Mixing ofνeandνuin SO(10) models

We found previously in SO(10) grand unified theories that if the neutrinos have a Dirac mass and a right-handed Majorana mass (∼${10}^{15}$ GeV) but no left-handed Majorana mass, there is small ${\nu }_e$ mixing but ${\nu }_{\mu }-{\nu }_{\tau }$ mixing can be substantial. We reexamine this problem on the basis of a formalism that assumes that the up, down, lepton, and neutrino mass matrices arise from a single complex 10 and a single 126 Higgs boson. This formalism determines the Majorana mass matrix in terms of quark mass matrices. Adopting three different sets of quark mass matrices that produce acceptable fermion mass ratios and Cabibbo mixing, we obtain results consistent with the above; however, in the optimum case, ${\nu }_e-{\nu }_{\mu }$ mixing can be of the order of the Cabibbo angle. In an extension of this model wherein the Witten mechanism generates the Majorana mass, we illustrate quantitatively how the parameter characterizing the Majorana sector must be tuned in order to achieve large ${\nu }_e-{\nu }_{\mu }$ mixing.