Two Higgs doublet models with an $S_3$ symmetry

TL;DR

This paper systematically explores all $S_3$ symmetry implementations in two Higgs doublet models with quarks, analyzing their implications for quark masses, CKM matrix structure, and symmetry breaking patterns.

Contribution

It classifies possible $S_3$ symmetry assignments in two Higgs doublet models and examines their phenomenological consequences, including relations between mixing angles and symmetry breaking.

Findings

Only two consistent $S_3$ assignments are possible: all sectors as singlets or all as doublets.

A relation between $ aneta$ and $ aneta$ is identified in the models.

Certain soft-breaking terms influence the vacuum structure and mixing angles.

Abstract

We study all implementations of the $S_3$ symmetry in the two Higgs doublet model with quarks, consistent with non-zero quark masses and a Cabibbo-Kobayashi-Maskawa (CKM) matrix which is not block diagonal. We study the impact of the various soft-breaking terms and vacuum expectation values, and find an interesting relation between $\alpha$ and $\beta$. We also show that, in this minimal setting, only two types of assignments are possible: either all field sectors are in singlets or all field sectors have a doublet.