Debye screening at finite temperature reexamined

We present an alternative way to calculate the screening of the static potential between two charges in (non)abelian gauge theories at high temperatures. Instead of a loop expansion of a gauge boson self-energy, we evaluate the energy shift of the vacuum to order e^2 after applying an external static magnetic field and extract a temperature- and momentum-dependent dielectric permittivity. The Hard Thermal Loop (HTL) gluon and photon Debye masses are recovered from the lowest lying Landau levels of the perturbed vacuum. In QED, the complete calculation exhibits an interesting cancellation of terms, resulting in a logarithmic running alpha(T). In QCD, a Landau pole in alpha_s arises in the infrared from the sign of the gluon contribution, as in more sophisticated thermal renormalization group calculations.