3D PHYSICS AND THE ELECTROWEAK PHASE-TRANSITION - PERTURBATION-THEORY

We develop a method for the construction of the effective potential at high temperatures, based on the effective field theory approach and renormalization group. It makes it possible to sum up the leading logarithms in all orders of perturbation theory. The method reproduces the known one-loop and two-loop results in a very simple and economic way and clarifies the issue of the convergence of the perturbation theory. We also discuss the assumptions being made for the determination of the critical temperature of the electroweak phase transition, and analyse different perturbative uncertainties in its determination. These results will then be used for the non-perturbative lattice Monte Carlo simulations of the EW phase transition in a forthcoming paper.