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

Abstract

For over thirty years, a $\sim20\%$ deficit, now exceeding $5σ$, 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 $^{71}{\textrm{Ge}}$, we find that the revised cross-section can be significantly reduced, potentially resolving the gallium anomaly without invoking new physics.

Figures (1)

• Figure 1: Transition densities corresponding to the best fit parameters reported in Tab. \ref{['tab:summaryTable']} from the IBD+EC combined fit for the Single Gaussian (SG) parametrization, the Sum of Gaussians (SOG), Double Gaussian (DG) and a variation of it ($\rm DG_2$), as well as the two-parameter Fermi (2pF) one. For graphical reasons, SG and 2pF have been magnified by a factor of 10.