  Electroweak baryogenesis is an attractive scenario for the generation of the
baryon asymmetry of the universe as its realization depends on the presence at
the weak scale of new particles which may be searched for at high energy
colliders. In the MSSM it may only be realized in the presence of light stops,
and with moderate or small mixing between the left- and right-handed
components. Consistency with the observed Higgs mass around 125 GeV demands the
heavier stop mass to be much larger than the weak scale. Moreover the lighter
stop leads to an increase of the gluon-gluon fusion Higgs production cross
section which seems to be in contradiction with indications from current LHC
data. We show that this tension may be considerably relaxed in the presence of
a light neutralino with a mass lower than about 60 GeV, satisfying all present
experimental constraints. In such a case the Higgs may have a significant
invisible decay width and the stop decays through a three or four body decay
channel, including a bottom quark and the lightest neutralino in the final
state. All these properties make this scenario testable at a high luminosity
LHC.
