Nearest-Neighbour Interaction from an Abelian Symmetry and Deviations from Hermiticity

TL;DR

This paper demonstrates how Abelian flavour symmetry, specifically Z_4, can generate Nearest-Neighbour Interaction textures in quark mass matrices within a two Higgs doublet model, aligning with experimental data when allowing for some non-Hermiticity.

Contribution

It introduces a minimal Z_4 symmetry framework to produce NNI textures compatible with quark data, including deviations from Hermiticity.

Findings

NNI textures can be derived from Z_4 symmetry.

Compatibility with experimental quark data requires ~20% Hermiticity deviations.

Two Higgs doublet model supports the proposed symmetry and textures.

Abstract

We show that Nearest-Neighbour Interaction (NNI) textures for the quark mass matrices can be obtained through the introduction of an Abelian flavour symmetry. The minimal realisation requires a Z_4 symmetry in the context of a two Higgs doublet model. It is further shown that the NNI textures can be in agreement with all present experimental data on quark masses and mixings, provided one allows for deviations of Hermiticity in the quark mass matrices at the 20% level.