Neutrino mass and mixing models with eclectic flavor symmetry Δ(27) (sic) T'

The Kahler potentials of modular symmetry models receive unsuppressed contributions which may be controlled by a flavor symmetry, where the combination of the two symmetry types is referred to as eclectic flavor symmetry. After briefly reviewing the consistency conditions of eclectic flavor symmetry models, including those with generalised (g)CP, we perform a comprehensive bottom-up study of eclectic flavor symmetry models based on Omega(1) congruent to Delta(27) (sic) T', consisting of the flavor symmetry Delta(27) in a semi-direct product with the modular symmetry T'. The modular transformations of different Delta(27) multiplets are given by solving the consistency condition. The eight nontrivial singlets of Delta(27) are related by T' modular symmetry, and they have to be present or absent simultaneously in any Omega(1) model. The most general forms of the superpotential and Kahler potential invariant under Omega(1) are discussed, and the corresponding fermion mass matrices are presented. Based on the eclectic flavor group Omega(1), two concrete lepton models which can successfully describe the experimental data of lepton masses and mixing parameters are constructed. For the two models without gCP, all six mixing parameters vary in small regions. A nearly maximal atmospheric mixing angle theta(23) and Dirac CP phase delta(CP) are obtained in the first model. After considering the compatible gCP symmetry and the assumption of R tau = 0 in the first model, the mu - tau reflection symmetry is preserved in the charged lepton diagonal basis. As a consequence, the atmospheric mixing angle and Dirac CP phase are predicted to be maximal, and two Majorana CP phases are predicted to be pi.