Exploring the Quark Flavour Puzzle within the 3 Higgs Model

We extend the standard model with two extra Higgs doublets. Making use of a symmetry principle, we present flavour symmetries based on cycle groups $Z_N$ that oblige each Higgs doublet to contribute to the mass of only one generation, thus accommodating the quark mass hierarchy. We systematically search for all charge configurations that naturally lead to the alignment in flavour space of the quark sectors, resulting in a CKM matrix near to the identity, determined by the quark mass hierarchy, and with the correct overall phenomenological features. The minimal realisation is by the group $Z_7$. We show that only a limited number of solutions exist, and that any accidental global symmetry that may occur together with the discrete symmetry is necessarily anomalous. A phenomenological study of each class of solutions concerning predictions to the flavour changing neutral current (FCNC) phenomena is also performed: for some solutions, it is possible to obtain realistic quark masses and mixing, while the flavour violating neutral Higgs are sufficient lighter to be accessible at LHC.