Fermi matrix element with isospin breaking

TL;DR

This paper examines how isospin breaking and in-medium effects influence the Fermi matrix element in neutron beta decay, which is crucial for precise tests of CKM unitarity, revealing potential corrections at the level of 10^-4.

Contribution

It introduces a detailed analysis of isospin violating corrections to the Fermi matrix element, highlighting their significance for CKM matrix unitarity tests.

Findings

Nuclear modifications are very small when respecting the Behrends-Sirlin-Ademollo-Gatto theorem.

The u-d mass difference significantly affects the value of V_ud.

Corrections to the unitarity sum are at the level of 10^-4.

Abstract

Prompted by the level of accuracy now being achieved in tests of the unitarity of the CKM matrix, we consider the possible modification of the Fermi matrix element for the $\beta$-decay of a neutron, including possible in-medium and isospin violating corrections. While the nuclear modifications lead to very small corrections once the Behrends-Sirlin-Ademollo-Gatto theorem is respected, the effect of the $u-d$ mass difference on the conclusion concerning $V_{ud}$ is no longer insignificant. Indeed, we suggest that the correction to the value of $|V_{ud}|^2 \, + \, |V_{us}|^2 \, + \, |V_{ub}|^2$ is at the level of $10^{-4}$.