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

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.

Figure 1

Feynman diagrams for the four-point quark gluon vertex.