Data-driven reevaluation of $ft$-values in superallowed $\beta$ decays

Abstract

We present a comprehensive re-evaluation of the $ft$ values in superallowed nuclear $\beta$ decays crucial for the precise determination of $V_{ud}$ and low-energy tests of the electroweak Standard Model. It consists of the first, fully data-driven analysis of the nuclear $\beta$ decay form factor, that utilizes isospin relations to connect the nuclear charged weak distribution to the measurable charge distributions. This prescription supersedes previous shell-model estimations, and allows for a rigorous quantification of theory uncertainties in $f$ which is absent in the existing literature. Our new evaluation shows an overall downward shift of the central values of $f$ at the level of 0.01\%.