Next-to-leading order static gluon self-energy for anisotropic plasmas

TL;DR

This paper investigates the next-to-leading order static gluon self-energy in anisotropic plasmas, deriving a compact form and highlighting the importance of including vertices for accurate results, especially regarding magnetic instabilities.

Contribution

It provides a detailed derivation of the NLO static gluon self-energy in anisotropic plasmas, emphasizing the role of vertices and setting the stage for comprehensive numerical analysis.

Findings

Both positive and negative contributions from HL vertices.

The imaginary part of the structure function is nonzero.

The results highlight the need for full numerical evaluation.

Abstract

In this paper the structure of the next-to-leading (NLO) static gluon self energy for an anisotropic plasma is investigated in the limit of a small momentum space anisotropy. Using the Ward identities for the static hard-loop (HL) gluon polarization tensor and the (nontrivial) static HL vertices, we derive a comparatively compact form for the complete NLO correction to the structure function containing the space-like pole associated with magnetic instabilities. On the basis of a calculation without HL vertices, it has been conjectured that the imaginary part of this structure function is nonzero, rendering the space-like poles integrable. We show that there are both positive and negative contributions when HL vertices are included, highlighting the necessity of a complete numerical evaluation, for which the present work provides the basis.