No strong $CP$ violation up to the one-loop level in a two-Higgs-doublet model

TL;DR

This paper proposes a two-Higgs-doublet model with a $Z_3$ symmetry where $CP$ is conserved at the Lagrangian level and only violated by the CKM matrix, with no strong $CP$ violation up to one-loop level.

Contribution

The model introduces a $Z_3$ symmetric two-Higgs-doublet framework with softly broken $CP$, avoiding strong $CP$ violation at tree and one-loop levels, and explores its phenomenological implications.

Findings

Strong $CP$ violation is absent at tree and one-loop levels.

New scalar particles can be lighter than 500 GeV.

Model constraints allow flavor-changing neutral currents.

Abstract

We put forward a two-Higgs-doublet model, furnished with a $Z_3$ symmetry, wherein $CP$ is conserved in the dimension-four terms of the Lagrangian and is softly broken in the scalar potential. The new particles of our model are one neutral scalar $H$, one neutral pseudoscalar $A$, and two charged scalars $H^\pm$. In our model the only locus of $CP$ violation is the CKM matrix. Strong $CP$ violation is absent both at the tree and one-loop levels. We work out the phenomenological constraints on our model, which features flavour-changing neutral Yukawa interactions, showing that the new scalar particles may in some cases be lighter than 500\,GeV.