CRITICAL BUBBLES AND FLUCTUATIONS AT THE ELECTROWEAK PHASE-TRANSITION

We discuss the critical bubbles of the electroweak phase transition using an effective high-temperature 3-dimensional action for the Higgs field phi. The separate integration of gauge and Goldstone boson degrees of freedom is conveniently described in the 't Hooft-Feynman covariant background gauge. The effective dimensionless gauge coupling g(3)(T)(2) in the broken phase is well behaved throughout the phase transition. However, the behavior of the one-loop Z(phi) factors of the Higgs and gauge kinetic terms signalizes the breakdown of the derivative expansion and of the perturbative expansion for a range of small phi values increasing with the Higgs mass m(H). Taking a functional S-z[phi] with constant Z(phi) = z instead of the full non-local effective action in some neighborhood of the saddle point we are calculating the critical bubbles for several temperatures. The fluctuation determinant is calculated to high accuracy using a variant of the heat kernel method. It gives a strong suppression of the transition rate compared to previous estimates.