Thermo-magnetic behavior of the quark-gluon vertex

TL;DR

This paper calculates the thermo-magnetic corrections to the quark-gluon vertex in a weak magnetic field at high temperature, revealing modifications to the longitudinal components and implications for the effective coupling and inverse magnetic catalysis.

Contribution

It provides a first-principles calculation of the thermo-magnetic quark-gluon vertex and coupling in the weak magnetic field regime within the Hard Thermal Loop approximation.

Findings

Longitudinal vertex components are modified by the magnetic field.

The effective quark-gluon coupling decreases with increasing magnetic field.

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

Abstract

The thermo-magnetic corrections to the quark-gluon vertex in the presence of a weak magnetic field are calculated in the frame of the Hard Thermal Loop approximation. The vertex satisfies a QED-like Ward identity with the quark self-energy calculated within the same approximation. It turns out that only the longitudinal vertex components get modified. The calculation provides a first principles result for the quark anomalous magnetic moment at high temperature in a weak magnetic field. The effective thermo-magnetic quark-gluon coupling shows a decreasing behavior as function of the field strength. This result supports the observation that the behavior of the effective quark-gluon coupling in the presence of a magnetic field is an important ingredient in order to understand the inverse magnetic catalysis phenomenon recently observed in the lattice QCD simulations.