U(1)' Symmetry Breaking in Supersymmetric E6 Models

Abstract

We study the electroweak and $U(1{)}^{{}^{\prime }}$ 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 $U(1{)}^{{}^{\prime }}$ 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 $M_{Z^{{}^{\prime }}}$ and the $Z-Z^{{}^{\prime }}$ mixing angle. In addition, by varying the $U(1{)}^{{}^{\prime }}$ 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.

24 pages, 6 figures, 4 tables, LaTex; minor revision of the numerical results, typos corrected, reference added

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