U(1)' Symmetry Breaking in Supersymmetric E6 Models

We study the electroweak and $U(1)^{'}$ symmetry breaking patterns in models with the particle content of supersymmetric $E_{6}$, including standard model singlets $S$ and exotic quarks $D,~\bar{D}$. Motivated by free fermionic string models, we do not require $E_{6}$-type relations between Yukawa couplings. In particular, we assume that baryon and lepton numbers are conserved, so that the exotic quarks can be light. Gauge invariance allows Yukawa interactions between $S$ and Higgs doublets, and between $S$ and the exotic quarks, allowing radiative $U(1)^{'}$ symmetry breaking and the generation of an effective $\mu$ parameter at the electroweak scale. For both the $E_{6}$ $\psi$ and $\eta$ models, universal soft supersymmetry breaking parameters and Yukawa universality at the high (string) scale do not yield acceptable low energy phenomenology. Relaxing universality, we find solutions with phenomenologically acceptable values of $M_{Z^{'}}$ and the $Z-Z^{'}$ mixing angle. In addition, by varying the $U(1)^{'}$ charge assignments due to the mixing of $U(1)_{\chi}$ and $U(1)_{\psi}$ of $E_{6}$, it is possible to have acceptable low energy phenomenology with universal boundary conditions.Comment: 24 pages, 6 figures, 4 tables, LaTex; minor revision of the numerical results, typos corrected, reference adde