Neutrino mixing matrix and masses from a generalized Friedberg-Lee model

The overall characteristics of the solar and atmospheric neutrino oscillation are approximately consistent with a tribimaximal form of the mixing matrix $U$ of the lepton sector. Exact tribimaximal mixing leads to $\theta_{13}=0$. However, recent results from Daya Bay and RENO experiments have established a nonzero value for $\theta_{13}$. Keeping the leading behavior of $U$ as tribimaximal, we use a generalized Fridberg-Lee neutrino mass model along with a complementary ansatz to incorporate a nonzero $\theta_{13}$ along with CP violation. We generalize this model in two stages: In the first stage we assume $\mu-\tau$ symmetry and add imaginary components which leads to nonzero phases. In the second stage we add a perturbation with real components which breaks the $\mu-\tau$ symmetry and this leads to a nonzero value for $\theta_{13}$. The combination of these two generalizations leads to CP violation. Using only two of the experimental data, we can fix all of the parameters of our model and predict not only values for the other experimental data, which agree well with the available data, but also the masses of neutrinos and the CP violating phases and parameters. These predictions include the following: $\langle m_{\nu_e} \rangle\approx(0.033-0.037)~eV$, $\langle m_{\nu_\mu} \rangle\approx(0.043-0.048)~ eV$, $\langle m_{\nu_\tau} \rangle\approx(0.046-0.051)~ eV$, and $59.21^{\circ}\lesssim \delta\lesssim 59.34^{\circ}$