<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="script">F</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:math> values of the mirror <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math> transitions and the weak-magnetism-induced current in allowed nuclear <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math> decay
N. Severijns, L. Hayen, V. De Leebeeck, S. Vanlangendonck, K. Bodek, D. Rozpędzik, I. S. Towner
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.