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

Abstract We study a toy $$\textrm{SU}(6)$$ SU ( 6 ) model with the symmetry breaking pattern of the extended 331 symmetry of $$\textrm{SU}(3)_c \otimes \textrm{SU}(3)_W \otimes \textrm{U}(1)_X$$ SU ( 3 ) c ⊗ SU ( 3 ) W ⊗ 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 $$125\,\textrm{GeV}$$ 125 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 $$\sim {{{\mathcal {O}}}}(10)\,\textrm{TeV}$$ ∼ O ( 10 ) TeV .