SO(10) Symmetry Breaking and Type II Seesaw

Abstract

A minimal SO(10) model with {\bf 126} Higgs field breaking B-L symmetry has been shown recently to predict large solar and atmospheric mixings in agreement with observations if it is assumed that the neutrino mass follows from the triplet dominated type II seesaw formula. No additional symmetries need to be assumed for this purpose. We discuss the conditions on the way SO(10) symmetry breaks down to MSSM and the Higgs multiplets in the model, required for the triplet dominated type II seesaw formula to hold. We find that (i) SO(10) must break to a nonminimal SU(5) before breaking to the standard model; (ii) $B-L$ symmetry must break at the time of SO(10) breaking and (iii) constraints of unification seem to require that the minimal model must have a {\bf 54} dimensional Higgs field together with a {\bf 210} and {\bf 126} to break the GUT symmetry.