Bottom quark and tau lepton masses in a toy ${\rm SU}(6)$

TL;DR

This paper explores a toy SU(6) model with a specific symmetry breaking pattern that naturally generates masses for the bottom quark and tau lepton, aligning with observed Higgs couplings and suggesting a symmetry breaking scale around 10 TeV.

Contribution

It introduces a novel symmetry breaking pattern in an SU(6) model that produces realistic fermion masses and Higgs couplings consistent with LHC observations.

Findings

Top quark mass generated at tree level by a single Higgs doublet.

Bottom quark and tau lepton masses arise from VEV splittings in the Higgs fields.

Predicted symmetry breaking scale is around 10 TeV, compatible with Higgs coupling measurements.

Abstract

We study a toy ${\rm SU}(6)$ model with the symmetry breaking pattern of the extended $331$ symmetry of ${\rm SU}(3)_c \otimes {\rm SU}(3)_W \otimes {\rm U}(1)_X$. A "fermion-Higgs mismatching" symmetry breaking pattern is proposed for more realistic model building. Within such symmetry breaking pattern, only one Higgs doublet develops vacuum expectation value for the spontaneous electroweak symmetry breaking, and gives tree-level top quark mass. A natural VEV splittings in the $331$ breaking Higgs fields gives tree-level masses to both bottom quark and tau lepton. The $125\,{\rm GeV}$ SM-like Higgs boson discovered at the LHC can have Yukawa couplings to bottom quark and tau lepton as in the SM prediction, and this suggests the $331$ symmetry breaking scale to be $\sim {\cal O}(10)\,{\rm TeV}$.