Neutrino mixing matrix and masses from a particular two-zero texture based on A 4 symmetry

Abstract

Abstract The current study aims to investigate the particular case of two zeros in a Majorana neutrino mass matrix based on A 4 symmetry, where charged lepton mass matrix is diagonal. The texture is M ν S 7 with (μ, μ) and (τ, τ) vanishing element of the neutrino mass matrix. The texture M ν S 7 has magic and μ − τ symmetry, with a tribimaximal form of the mixing matrix, which leads to θ 13 = 0 that it is not consistent with experimental data and at first, does not seem to be allowed. Since θ 13 a small mixing angle compared to others neutrino mixing angles justifies the use of perturbation theory. We propose that, θ 13, and the Dirac phase δ, and two Majorana phases ρ and σ could be generated by using a complex symmetric perturbation mass matrix in the mass basis and find that δ m 2 ≡ m 2 2 − m 1 2 ≠ 0 affect to the atmospheric mixing angle. We show that only the predictions of the case I, with Δ < 0 and Re ( α ) < 0 , are consistent with the experimental data. Furthermore, the allowed range of our parameter space and complex elements of perturbation mass matrix are found, which led to finding the allowed region of the neutrino masses, the Majorana phases, the effective neutrino mass for the neutrinoless double beta decay, the allowed deviation of θ 23 from 45°, and to predict the normal neutrino mass hierarchy. The predicted region of 〈 m ν β β 〉 and θ 23 are in line with the current experimental data which indicate the accuracy of our model and its results. The results of the case II, with Δ > 0 and Re ( α ) > 0 , are ruled out.