Dilepton production spectrum above Tc with a lattice quark propagator

The dilepton production rate from the deconfined medium is analyzed with the photon self-energies constructed from quark propagators obtained by lattice numerical simulation for two values of temperature $T=1.5T_{\rm c}$ and $3T_{\rm c}$ above the critical temperature $T_{\rm c}$. The photon self-energy is calculated by the Schwinger-Dyson equation with the lattice quark propagtor and a vertex function determined so as to satisfy the Ward-Takahashi identity. The obtained dilepton production rate at zero momentum exhibits divergences reflecting van Hove singularity, and is significantly enhanced around $\omega\simeq T$ compared with the rate obtained by the perturbative analysis.