  Electroweak baryogenesis in the minimal supersymmetric extension of the
Standard Model may be realized within the light stop scenario, where the
right-handed stop mass remains close to the top-quark mass to allow for a
sufficiently strong first order electroweak phase transition. All other
supersymmetric scalars are much heavier to comply with the present bounds on
the Higgs mass and the electron and neutron electric dipole moments. Heavy
third generation scalars render it necessary to resum large logarithm
contributions to perform a trustable Higgs mass calculation. We have studied
the one--loop RGE improved effective theory below the heavy scalar mass scale
and obtained reliable values of the Higgs mass. Moreover, assuming a common
mass $\tilde m$ for all heavy scalar particles, and values of all gaugino
masses and the Higgsino mass parameter about the weak scale, and imposing gauge
coupling unification, a two-loop calculation yields values of the mass $\tilde
m$ in the interval between three TeV and six hundred TeV. Furthermore for a
stop mass around the top quark mass, this translates into an upper bound on the
Higgs mass of about 150 GeV. The Higgs mass bound becomes even stronger, of
about 129 GeV, for the range of stop and gaugino masses consistent with
electroweak baryogenesis. The collider phenomenology implications of this
scenario are discussed in some detail.
