Two-loop Compton and annihilation processes in thermal QCD

TL;DR

This paper calculates two-loop contributions to soft lepton pair production in a quark-gluon plasma, showing they are as significant as one-loop terms and essential for consistent perturbative results.

Contribution

It introduces a detailed two-loop calculation within the hard thermal loop resummation framework, highlighting the importance of higher-order corrections in thermal QCD processes.

Findings

Two-loop diagrams contribute equally as one-loop diagrams.

Higher-order corrections are necessary for consistent perturbative expansion.

Proper subtraction of counterterms avoids double counting.

Abstract

We calculate the Compton and annihilation production of a soft static lepton pair in a quark-gluon plasma in the two-loop approximation. We work in the context of the effective perturbative expansion based on the resummation of hard thermal loops. Double counting is avoided by subtracting appropriate counterterms. It is found that the two-loop diagrams give contributions of the same order as the one-loop diagram. Furthermore, these contributions are necessary to obtain agreement with the naive perturbative expansion in the limit of vanishing thermal masses.