Electroweak phase transitions

Abstract

An analytic treatment of the one Higgs doublet, electroweak phase transition is given. The phase transition is first order, occurs by the nucleation of thin walled bubbles and completes at a temperature where the order parameter, <Φ>T is significantly smaller than it is when the origin becomes absolutely unstable. The rate of anomalous baryon number violation is an exponentially function of <Φ>T. In very minimal extensions of the standard model it is quite easy to increase <Φ>T so that anomalous baryon number violation is suppressed after completion of the phase transition. Hence baryogenesis at the electroweak phase transition is tenable in minimal of the standard model. In some cases additional phase transitions are possible. For a light Higgs boson, when the top quark mass is sufficiently large, the state where the Higgs field has a vacuum expectation value <Φ> = 246 GeV is not the true minimum of the Higgs potential. When this is the case, and when the top quark mass exceeds some critical value, thermal fluctuations in the early universe would have rendered the state <Φ> = 246 GeV unstable. The requirement that the state <Φ> = 246 GeV is sufficiently long lived constrains the masses of the Higgs boson and the top quark. Finally, we consider whether local phase transitions can be induced by heavy particles which act as seeds for deformations in the scalar field.