Enhanced thermal production of hard dileptons by $3\to 2$ processes

In the framework of the Hard Thermal Loop effective theory, we calculate the two-loop contributions to hard lepton pair production in a quark-gluon plasma. We show that the result is free of any infrared and collinear singularity. We also recover the known fact that perturbation theory leads to integrable singularities at the location of the threshold for $q\bar{q}\to\gamma^*$. It appears that the process calculated here significantly enhances the rate of low mass hard dileptons.