Thermal 2-loop master spectral function at finite momentum

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 similar to (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 similar to (pi T)(2).