  The predictions for the mass of the light CP-even Higgs are investigated in
the context of a simple extension of the Minimal Supersymmetric Standard Model
where the baryon and lepton numbers are local gauge symmetries. This theory
predicts the existence of light charged and neutral leptons which give extra
contributions to the Higgs mass at the one-loop level. We show the possibility
to satisfy the LEP2 bound and achieve a Higgs mass around 125 GeV in a
supersymmetric spectrum with light sfermions and small left-right mixing in the
stop sector. We make a brief discussion of the unique leptonic signals at the
Large Hadron Collider. This theory predicts baryon number violation at the low
scale and one could avoid the current LHC bounds on the supersymmetric mass
spectrum.
