Jihn E. Kim, Seodong Shin
A general electroweak scale $Z'$ is applied in a supersymmetric
SU(6)$\timesSU(2)_h$ 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 $\rho_0$ parameter. We conclude that $Z'$ 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 $Z'$ 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)$'$ effect
on the tree level mass of the lightest MSSM Higgs boson.
View original:
http://arxiv.org/abs/1104.5500
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