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 $H_{2}L{\nu }^c$. 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. For Dirac masses of the neutrinos of order ${10}^{-4}\mathrm{GeV}$, eigenvalues reproducing the correct scale of neutrino masses are obtained.