Solving the gallium anomaly: New calculation may explain neutrino shortfall without invoking new particles

October 16, 2026 feature Solving the gallium anomaly: New calculation may explain neutrino shortfall without invoking new particles David Appell Author Sadie Harley Scientific Editor Robert Egan Senior Editor Glimpses of the "gallium anomaly" were first seen in the mid-1990s, but it was first clearly discovered and stated in 2007 by neutrino physicist Carlo Giunti of Italy. The problem is simple to state but potentially very important: about 20% fewer electron neutrinos were seen to be captured by gallium nuclei than expected. But now the anomaly looks to be explained with a new calculation by a collaboration of physicists at Italian universities and research laboratories—and the calculation agrees with the observed number of electron neutrinos captured. Their work is published in the journal Physical Review Letters. When an electron neutrino (one of the three types of neutrinos) collides with a neutron in the nucleus of gallium-71 (⁷¹Ga), an electron is produced and the neutron transforms to a proton as a down quark converts to an up quark. The gallium nucleus then becomes a germanium-71 (⁷¹Ge) nucleus. This is a weak force interaction with a W+ particle exchange, a so-called charged-current weak interaction, and was historically important to the solar neutrino problem recognized in the 1960s. Sterile neutrinos faced conflicting evidence The 20% puzzle persisted for years. One interpretation took it as evidence for oscillations between electron neutrinos and so-called sterile neutrinos; the latter were hypothesized to interact only by their meager gravitational force, not by any of the other three forces in the Standard Model. The gallium anomaly was experimentally reaffirmed as recently as 2022 by the Baksan Experiment on Sterile Transitions with an international group of collaborators. "The gallium anomaly has been something of a personal obsession of mine for a very long time," lead author Matteo Cadeddu of the National Institute for Nuclear Physics in Italy told Phys.org. He worked on it during his master's thesis under the supervision of Giunti. "I was never completely convinced that sterile neutrinos were the only possible explanation." Indeed, the sterile neutrino explanation for the gallium anomaly conflicted with other neutrino results such as reactor antineutrino experiments, a bound found for solar neutrinos, neutrino mass measurements and more. Revisiting the calculation from scratch After leaving the problem for some time, Cadeddu started again about three years ago, "essentially from zero ... reconsidering the problem as broadly as possible: the theoretical prediction, the nuclear and atomic physics entering it, the experimental procedure, and any possible systematic effect that could mimic or contribute to the anomaly." Eventually he involved some master's students—current and former—in the project, many of whom are now Ph.D. students and postdoctoral physicists working with him on the topic. Theoretical physics can be a long and lonely road that one follows only in their mind. "We explored many possibilities that led nowhere," Cadeddu said. "At some point you find yourself questioning things that are so standard that you normally no longer notice that they are assumptions." Rethinking electrons inside the nucleus Although the theoretical calculation of the reaction had been honed and refined over the years, one issue that remained was a simplification that could be improved: the behavior of the gallium nucleus had been separated from that of the neutrino and electron. Incorporating earlier work that served as an intermediate step, Cadeddu and colleagues separated the wave functions of the electron and neutrino from the nuclear part of the calculation's setup. They also incorporated the laws of special relativity, which in practice meant starting with the Dirac equation, which was derived specifically to be in accord with special relativity, instead of the nonrelativistic Schrödinger equation. The Dirac equation is more complex, based on four-dimensional spinors that are consistent with the demands of special relativity. While this allowed more accurate electron wave functions, the gallium anomaly remained. "But that work was not a dead end," Cadeddu said. "It taught us in detail how the electron behaves inside the nucleus, and it was one of the steps that eventually led us to ask a different question: what if the electron and the nuclear transition cannot always be treated as two essentially independent pieces of the calculation?" That change turned out to have deep implications. "Details of the nuclear transformation that were previously hidden become directly relevant," said Cadeddu. "It opened a different way of thinking about this class of weak nuclear processes, because information that is normally compressed into a single nuclear matrix element may actually matter." A numerical fit to the anomaly With this, Cadeddu and his co-authors were able to solve the problem numerically with a software package they developed. More electron neutrinos were expected from the reaction—just enough to fit the gallium anomaly and solve it. Besides his co-authors and colleagues, Cadeddu credits his wife, Francesca Dordei, a physicist and co-author as well. "We spent countless days discussing this problem and trying to attack our own ideas from every possible direction," he said. "We would often take opposite sides just to see whether an argument survived." He added, "There were also a few sleepless nights along the way!" Written for you by our author David Appell, edited by Sadie Harley, and fact-checked and reviewed by Robert Egan—this article is the result of careful human work. We rely on readers like you to keep independent science journalism alive. If this reporting matters to you, please consider a donation (especially monthly). You'll get an ad-free account as a thank-you. Publication details M. Cadeddu et al., Possible Solution to the Gallium Anomaly Moving beyond the Leptonic Wave-Function Factorization, Physical Review Letters (2026). DOI: 10.1103/5pvf-mcr1 Journal information: Physical Review Letters © 2026 Science X Network