Bounds on the Neutrino Mixing Angles and CP Phase for an SO(10) Model with Lopsided Mass Matrices

Abstract

The bounds on the neutrino mixing angles and CP Dirac phase for an SO(10) model with lopsided mass matrices, arising from the presence of ${\bf 16}_H$ and $\bar{\bf 16}_H$ Higgs representations, are studied by variation of the one real and three unknown complex input parameters for the right-handed Majorana neutrino mass matrix. The scatter plots obtained favor nearly maximal atmospheric neutrino mixing, while the reactor neutrino mixing lies in the range $10^{-5} \lsim \sin^2 \theta_{13} \lsim 1 \times 10^{-2}$ with values greater than $10^{-3}$ most densely populated. A rather compelling scenario within the model follows, if we restrict the three unknown complex parameters to their imaginary axes and set two of them equal. We then find the scatter plots are reduced to narrow bands, as the mixing angles and CP phase become highly correlated and predictive. The bounds on the mixing angles and phase then become $0.45 \lsim \sin^2 \theta_{23} \lsim 0.55$, $0.38 \lsim \tan^2 \theta_{12} \lsim 0.50$, $0.002 \lsim \sin^2 \theta_{13} \lsim 0.003$, and $60^\circ \lsim \pm \delta_{CP} \lsim 85^\circ$. Moreover, successful leptogenesis and subsequent baryogenesis are also obtained, with $\eta_B$ increasing from $(2.7 to 6.3) \times 10^{-10}$ as $\sin^2 \theta_{23}$ increases from 0.45 to 0.55.