A Critical Look at the Electroweak Phase Transition

The electroweak phase transition broke the electroweak symmetry. Perturbativemethods used to calculate observables related to this phase transition suffer from severeproblems such as gauge dependence, infrared divergences, and a breakdown of perturbationtheory. 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. Wecalculate the finite temperature effective potential to two loops for general gauge-fixingparameters in a generic model. We demonstrate gauge invariance, and perform numericalcalculations for the Standard Model in Fermi gauge