Model of the Neutrino Mass Matrix With δ=-π/2 and θ_(23)=π/4

Abstract

Experimental data have provided stringent constraints on the neutrino mixing parameters. In the standard parameterization the mixing angle θ_(23) is close to π/4. There is also evidence which shows that the CP violating phase is close to -π/2. We study the 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/√3, consistent with the data. With complex Yukawa couplings the values for δ and θ_(23) can significantly deviate away from the symmetry values -π/2 and π/4, respectively. But |V_(e2)| = 1/√3 is not altered. This matrix is an excellent lowest order approximation for theoretical model buildings of the neutrino mass matrix.