Neutrino Masses and Mixing Angles in a Supersymmetric SU(4)$\otimes$SU(2)$_L\otimes$SU(2)$_R$ Model

Abstract

We consider the problem of neutrino masses and mixing angles in a supersymmetric model based on the gauge group SU(4)$\otimes$SU(2)$_L\otimes$SU(2)$_R$ broken at the scale $M_X\approx 10^{16}$ GeV. We extend a previous operator analysis of the charged lepton and quark masses and mixing angles in this model to include the neutrino sector, assuming a universal Majorana mass $M$ for the right-handed neutrinos. The Dirac part of the neutrino matrix is then fixed and the physical neutrino masses and magnitudes of all of the elements of the leptonic mixing matrix are then predicted in terms of the single additional parameter $M$. The successful ansatze predict a tau neutrino mass in the relevant range for the dark matter problem and structure formation, muon and electron neutrinos consistent with the MSW solution to the solar neutrino problem, and tau-muon neutrino mixing at a level which should soon be observed by the CHORUS and NOMAD experiments.