CKMCPviolation in a minimal SO(10) model for neutrinos and its implications

A minimal supersymmetric SO(10) model with one 10 and one 126 Higgs superfield has recently been shown to predict all neutrino mixings as well as the solar mass difference squared in agreement with observations. Two assumptions critical to the predictivity and success of the model are that (i) the superpotential includes only renormalizable terms, thereby limiting the number of free parameters, and (ii) the triplet term in the type II seesaw formula for neutrino mass dominates, leading to the sum rule $M_{\nu }{=c(M}_d-M_e),$ which is responsible for large mixings. However, the CKM CP phase is constrained to be in the second or third quadrant, requiring a significant non-CKM component to CP violation to explain observations. We reexamine this issue using a type I seesaw formula for neutrino masses and obtain the following results. (i) We show that the above sum rule responsible for large mixing angles can also emerge in type I seesaw models; the detailed predictions are, however, not compatible with present data for any choice of CP phases. (ii) We then show that addition of a nonrenormalizable term restores compatibility with neutrino data and CKM CP violation both in type I and type II cases. We further find (iii) the MSSM parameter $\tan \beta >~30$ in the type I model and (iv) lepton flavor violation and lepton electric dipole moments that are accessible to proposed experiments in both type I and type II models. We also discuss the unification of the gauge couplings in the type I model, which requires an intermediate scale.