Self-consistent treatment of bubble nucleation at the electroweak phase transition

Abstract

In the standard procedure for calculating the decay rate of a metastable vacuum the solution of the classical Euclidean equation of motion of the background field is needed. On the other hand radiative corrections have to be taken into account already in the equation of motion. Hence, the latter one has to be the functional derivative of the effective action with respect to the background field. This is of crucial importance in theories in which the symmetry breaking is due to radiative corrections. Usually the effective potential is considered only, neglecting the corrections due to the derivative terms of the effective action. In this article a bounce solution from an equation of motion which takes into account the full effective action in the one-loop approximation is calculated. A computational method that yields a strict separation of the divergent contributions to the effective action from the convergent ones is obtained. This allows a wide freedom in the choice of regularization and renormalization schemes. The model under consideration is the SU(2)-Higgs model. The fluctuations of the complete bosonic sector, i.e., gauge field, Higgs, and Goldstone boson contributions, are taken into account. The bounce is then self-consistent to one-loop order. The obtained results for characteristic quantities of the transition such as the nucleation rate and the number of nucleated bubbles per volume are compared to other, non-self-consistent approaches.