Neutrino masses in the effective rank-5 subgroups ofE6. II. Supersymmetric case

We present a complete analysis of the neutral fermion sector of supersymmetric $E_6$-inspired low-energy models containing an extra $SU(2)$, concentrating on the alternative left-right and inert models. We show that the $R$-parity conserving scenario always exhibits a large Dirac mass for ${\nu }_L$ with maximal mixing with an isosinglet neutrino, and that $R$-parity violating scenarios do not change the picture other than allowing further mixing with another isosinglet. In order to recover standard model phenomenology, additional assumptions in the form of discrete symmetries and/or new interactions are needed. We introduce and investigate the discrete symmetry method and higher-dimensional operators as mechanisms for solving the neutrino mass and mixing problems in these models.