Three generations of Higgses and the cyclic groups

TL;DR

This paper explores multi-Higgs doublet models with cyclic flavor symmetries, identifying the minimal cyclic group order needed for specific quark mass textures and analyzing the Higgs spectrum and flavor constraints.

Contribution

It demonstrates that for renormalizable flavor models with cyclic symmetry, the smallest N for NNI textures with one Higgs per generation is N=5, and provides Higgs spectrum and flavor analysis for Z_5.

Findings

Minimal cyclic group order N=5 for NNI textures with one Higgs per generation.

Higgs spectrum analysis within the Z_5 model.

Consistency with K - anti-K mixing constraints.

Abstract

Multi Higgs doublet models are interesting extensions of the Standard Model that can be related to flavor. The reason is that most flavor models usually involve the presence of several additional scalar fields. In this work we present an analysis that shows that for renormalizable flavor models based on the cyclic group of order $N$, if there is one flavored SU(2) double Higgs per generation, the smallest $N$ that can be used to reproduce the Nearest-Neighbor-Interaction texture for the quark mass matrices is N=5. Results for the Higgs spectrum and consistency under $K - \bar{K}$ mixing in a specific model with $Z_5$ are also presented.