  The generation of the observed baryon asymmetry may have taken place during
the electroweak phase transition, thus involving physics testable at LHC, a
scenario dubbed electroweak baryogenesis. In this paper we point out that the
magnetic field which is produced in the bubbles of a first order phase
transition endangers the baryon asymmetry produced in the bubble walls. The
reason being that the produced magnetic field couples to the sphaleron magnetic
moment and lowers the sphaleron energy; this strengthens the sphaleron
transitions inside the bubbles and triggers a more effective wash out of the
baryon asymmetry. We apply this scenario to the Minimal Supersymmetric
extension of the Standard Model (MSSM) where, in the absence of a magnetic
field, successful electroweak baryogenesis requires the lightest CP-even Higgs
and the right-handed stop masses to be lighter than about 127 GeV and 120 GeV,
respectively. We show that even for moderate values of the magnetic field, the
Higgs mass required to preserve the baryon asymmetry is below the present
experimental bound. As a consequence electroweak baryogenesis within the MSSM
should be confronted on the one hand to future measurements at the LHC on the
Higgs and the right-handed stop masses, and on the other hand to more precise
calculations of the magnetic field produced at the electroweak phase
transition.
