Z−Z′mass hierarchy in a supersymmetric model with a secludedU(1)′-breaking sector

We consider the $Z^{\prime }/Z$ mass hierarchy in a supersymmetric model in which the ${U\left(1\right)\mathrm{}}^{\prime }$ is broken in a secluded sector coupled to the ordinary sector only by gauge and possibly soft terms. A large mass hierarchy can be achieved while maintaining the normal sparticle spectra if there is a direction in which the tree level potential becomes flat when a particular Yukawa coupling vanishes. We describe the conditions needed for the desired breaking pattern, to avoid unwanted global symmetries, and for an acceptable effective μ parameter. The electroweak breaking is dominated by A terms rather than scalar masses, leading to $\tan \beta \simeq 1.$ The spectrum of the symmetry breaking sector is displayed. There is significant mixing between the MSSM particles and new standard model singlets, for both the Higgs scalars and the neutralinos. A larger Yukawa coupling for the effective μ parameter is allowed than in the NMSSM because of the ${U\left(1\right)\mathrm{}}^{\prime }$ contribution to the running from a high scale. The upper bound on the tree-level mass of the lightest $\mathrm{CP}$ even Higgs doublet mass is about $c\times 174\hspace{0.5em}\mathrm{GeV},$ where c is of order unity, but the actual mass eigenvalues are generally smaller because of singlet mixing.