The Higgs sector in the Next-to-MSSM
  We study the Higgs sector in the Next-to-Minimal Supersymmetric Standard Model with and without explicit CP violation, focusing on the case of weak scale expectation value of the singlet field. We scan a wide range of the parameter space to find out allowed regions by requiring that the electroweak vacuum be the global minimum of the effective potential and that the neutral Higgs bosons with moderate gauge coupling be heavier than the lower bound on the Higgs boson in the standard model. Among the allowed parameters, some sets admit the situation in which the light Higgs bosons couple with the $Z$ boson too weak to be found in present collider experiments. For such parameter sets, we find an upper bound on the charged Higgs mass which is reachable in LHC. 
Koichi Funakubo and Shuichiro Tao