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

We put forward a two-Higgs-doublet model, furnished with a \(\mathbb {Z}_3\) 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.