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

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 {${\mathring{g}}_A=-1.2754(13{)}_{\exp }(2{)}_{\mathrm{RC}}$} based on the PDG average $\lambda =-1.2756(13)$

Revised manuscript

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