Speaker
Description
The most precise determination of the top-left corner element of the CKM quark mixing matrix $V_{ud}$ is obtained from accurate measurements of superallowed nuclear $\beta$ decays. Among the theoretical ingredients in this determination, the isospin symmetry-breaking (ISB) correction $\delta_\mathrm{C}$ plays a crucial role in aligning the $Ft$-values across all superallowed transitions. This alignment allows for a joint analysis of many transitions in terms of $V_{ud}$, while remaining misalignments are used to set stringent limits on BSM scalar currents. Until recently, $\delta_\mathrm{C}$ could not be directly constrained by observables remaining a purely theoretical input, and the respective uncertainty was hard to estimate reliably. In a series of recent works, we construct combinations of the nuclear charge and weak radii which are connected to $\delta_\mathrm{C}$. These nuclear radii can be obtained experimentally from a combination of muonic atom spectroscopy, isotope shift measurements, and parity violation in electron scattering, and the corresponding experimental uncertainties can be used for a robust, data-driven and model-independent uncertainty on $\delta_\mathrm{C}$, empowering tests of CKM unitarity and constraints on BSM with nuclear $\beta$ decays.
