A Model of Neutrino Mass Matrix With $δ= -π/2$ and $θ_{23} = π/4$

Abstract

Experimental data have provided stringent constraints on neutrino mixing parameters. In the standard parameterization the mixing angle $θ_{23}$ is close to $π/4$. There are also evidences show that the CP violating phase is close to $-π/2$. We study neutrino mass matrix reconstructed using this information and find several interesting properties. We show that a theoretical model based on the $A_4$ symmetry naturally predicts $δ= -π/2$ and $θ_{23} = π/4$ when the Yukawa couplings and scalar vacuum expectation values are real reaching a $μ-τ$ exchange and CP conjugate symmetry limit. In this case CP violation solely comes from the complex group theoretical Clebsh-Gordan coefficients. The model also predicts $|V_{e2}|=1/\sqrt{3}$ consistent with data. With complex Yukawa couplings the values for $δ$ and $θ_{23}$ can be significantly deviate away from the symmetry values $-π/2$ and $π/4$, respectively. But $|V_{e2}|= 1/\sqrt{3}$ is not altered. This matrix is an excellent lowest order approximation for theoretical model buildings of neutrino mass matrix.