Clockwork Mechanism for Flavour Hierarchies

TL;DR

This paper introduces a clockwork mechanism into the Standard Model to naturally generate fermion mass hierarchies and mixing patterns without fine-tuning, using vectorlike fermions as gears.

Contribution

It demonstrates how the clockwork mechanism can reproduce observed flavor hierarchies and relates it to a generalized Froggatt-Nielsen framework.

Findings

Fermion mass hierarchies are controlled by the number of clockwork gears.

The mechanism can produce both strong and mild hierarchies.

It provides a natural explanation for flavor structure without small parameters.

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.