Cabibbo-Kobayashi-Maskawa unitarity deficit reduction via finite nuclear size

Abstract

We revisit the extraction of the $|V_{ud}|$ CKM matrix element from the superallowed transition decay rate of $^{26m}$Al$\rightarrow$$^{26}$Mg, focusing on finite nuclear size effects. The decay rate dependence on the $^{26m}$Al charge radius is found to be four times higher than previously believed, necessitating precise determination. However, for a short-lived isotope of an odd $Z$ element such as $^{26m}$Al, radius extraction relies on challenging many-body atomic calculations. We performed the needed calculations, finding an excellent agreement with previous ones, which used a different methodology. This sets a new standard for the reliability of isotope shift factor calculations in many-electron systems. The $\mathcal{F}t$ value obtained from our analysis is lower by $2.2\,\sigma$ than the corresponding value in the previous critical survey, resulting in an increase in $|V_{ud}|^2$ by $0.9\,\sigma$. Adopting $|V_{ud}|$ from this decay alone reduces the CKM unitarity deficit by one standard deviation, irrespective of the choice of $|V_{us}|$.