Axial coupling constant in a magnetic background

TL;DR

This paper investigates how an external magnetic field influences the nucleon axial coupling constant $g_A$ by employing finite energy sum rules to analyze proton, neutron, and axial-vector correlators within QCD and hadronic frameworks.

Contribution

It introduces a method to calculate $g_A$ in a magnetic background using sum rules, highlighting the magnetic field's effect on current-nucleon couplings and thresholds.

Findings

$g_A$ decreases with increasing magnetic field

Magnetic effects mainly through in-medium coupling constants and thresholds

Sum rule approach effectively captures magnetic field influence

Abstract

The nucleon axial coupling constant $g_A$ is calculated in the presence of an external uniform magnetic field using finite energy sum rules. The correlation function of proton, neutron and axial-vector currents is calculated both the hadronic and the QCD sector. Once the axial contribution in the form factor is isolated, a double sum rule is considered, i.e., the usual QCD contour integration for the external moments of both the proton and neutron current. The effects of the external magnetic field come mainly through the in-medium current-nucleon coupling constants $\lambda_N(B)$ and the hadronic thresholds $s_0(B)$ provided by the nucleon-nucleon correlators. As a result, the axial coupling constant decreases in the presence of the magnetic field.