Higgs bosons in a nonminimal supersymmetric model

The minimal supersymmetric standard model contains two Higgs doublets which must mix via a mass parameter whose magnitude remains to be explained. We explore an extension of the minimal model to include a singlet Higgs field whose vacuum expectation value determines the mixing. We study the spectrum and couplings of Higgs bosons in this extended model and compare them with those in the minimal model. We examine a number of limiting cases analytically and also make numerical studies of the extended model both with and without constraints from the renormalization-group analysis of a parent superstring-inspired grand-unified-theory model. We establish the conditions for there to be a charged Higgs boson lighter than the $W^{\pm }$ and the circumstances under which there is no light neutral Higgs boson. With a particularly simple set of boundary conditions at the unification scale, the renormalization-group equations imply that one or more Higgs bosons are light enough to be found at the CERN LEP or SLAC Linear Collider and that many supersymmetric particles should be accessible to these accelerators and the Fermilab Tevatron; relatively few would require the Superconducting Super Collider, Large Hadron Collider, or a TeV-scale $e^{+}$ $e^{\mathrm{-}}$ collider for discovery. Finally, we analyze the possible production mechanisms and phenomenological signatures of the different Higgs bosons at these machines.