Phenomenology of the General NMSSM with Gauge Mediated Supersymmetry Breaking

We investigate various classes of Gauge Mediated Supersymmetry Breaking models and show that the Next-to-Minimal Supersymmetric Standard Model can solve the mu-problem in a phenomenologically acceptable way. These models include scenarios with singlet tadpole terms, which are phenomenologically viable, e.g., in the presence of a small Yukawa coupling <~ 10^{-5}. Scenarios with suppressed trilinear A-terms at the messenger scale lead naturally to light CP-odd scalars, which play the r\^ole of pseudo R-axions. A wide range of parameters of such models satisfies LEP constraints, with CP-even Higgs scalars below 114 GeV decaying dominantly into a pair of CP-odd scalars.