The static hard-loop gluon propagator to all orders in anisotropy

TL;DR

This paper derives the static hard-loop gluon propagator in an anisotropic quark-gluon plasma to all orders in anisotropy, revealing infrared-finite results and extending previous approximations.

Contribution

It provides the first all-orders in anisotropy calculation of the static gluon propagator, including new results for the Feynman self-energy and propagator.

Findings

All-orders Feynman propagator free from infrared singularities

Extended retarded and advanced self-energy calculations to next-to-leading order

Comparison shows previous Taylor-expansion results are approximate and infrared-divergent

Abstract

We calculate the (semi-)static hard-loop self-energy and propagator using the Keldysh formalism in a momentum-space anisotropic quark-gluon plasma. The static retarded, advanced, and Feynman (symmetric) self-energies and propagators are calculated to all orders in the momentum-space anisotropy parameter $\xi$. For the retarded and advanced self-energies/propagators, we present a concise derivation and comparison with previously-obtained results and extend the calculation of the self-energies to next-to-leading order in the gluon energy, $\omega$. For the Feynman self-energy/propagator, we present new results which are accurate to all orders in $\xi$. We compare our exact results with prior expressions for the Feynman self-energy/propagator which were obtained using Taylor-expansions around an isotropic state. We show that, unlike the Taylor-expanded results, the all-orders expression for the Feynman propagator is free from infrared singularities. Finally, we discuss the application of our results to the calculation of the imaginary-part of the heavy-quark potential in an anisotropic quark-gluon plasma.