We address two closely related problems associated with the singlet scalars potential that are often present in supersymmetric U(1) models, especially those which maintain the gauge unification of the MSSM in a simple way. The first is the possibilit
y of an accidental global symmetry which results in a light Goldstone boson. The second is the problem of generating a vacuum expectation value for more than one field without reintroducing the $mu$ problem. We give sufficient conditions for addressing both issues and provide a concrete example to generate them.
Gauge singlet extensions of the Standard Model (SM) scalar sector may help remedy its theoretical and phenomenological shortcomings while solving outstanding problems in cosmology. Depending on the symmetries of the scalar potential, such extensions
may provide a viable candidate for the observed relic density of cold dark matter or a strong first order electroweak phase transition needed for electroweak baryogenesis. Using the simplest extension of the SM scalar sector with one real singlet field, we analyze the generic implications of a singlet-extended scalar sector for Higgs boson phenomenology at the Large Hadron Collider (LHC). We consider two broad scenarios: one in which the neutral SM Higgs and singlet mix and the other in which no mixing occurs and the singlet can be a dark matter particle. For the first scenario, we analyze constraints from electroweak precision observables and their implications for LHC Higgs phenomenology. For models in which the singlet is stable, we determine the conditions under which it can yield the observed relic density, compute the cross sections for direct detection in recoil experiments, and discuss the corresponding signatures at the LHC.
