A Critical Look at the Electroweak Phase Transition

The electroweak phase transition broke the electroweak symmetry. Perturbative methods used to calculate observables related to this phase transition suffer from severe problems such as gauge dependence, infrared divergences, and a breakdown of perturbation theory. In this paper we develop robust perturbative tools for dealing with phase transitions. We argue that gauge and infrared problems are absent in a consistent power-counting. We calculate the finite temperature effective potential to two loops for general gauge-fixing parameters in a generic model. We demonstrate gauge invariance, and perform numerical calculations for the Standard Model in Fermi gauge.