We give an analytic treatment of the one-Higgs-doublet, electroweak phase transition which demonstrates that the phase transition is first order. The phase transition occurs by the nucleation of thin-walled bubbles and completes as a temperature where the order parameter 〈φ${\mathrm{〉}}_{\mathit{T}}$ is significantly smaller than it is when the origin becomes absolutely unstable. The rate of anomalous baryon-number violation is an exponentially sensitive function of 〈φ${\mathrm{〉}}_{\mathit{T}}$. In very minimal extensions of the standard model it is quite easy to increase 〈φ${\mathrm{〉}}_{\mathit{T}}$ so that anomalous baryon-number violation is suppressed after the completion of the phase transition. Hence, baryogenesis at the electroweak phase transition is tenable in minimal extensions of the standard model with one Higgs doublet.

• Received 23 September 1991

DOI:https://doi.org/10.1103/PhysRevD.45.2685