  We compute corrections to the hard thermal (or dense) loop photon
polarization tensor associated to a small mass $m$ of the fermions of an
electromagnetic plasma at high temperature $T$ (or chemical potential $\mu$).
To this aim we use the on-shell effective field theory, amended with mass
corrections. We also carry out the computation using transport theory, reaching
to the same result. Interemediate steps in the computations reveal the presence
of potential infrared divergencies. We use dimensional regularization, as it is
respectful with the gauge symmetry, and then show that all infrared
divergencies cancel in the final result. We compare the mass corrections with
both the power and two-loop corrections, and claim that they are equally
important if the mass is soft, that is, of order $e T$ (or $e \mu$), where $e$
is the gauge coupling constant, but are dominat if the mass obeys $ e T < m \ll
T $ (or $e \mu < m \ll \mu)$.
