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

TL;DR

This paper presents the first extit{ab initio} calculation of the nuclear-structure-dependent radiative correction for the $^{10}$C to $^{10}$B superallowed transition, reducing uncertainty and enabling more precise $V_{ud}$ extraction.

Contribution

It introduces a systematic extit{ab initio} approach using the no-core shell model and chiral EFT to compute nuclear corrections for superallowed beta decays.

Findings

Calculated $ ext{delta}_{ ext{NS}}$ with reduced uncertainty

Achieved 1.6 times lower total uncertainty than previous models

Supports more precise determination of $V_{ud}$

Abstract

We report the first \textit{ab initio} calculation of the nuclear-structure-dependent radiative correction $ \delta_{ \mathrm{NS} } $ to the $ {}^{10}\mathrm{C} \rightarrow {}^{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.