We examined the neutrino sector in $E_6\times SU(2{)}_F$ supersymmetric grand unified theory with spontaneous $CP$ violation. At first glance, the discrete symmetry, which is introduced in order to solve the supersymmetric $CP$ problem, constrains the allowed operators too strongly for the neutrino sector to be consistent with the experimental data, i.e., the $\mu$ neutrino becomes massless as commented in the previous paper. We showed that this issue can be solved if some operators are taken into account. And we saw that such operators do not play an important role in studying quark and charged lepton sectors. The predictions on the neutrino masses and mixings are the same as the $E_6$ models, which are consistent with various experiments on the neutrino oscillations.

• Received 5 March 2012

DOI:https://doi.org/10.1103/PhysRevD.85.095015