Flavour-alignment in an $S_3$-symmetric Higgs sector and its RG-behaviour

TL;DR

This paper explores an $S_3$-symmetric three Higgs-doublet model that explains quark masses and mixings, addresses flavor-changing neutral currents via soft symmetry breaking, and examines the model's parameter space through flavor observables and RG analysis.

Contribution

It introduces a soft $S_3$-breaking mechanism in a three Higgs-doublet model to control FCNCs and studies the model's parameter space with flavor data and RG evolution.

Findings

Constraints on FCNC-related Yukawa parameters from meson decay data

Identification of parameter regions compatible with flavor observables

RG analysis validates the stability of the model parameters

Abstract

A three Higgs-doublet model admitting an $S_3$-symmetry can predict the observed pattern of the quark masses and their mixings. However the same symmetry also introduces potential flavour-changing neutral currents at the tree level. We assume in this work that the scalar potential contains appropriate \emph{soft} $S_3$-breaking terms in order to keep the choices of the scalar masses flexible. We identify the parameters in the Yukawa Lagrangian in the quark sector responsible for such FCNCs and constrain them using data from some of the flavour physics observables like meson-decays and meson-mixings. We also validate the corresponding model parameter space with renormalisation group (RG) evaluation.