Proposal for a supersymmetric standard model.

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 H2Lnuc. 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 nuc H1H2 in the superpotential may carry out this task spontaneously through neutrino vacuum expectation values. In addition, terms of the type (nuc)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. For Dirac masses of the neutrinos of order 10(-4) GeV, eigenvalues reproducing the correct scale of neutrino masses are obtained.