  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.
