The Electroweak Phase Transition in the Minimal Supersymmetric Standard Model

Using dimensional reduction we construct an effective 3D theory of the Minimal Supersymmetric Standard Model at finite temperature. The final effective theory is obtained after three successive stages of integration out of massive particles. We obtain the full 1-loop relation between the couplings of the reduced theory and the underlying 4D couplings and masses. The procedure is also applied to a general two Higgs doublet model and the Next to Minimal Supersymmetric Standard Model. We analyze the effective 3D theory constructed for the MSSM to determine the regions of parameter space for which electroweak baryogenesis is possible. We find that the inclusion of all supersymmetric scalars has the effect of enhancing the strength of the phase transition. The requirement of a very light stop is not necessary for baryogenesis. The phase transition is sufficiently first order if the lightest Higgs mass, $m_{h} ~< 70$ GeV. We note the existence of potentially interesting regions of parameter space for which existing analysis techniques are inadequate to decide the question.