Neutral Scalar Higgs Masses and Production Cross Sections in an Extended Supersymmetric Standard Model

Upper bounds on the three neutral scalar Higgs masses are considered in the supersymmetric standard model with a gauge singlet Higgs field. When the lightest Higgs is singlet-dominated the second lightest Higgs is shown to lie near or below the theoretical upper bound on the lightest Higgs mass. We also consider detectability of these Higgs bosons at a future $e^+ e^-$ linear collider with $\sqrt{s}\sim 300 $ GeV and show that at least one of the neutral scalar Higgs has a production cross section larger than 0.04~pb.