Thermal Dileptons from pi - rho Interactions in a Hot Pion Gas

A systematic study of low mass dilepton production from $\pi-\rho$ interactions in a hot medium is presented. Applying finite temperature perturbation theory the dilepton rate, respectively the virtual photon rate, is computed up to order $g_\rho^2$. For dilepton masses below the $\rho$ the two-body reactions $\pi\pi\to \rho \gamma^*$, $\pi\rho\to \pi \gamma^*$, and the decay process $\rho \to \pi \pi \gamma^*$ give significant contributions. Non-equilibrium contributions to the thermal rate are estimated, including the modification of the particle distribution function with non-zero pion chemical potential. The comparison of the dilepton rate with the recent data measured in nucleus-nucleus collisions at SPS energy by the CERES Collaboration is also performed. It is shown that the additional thermal dileptons from $\pi-\rho$ interactions can partially account for the access of the soft dilepton yield seen experimentally.