Soft photon propagation in a hot and dense medium to next-to-leading order

TL;DR

This paper provides a comprehensive next-to-leading order calculation of soft photon self-energy in hot/dense QED plasma, crucial for advancing perturbative pressure calculations and setting the stage for future QCD studies.

Contribution

It delivers the first complete NLO calculation of soft photon self-energy in hot/dense QED using real-time formalism and dimensional regularization.

Findings

Explicit $O(\epsilon)$ terms reported at zero temperature.

Results enable higher-order perturbative calculations of QED matter pressure.

Lays groundwork for similar calculations in QCD.

Abstract

We present the first complete calculation of the soft photon self-energy to the next-to-leading order in a hot and/or dense ultrarelativistic plasma in Quantum Electrodynamics (QED). The calculation is performed within the real-time formalism utilizing dimensional regularization in $4-2\epsilon$ dimensions, while the result is reported including explicit $O(\epsilon)$ terms in the zero-temperature limit. This information is required to extend the perturbative calculation of the pressure of cold and dense QED matter to partial next-to-next-to-next-to-leading order in a weak-coupling expansion, reported in a companion paper. These results pave the way for a similar future calculation in Quantum Chromodynamics.