Radiatively generated fermion mass hierarchy from flavour non-universal gauge symmetries

TL;DR

This paper proposes a model where third-generation fermions get masses at tree level, while first and second generations acquire masses radiatively through flavor non-universal gauge symmetries, explaining the fermion mass hierarchy.

Contribution

The paper introduces a renormalizable model with two U(1) gauge symmetries that reproduces the Standard Model fermion mass spectrum via radiative corrections and flavor non-universal interactions.

Findings

First and second generation fermion masses are loop suppressed.

Hierarchy between the first two generations arises from gauge boson mass gaps.

Lower bounds on vector boson masses are established.

Abstract

A framework based on a class of abelian gauge symmetries is proposed in which the masses of only the third generation quarks and leptons arise at the tree level. The fermions of the first and second families receive their masses through radiative corrections induced by the new gauge bosons in the loops. It is shown that the class of abelian symmetries which can viably implement this mechanism are flavour non-universal in nature. Taking the all-fermion generalization of the well-known leptonic $L_\mu-L_\tau$ and $L_e - L_\mu$ symmetries, we construct an explicit renormalizable model based on two $U(1)$ which is shown to reproduce the observed fermion mass spectrum of the Standard Model. The first and second generation fermion masses are loop suppressed while the hierarchy between these two generations results from a gap between the masses of two vector bosons of the extended gauge symmetries. Several phenomenological aspects of the flavourful new physics are discussed and lower limits on the masses of the vector bosons are derived.