Dileptons, spectral weights, and conductivity in the Quark-Gluon Plasma

TL;DR

This paper re-examines soft dilepton emission in the Quark-Gluon Plasma, correcting previous results and analyzing spectral weights and conductivity at small energies using kinetic theory, highlighting the challenges in extracting electrical conductivity.

Contribution

It corrects the coefficient in the dilepton rate at small energies and analyzes spectral weight behavior at very low energies using kinetic theory.

Findings

Dilepton rate rises as E^-4 at small energies, with corrected coefficients.

Spectral weight scales as 1/E at small energies, moderating to 1/E^2 at very low energies.

Finite electrical conductivity is consistent with the spectral weight behavior.

Abstract

We re-examine soft dilepton emission from a weakly coupled Quark-Gluon Plasma. We show that Braaten, Pisarski, and Yuan's result that the dilepton rate rises as E^-4 (and the spectral weight scales as 1/E) at small energy E<<gT is correct, but that the coefficient they found for this behavior is not correct, because their analysis was incomplete. At still smaller scales, the behavior moderates to ~1/E^2 for E <= g^4 T, consistent with a finite electrical conductivity. We evaluate the spectral weight in the E~g^4 T region by kinetic theory techniques and show that it satisfies a sum rule, which makes the determination of electrical conductivity from the Euclidean correlation function very challenging.