Quark and gluon distribution functions in a viscous quark-gluon plasma medium and dilepton production via $q\bar{q}$-- annihilation

Viscous modifications to the thermal distributions of quark-antiquarks and gluons have been studied in a quasi-particle description of the quark-gluon-plasma medium created in relativistic heavy-ion collision experiments. The model is described in terms of quasi-partons that encode the hot QCD medium effects in their respective effective fugacities. Both shear and bulk viscosities have been taken in to account in the analysis and the modifications to thermal distributions have been obtained by modifying the the energy momentum tensor in view of the non-trivial dispersion relations for the gluons and quarks. The interactions encoded in the equation of state induce significant modifications to the thermal distributions. As an implication, dilepton production rate in the $q\bar{q}$ annihilation process has been investigated. The equation of state is found to have significant impact on the dilepton production rate along with the viscosities.