Charged Fermion Masses and Mixing from a SU(3) Family Symmetry Model

TL;DR

This paper presents a model with an $SU(3)$ family symmetry that explains fermion masses and mixing by combining tree-level mechanisms and loop corrections, predicting new particles around 2 TeV.

Contribution

It introduces a novel $SU(3)$ family symmetry framework with a detailed fit to fermion masses and mixings, including neutrinos, using a combination of Dirac See-saw and radiative corrections.

Findings

Heavy fermions gain mass at tree level via Dirac See-saw.

Light fermions and neutrinos acquire mass through loop corrections.

Predicted new gauge bosons have masses around 2 TeV.

Abstract

Within the framework of a Beyond Standard Model (BSM) with a local $SU(3)$ family symmetry, we report an updated fit of parameters which account for the known spectrum of quarks and charged lepton masses and the quark mixing in a $4\times 4$ non-unitary $V_{CKM}$. In this scenario, ordinary heavy fermions, top and bottom quarks and tau lepton, become massive at tree level from Dirac See-saw mechanisms implemented by the introduction of a new set of $SU(2)_L$ weak singlet vector-like fermions, $U,D,E,N$, with $N$ a sterile neutrino. The $N_{L,R}$ sterile neutrinos allow the implementation of a $8\times 8$ general See-saw Majorana neutrino mass matrix with four massless eigenvalues at tree level. Hence, light fermions, including neutrinos, obtain masses from loop radiative corrections mediated by the massive $SU(3)$ gauge bosons. $SU(3)$ family symmetry is broken spontaneously in two stages, whose hierarchy of scales yield an approximate $SU(2)$ global symmetry associated with the $Z_1, Y_1^\pm$ gauge boson masses of the order of 2 TeV. A global fit of parameters to include neutrino masses and lepton mixing is in progress.