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

Oleksandr Tomalak, Yi-Bo Yang

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 $3.5(2.1)\%$ ($5.6(7)\%$). 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.

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 and 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 , finding a total radiative correction of (). This leads to an expected lattice-QCD result of () 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.
Paper Structure (2 sections, 6 equations, 1 figure)

This paper contains 2 sections, 6 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Materials and Methods

Figures (1)

  • Figure S1: Perturbatively improved relative radiative correction to the nucleon low-energy coupling constants $\delta g^{\rm LL}_V \mathopen{}\mathclose{\left( \mu_\chi = m_e \right)$ and $\frac{\delta g^{\rm LL}}_A \mathopen{}\mathclose{\left( \mu_\chi = m_e \right)}{g_A^{\mathopen{}\mathclose{\left( 0 \right)}}}}$ is shown as a function of the hadronic scale $\mu_0$.