Two-loop thermal spectral functions with general kinematics

TL;DR

This paper calculates finite-temperature two-loop spectral functions for massless particles in various kinematic regions, providing analytical divergence handling and numerical evaluation, with applications to QCD vector channels.

Contribution

It introduces a comprehensive method for computing two-loop thermal spectral functions with general kinematics, including divergence analysis and numerical techniques, applicable to QCD.

Findings

Derived analytical expressions for divergences in spectral functions.

Numerical evaluation of finite parts of spectral functions.

Application to transverse and longitudinal QCD vector channels.

Abstract

Spectral functions at finite temperature and two-loop order are investigated, for a medium consisting of massless particles. We consider them in the timelike and spacelike domains, allowing the propagating particles to be any valid combination of bosons and fermions. Divergences (if present) are analytically derived and set aside for the remaining finite part to be calculated numerically. To illustrate the utility of these 'master' functions, we consider transverse and longitudinal parts of the QCD vector channel spectral function.