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 $M_{\nu }^{}$. We show that a favorable neutrino mixing pattern (with ${\theta }_{12}^{}\approx 35.3^{\circ }$, ${\theta }_{23}^{}=45^{\circ }$, ${\theta }_{13}^{}\ne 0^{\circ }$ and $\delta =90^{\circ }$) can naturally be derived from $M_{\nu }^{}$, if it has an approximate or softly-broken $\mu$-$\tau$ symmetry. We point out a different way to obtain the nearly tri-bimaximal neutrino mixing with $\delta =0^{\circ }$ and non-vanishing Majorana phases. The most general case, in which all the free parameters of $M_{\nu }^{}$ are complex and the resultant neutrino mixing matrix contains both Dirac and Majorana phases of CP violation, is also discussed.

Comments: REVTeX 16 pages, 8 PS figures. A numerical error in FIG.1 removed; the parameter space of Majorana phases in Scenario (B) plotted; more discussions added; figures and references updated