Perturbative generation of CP violation and solar mass splitting from Fridberg-Lee model on the basic tribimaximal structure

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, the 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 an approximated Fridberg-Lee neutrino mass model. We characterize a perturbation mass matrix which is responsible for a nonzero $\theta_{13}$ along with CP violation, besides the solar neutrino mass splitting has been resulted from it. We consider this model in two stages: In the first stage, we obtain the perturbation mass matrix with real components which breaks softly the $\mu-\tau$ symmetry and this leads to a nonzero value for $\theta_{13}$. In the second stage, we extend the perturbation mass matrix to a complex symmetric matrix which leads to CP violation. Therefore obtain a realistic neutrino mixing matrix with with $\delta\neq0$ and $\theta_{23}=45^\circ$. We obtain in our model that the solar mass splitting term is more imaginary, the ordering of the neutrino masses is normal, however near the end of the allowed range of masses is more degenerate ($97\%$). Using only three sets of the experimental data, we can fix all of the parameters of our model and show that the order of $\theta_{13}$ in our model is consistent with the experimental data. We 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: