Electroweak phase transition, critical bubbles, and sphaleron decoupling condition in the MSSM

Abstract

The electroweak phase transition and the sphaleron decoupling condition in the minimal supersymmetric standard model are revisited taking the latest experimental data into account. The light Higgs boson scenario and the ordinary decoupling limit, which are classified by the relative size between the $CP$-odd Higgs boson mass and $Z$ boson mass, are considered within the context of electroweak baryogenesis. We investigate $v/T$ at not only the critical temperature at which the effective potential has two degenerate minima but also the nucleation temperature of the critical bubbles, where $v$ is a vacuum expectation value of the Higgs boson and $T$ denotes a temperature. It is found that $v/T$ at the nucleation temperature can be enhanced by about 10% compared to that at the critical temperature. We also evaluate the sphaleron decoupling condition including the zero mode factors of the fluctuations around sphaleron. It is observed that the sphaleron decoupling condition at the nucleation temperature is given by $v/T\ensuremath{\gtrsim}1.38$ for the typical parameter sets. In any phenomenologically allowed region, $v/T$ at both the critical and nucleation temperatures cannot be large enough to satisfy such a sphaleron decoupling condition.