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

TL;DR

This paper explores the structure and implications of the eclectic flavor group (27) times S_3, analyzing its representations, symmetries, and applications to lepton mass models, successfully fitting experimental data.

Contribution

It systematically studies the eclectic flavor group (27) times S_3, including its representations, symmetries, and application to lepton mass modeling, which is a novel extension of flavor symmetry analysis.

Findings

Determined modular transformation matrices for (27) multiplets.

Constructed invariant Ke4hler potential and superpotential.

Developed a lepton mass model consistent with experimental data.

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.