Finite temperature quark-gluon vertex with a magnetic field in the Hard   Thermal Loop approximation
  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. 
Alejandro Ayala, J.J. Cobos-Martinez, M. Loewe, Maria Elena   Tejeda-Yeomans, R. Zamora
hep-ph hep-lat hep-th nucl-th