Lepton Flavor Model from Delta(54) Symmetry

Abstract

We present the lepton flavor model with $\Delta (54)$, which appears typically in heterotic string models on the $T^2/Z_3$ orbifold. Our model reproduces the tri-bimaximal mixing in the parameter region around degenerate neutrino masses or two massless neutrinos. We predict the deviation from the tri-bimaximal mixing by putting the experimental data of neutrino masses in the normal hierarchy of neutrino masses. The upper bound of ${\sin }^2{\theta }_{13}$ is 0.01. There is the strong correlation between ${\theta }_{23}$ and ${\theta }_{13}$. Unless ${\theta }_{23}$ is deviated from the maximal mixing considerably, ${\theta }_{13}$ remains to be tiny.

Comments: 19 pages, 7 figures; some discussions are modified