More missing VEV mechanism in supersymmetric SO(10) model

Abstract

The anomalous gauge U (1) A symmetry can be a very useful ingredient towards building the complete supersymmetric SO (10) theory. We present an example of the SO (10) × U (1) A model which provides “all order” solution to the doublet-triplet splitting problem via the missing VEV mechanism. An interesting feature of the model is that all relevant GUT scales are related to a single dimensional parameter in the Higgs superpotential, which could have a dynamical origin. In this situation the SO (10) symmetry breaks down to the MSSM practically at one step, without intermediate stages. We also present a variant of the model where the colour Higgsino mediated d = 5 operators are naturally suppressed. We also extend the model by implementing U (1) A as a horizontal symmetry for explaining the fermion mass and mixing hierarchy. The obtained pattern of the fermion mass matrices implies a moderate value of tan β (∼ 6–10) and leads to the consistent picture for the low energy observables. It also suggests the neutrino mass and mixing pattern that could naturally explain both the solar and atmospheric neutrino problems, respectively through the ν e - ν μ and ν μ - ν τ oscillations.