Supersymmetric Electroweak Phase Transition: Baryogenesis versus Experimental Constraints

We use the two-loop effective potential to study the first order electroweak phase transition in the minimal supersymmetric standard model. A global search of the parameter space is made to identify parameters compatible with electroweak baryogenesis. We improve on previous such studies by fully incorporating squark and Higgs boson mixing, by using the latest experimental constraints, and by computing the latent heat and the sphaleron rate. We find the constraints $\tan \beta >2.1\mathrm{}$, $m_{\tilde{t}}<172\mathrm{}\mathrm{GeV}$, and $m_h<107\mathrm{}\mathrm{GeV}$ (becoming more or less restrictive if the heavy stop has mass less than or greater than 1 TeV). We also find that the change in $\tan \beta$ in the bubble wall is rarely greater than ${10}^{-3\mathrm{}}$, which severely constrains the mechanism of baryogenesis.