Two-loop hard thermal loops for any model

TL;DR

This paper derives two-loop hard thermal loop self-energies for generic models, enabling more accurate calculations of plasma properties in high-temperature quantum field theories.

Contribution

It provides the first comprehensive derivation of two-loop self-energies for a wide class of models, extending the applicability of thermal field theory calculations.

Findings

Two-loop self-energies are explicitly calculated for generic models.

Results include higher-point functions at two-loop order.

Examples demonstrate the use of the derived formulas.

Abstract

Hard thermal loops describe how soft gauge fields are screened and damped in hot plasmas. As such they are used to calculate transport coefficients, Sphaleron rates, equations of state, and particle production. However, most calculations are done using one-loop self-energies. And two-loop contributions can be large. To that end this paper provides vector two-loop self-energies for generic models: Any scalar, fermion, or vector representation; and all possible renormalizable terms. Several examples are given to showcase the results. Two-loop results for higher-point functions are also given.