Debye Screening at Finite Temperature , Revisited ∗ )

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 in a first, though incomplete approximation. In QED, the complete calculation exhibits an interesting cancellation of terms, resulting in a logarithmic running α(T). Debye screening is then caused by the modified index of refraction of the vacuum. In QCD, a Landau pole in αs arises in the infrared from the sign of the gluon contribution, as in more sophisticated thermal renormalization group calculations.