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Light Higgs Boson in the Spontaneously CP Violating NMSSM

We consider spontaneous CP violation in the Next to Minimal Supersymmetric Standard Model, without the usual $Z_3$ discrete symmetry. CP violation can occur at tree level, raising a potential conflict with the experimental bounds on the electric dipole moments of the electron and neutron. One escape from this is to demand that the CP violating angles are small, but we find that this entails a light neutral Higgs particle. This is almost pseudoscalar, can have a high singlet content, and will be hard to detect experimentally.