Electroweak Baryogenesis and Higgs and Stop Searches at LEP and the Tevatron ∗

It has been recently shown that the observed baryon number may originate at the electroweak phase transition, provided that the Higgs boson and the lightest stop are sufficiently light. In this work, we perform a detailed analysis , including all dominant two-loop finite temperature corrections to the Higgs effective potential, as well as the non-trivial effects proceeding from the mixing in the stop sector, to define the region of parameter space for which electroweak baryogenesis can happen. The limits on the stop and Higgs masses are obtained by taking into account the experimental bounds on these quantities, as well as those coming from the requirement of avoiding dangerous color breaking minima. We find for the Higgs mass m h < ∼ 105 GeV, while the stop mass may be close to the present experimental bound and must be smaller than, or of order of, the top quark mass. These results provide a very strong motivation for further non-perturbative analysis of the electroweak phase transition, as well as for the search for Higgs and stop particles at the LEP and Tevatron colliders.