$Z^{\prime }$ bosons in supersymmetric $E_6$ models confront electroweak data

Abstract

We study constraints on additional $Z^{\prime }$ bosons predicted in the supersymmetric (SUSY) $E_6$ models by using the updated results of electroweak experiments -- $Z$-pole experiments, $m_W$ measurements and low-energy neutral current (LENC) experiments. We find that the effects of $Z$-$Z^{\prime }$ mixing are parametrized by (i) a tree-level contribution to the $T$-parameter, (ii) the effective $Z$-$Z^{\prime }$ mass mixing angle $\text{xibar}$. In addition, the effect of the direct exchange of the heavier mass eigenstate $Z_2$ in the LENC processes is parametrized by (iii) a contact term $\text{contact}$. We give the theoretical predictions for the observables in the electroweak experiments together with the standard model radiative corrections. Constraints on $T_{\mathrm{new}}$ and $\text{xibar}$ from the $Z$-pole and $m_W$ experiments and those on $\text{contact}$ from the LENC experiments are separately shown. Impacts of the kinetic mixing between the ${\mathrm{U}(1)}_Y$ and $\mathrm{U}(1{)}^{\prime }$ gauge bosons on the ${\chi }^2$-analysis are studied. We show the 95% CL lower mass limit of $Z_2$ as a function of the effective $Z$-$Z^{\prime }$ mixing parameter $\zeta$, a combination of the mass and kinetic mixings. Theoretical prediction on $\zeta$ and $g_E$ is found for the $\chi ,\psi ,\eta$ and $\nu$ models by assuming the minimal particle content of the SUSY $E_6$ models. In a certain region of the parameter space, the $Z_2$ boson mass in the detectable range of LHC is still allowed.

Comments: LaTeX, 36pages, 4 figures. One referece added. Final version to appear in Nucl. Phys. B