Dilepton rate and quark number susceptibility with the Gribov action

We use a recently obtained resummed quark propagator at finite temperature which takes into account both the chromoelectric scale gT and the chromomagnetic scale g^2T through the Gribov action. The electric scale generates two massive modes whereas the magnetic scale produces a new massless spacelike mode in the medium. Moreover, the non-perturbative quark propagator is found to contain no discontinuity in contrast to the standard perturbative hard thermal loop approach. Using this non-perturbative quark propagator and self-consistent vertices, we compute the non-perturbative dilepton rate at vanishing three-momentum at one-loop order. The resulting rate has a rich structure at low energies due to the inclusion of the non-perturbative magnetic scale. We also calculate the quark number susceptibility, which is related to the conserved quark number density fluctuation in the deconfined state. Both the dilepton rate and quark number susceptibility are compared with results from lattice quantum chromodynamics and the standard hard thermal loop approach. Finally, we discuss how the absence of a discontinuity in the imaginary part of the non-perturbative quark propagator makes the results for both dilepton production and quark number susceptibility dramatically different from those in perturbative approaches and seemingly in conflict with known lattice data.