Gauged $SU(3)_F$ and loop induced quark and lepton masses

TL;DR

This paper proposes a model with a gauged $SU(3)_F$ flavor symmetry that generates quark and lepton masses through radiative corrections, explaining mass hierarchies and mixing while predicting large flavor violations and heavy gauge bosons.

Contribution

It introduces a novel $SU(3)_F$ flavor symmetry model that naturally produces fermion mass hierarchies and mixing angles via quantum corrections, with explicit viability analysis.

Findings

Reproduces realistic charged fermion masses and quark mixing parameters.

Predicts a strange quark mass of approximately 16 MeV at $M_Z$, close to experimental values.

Indicates new gauge bosons must be heavier than 1000 TeV due to flavor violation constraints.

Abstract

We investigate a local $SU(3)_F$ flavour symmetry for its viability in generating the masses for the quarks and charged leptons of the first two families through radiative corrections. Only the third-generation fermions get tree-level masses due to specific choice of the field content and their gauge charges. Unprotected by symmetry, the remaining fermions acquire non-vanishing masses through the quantum corrections induced by the gauge bosons of broken $SU(3)_F$. We show that inter-generational hierarchy between the masses of the first two families arises if the flavour symmetry is broken with an intermediate $SU(2)$ leading to a specific ordering in the masses of the gauge bosons. Based on this scheme, we construct an explicit and predictive model and show its viability in reproducing the realistic charged fermion masses and quark mixing parameters in terms of not-so-hierarchical fundamental couplings. The model leads to the strange quark mass, $m_s \approx 16$ MeV at $M_Z$, which is $\sim 2.4 \sigma$ away from its current central value. Large flavour violations are a generic prediction of the scheme which pushes the masses of the new gauge bosons to $10^3$ TeV or higher.