OSEFT or how to go beyond hard thermal loops

TL;DR

This paper develops an effective field theory framework, OSEFT, to improve the description of high-temperature plasma physics beyond traditional hard thermal loop approximations, capturing both hard and soft scale effects.

Contribution

The paper introduces the on-shell effective field theory (OSEFT) that systematically incorporates corrections beyond HTL in high-temperature plasmas.

Findings

OSEFT accurately reproduces HTL photon polarization tensor in QED.

The theory provides 1/T corrections to HTL results.

Soft scale corrections are perturbative modifications to HTL.

Abstract

We show that effective field theory techniques can be applied in the high temperature $T$ regime of plasmas to improve the accuracy of the physics of the hard scales (or scales of order $T$), and as a by-product, also that of the soft scales (or scales of order $gT$). At leading order in the coupling constant the hard scales of the plasma can be viewed as on-shell classical particles. Based on this observation, and without any reference to the state of the system, we derive an effective field theory describing the quantum fluctuations around an on-shell fermion with energy $p$, described as a set of high dimension operators over the on-shell energy $p$. When applied to systems close to thermal equilibrium, where for most on-shell particles $p \sim T$, we show that the on-shell effective field theory (OSEFT) properly describes the HTL photon polarization tensor of QED, and its 1/T corrections. For the soft scales the first non-vanishing power correction turns out to be a perturbative correction to the HTL result.