Z ^′ boson from SU(6)×SU(2) _h grand unified theory, CDF Wjj excess and Higgs boson mass bound

A general electroweak scale Z ^′ is applied in a supersymmetric SU(6)×SU(2) _h grand unification model, to have a Z ₆ for the hexality. We briefly show that there cannot exist any baryonic U(1)B′ in any subgroup of E ₆. Any effect that requires sizable Z ^′ couplings to quarks like the reported Wjj anomaly of CDF, if observed, implies a substantial Z ^′ coupling to leptons or Higgs doublets. The kinetic mixing considered in a supersymmetric model from E ₆ is restricted by the gauge coupling unification and neutrino mixing. The mass of Z ^′ is strongly constrained by the electroweak ρ ₀ parameter. We conclude that a Z ^′ mass much above 10TeV is favored by considering the neutrino mixing and proton decay constraint in supersymmetric models. In this sense, the CDF Wjj anomaly cannot be fitted to any electroweak model descending from E ₆. Furthermore, if Z ^′ is found at several hundred GeV, any grand unification group embedded in E ₆ such as SU(6)×SU(2), SO(10), SU(5)×U(1), SU(5), SU(4)×SU(4), and SU(3)3, needs fine-tuned gauge couplings. We also discuss the U(1) ^′ effect on the tree level mass of the lightest MSSM Higgs boson.