Resolving the constrained minimal and next-to-minimal supersymmetric standard models.

We perform a detailed analysis of the next-to-minimal supersymmetric standard model (NMSSM), imposing the constraints of two-loop gauge coupling unification, universal soft supersymmetry breaking, and the correct pattern of electroweak symmetry breaking. We compare our results with those for the minimal supersymmetric standard model (MSSM) using closely related techniques and, as far as possible, a common set of input and output variables. In general, in the constrained NMSSM, there are much stronger correlations between parameters than in the constrained MSSM, and we map out the allowed parameter space. We also give a detailed discussion of how to resolve the two models experimentally, concentrating primarily on the prospects at CERN LEP II. We find that, for a top quark mass {approx_gt}150 GeV, the constrained NMSSM is only viable in regions where its spectrum is in general very similar to that of the MSSM, although there are exceptions which we explore. For example, in some corners of parameter space the lightest {ital CP}-even Higgs boson in the constrained NMSSM may be detected at LEP II with singlet-diluted couplings which may allow it to be distinguished from that of the MSSM. However, if small universal gaugino mass {ital M}{sub 1/2} is required, thenmore » we expect a standard-model-like Higgs boson which may be detected at LEP II, together with a very characteristic Higgs boson and SUSY spectrum. We also study fine-tuning in the constrained NMSSM, which is typically a more severe constraint than in the MSSM, and give a simple analytical discussion of the potential and spectrum.« less