Electrical conductivity of the quark-gluon plasma from the low energy limit of photon and dilepton spectra

Fluid dynamic considerations are used to determine the electric current spectral density in the regime of small energies and momenta. The spectral density in this regime is parameterized by the electric conductivity, the charge susceptibility, and the relaxation time for the electric current, which is needed for relativistic causality. Experimentally, the spectral function can be accessed through the production rates of photons and dileptons in the expanding quark-gluon plasma. We use fluid dynamic simulations of high energy nuclear collisions, together with the transport limit of the spectral density, to obtain photon and dielectron spectra for different values of the conductivity and relaxation times. The yields of photon and dileptons produced in the plasma are compared to the background from decays of short-lived hadrons. We discuss how experiments can constrain the electrical conductivity and associated relaxation time of the quark-gluon plasma.