# Finite temperature QCD four-point function in the presence of a weak magnetic field within the hard thermal loop approximation

## TL;DR

This paper calculates how a weak magnetic field affects the four-point quark-gluon vertex at finite temperature and chemical potential, ensuring consistency with Ward identities within the hard thermal loop approximation.

## Contribution

It provides the first detailed computation of the magnetic field correction to the four-point quark-gluon vertex in hot QCD within the HTL framework.

## Key findings

- The four-point vertex correction satisfies the Ward identity with the three-point vertex.
- The correction is computed explicitly within the HTL approximation.
- Results are relevant for understanding QCD in magnetic fields at finite temperature.

## Abstract

We compute the weak magnetic field correction to the four-point quark-gluon vertex at finite temperature and chemical potential within the hard thermal loop approximation. The resulting four-point quark-gluon vertex satisfies the Ward identity with the three-point quark-gluon vertex.