On electric fields in hot QCD: perturbation theory

TL;DR

This paper studies how a hot quark gas responds to external electric fields using perturbation theory, calculating electric susceptibility and exploring discrepancies in different calculation methods.

Contribution

It provides a leading-order perturbative analysis of electric susceptibility in hot QCD and discusses the mismatch between different susceptibility calculations.

Findings

Derived high-temperature expansion of electric susceptibility for arbitrary quark mass.

Identified and analyzed the mismatch between direct susceptibility determination and weak-field expansion.

Discussed implications for extending results to full QCD in electric fields.

Abstract

We investigate the response of a hot gas of quarks to external electric fields via leading-order perturbation theory. In particular, we discuss how equilibrium is maintained in the presence of the electric field and calculate the electric susceptibility, providing its high-temperature expansion for arbitrary quark mass. Furthermore, we point out that there is a mismatch between this, direct determination of the susceptibility at zero field and the weak-field expansion of the effective action at nonzero electric fields, as obtained using Schwinger's exact propagator. We discuss the origin of this mismatch and elaborate on the generalization of our results to full QCD in electric fields.