Ft values of the mirror β transitions and the weak-magnetism-induced current in allowed nuclear β decay

Abstract

The precision of correlation measurements in neutron and nuclear $\ensuremath{\beta}$ decay has now reached the level of about 1% and better. At this level of precision, higher-order corrections such as recoil-order corrections induced by the strong interaction and radiative corrections cannot necessarily be neglected anymore. We provide here an update of the $\mathcal{F}t$ values of the isospin $T=1/2$ mirror $\ensuremath{\beta}$ decays including the neutron, of interest to determine the ${V}_{\mathrm{ud}}$ quark-mixing matrix element. We also provide an overview of current experimental and theoretical knowledge of the most important recoil term, weak magnetism, for both these mirror $\ensuremath{\beta}$ decays and a large set of $\ensuremath{\beta}$ decays in higher isospin multiplets. The matrix elements determining weak magnetism were calculated in the nuclear shell model and cross-checked against experimental data, showing overall good agreement. We show that the neutron and the mirror nuclei now effectively contribute to the value of ${V}_{\mathrm{ud}}$, but we also stress the need for further work on the radiative correction ${\mathrm{\ensuremath{\Delta}}}_{R}^{V}$. Our results provide new insight into the size of weak magnetism, extending the available information to nuclei with masses up to $A=$ 75. This provides important guidance for planning and improved sensitivity for interpreting correlation measurements in searches for new physics or to extract ${V}_{\mathrm{ud}}$ in mirror $\ensuremath{\beta}$ decays. It can also be of interest for further theoretical work related to the reactor neutrino problem.