Dispersion relation analysis of the radiative corrections to $g_A$ in the neutron $\beta$-decay

TL;DR

This paper performs a comprehensive dispersion relation analysis of radiative corrections to the axial coupling in neutron beta decay, achieving high-precision determination of the $ ext{γ}W$-box contribution and implications for the bare axial coupling constant.

Contribution

It provides the first complete dispersion relation calculation of the inner radiative corrections to $g_A$ in neutron beta decay, with improved precision and insights into the ratio $ ext{g}_A/ ext{g}_V$.

Findings

Inner radiative corrections to $g_A$ and $g_V$ are nearly identical.

The $ ext{γ}W$-box contribution is determined with better than $10^{-4}$ precision.

The bare axial coupling constant is predicted as $ extstyle ext{ extmathring{g}}_A = -1.2754(15)$.

Abstract

We present the first and complete dispersion relation analysis of the inner radiative corrections to the axial coupling constant $g_A$ in the neutron $\beta$-decay. Using experimental inputs from the elastic form factors and the spin-dependent structure function $g_1$, we determine the contribution from the $\gamma W$-box diagram to a precision better than $10^{-4}$. Our calculation indicates that the inner radiative corrections to the Fermi and the Gamow-Teller matrix element in the neutron $\beta$-decay are almost identical, i.e. the ratio $\lambda=g_A/g_V$ is almost unrenormalized. With this result, we predict the bare axial coupling constant to be {$\mathring{g}_A=-1.2754(13)_\mathrm{exp}(2)_\mathrm{RC}$} based on the PDG average $\lambda=-1.2756(13)$