Neutrino oscillation data versus minimal supersymmetric SO(10) model

Abstract

We reconsider the minimal supersymmetric SO(10) model, where only one {\bf 10} and one $\bar{\bf 126}$ Higgs multiplets have Yukawa couplings with matter multiplets. The model is generalized to include CP-violating phases, and examined how well its predictions can meet the current neutrino oscillation data. Using the electroweak scale data about six quark masses, three angles and one CP-phase in the Cabibbo-Kobayashi-Maskawa matrix and three charged-lepton masses and given $\tan \beta$ (the ratio of vacuum expectation values of a pair of Higgs doublets), we obtain the Pontecorvo-Maki-Nakagawa-Sakata matrix and the ratio, $\Delta m_\odot^2/\Delta m_\oplus^2 $, as functions of only one free parameter in the model. In our analysis, one-loop renormalization group equations for the gauge couplings, the Yukawa couplings and the effective dimension-five operator are used to connect the data between the electroweak scale and the grand unification scale. Fixing the free parameter appropriately, we find, for example, $\sin^2 2 \theta_{12} \sim 0.72$, $\sin^2 2 \theta_{23} \sim 0.90$, $\sin^2 2 \theta_{13} \sim 0.16$ and $\Delta m_\odot^2/\Delta m_\oplus^2 \sim 0.19$ with $\tan \beta = 45$, which are in agreement with the current neutrino oscillation data.