Electroweak axial structure functions and improved extraction of the $V_{ud}$ CKM matrix element

TL;DR

This paper refines the calculation of radiative corrections to neutron beta decay using dispersion relations, leading to a more precise estimate of the CKM matrix element $V_{ud}$ and highlighting a potential unitarity violation.

Contribution

It provides an improved, data-driven calculation of the $ox^{ ext{ extgamma W}}_A$ correction to neutron beta decay, impacting the determination of $V_{ud}$.

Findings

Calculated $ox^{ ext{ extgamma W}}_A$ as 3.90(9) x 10^{-3}

Updated $|V_{ud}|^2$ to 0.94805(26)

Indicates a 4$\sigma$ unitarity violation in CKM matrix

Abstract

We present a comprehensive analysis of the $\gamma W$ interference radiative correction to the neutron $\beta$-decay matrix element. Within a dispersion relations approach, we compute the axial-vector part of the $\gamma W$ box amplitude $\Box^{\gamma W}_{A}$ in terms of the isoscalar part of the $F_3^{\gamma W}$ interference structure function. Using the latest available phenomenology for $F_3^{\gamma W}$ from the nucleon elastic, resonance, deep-inelastic, and Regge regions, we find the real part of the box correction to be $\Box^{\gamma W}_A = 3.90(9) \times 10^{-3}$. This improved correction gives a theoretical estimate of the CKM matrix element $|V_{ud}|^2=0.94805(26)$, which represents a 4$\sigma$ violation of unitarity.