Two A4 modular symmetries for Tri-Maximal 2 mixing

TL;DR

This paper develops lepton flavor models using two $A_4$ modular symmetries broken to a diagonal subgroup, leading to TM2 mixing with minimal field content and two moduli as stabilizers.

Contribution

It introduces a novel approach with two $A_4$ modular symmetries broken to a diagonal subgroup, achieving TM2 mixing without flavons.

Findings

Successful construction of TM2 mixing models

Minimal field content achieved

Two moduli serve as stabilizers for residual symmetries

Abstract

We construct lepton flavour models based on two $A_4$ modular symmetries. The two $A_4$ are broken by a bi-triplet field to the diagonal $A_4$ subgroup, resulting in an effective modular $A_4$ flavour symmetry with two moduli. We employ these moduli as stabilisers, that preserve distinct residual symmetries, enabling us to obtain Tri-Maximal 2 (TM2) mixing with a minimal field content (without flavons).