Eclectic flavor group $\Delta (27)⋊S_3$ and lepton model building

Abstract

We have performed a systematical study of the eclectic flavor group $\Delta (27)⋊S_3$ which is the extension of the traditional flavor symmetry $\Delta (27)$ by the finite modular symmetry $S_3$. Consistency between $\Delta (27)$ and $S_3$ requires that the eight nontrivial singlet representations of $\Delta (27)$ should be arranged into four reducible doublets. The modular transformation matrices are determined for various $\Delta (27)$ multiplets, and the CP-like symmetry compatible with $\Delta (27)⋊S_3$ are discussed. We study the general form of the Kähler potential and superpotential invariant under $\Delta (27)⋊S_3$, and the corresponding fermion mass matrices are presented. We propose a bottom-up model for lepton masses and mixing based on $\Delta (27)⋊S_3$, a numerical analysis is performed and the experimental data can be accommodated.

Comments: 36 pages, 2 figures