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

We present a comprehensive reevaluation 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%.

Figure 1

A plot of the Fermi function $F\left(E\right)$ with respect to the magnitude of the positron momentum $\mathbf{p}$ (in units of $m_e$) for ${}^{22}\mathrm{Mg}$. The error band due to uncertainties from the nuclear charged distribution parameters is too small to be visible.

Figure 2

Plot of the nuclear charge distribution ${\rho }_{\text{ch}}\left(r\right)$ in atomic units ($\hslash =c=m_e=1$) for ${}^{22}\mathrm{Mg}$ (blue) and ${}^{22}\mathrm{Ne}$ (red), and the corresponding charged weak distribution ${\rho }_{\text{cw}}\left(r\right)$ (green). The selection of nuclear charge distribution data is explained in Sec. 4.