  The fact that neutrinos are massive suggests that the minimal supersymmetric
standard model (MSSM) might be extended in order to include three gauge-singlet
neutrino superfields with Yukawa couplings of the type $H_2 L \nu^c$. We
propose to use these superfields to solve the $\mu$ problem of the MSSM without
having to introduce an extra singlet superfield as in the case of the
next-to-MSSM (NMSSM). In particular, terms of the type $\nu^c H_1 H_2$ in the
superpotential may carry out this task spontaneously through sneutrino vacuum
expectation values. In addition, terms of the type $(\nu^c)^3$ avoid the
presence of axions and generate effective Majorana masses for neutrinos at the
electroweak scale. On the other hand, these terms break lepton number and
R-parity explicitly implying that the phenomenology of this model is very
different from the one of the MSSM or NMSSM. For example, the usual neutralinos
are now mixed with the neutrinos. For Dirac masses of the latter of order
$10^{-4}$ GeV, eigenvalues reproducing the correct scale of neutrino masses are
obtained.
