Low-mass dilepton rate from the deconfined phase

Abstract

We discuss low-mass dilepton rates ($\ensuremath{\leqslant}1$ GeV) from the deconfined phase of QCD using both perturbative and nonperturbative models and compare them with those from lattice gauge theory and in-medium hadron gas. Our analysis suggests that the rate at very low invariant mass ($M\ensuremath{\leqslant}200$ MeV) using the nonperturbative gluon condensate in a semiempirical way within the Green function approach dominates over the Born rate, independent of any uncertainty associated with the choice of the strong coupling in perturbation theory. On the other hand, the rate from $\ensuremath{\rho}$-$q$ interaction in the deconfined phase is important at $200$ MeV $\ensuremath{\leqslant}M\ensuremath{\leqslant}$ $1$ GeV as it is almost of same order as the Born rate as well as the in-medium hadron gas rate. Also, the higher order perturbative rate, leaving aside its various uncertainties, from the hard-thermal-loop approximation becomes reliable at $M\ensuremath{\geqslant}200$ MeV and also becomes comparable with the Born rate and the lattice rate for $M\ensuremath{\geqslant}500$ MeV, constraining on the broad resonance structures in the dilepton rate at large invariant mass. We also discuss the lattice constraints on the low-mass dilepton rate. Furthermore, we discuss a realistic way to advocate the quark-hadron duality hypothesis based on the dilepton rates from quark-gluon plasma and hadron gas.