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 $2.2\,σ$ than the corresponding value in the previous critical survey, resulting in an increase in $|V_{ud}|^2$ by $0.9\,σ$. Adopting $|V_{ud}|$ from this decay alone reduces the CKM unitarity deficit by one standard deviation, irrespective of the choice of $|V_{us}|$.

Figures (2)

• Figure 1: Schematic representation of the approach taken in this work to connect the measurements of the nuclear $^{26m}$Al$\,\rightarrow^{26}$Mg beta-transition to the atomic transitions used to determine the nuclear charge radii and to $V_{ud}$. A detailed explanation of all ingredients is given in the main text.
• Figure 2: Effect of the updated value of $|V_{ud}|$ form this work on the CKM unitarity test. The bands span the 67% confidence interval.