriguing. Models in which only the lightest mass eigenstate ${\nu }_1$ is essentially stable while the heavier states decay rapidly on cosmological timescales remain viable. They would predict that the cosmic neutrino background today is composed dominantly of ${\nu }_1$, with consequences for the spectral shape of CMB and large-scale-structure imprints of neutrinos. Distinguishing this scenario from the standard expectation is one of the targets of next-generation cosmology surveys.

Models that allow visible decays to be near current experimental limits could produce signatures in supernova neutrino bursts — a future galactic supernova would, if its neutrinos travelled the few kiloparsecs to Earth slightly faster than expected, hint at decay-induced spectrum modifications. PTOLEMY, the proposed detector targeting the cosmic neutrino background, would be sensitive to whether the relic neutrinos arriving at Earth are dominantly the lightest mass eigenstate or carry the standard mass-eigenstate composition expected from CMB-era physics. Either result would inform the lifetime question.

What might break the picture

The most likely venue for surprise is cosmological. If neutrinos decay on timescales between the CMB epoch and today, the cosmic neutrino background’s contribution to structure growth and to the CMB anisotropies would be modified. CMB-S4 and the Simons Observatory will achieve substantially better sensitivity to such effects than Planck did, and combined with galaxy-clustering measurements from DESI and Euclid, the cosmological constraint on neutrino lifetimes will sharpen by an order of magnitude over the coming decade.

A subtler test concerns the flavor composition of the diffuse supernova neutrino background, currently being probed by SK-Gd. If the heavier mass eigenstates decay invisibly during the gigayear-scale propagation from distant supernovae, the arriving flavor mix at Earth shifts measurably. SK-Gd’s projected sensitivity to the diffuse background opens up this avenue, and a detected DSNB signal with a flavor ratio inconsistent with stable-neutrino expectations would point directly at decay.

Summary

Neutrinos are essentially stable in the Standard Model — radiative lifetimes around $10^{43}$ years, well beyond any conceivable observation. But many extensions of the Standard Model, particularly those with new light scalars such as Majorons, predict observable decay rates. The strongest current lower bounds come from a remarkable diversity of sources: SN1987A’s non-observation of correlated gamma rays gives $\tau /m>10^5$ s/eV for radiative decay; solar neutrinos give ${\tau }_2/m_2>10^{-4}$ s/eV for invisible decay of ${\nu }_2$; atmospheric neutrinos give a bound on ${\nu }_3$ near $10^{-10}$ s/eV; and IceCube’s astrophysical flavor ratio gives ${\tau }_3/m_3>10$ s/eV. The combination already rules out wide regions of beyond-Standard-Model parameter space, and next-generation cosmology surveys plus the diffuse supernova background detection at SK-Gd will push the bounds further. Whether neutrinos turn out to be eternal — or whether decay reveals new light degrees of freedom in the lepton sector — remains one of the open questions of the field.