Thermal dilepton rates and electrical conductivity of the QGP from the lattice

We investigate the temperature dependence of the thermal dilepton rate and the electrical conductivity of the gluon plasma at temperatures of 1.1, 1.3, and 1.5T(c) in quenched QCD. Making use of nonperturbatively clover-improved Wilson valence quarks allows for a clean extrapolation of the vector meson correlation function to the continuum limit. We found that the vector correlation function divided by T-3 is almost temperature independent in the current temperature window. The spectral functions are obtained by chi(2) fitting of phenomenologically inspired Ansatze for the spectral function to the continuum extrapolated correlator data, where the correlations between the data points have been included. Systematic uncertainties arising from varying the Ansatze motivated from strong coupling theory as well as perturbation theory are discussed and estimated. We found that the electrical conductivity of the hot medium, related to the slope of the vector spectral function at zero frequency and momentum, is 0.2C(em) less than or similar to sigma/T less than or similar to 0.7C(em) for T = 1.1T(c) and 0.2C(em) less than or similar to sigma/T less than or similar to 0.4C(em) for the higher temperatures. The dilepton rates and soft photon rates, resulting from the obtained spectral functions, show no significant temperature dependence, either.