Thermal 2-loop master spectral function at finite momentum

TL;DR

This paper develops a method to compute the 2-loop spectral function at finite momentum for thermal particle production, enabling more accurate NLO calculations relevant for cosmology and QCD plasmas.

Contribution

It introduces a convergent integral representation for the complex 2-loop spectral function, applicable to both bosonic and fermionic statistics, improving NLO thermal rate computations.

Findings

Non-relativistic approximation is accurate only for K^2 > (8 pi T)^2.

Zero-momentum approximation is surprisingly effective.

Method facilitates NLO calculations for neutrino and dilepton production rates.

Abstract

When considering NLO corrections to thermal particle production in the "relativistic" regime, in which the invariant mass squared of the produced particle is K^2 ~ (pi T)^2, then the production rate can be expressed as a sum of a few universal "master" spectral functions. Taking the most complicated 2-loop master as an example, a general strategy for obtaining a convergent 2-dimensional integral representation is suggested. The analysis applies both to bosonic and fermionic statistics, and shows that for this master the non-relativistic approximation is only accurate for K^2 > (8 pi T)^2, whereas the zero-momentum approximation works surprisingly well. Once the simpler masters have been similarly resolved, NLO results for quantities such as the right-handed neutrino production rate from a Standard Model plasma or the dilepton production rate from a QCD plasma can be assembled for K^2 ~ (pi T)^2.