Constraints from Unrealistic Vacua in the Next-to-Minimal Supersymmetric   Standard Model
  We study constraints to avoid deep unrealistic minima in the next-to-minimal supersymmetric standard model. We analyze a scalar potential along directions where all of and one of the three Higgs fields develop their vacuum expectation values, and find unrealistic minima deeper than the electroweak symmetry breaking (EWSB) vacuum. These unrealistic minima threaten the realization of the successful EWSB and therefore should be avoided. Necessary conditions to avoid these minima result in constraints of parameters. We show that a wide and significant region of the parameter space, especially large \lambda, is ruled out by our constraints. 
Yoshimi Kanehata, Tatsuo Kobayashi, Yasufumi Konishi, Osamu Seto and   Takashi Shimomura
hep-ph