Robust treatment of finite nuclear size reduces CKM unitarity deficit

Mikhail Gorchtein, Vaibhav Katyal, B. Ohayon, B. K. Sahoo, Chien-Yeah Seng


[arXiv:2502.17070]

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 \(|V{us}|\).

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