Power corrections to the photon polarization tensor in a hot and dense medium of massive fermions

TL;DR

This paper calculates the first nonzero mass-dependent power corrections to the photon polarization tensor in a hot, dense medium, revealing their impact on electromagnetic susceptibilities relevant for equilibrium conditions.

Contribution

It introduces the calculation of mass corrections to the photon polarization tensor within the hard thermal loop approximation, extending previous massless analyses.

Findings

Mass corrections influence temperature dependence of photon polarization.

Results impact calculations of electric and magnetic susceptibilities.

Comparison with previous massless results highlights the significance of finite mass effects.

Abstract

We compute the $\mathcal{O}(k^2)$ terms (power corrections) of the photon polarization tensor in a hot and dense medium of particles with a small but finite mass, i.e., $0< m\ll T, \mu$. We perform our calculations within the hard thermal loop approximation in the real-time formalism, and evaluate the first nonzero mass corrections. For a renormalization scale $\bar{\Lambda}\sim T$, these mass contributions determine the temperature dependence of the power corrections. These results have direct implications in the computation of electric and magnetic susceptibilities of hot and dense media in equilibrium. We address such implications and make comparisons with previous results.