FCNC-free multi-Higgs-doublet models from broken family symmetries

TL;DR

This paper shows how residual flavour symmetries in multi-Higgs-doublet models can naturally suppress FCNCs without relying on mass hierarchies, linking flavour predictivity with FCNC control.

Contribution

It introduces a symmetry-based mechanism to control FCNCs in MHDM, connecting flavour symmetry breaking to FCNC suppression without mass hierarchy assumptions.

Findings

Residual flavour symmetries can suppress FCNCs in MHDM.

A model-independent framework for fermionic mixing control.

An explicit $A_4$ toy model demonstrating the approach.

Abstract

We demonstrate how residual flavour symmetries, infrared signatures of symmetry breaking in complete models of flavour, can naturally forbid (or limit in a flavour specific way) flavour-changing neutral currents (FCNC) in multi-Higgs-doublet models (MHDM) without using mass hierarchies. We first review how this model-independent mechanism can control the fermionic mixing patterns of the Standard Model, and then implement the symmetries in the Yukawa sector of MHDM, which allows us to intimately connect the predictivity of a given flavour model with its ability to sequester FCNC. Finally, after discussing various subtleties of the approach, we sketch an $A_4$ toy model that realises an explicit example of these simplified constructions.