Clockwork Mechanism for Flavour Hierarchies

Abstract

We incorporate clockwork mechanism into the Standard Model flavour sector and show that the observed pattern of fermion masses and mixing can be obtained without any unnaturally small or large parameter in the fundamental theory. By introducing $N_f$ pairs of vectorlike fermions, as clockwork gears, for each generation of the Standard Model fermions and setting up a characteristic clockwork potential, it is shown that the inter-generational mass hierarchies are determined by $N_f$. For a given type of fermions, strong or mild hierarchy in the masses and mixing parameters can be obtained by taking the large or small value of $N_f$. The mechanism is shown to lead to a generalized version of the Froggatt-Nielsen mechanism as an effective description.