Nearly Tri-bimaximal Neutrino Mixing and CP Violation from mu-tau Symmetry Breaking

Abstract

Assuming the Majorana nature of massive neutrinos, we generalize the Friedberg-Lee neutrino mass model to include CP violation in the neutrino mass matrix $M^{}_ν$. We show that a favorable neutrino mixing pattern (with $θ^{}_{12} \approx 35.3^\circ$, $θ^{}_{23} = 45^\circ$, $θ^{}_{13} \neq 0^\circ$ and $δ= 90^\circ$) can naturally be derived from $M^{}_ν$, if it has an approximate or softly-broken $μ$-$τ$ symmetry. We point out a different way to obtain the nearly tri-bimaximal neutrino mixing with $δ= 0^\circ$ and non-vanishing Majorana phases. The most general case, in which all the free parameters of $M^{}_ν$ are complex and the resultant neutrino mixing matrix contains both Dirac and Majorana phases of CP violation, is also discussed.