The BEST Anomaly: Gallium Doubles Down on a Missing Calibration Signal

The history of neutrino physics has a recurring pattern: a small persistent anomaly sits at the edge of statistical significance for decades, gets dismissed as a calibration or modeling problem, and then either dissolves into the noise or hardens into a discovery. The solar neutrino problem followed that arc from the 1960s through the SNO measurement of 2002. The atmospheric anomaly did the same on the route to Super-Kamiokande in 1998. The current candidates — the gallium anomaly, the reactor antineutrino anomaly, and the MiniBooNE excess — are still on the curve, none yet resolved.

In 2022 the Baksan Experiment on Sterile Transitions (BEST) added the freshest data point to that lineage. Designed as a dedicated calibration measurement, BEST exposed a two-zone gallium target to a chromium-51 neutrino source and counted germanium-71 atoms produced in each zone. The result, after three years of running, was a count rate of about 80 per cent of the theoretical expectation in both zones — a four-sigma shortfall consistent with what the original SAGE and GALLEX calibrations had hinted at three decades earlier. The deficit is one of the cleanest live anomalies in neutrino physics, and the sterile-neutrino interpretation it favours is in increasingly sharp tension with everything else the field has measured.

This post is about how BEST works, what the gallium anomaly actually is, and why the answer matters even though no other experiment quite agrees.

The historical setup

The earliest radiochemical solar-neutrino experiments — Davis’s chlorine detector in the Homestake mine and the two gallium experiments SAGE at Baksan and GALLEX/GNO at Gran Sasso — were calibrated using artificial neutrino sources. SAGE and GALLEX both used chromium-51, a radioactive isotope that decays by electron capture to vanadium-51 and emits monoenergetic electron neutrinos at four discrete energies clustered around 750 keV. The cross-section for ${\nu }_e{+}^{71}\mathrm{Ga}{\to }^{71}\mathrm{Ge}+e^{-}$ at these energies is calculable from nuclear physics, and the source activity is measured calorimetrically before deployment, so the expected count rate is, in principle, a well-defined number.

When SAGE and GALLEX measured their calibration rates in the 1990s, they came in slightly low — at the level of 87 per cent of expectation for SAGE and 93 per cent for GALLEX, each with uncertainties of about 10 per cent. The deficit was small and consistent with the unconfirmed possibilities that the cross-section had been overestimated or the source activity slightly mismeasured. SAGE later repeated the calibration with argon-37, getting a similar low rate. Across the four measurements the combined deficit hovered near 84 per cent of expectation, with a combined significance of about 2 to 3 standard deviations depending on the cross-section adopted.

That sat in the limbo of “interesting but not conclusive” for nearly twenty years. Cleaning up the question motivated BEST, a successor measurement at Baksan that was designed from the ground up to resolve the gallium anomaly with a single, well-controlled exposure.

The BEST geometry

BEST’s central design choice was its two-zone target. The chromium-51 source, a cylindrical chromium pellet activated by neutron irradiation in a fast reactor and with a starting activity of 3.4 megacuries, was placed at the centre of an inner spherical volume of metallic gallium. Surrounding the inner sphere was a concentric outer cylindrical zone of gallium. The two zones together held 47 tons of gallium. Mean distances from the source to gallium atoms differed between the zones — about 50 cm for the inner sphere and about 1 metre for the outer cylinder.

The geometry matters because of the oscillation hypothesis being tested. An eV-scale sterile neutrino with mass-squared difference $\Delta m^2\sim 1\text{–}10$ eV² would have an oscillation length on the order of $L_{\mathrm{osc}}=2.48E/\Delta m^2$ in convenient units of metres, eV²-eV. For 750 keV neutrinos and $\Delta m^2\sim 2$ eV², the oscillation length is about a metre. That means the survival probability $P({\nu }_e\to {\nu }_e)$ varies over the scale of the BEST geometry. The inner zone, with shorter average distance, should show a smaller deficit than the outer zone if oscillations are occurring on that scale, in addition to an overall deficit relative to the standard cross-section.

After each run cycle the germanium atoms produced inside each gallium volume were extracted chemically and counted in low-background proportional counters specifically designed for the few-atom-per-cycle yield. Ten extraction cycles between July 2019 and December 2020 — covering both Cr-51 source-active and source-decayed periods — provided the final dataset.

The result

The measured germanium production rates were, after correcting for chemistry efficiency and background:

• inner zone: $0.79\pm 0.05$ of expectation
• outer zone: $0.77\pm 0.05$ of expectation

Both zones came in low at essentially the same level. Combined with the previous SAGE and GALLEX gallium-source calibrations, the global deficit is approximately $0.80\pm 0.05$ of expectation, a $\sim 4\sigma$ shortfall.

The first observation is that the inner and outer rates are statistically identical. By itself this disfavours the simplest oscillation patterns that would give very different rates in the two zones at the BEST length scale — though it does not rule them out, because the geometric averaging over the extended source and the extended gallium volume washes out fine oscillation features. The two-zone design was not able to definitively resolve an oscillation length, only to test it.

The second observation is that the combined deficit is clean. The chromium-51 source activity is calorimetrically measured with sub-percent precision. The gallium-71 cross-section is calculable; even with the uncertainty from nuclear matrix elements at the few-percent level, the deficit comfortably exceeds it. Pulling the gallium anomaly out of the data with conventional nuclear-physics adjustments now requires a cross-section shift larger than the modern uncertainty estimates allow.

Interpreted as a sterile-neutrino oscillation, the deficit favours a region of parameter space with $\Delta m^2\sim 2\text{–}10$ eV² and a sizable mixing angle ${\sin }^{2}2\theta \sim 0.3\text{–}0.5$. That region is uncomfortably large for any sterile state and squarely in tension with multiple other measurements.

The tension with everything else

BEST does not exist in a vacuum. The same parameter space that explains its deficit makes specific predictions for other experiments, and those predictions are not borne out.

The reactor antineutrino anomaly had once hinted at a sterile oscillation in roughly the same region, but later analyses with new precision reactor measurements (Daya Bay, RENO, STEREO, PROSPECT) found the deficit to be consistent with mis-modelled reactor flux rather than oscillations. PROSPECT and STEREO directly searched for sterile-neutrino oscillations at short baselines from their reactor cores and reported null results that exclude a large portion of the gallium-favoured region.

The MicroBooNE result on the MiniBooNE low-energy excess showed that the excess is dominantly photon-like, not electron-like, ruling out the simplest sterile-neutrino interpretation of MiniBooNE and tightening the available space.

The cosmological constraints on light sterile species from the CMB and large-scale structure require that any sterile state with parameters favoured by BEST be only partially thermalised in the early universe — possible but requiring additional new physics to evade.

Combining BEST with these results in a global fit produces a fundamental tension at the few-sigma level. The gallium-anomaly explanation that BEST favours is incompatible with what reactor short-baseline experiments and accelerator-based searches are seeing. Either BEST is signalling new physics that the others should also see (so something is being missed there), or it is reflecting a systematic that has not been adequately bounded.

Possible resolutions

Three classes of resolution are being pursued.

The first is more precise nuclear cross-sections. The dominant uncertainty in the predicted gallium count rate comes from the matrix elements of two excited-state transitions in ${}^{71}$Ge. Several groups have re-evaluated these in the past two years, and the calculations have tended to lower the predicted rate by a few percent — reducing the deficit but not eliminating it. Further nuclear-structure work, including independent measurements of the relevant matrix elements via ${}^{71}$Ge electron capture, may eventually settle the question.

The second is direct measurement of the relevant cross-section via a new neutrino source. Proposals to use an argon-37 calibration on a tonne-scale gallium target, or to use new tritium sources for ${}^3\mathrm{H}\to {}^3\mathrm{He}$ reverse-checking, are under discussion. None has been funded.

The third is to accept that BEST is showing new physics and look for the corresponding signal elsewhere — in tritium beta-decay spectra near the endpoint (KATRIN, Project 8), in beam-dump heavy-neutral-lepton searches, or in further reactor-baseline searches at the very-short-baseline end. None of these has yet seen anything compatible with the gallium-favoured region.

Why it still matters

The gallium anomaly is now thirty years old and BEST has both clarified and complicated the picture. The clean experimental story — a 4σ deficit in a well-controlled calibration, agreement between SAGE, GALLEX, and BEST, and a tight overall constraint that no longer fits within standard nuclear-physics uncertainties — would, in isolation, be a strong claim for new physics. The complicating story is that the favoured new physics is increasingly squeezed by every other measurement of comparable precision.

This is the kind of situation that historically has gone one of two ways. It either dissolves when one specific cross-section turns out to have been mis-evaluated, in which case the field will look back at BEST as a useful sharpening of the limits on a hypothesis that ultimately fell. Or it eventually breaks open into a genuine discovery, with the surrounding null results turning out to have been less constraining than they appeared. Which way the resolution falls is one of the open questions of contemporary neutrino physics, and BEST has made it impossible to look away.

Summary

BEST’s chromium-51 calibration produced a $\sim 4\sigma$ deficit in the germanium-71 production rate, consistent in both its inner and outer gallium zones and confirming the earlier SAGE and GALLEX gallium-source deficits. The measurement is one of the cleanest persistent anomalies in neutrino physics because the source activity and the relevant cross-section are both calculable. Interpreted as sterile-neutrino oscillation, it favours a region of parameter space now squarely in tension with reactor short-baseline searches, MicroBooNE’s resolution of the MiniBooNE excess, and cosmological constraints on light sterile species. Resolution likely requires either improved nuclear cross-section calculations, a direct independent cross-section measurement, or a confirming signal in another experimental channel. Until then BEST remains the most pointed live hint that the three-neutrino picture may be incomplete.