Thermal 2-loop master spectral function at finite momentum

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 ∼ (πT ) 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 > ∼ (8πT ) 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 ∼ (πT ) 2 .

Two-loop thermal spectral functions with general kinematics

“…(This figure confirms Ref. [16] above the light cone.) The curves appear continuous across the light cone because For m = n = 1 , there is a leading vacuum term in (D.18).…”

“…Let us define, for generic sum-integrals I as functions of the external four-momentum K = (k 0 , k) , a uniform notation (for m = n = 0, cf. [16])…”

“…In Ref. [16], the function Im I (0) 11111 (it was labelled with 'j' there) was computed above the light cone. For that case, with m = n = 0 , we do not need to worry about ultraviolet divergences.…”

Interpolation of hard and soft dilepton rates

“…The current study is the continuation of a recent project [17,18] which led to the determination of the NLO dilepton rate for generic momenta and invariant masses k, M ∼ πT [11]. The goal of the present study is to present a smooth interpolation between these hard NLO expressions, and leading-order LPM resummation in the soft regime M ∼ gT , k ≫ M .…”

On the infrared behavior of the shear spectral function in hot Yang-Mills theory

“…Since then, the techniques developed in these papers have been further generalized to include the case of non-vanishing external three-momenta [22], motivated by applications beyond QCD, most importantly studies of the leptogenesis scenario.…”