We propose a non-minimal left-right symmetric model with parity symmetry where the fermion mixings arise as a result of imposing an S 3 ⊗ Z 2 flavor symmetry, and an extra Z e 2 symmetry is considered in the lepton sector. Then the neutrino mass matrix possesses approximately the μ-τ symmetry. The breaking of the μ-τ symmetry induces sizable non-zero θ 13 , and the deviation of θ 23 from 45 • is strongly controlled by an free parameter and the neutrino masses. So, an analytic study of the CP parities in the neutrino masses is carried out to constrain the parameter and the lightest neutrino mass that accommodate the mixing angles. The results are: (a) the normal hierarchy is ruled out for any values of the Majorana phases; (b) for the inverted hierarchy the values of the reactor and atmospheric angles are compatible up to 2, 3 σ C.L.; (c) the degenerate ordering is the most favorable such that the reactor and atmospheric angle are compatible with the experimental data for a large set of values of the free parameters. The model predicts defined regions for the effective neutrino mass, the neutrino mass scale and the sum of the neutrino masses for the favored cases. Therefore, this model may be testable by the future experiments.

Neutrino oscillations data indicates that neutrino mixings are consistent with an apparent À exchange symmetry in neutrino mass matrix. We observe that in the minimally extended standard model with the seesaw mechanism, one can impose $ symmetry at the tree level on all Lagrangian terms, but for the mass difference among and leptons. In the absence of any new extra physics, this mass difference becomes the only source for the breaking of such a symmetry, which induces, via quantum corrections, small but predictable values for 13 , and for the deviation of ATM from maximality. In the CP conserving case, the predictions only depend on neutrino mass hierarchy and may provide a unique way to test for new physics with neutrino experiments.

We make a scalar extension of the B-L gauge model where the S 3 non-abelian discrete group drives mainly the Yukawa sector. Motived by the large and small hierarchies among the quark and active neutrino masses, respectively, the quark and lepton families are not treated on the same footing under the assignment of the discrete group. As a consequence, the nearest neighbor interaction (NNI) textures appear in the quark sector, leading to the CKM mixing matrix, whereas in the lepton sector, a soft breaking of the μ ↔ τ symmetry in the effective neutrino mass, which comes from type I seesaw mechanism, provides a non-maximal atmospheric angle and a non-zero reactor angle.