Thermomagnetic corrections to the quark gluon vertex in the hard thermal loop approximation

We compute the thermomagnetic corrections to the quark gluon vertex in 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 We extract the effective thermomagnetic quark gluon coupling and show that it decreases as 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 for understanding the inverse magnetic catalysis phenomenon