  In collaboration with G.D. Moore, the electroweak phase transition in the
minimal supersymmetric standard model is studied using the two-loop effective
potential. We make a comprehensive search of the MSSM parameter space
consistent with electroweak baryogenesis, taking into account various factors:
the latest experimental constraints on the Higgs boson mass and the rho
parameter, the possibility of significant squark and Higgs boson mixing, and
the exact rate of bubble nucleation and sphaleron transitions. Most of the
baryogenesis-allowed regions of parameter space will be probed by LEP 200,
hence the Higgs boson is likely to be discovered soon if the baryon asymmetry
was indeed created during the electroweak phase transition.
