Electroweak nuclear radii constrain the isospin breaking correction to $V_{ud}$

TL;DR

This paper introduces a new formalism linking isospin-symmetry breaking corrections in nuclear beta decay to electroweak nuclear radii, enabling experimental tests to refine theoretical models of these corrections.

Contribution

It presents a novel formalism connecting isospin-breaking corrections to measurable electroweak radii, aiding model discrimination in nuclear beta decay studies.

Findings

Proposes a formalism linking $ ext{delta}_C$ to electroweak radii.

Identifies key transitions where neutron skin measurements can discriminate models.

Connects theoretical corrections with experimental observables.

Abstract

We lay out a novel formalism to connect the isospin-symmetry breaking correction to the rates of superallowed nuclear beta decays, $\delta_\text{C}$, to the isospin-breaking sensitive combinations of electroweak nuclear radii that can be accessed experimentally. We individuate transitions in the superallowed decay chart where a measurement of the neutron skin of a stable daughter even at a moderate precision could already help discriminating between models used to compute $\delta_\text{C}$. We review the existing experimental situation and make connection to the existing and future experimental programs.