New Calculation Closes the 20% Gallium Neutrino Gap Without Inventing a New Particle

For about three decades, an experiment with a metal that melts in your hand has bothered neutrino physicists. A new calculation says the puzzle may not need new physics at all.

The "gallium anomaly" is simple to state. In experiments using gallium, about 20% fewer electron neutrinos were captured by gallium nuclei than theory predicted. Hints of the shortfall first appeared in the mid-1990s, and it was clearly laid out in 2007 by Italian neutrino physicist Carlo Giunti. The Baksan Experiment on Sterile Transitions reaffirmed it as recently as 2022.

Here is the reaction involved. An electron neutrino strikes a neutron in a gallium-71 nucleus. A down quark inside the neutron converts to an up quark through the exchange of a W+ particle, the neutron becomes a proton, and an electron flies out. The nucleus turns into germanium-71. It is the same kind of charged-current weak interaction that was central to the solar neutrino problem recognized in the 1960s.

The favorite explanation for the missing 20% was a sterile neutrino, a hypothesized particle that would interact only through its feeble gravity and none of the Standard Model's other three forces. Electron neutrinos would oscillate into it and vanish from the count. But that idea clashed with other results, including reactor antineutrino experiments, a bound from solar neutrinos and neutrino mass measurements.

Now a collaboration of physicists at Italian universities and research laboratories reports in Physical Review Letters that a new calculation matches the observed capture rate. Lead author Matteo Cadeddu of Italy's National Institute for Nuclear Physics said he had long doubted the sterile-neutrino story. "The gallium anomaly has been something of a personal obsession of mine for a very long time," he told Phys.org. "I was never completely convinced that sterile neutrinos were the only possible explanation."

About three years ago, Cadeddu restarted the problem "essentially from zero," rechecking the theory, the nuclear and atomic physics, and the experimental procedure. The sticking point was a simplification baked into earlier calculations: the behavior of the gallium nucleus was treated separately from that of the neutrino and the electron. His team first moved to the relativistic Dirac equation to model the electron more accurately, which improved the picture but left the anomaly in place.

That work taught them how the electron behaves inside the nucleus, and it led to a different question. "What if the electron and the nuclear transition cannot always be treated as two essentially independent pieces of the calculation?" Cadeddu said. When they stopped factorizing the electron's wave function from the nuclear part, details of the nuclear transformation that were previously hidden became relevant. Using a software package they developed, the team solved the problem numerically. The result predicts more electron-neutrino captures than older calculations, just enough to fit the data.

The paper, titled "Possible Solution to the Gallium Anomaly Moving beyond the Leptonic Wave-Function Factorization," has Cadeddu's wife, physicist Francesca Dordei, among its co-authors. The word "possible" is deliberate. Other groups will need to check the method, and experiments will keep testing whether sterile neutrinos exist. But if the calculation holds, one of the longest-running hints of new particles in neutrino physics goes away.