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

Cai-Chang Li; Gui-Jun Ding

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arXiv · 2308.16901

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

Cai-Chang Li·Gui-Jun Ding

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Abstract

We have performed a systematical study of the eclectic flavor group $\Delta(27)\rtimes S_3$ 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 $\Delta(27)\rtimes S_3$ are discussed. We study the general form of the K\"ahler potential and superpotential invariant under $\Delta(27)\rtimes S_3$, and the corresponding fermion mass matrices are presented. We propose a bottom-up model for lepton masses and mixing based on $\Delta(27)\rtimes S_{3}$, a numerical analysis is performed and the experimental data can be accommodated.

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Cai-Chang Li, Gui-Jun Ding. 2023-08-31. Eclectic flavor group $\Delta(27)\rtimes S_3$ and lepton model building. https://arxiv.org/abs/2308.16901

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