Sterile Neutrinos and the Gallium Anomaly: What the Evidence Shows

Sterile neutrinos have not been discovered, and the gallium anomaly does not by itself establish that they exist. Gallium source experiments measured fewer neutrino captures than expected. A peer-reviewed September 2026 study offers a possible explanation within known physics by revisiting the predicted capture cross section.

That changes the interpretation, not the recorded counts. Meanwhile, MicroBooNE and KATRIN have placed important limits on simple sterile-neutrino explanations of other anomalies. Their results constrain particular models and parameter regions. They do not exclude every additional neutrino, even at the eV scale.

What is the gallium anomaly?

The gallium anomaly is the difference between measured and predicted production of germanium-71 in detectors exposed to calibrated radioactive neutrino sources. The relevant reaction is

Experiments chemically extract the germanium and count its subsequent decays. GALLEX and SAGE first found deficits in source calibrations. BEST tested the effect using a chromium-51 source surrounded by two liquid-gallium zones.

In BEST’s detailed 2022 analysis, the measured-to-predicted ratios were 0.79 ± 0.05 in the inner zone and 0.77 ± 0.05 in the outer zone, using the paper’s adopted capture cross section. Both were low; the two zones did not show a significant difference from one another. That is evidence for a deficit relative to the prediction, without a resolved oscillation pattern between the zones.

Why does the predicted capture rate matter?

A count prediction combines several ingredients. In schematic form, the expected signal is proportional to the number of target nuclei, the neutrino flux, the capture cross section and the exposure, with geometry, decay and extraction effects handled in the analysis. A calibrated source fixes an important part of that calculation; it does not independently determine the nuclear capture probability.

The often-quoted deficit is a ratio, R = measured/predicted. Changing the denominator changes the anomaly even if the numerator stays fixed. For an arithmetic illustration, 80 observed captures against 100 predicted gives R = 0.80. If a justified calculation instead predicts 80, the same observations give R = 1.

The illustration is deliberately not a fit to BEST. A real revision needs its own uncertainty budget and must be consistent with independent nuclear information. Choosing a lower denominator simply because it removes the deficit would not constitute a prediction.

What the new gallium calculation changes

Cadeddu and colleagues’ paper, published in Physical Review Letters on 24 September 2026, revisits an approximation that factors the lepton wave functions out of the nuclear transition integral. Keeping their spatial dependence changes how the nuclear transition is weighted in neutrino capture and in germanium electron capture.

The authors explore phenomenological Gamow–Teller transition densities that can accommodate the source data while reproducing the measured germanium-71 half-life. Some give substantially lower capture cross sections. The paper does not overturn microscopic reversibility; it questions an approximation used to relate the two processes.

The crucial limit is that this is not an independent, first-principles nuclear prediction. The transition-density parameters are fitted using capture information and the half-life. The authors leave a microscopic nuclear-structure calculation for future work. The result demonstrates a possible conventional explanation, not a settled solution.

An earlier paper from the group, published in February 2026, improved the electron wave functions while retaining a different level of approximation. The September study goes further by examining the factorization itself. These are distinct steps, not new detector measurements.

Does a five-sigma deficit mean a new neutrino?

No. A significance quantifies disagreement with a stated prediction and uncertainty model. It does not identify the cause. If a cross-section model is biased, increasing the exposure can make the discrepancy more statistically striking without revealing a new particle.

For this reason, the questions “is the ratio low?” and “is sterile-neutrino oscillation responsible?” require different tests. A convincing oscillation interpretation should predict how the signal changes with distance and energy, and agree with other channels using the same mixing parameters. Our five-sigma guide explains why a significance is conditional on the hypothesis being tested.

The calculation motivates a concrete next step: obtain nuclear information that constrains the capture probability independently of the deficit being explained. That would help distinguish a corrected prediction from a flexible fit.

What does “sterile neutrino” mean?

A sterile neutrino is a hypothetical neutral fermion without the ordinary Standard Model weak interaction of an active neutrino. Through mixing or other specified interactions, it could still produce detectable effects. “Sterile” describes its interaction properties, not one particular mass.

In a minimal 3+1 oscillation model, three mostly active mass states are supplemented by one additional state. At short baselines, the approximate electron-neutrino survival probability is

Use Δm² in eV², L in metres and E in MeV. The mass-squared splitting sets the oscillation scale; the mixing controls the amplitude. Source size, detector volume and energy distribution average the probability. A deficit alone does not separately determine all these quantities. Dasgupta and Kopp’s review surveys the wider model family.

What did MicroBooNE and KATRIN rule out?

MicroBooNE’s two-beam search, published in Nature in December 2025, used a liquid-argon detector exposed to the Booster and NuMI beams. The combination helps break a degeneracy between electron-neutrino appearance and disappearance. The collaboration excludes the single light sterile-neutrino interpretation of the LSND and MiniBooNE anomalies at 95% confidence and constrains a substantial part of gallium’s preferred parameter space.

That is a statement about the tested explanation. It does not remove the earlier observations from the record or rule out arbitrary extensions with additional particles and interactions.

KATRIN’s 259-day analysis examined 36 million tritium beta-decay electrons for the spectral distortion of an additional mass state. It found no supporting signal. The reported exclusions include the Neutrino-4 best-fit point at 99.99% confidence and a combined gallium best-fit point at 96.56% confidence.

The latter is a specific point from an oscillation interpretation, not a 96.56% probability that the gallium experiment is wrong. Changing the capture calculation changes the gallium-preferred region that should be compared with KATRIN. It does not change KATRIN’s measured spectrum.

Different tests constrain different quantities

On a phone, swipe the table sideways. The first column stays visible.

Why do the other anomalies still matter?

LSND, MiniBooNE, gallium sources and reactors do not measure the same observable. Appearance searches ask whether an unexpected flavour shows up. Disappearance searches ask whether an expected flavour is missing. In a specified mixing model, those channels are connected, which makes their compatibility a meaningful test.

Reactor rate deficits also depend on predicted fluxes. A May 2026 preprint by Giunti, Li and Zhang finds a 2.2σ reactor deficit with a particular summation flux model. In its 3+1 comparison, gallium is in 3.8σ tension with the other included datasets; an illustrative enlargement of gallium uncertainties lowers that tension to 1.3σ.

Those figures answer different statistical questions and should not be ranked on one “discovery significance” bar chart. Nor does increasing an assumed error demonstrate that the larger error is physically correct. The preprint’s sensitivity study is a reminder to examine the uncertainty model.

Do these searches exclude sterile-neutrino dark matter?

No. The eV-scale states invoked for short-baseline oscillations and the keV-scale candidates studied as dark matter occupy different parameter ranges. A null oscillation search cannot be transferred across those ranges without a model.

For a sufficiently long-lived keV sterile neutrino, radiative decay can produce an X-ray photon with energy close to half the particle’s mass. X-ray limits and the small-scale distribution of matter constrain this possibility. The implications depend on the abundance and momentum distribution, which in turn depend on production. Boyarsky and colleagues’ review explains that connection.

One specific check is XRISM’s stacked spectrum of ten galaxy clusters. It found no unidentified line in 3.75 million seconds of observations. For a 7.1 keV decaying dark-matter particle, its quoted 3σ rate limit is about 10⁻²⁷ s⁻¹. In that analysis the limit remains about five times above the rate inferred from the earlier XMM-Newton cluster claim. This dataset therefore does not independently settle that claim.

Heavier singlet neutrinos can also enter mass-generation and leptogenesis models extending the Standard Model. Those motivations do not depend on gallium. Conversely, a successful calculation of neutrino masses is not experimental evidence that the proposed heavy particles exist.

What would resolve the evidence?

There are complementary routes forward: a nuclear calculation with controlled uncertainties, source measurements testing the predicted energy dependence, and oscillation searches resolving distance and energy together. Agreement across these methods would be more informative than another isolated deficit.

Cosmology adds a further consistency test. A fully thermalised extra light species changes the radiation density and, once nonrelativistic, the matter density. Planck’s cosmological analysis strongly constrains the simplest versions of that history. As in other cosmological neutrino bounds, the inference depends on the assumed cosmology and production history; it is not a direct census of every possible sterile state.

The measured gallium rates are established. Their interpretation remains contested: the conventional cross section, its uncertainty and an oscillation explanation must all face independent tests. No sterile neutrino has been established by these results. The September calculation makes a conventional explanation worth testing more closely, while the accelerator and beta-decay searches continue to restrict the particle alternatives.