Generalized Friedberg-Lee model for CP violation in neutrino physics

Abstract

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: $B=\pm \sqrt{3/4(a-b_r{)}^2{\sin }^{2}2{\theta }_{13}{\cos }^2{\theta }_{12}}$. 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: $35.06^{\circ }\lesssim {\theta }_{12}\lesssim 36.27^{\circ }$, ${\theta }_{23}=45^{\circ }$, $7.27^{\circ }\lesssim {\theta }_{13}\lesssim 11.09^{\circ }$, and $82.03^{\circ }\lesssim \delta \lesssim 85.37^{\circ }$. We get mildly broken $\mu -\tau$ 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 $0.027\lesssim J\lesssim 0.044$.

Comments: 8 pages, 3 figures, published in Phys. Rev. D