THE WEAK ELECTROWEAK PHASE-TRANSITION

We present a detailed analysis of the phase transition in the standard model at finite temperature. Using an improved perturbation theory, w here plasma masses are determined from a set of one-loop gap equations , we evaluate the effective potential V-eff(phi,T) in next-to-leading order, i.e., including terms cubic in the gauge coupling g, the scalar self-coupling lambda(1/2), and the top-quark Yukawa coupling f(t). Th e gap equations yield a non-vanishing magnetic plasma mass for the gau ge bosons, originating from the non-abelian self-interactions. We disc uss in detail size and origin of higher order effects and conclude tha t the phase transition is weakly first-order up to Higgs masses of abo ut 70 GeV, above which our calculation is no longer self-consistent. F or larger Higgs masses even an approximation containing all g(4) contr ibutions to V-eff is not sufficient, at least a full calculation to or der g(6) is needed. These results turn out to be rather insensitive to the top-quark mass in the range m(top)=100-180 GeV. Using Langer's th eory of metastability we calculate the nucleation rate of critical dro plets and discuss some aspects of the cosmological electroweak phase t ransition. (C) 1994 Academic Press, Inc.