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

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.