Finite temperature quark-gluon vertex with a magnetic field in the Hard Thermal Loop approximation

TL;DR

This paper calculates the thermo-magnetic correction to the quark-gluon vertex at high temperature with a weak magnetic field, revealing how the effective coupling decreases with field strength and relates to inverse magnetic catalysis.

Contribution

It provides a first-principles calculation of the thermo-magnetic quark-gluon vertex within the Hard Thermal Loop approximation, highlighting the behavior of the effective coupling under magnetic fields.

Findings

Longitudinal vertex components are modified by the magnetic field.

The effective quark-gluon coupling decreases as magnetic field strength increases.

Results support the role of the coupling in inverse magnetic catalysis.

Abstract

We compute the thermo-magnetic correction to the quark-gluon vertex in the presence of a weak magnetic field within the Hard Thermal Loop approximation. The vertex satisfies a QED-like Ward identity with the quark self-energy. The only vertex components that get modified are the longitudinal ones. The calculation provides a first principles result for the quark anomalous magnetic moment at high temperature in a weak magnetic field. We extract the effective thermo-magnetic quark-gluon coupling and show that this decreases as a function of the field strength. The result supports the idea that the properties of the effective quark-gluon coupling in the presence of a magnetic field are an important ingredient to understand the inverse magnetic catalysis phenomenon.