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Generalized Friedberg-Lee model for CP violation in neutrino physics

We propose a phenomenological model of Dirac neutrino mass operator based on the Fridberg-Lee (FL) neutrino mass model to include CP violation. By considering the most general set of complex coefficients, and imposing the condition that the mass eigenvalues are real, we find a neutrino mass matrix which is non-hermitian, symmetric and magic. In particular, we find that the requirement of obtaining real mass eigenvalues by transferring the residual phases to the mass eigenstates self-consistently, dictates the following relationship between the imaginary part of the mass matrix elements $B$ and the parameters of the FL model: $B=\pm\sqrt{3/4(a-b_{r})^{2}\sin^{2}2θ_{13}\cos^{2}θ_{12}}$. We obtain inverted neutrino mass hierarchy, $m_{3}=0$. Making a correspondence between our model and the experimental data produces stringent conditions on the parameters as follows: $35.06^{\circ}\lesssimθ_{12}\lesssim36.27^{\circ}$, $θ_{23}= 45^{\circ}$, $7.27^{\circ}\lesssimθ_{13}\lesssim11.09^{\circ}$, and $82.03^{\circ}\lesssimδ\lesssim85.37^{\circ}$. We get mildly broken $μ-τ$ symmetry, which reduces the resultant neutrino mixing pattern from tribimaximal (TBM) to trimaximal (TM). The CP violation as measured by the Jarlskog parameter is restricted by $0.027\lesssim J\lesssim0.044$.