Three-loop HTL Free Energy for QED

TL;DR

This paper computes the three-loop free energy of a hot QED plasma using hard-thermal-loop perturbation theory, demonstrating improved convergence and gauge invariance, and providing an analytic resummed thermodynamic potential.

Contribution

It presents a three-loop calculation of QED free energy with a novel reorganization that enhances convergence and maintains gauge invariance, offering an analytic result.

Findings

Improved convergence of free energy calculations at large coupling.

Gauge-invariant three-loop resummed thermodynamic potential.

Analytic expression for the thermodynamic potential.

Abstract

We calculate the free energy of a hot gas of electrons and photons to three loops using the hard-thermal-loop perturbation theory reorganization of finite-temperature perturbation theory. We calculate the free energy through three loops by expanding in a power series in m_D/T, m_f/T, and e^2, where m_D and m_f are thermal masses and e is the coupling constant. We demonstrate that the hard-thermal-loop perturbation reorganization improves the convergence of the successive approximations to the QED free energy at large coupling, e ~ 2. The reorganization is gauge invariant by construction, and due to cancellation among various contributions, we obtain a completely analytic result for the resummed thermodynamic potential at three loops. Finally, we compare our result with similar calculations that use the Phi-derivable approach.