Minimal E_6 Supersymmetric Standard Model

Abstract

We propose a Minimal E_6 Supersymmetric Standard Model (ME${}_6$SSM) which allows Planck scale unification, provides a solution to the $\mu$ problem and predicts a new Z'. Above the conventional GUT scale $M_{GUT}\sim 10^{16}$ GeV the gauge group corresponds to a left-right symmetric Supersymmetric Pati-Salam model, together with an additional $U(1{)}_{\psi }$ gauge group arising from an E_6 gauge group broken near the Planck scale. Below $M_{GUT}$ the ME${}_6$SSM contains three reducible $27$ representations of the Standard Model gauge group together with an additional U(1)_X gauge group, consisting of a novel and non-trivial linear combination of $U(1{)}_{\psi }$ and two Pati-Salam generators, which is broken at the TeV scale by the same singlet which also generates the effective $\mu$ term, resulting in a new low energy Z' gauge boson. We discuss the phenomenology of the new Z' gauge boson in some detail.

Minor corrections,32 pages, 2 figures

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