The Electroweak Phase Transition in the MSSM

The construction of an effective 3D theory at high temperatures for the MSSM as a model of electroweak baryogenesis is discussed. The analysis for a single light scalar field shows, that given the experimental constraints, there is no value of the Higgs mass for which a sufficiently first-order phase transition is obtained. A precise determination of the 3D parameters of the effective theory for the case of a light right-handed stop allows us to obtain an upper bound on the masses of the lightest Higgs and right-handed stop using the two-loop effective potential. A two-stage phase transition persists for a small range of values of $m_{\tilde{t}_{R}}$.