Higgs bosons in the NMSSM with exact and slightly broken PQ-symmetry

We explore the Higgs sector of the NMSSM in the limit when the Peccei--Quinn symmetry is exact or only slightly broken. In this case the Higgs spectrum has a hierarchical structure which is caused by the stability of the physical vacuum. We find a strong correlation between the parameters of the NMSSM if $\kappa=0$ or $\kappa\lesssim \lambda^2$. It allows one to distinguish the NMSSM with exact or softly broken PQ-symmetry from the MSSM even when extra scalar and pseudoscalar Higgs states escape direct detection.