Covariant formulation of gluon self-energy in presence of ellipsoidal anisotropy

TL;DR

This paper develops a covariant framework for gluon self-energy in anisotropic media, revealing new unstable modes due to ellipsoidal anisotropy, with potential implications for understanding quark-gluon plasma behavior.

Contribution

It introduces a covariant formulation of gluon self-energy with ellipsoidal anisotropy and analyzes the resulting collective modes and instabilities.

Findings

Six independent projection tensors describe the gluon self-energy structure.

Mass scales depend on angular parameters in the anisotropic medium.

Additional unstable modes can emerge with ellipsoidal anisotropy.

Abstract

In this work, a covariant formulation of the gluon self-energy in presence of ellipsoidal anisotropy is considered. It is shown that the general structure of the gluon self-energy can be written in terms of six linearly independent projection tensors. Similar to the spheroidal anisotropy, mass scales can be introduced for each of the collective modes considering the static limits. With a simplified ellipsoidal generalization of the Romatschke-Strickland form, the angular dependencies of the mass scales are studied. It is observed that, compared to the spheroidal case, additional unstable mode may appear in presence of ellipsoidal anisotropy depending upon the choice of the parameters.