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

TL;DR

This paper calculates the refractive index of the quark-gluon plasma using HTL perturbation theory, revealing negative refraction in magnetizable plasmas and contrasting weakly and strongly coupled regimes.

Contribution

It provides the first calculation of the refractive index in QGP within HTL perturbation theory, highlighting the conditions for negative refraction and differences between magnetizable and non-magnetizable plasmas.

Findings

Negative refraction occurs in magnetizable plasma within a specific frequency range.

Magnetic permeability remains positive in non-magnetizable plasma.

Weakly coupled plasma shows no propagating modes with negative refraction.

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.