Electric conductivity of the quark-gluon plasma investigated using a perturbative QCD based parton cascade

TL;DR

This paper calculates the electric conductivity of a quark-gluon plasma using perturbative QCD and the Boltzmann equation, providing new numerical results that agree with lattice QCD data.

Contribution

It introduces a novel numerical approach to compute electric conductivity in a quark-gluon plasma using perturbative QCD and the Boltzmann equation, including inelastic scattering effects.

Findings

Numerical validation of the Drude formula for ultrarelativistic gases.

Electric conductivity results agree with recent lattice QCD data.

Inclusion of inelastic scattering effects enhances the model's realism.

Abstract

Electric conductivity is sensitive to effective cross sections among the particles of the partonic medium. We investigate the electric conductivity of a hot plasma of quarks and gluons, solving the relativistic Boltzmann equation. In order to extract this transport coefficient, we employ the Green-Kubo formalism and, independently, a method motivated by the classical definition of electric conductivity. To this end we evaluate the static electric diffusion current upon the influence of an electric field. Both methods give identical results. For the first time, we obtain numerically the Drude electric conductivity formula for an ultrarelativistic gas of quarks and gluons employing constant isotropic binary cross sections. Furthermore, we extract the electric conductivity for a system of massless quarks and gluons including screened binary and inelastic, radiative $2\leftrightarrow 3$ perturbative QCD scattering. Comparing with recent lattice results, we find an agreement in the temperature dependence of the conductivity.