The T7 flavor symmetry in 3-3-1 model with neutral leptons

Abstract

We construct a 3-3-1 model based on non-Abelian discrete symmetry $T_7$ responsible for the fermion masses. Neutrinos get masses from only anti-sextets which are in triplets $\underline{3}$ and $\underline{3}^*$ under $T_7$. The flavor mixing patterns and mass splitting are obtained without perturbation. The tribimaximal form obtained with the breaking $T_7 \rightarrow Z_3$ in charged lepton sector and both $T_7 \rightarrow Z_3$ and $Z_3 \rightarrow \{\mathrm{Identity}\}$ must be taken place in neutrino sector but only apart in breakings $Z_3 \rightarrow \{\mathrm{Identity}\}$ (without contribution of $\si'$), and the upper bound on neutrino mass $\sum_{i=1}^3m_i$ at the level is presented. The Dirac CP violation phase $δ$ is predicted to either $\fracπ{2}$ or $\frac{3π}{2}$ which is maximal CP violation. From the Dirac CP violation phase we obtain the relation between Euler's angles which is consistent with the experimental in PDG 2012. On the other hand, the realistic lepton mixing can be obtained if both the direction for breakings $T_7 \rightarrow Z_3$ and $Z_3 \rightarrow \{\mathrm{Identity}\}$ are taken place in neutrino sectors. The CKM matrix is the identity matrix at the tree-level.