On the screening of static electromagnetic fields in hot QED plasmas

We study the screening of static magnetic and electric fields in massless quantum electrodynamics (QED) and massless scalar electrodynamics (SQED) at temperature $T$. Various exact relations for the static polarisation tensor are first reviewed and then verified perturbatively to fifth order (in the coupling) in QED and fourth order in SQED, using different resummation techniques. The magnetic and electric screening masses squared, as defined through the pole of the static propagators, are also calculated to fifth order in QED and fourth order in SQED, and their gauge-independence and renormalisation-group invariance is checked. Finally, we provide arguments for the vanishing of the magnetic mass to all orders in perturbation theory.