Radiative corrections to the nucleon isovector $g_V$ and $g_A$

TL;DR

This paper calculates radiative corrections to nucleon coupling constants $g_V$ and $g_A$, updating their relation between lattice QCD and physical values, with implications for future theoretical and experimental studies.

Contribution

It provides a comprehensive update on radiative corrections to nucleon couplings, incorporating large logarithms and pion-mass effects, refining the connection between lattice QCD and physical constants.

Findings

Total radiative correction to $g_A$ is approximately 3.5% to 5.6%.

Updated lattice-QCD estimate of $g_A$ is around 1.24 to 1.27.

Future studies can improve the accuracy of these corrections.

Abstract

Electroweak, QCD, and QED radiative corrections to the nucleon low-energy coupling constants $g_V$ and $g_A$ are enhanced by large perturbative logarithms between the electroweak and hadronic scale, as well as between the hadronic scale and the low-energy MeV scale. Additionally, higher-order pion-mass splitting corrections to the nucleon axial-vector charge might be large. By consistently incorporating these effects, we provide an updated relation between the lattice-QCD and physical $g_A$, finding a total radiative correction of $3.5(2.1)\%$ ($5.6(0.7)\%$). This leads to an expected lattice-QCD result of $g^{\mathrm{QCD}}_A = 1.265(26)$ ($g^{\mathrm{QCD}}_A = 1.240(9)$) when based on a combination of lattice-QCD and data-driven (or only data-driven) inputs, respectively. Future phenomenological, chiral perturbation theory, and lattice-QCD studies can improve both the central value and the uncertainty of this estimate.