Dilepton production at finite temperature: Perturbative treatment at orderαs

In the framework of finite-temperature perturbative QCD we examine the first-order corrections to the rate of lepton pairs produced in a thermalized quark-gluon plasma. The dilepton rate is calculated using the real-time formalism in two different ways by (i) applying the Feynman amplitude approach and by (ii) analyzing the relationship to the discontinuity of the two-loop photon self-energy at finite temperature. We mainly study the infrared and mass singular behavior and we show that up to order ${\alpha }_s$ the rate is free of these divergences in the limit of vanishing gluon and quark masses.