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

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 $g_A^{\mathrm{QCD}}=1.265(26)$ ($g_A^{\mathrm{QCD}}=1.240(9)$) 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.

Comments: 11 pages, 2 figures, version published in Universe, footnote 1 added, new sentence in footnote 3, corrected last equation in footnote 5, minor text changes