A possible solution to the gallium anomaly moving beyond the leptonic wave function factorization

Abstract

For over thirty years, a $\sim 20\%$ deficit, now exceeding $5\ddot{I}ƒ$, has persisted between measured and predicted neutrino capture rates on ${}^{71}$Ga, as observed in radioactive source experiments (namely GALLEX, SAGE, and more recently BEST) using ${}^{51}$Cr and ${}^{37}$Ar. This long-standing discrepancy, referred to as the gallium anomaly, has posed a significant challenge to our understanding of both experimental methods and theoretical predictions. In this work, we revisit the theoretical calculation of the neutrino capture cross-section by moving beyond the standard treatment of the leptonic wave functions, revealing limitations in the commonly used factorization approach based on the detailed balance principle. Incorporating phenomenologically constrained Gamow-Teller transition densities, able to correctly reproduce the precisely measured half-life of ${}^{71}\text{Ge}$, we find that the revised cross-section can be significantly reduced, potentially resolving the gallium anomaly without invoking new physics.

7 pages, 1 figure; added compact transition-density solutions and expanded discussion of their nuclear-structure motivation