An $\text{ab initio}$ strategy for taming nuclear-structure dependence of $V_{ud}$ extractions: the ${}^{10}\mathrm{C}\to {}^{10}\mathrm{B}$ superallowed transition

Abstract

We report the first \textit{ab initio} calculation of the nuclear-structure-dependent radiative correction ${\delta }_{\mathrm{NS}}$ to the ${}^{10}\mathrm{C}\to {}^{10}\mathrm{B}$ superallowed transition, computed with the no-core shell model and chiral effective field theory. We obtain ${\delta }_{\mathrm{NS}}=-0.422(29{)}_{\mathrm{nuc}}(12{)}_{n,\mathrm{el}}$ with a $1.6$-times reduction in the total uncertainty when compared to the current literature estimate based on the shell model and Fermi gas picture. This work paves the way for a precise determination of $V_{ud}$ from superallowed beta decays within a systematically improvable framework.

Comments: 10 pages, 6 figures