$T_7$ flavor symmetry scheme for understanding neutrino mass and mixing in 3-3-1 model with neutral leptons

Abstract

We construct a new version for the 3-3-1 model based on $T_7$ flavor symmetry where the left-handed leptons under $T_7$ differ from those of our previous work while the $\mathrm{SU}(3)_C \otimes \mathrm{SU}(3)_L \otimes \mathrm{U}(1)_X$ gauge symmetry is retain. The flavor mixing patterns and mass splitting are obtained without perturbation. The realistic lepton mixing can be obtained if both the direction of breakings $T_7 \rightarrow Z_3$ and $Z_3 \rightarrow \{\mathrm{Identity}\}$ are taken place in neutrino sector. Maximal CP violation is predicted and CKM matrix is the identity matrix at the tree-level.