On the imaginary parts and infrared divergences of two-loop vector boson self-energies in thermal QCD

TL;DR

This work computes the imaginary part of the retarded two-loop self-energy for a static vector boson in a thermal QCD plasma using imaginary-time formalism. By reassembling all cuts into physical tree-like processes and interpreting loop-containing cuts as interference with spectator contributions, the authors provide a coherent picture of dilepton production mechanisms in the $E\gg T$ regime. They show that, after summing all contributions, infrared and collinear divergences cancel, yielding a finite thermal rate proportional to $T^2$ and consistent with KLN-like expectations at finite temperature. The results unify multiple earlier approaches and offer a robust, infrared-safe prediction for dilepton production in a quark–gluon plasma.

Abstract

We calculate the imaginary part of the retarded two-loop self-energy of a static vector boson in a plasma of quarks and gluons of temperature T, using the imaginary time formalism. We recombine various cuts of the self-energy to generate physical processes. We demonstrate how cuts containing loops may be reinterpreted in terms of interference between Order $α$ tree diagrams and the Born term along with spectators from the medium. We apply our results to the rate of dilepton production in the limit of dilepton invariant mass E>>T. We find that all infrared and collinear singularities cancel in the final result obtained in this limit.

Figures (12)

• Figure 1: The first topology for the self-energy.
• Figure 2: The second topology for the self-energy.
• Figure 3: Heavy photon decay and formation.
• Figure 4: Heavy photon decay at first order in $\alpha$ and $\alpha_s$.
• Figure 5: Quark Compton scattering.