Constraining the Higgs sector from False Vacua in the Next-to-Minimal   Supersymmetric Standard Model
  We study the mass, the mixing and the coupling with $Z$ boson of the lightest Higgs boson in the next-to-minimal supersymmetric standard model. The vacuum structure of the Higgs potential is analyzed and the new false vacua are discussed. The significant parameter region can be excluded by requiring that the realistic vacuum is deeper than false vacua, which result in constraints on the properties of the lightest Higgs boson. 
Tatsuo Kobayashi, Takashi Shimomura and Tsubasa Takahashi
hep-ph