Next-to-Leading Order Debye-Screening in Spontaneously Broken Gauge Theories

The main role of the Debye screening mass in the perturbative treatment of the electro-weak phase transition is the reduction of the cubic term that determines the strength of a first-order transition. In this note I point out that the standard definition of the Debye mass is unphysical. Its next-to-leading order corrections in resummed perturbation theory are gauge dependent generally in nonabelian gauge theories, and even in Abelian theories when in the Higgs phase. A gauge independent definition can be obtained from a gap equation for the propagator rather than the self-energy, which turns out to be perturbatively under control in the Higgs phase, but sensitive to the nonperturbative magnetic mass scale in the symmetric phase of nonabelian theories. [Contributed talk at the NATO Advanced Research Workshop ``Electroweak Physics and the Early Universe'', 23 - 25 March 1994, Sintra, Portugal]