Refractive Index of Light in the Quark-Gluon Plasma with the Hard-Thermal-Loop Perturbation Theory

Abstract

The electric permittivity and magnetic permeability for the quark-gluon plasma (QGP) is calculated within the hard-thermal-loop (HTL) perturbation theory. The refractive indices in the magnetizable and non-magnetizable plasmas are calculated. In a magnetizable plasma, there is a frequency pole ${\omega }_{mp}$ in the magnetic permeability and the refractive index. The refractive index becomes negative in the range $\omega \in [k,{\omega }_{mp}]$, where $k$ is the wave number, but no propagating modes are found. In a non-magnetizable plasma, the magnetic permeability and the refractive index are always positive. This marks the main distinction of a weakly coupled plasma from a strongly coupled one, where the negative refraction is shown to exist in a holographic theory.

Comments: 12 pages, 5 figures; v2: published version, title changed in accordance with PRD editor's suggestion, minor clarifications and references added, figures updated, typos corrected