Z' from SU(6)$\times$SU(2)_h GUT, Wjj anomaly and Higgs boson mass bound

Abstract

A general electroweak scale $Z^{\prime }$ is applied in a supersymmetric SU(6)$\text{timesSU}(2{)}_h$ grand unification model, to have a ${\mathbb{Z}}_6$ for the hexality. We briefly show that there cannot exist any baryonic U(1)${}_B^{\prime }$ in any subgroup of E${}_6$. Any effect that requires sizable $Z^{\prime }$ couplings to quarks like the reported Wjj anomaly of CDF, if observed, implies a substantial $Z^{\prime }$ 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 $Z^{\prime }$ is strongly constrained by the electroweak ${\rho }_0$ parameter. We conclude that $Z^{\prime }$ mass much above 10 TeV 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 $Z^{\prime }$ is found at several hundred GeV, any grand unification group embedded in E${}_6$ such as SU(6)$\times$SU(2), SO(10), SU(5)$\times$U(1), SU(5), SU(4)$\times$SU(4), and SU(3)${}^3$, needs fine-tuned gauge couplings. We also discuss the U(1)${}^{\prime }$ effect on the tree level mass of the lightest MSSM Higgs boson.

Comments: 1 figure, 6 pages