Controlling the flavour changing neutral couplings of multi-Higgs doublets models through unitary matrices

Abstract In this paper, we introduce unitary flavour violation to produce multi-Higgs doublets models where all flavour par ameters are contained within three unitary matrices. After that, we identify two of its subclasses, the left and right models, which have naturally suppressed tree-lev el flavour changing neutral couplings that easily avoid the experimental constraints derived from neutral meson mi xing. Then, we show that left models can accomodate spontaneous CP violation when all quarks have flavour changing neutr al couplings. Finally, we illustrate these concepts by considering a specific implementation with three Higgs doublets.