GAUSSIAN EFFECTIVE POTENTIAL FOR THE U(1) HIGGS-MODEL

In order to investigate the Higgs mechanism nonperturbatively, we comp ute the Gaussian effective potential of the U(1) Higgs model (''scalar electrodynamics''). We show that the same simple result is obtained i n three different formalisms. A general covariant gauge is used, with Landau gauge proving to be optimal. The renormalization generalizes th e ''autonomous'' renormalization for lambda phi(4) theory and requires a particular relationship between the bare gauge coupling e(B) and th e bare scalar self-coupling lambda(B). When both couplings are small, then lambda is proportional to e(4) and the scalar/vector mass-squared ratio is of order e(2), as in the classic 1-loop analysis of Coleman and Weinberg. However, as lambda increases, e reaches a maximum value and then decreases, and in this ''nonperturbative'' regime the Higgs s calar can be much heavier than the vector boson. We compare our result s to the autonomously renormalized 1-loop effective potential, finding close agreement in the physical predictions. The main phenomenologica l implication is a Higgs mass of about 2 TeV.