Parton self-energies for general momentum-space anisotropy

TL;DR

This paper presents a fast, general method for calculating quark and gluon self-energies in anisotropic quark-gluon plasmas, enabling efficient analysis of collective modes and dispersion relations in complex momentum distributions.

Contribution

The authors develop a hypergeometric basis function method for calculating self-energies applicable to general anisotropic momentum distributions, improving speed and accuracy over numerical integration.

Findings

Derived self-energies and dispersion relations for anisotropic plasmas.

Numerical results for ellipsoidal momentum-space anisotropy.

First calculation of gluon unstable mode growth rate in this context.

Abstract

We introduce an efficient general method for calculating the self-energies, collective modes, and dispersion relations of quarks and gluons in a momentum-anisotropic high-temperature quark-gluon plasma. The method introduced is applicable to the most general classes of deformed anisotropic momentum distributions and the resulting self-energies are expressed in terms of a series of hypergeometric basis functions which are valid in the entire complex phase-velocity plane. Comparing to direct numerical integration of the self-energies, the proposed method is orders of magnitude faster and provides results with similar or better accuracy. To extend previous studies and demonstrate the application of the proposed method, we present numerical results for the parton self-energies and dispersion relations of partonic collective excitations for the case of an ellipsoidal momentum-space anisotropy. Finally, we also present, for the first time, the gluon unstable mode growth rate for the case of an ellipsoidal momentum-space anisotropy.