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.
Highlights
In a relativistic plasma, the rates of processes like particle production and damping are derivable from the imaginary part of a particle’s self-energy [1,2]
By applying (2.4) and (2.3) in sequence one can reduce pm0 for m ≥ 2 in (2.1) to a sum of powers of ðvEpÞ with simpler masters. (And the same strategy works for qn0.) The benefit of all this, is that the frequency sums are relatable to cases with m 1⁄4 n 1⁄4 0; any complications will move to the integration over the three momenta p and q that follows
We have computed a list of spectral functions that originate from self-energy diagrams with two loops, generalizing the results of Refs. [16,25] to below the light cone and considering a larger set of master integrals with m; n > 0
Summary
Albert Einstein Center, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland (Received 27 October 2019; published 20 December 2019). 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
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