  In this paper we study the production of energetic di-leptons. We calculate
the rate for 2 $\to$ 2 processes. The log term is obtained analytically and the
constant term is calculated numerically. When the photon mass is of the order
of the thermal quark mass, the result is insensitive to the photon mass and the
soft logarithmic divergence is regulated by the thermal quark mass, exactly as
in the case of real photons. We also consider the production of thermal
Drell-Yan dileptons (thermal quark and antiquark pairs produced by virtual
photons) and calculate the rate systematically in the context of the hard
thermal loop effective theory. We obtain analytic and numerical results. We
compare our results with those of previous calculations.
