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When considering NLO corrections to thermal particle production in the"relativistic" regime, in which the invariant mass squared of the producedparticle is K^2 ~ (pi T)^2, then the production rate can be expressed as a sumof a few universal "master" spectral functions. Taking the most complicated2-loop master as an example, a general strategy for obtaining a convergent2-dimensional integral representation is suggested. The analysis applies bothto bosonic and fermionic statistics, and shows that for this master thenon-relativistic approximation is only accurate for K^2 > (8 pi T)^2, whereasthe zero-momentum approximation works surprisingly well. Once the simplermasters have been similarly resolved, NLO results for quantities such as theright-handed neutrino production rate from a Standard Model plasma or thedilepton production rate from a QCD plasma can be assembled for K^2 ~ (pi T)^2.

Thermal 2-loop master spectral function at finite momentum