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 λ, is ruled out by our constraints.

We analyze a scalar potential of the minimal supersymmetric standard model (MSSM) with neutrino mass operators along Unbounded-From-Below (UFB) and Color and/or Charged Breaking (CCB) directions. We show necessary conditions to avoid the potential minima which can be deeper than the realistic vacuum. These conditions would constrain more strongly than conditions in the MSSM without taking into account neutrino mass operators, and can improve the predictive power of supersymmetric models with neutrino mass operators.

The forward-backward asymmetry of b-quark jets on the Z-pole measured at LEP/SLD experiments shows us −2.8-σ deviation from the Standard Model (SM) prediction. We examine a possibility of Kaluza-Klein (KK) gluon to explain the A b F B data in a scenario based on the warped extra dimension model by Randall and Sundrum. In this scenario, the KK gluon strongly couples to b-quark by an appropriate choice of the bulk quark mass terms. We find that the A b F B data could be explained if the KK gluon mass is few hundred GeV. Constraints on our scenario from the hadron collider experiments are discussed.