Two-Higgs-doublet models with a flavored Z2 symmetry

Two-Higgs-doublet models usually consider an ad-hoc Z2 discrete symmetry to avoid flavor changing neutral currents. We consider a new class of two-Higgs-doublet models where Z2 is enlarged to the symmetry group F⋊Z2, i.e., an inner semidirect product of a discrete symmetry group F and Z2. In such a scenario, the symmetry constrains the Yukawa interactions but goes unnoticed by the scalar sector. In the most minimal scenario, Z3⋊Z2=D3, 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 Cabibbo-Kobayashi-Maskawa matrix and a Pontecorvo-Maki-Nakagawa-Sakata matr…