Eclectic flavor group ∆(27) ⋊ S 3 and lepton model building

Abstract We have performed a systematical study of the eclectic flavor group ∆(27) ⋊ S 3 which is the extension of the traditional flavor symmetry ∆(27) by the finite modular symmetry S 3. Consistency between ∆(27) and S 3 requires that the eight nontrivial singlet representations of ∆(27) should be arranged into four reducible doublets. The modular transformation matrices are determined for various ∆(27) multiplets, and the CP-like symmetry compatible with ∆(27) ⋊ S 3 are discussed. We study the general form of the Kähler potential and superpotential invariant under ∆(27) ⋊ S 3, and the corresponding fermion mass matrices are presented. We propose a bottom-up model for lepton masses and mixing based on ∆(27) ⋊ S 3, a numerical analysis is performed and the experimental data can be accommodated.