Theory and Phenomenology of an Exceptional Supersymmetric Standard Model

We make a comprehensive study of the theory and phenomenology of a low energy supersymmetric standard model originating from a string-inspired $E_6$ grand unified gauge group. The Exceptional Supersymmetric Standard Model (ESSM) considered here is based on the low energy SM gauge group together with an extra $Z'$ corresponding to an extra $U(1)_{N}$ gauge symmetry under which right--handed neutrinos have zero charge. The low energy matter content of the ESSM corresponds to three 27 representations of the $E_6$ symmetry group, to ensure anomaly cancellation, plus an additional pair of Higgs--like doublets as required for high energy gauge coupling unification. The ESSM is therefore a low energy alternative to the MSSM or NMSSM. The ESSM involves extra matter beyond the MSSM contained in three $5+5^*$ representations of SU(5), plus three SU(5) singlets which carry $U(1)_{N}$ charges, one of which develops a VEV, providing the effective $\mu$ term for the Higgs doublets, as well as the necessary exotic fermion masses. We explore the RG flow of the ESSM and examine theoretical restrictions on the values of new Yukawa couplings caused by the validity of perturbation theory up to the Grand Unification scale. We then discuss electroweak symmetry breaking and Higgs phenomenology, and establish an upper limit on the mass of the lightest Higgs particle which can be significantly heavier than in the MSSM and NMSSM, in leading two--loop approximation. We also discuss the phenomenology of the $Z'$ and the extra matter, whose discovery will provide a smoking gun signal of the model.