The production of soft dileptons in the quark-gluon plasma in resummed perturbation theory

The production rate of soft dileptons in a quark-gluon plasma is calculated for the general case where the intermediate virtual photons have non-zero momenta using Braaten-Pisarski resummed perturbation theory. It is found that the physics is more complicated and the structures are somewhat richer than the special case where the photons produced are stationary in the plasma. These structures are found to be determined, to a large extent, by the dispersion relations of the two propagating modes of the soft quarks. However, the Van Hove singularities present in the zero-momentum case are no longer there. The dependence of the rate on the total momentum of the dilepton pairs is not very strong, unless the photon mass shell is approached. Comparison with the the results obtained from the one loop calculation shows that the resummed perturbation theory predicts more dileptons being produced from the plasma when the intermediate virtual photons are near their mass shell. (orig.)