Two-Higgs-Doublet Models with a Flavored $\mathbb{Z}_2$

TL;DR

This paper introduces a novel class of two-Higgs-doublet models with an enlarged flavor symmetry group, which naturally suppresses flavor-changing neutral currents and predicts specific quark and lepton mixing patterns.

Contribution

It proposes a new flavor symmetry structure in two-Higgs-doublet models that constrains Yukawa interactions without affecting the scalar sector, leading to predictive mixing matrices.

Findings

Flavor-changing neutral currents are absent at tree and one-loop levels.

Predicts a trivial CKM matrix and a maximal atmospheric mixing in the PMNS matrix.

Extensions can reproduce realistic mixing parameters, including cobimaximal mixing.

Abstract

Two Higgs-doublet models usually consider an ad-hoc $\mathbb{Z}_2$ discrete symmetry to avoid flavor changing neutral currents. We consider a new class of two Higgs-doublet models where $\mathbb{Z}_2$ is enlarged to the symmetry group ${\cal{F}}\rtimes \mathbb{Z}_2$, i.e. an inner semi-direct product of a discrete symmetry group ${\cal{F}}$ and $\mathbb{Z}_2$. In such a scenario the symmetry constrains the Yukawa interactions but goes unnoticed by the scalar sector. In the most minimal scenario, $\mathbb{Z}_3 \rtimes \mathbb{Z}_2 = D_3$, flavor changing neutral currents mediated by scalars are absent at tree and one-loop level, while at the same time predictions to quark and lepton mixing are obtained, namely a trivial CKM matrix and a PMNS matrix (upon introduction of three heavy right-handed neutrinos) containing maximal atmospheric mixing. Small extensions allow to fully reproduce mixing parameters, including cobimaximal mixing in the lepton sector (maximal atmospheric mixing and a maximal $CP$ phase).