  New models have recently been proposed in which a second Higgs doublet
couples only to the lepton doublets and right-handed neutrinos, yielding Dirac
neutrino masses. The vacuum value of this second "nu-Higgs" doublet is made
very small by means of a very softly-broken $Z_2$ or U(1) symmetry. The latter
is technically natural and avoids fine-tuning and very light scalars. We
consider a supersymmetric version of this model, in which two additional
doublets are added to the MSSM. If kinematically allowed, the decay of the
heavy MSSM scalar into charged nu-Higgs scalars will yield dilepton events
which can be separated from the W-pair background. In addition, the
nu-Higgsinos can lead to very dramatic tetralepton, pentalepton and hexalepton
events which have negligible background and can be detected at the LHC and the
Tevatron.
