Abstract
We study constraints to avoid deep unrealistic minima in the next-to-minimal supersymmetric standard model. We analyze the 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 successful EWSB and therefore should be avoided. Necessary conditions for avoiding these minima result in constraints on parameters. We show that a wide and significant region of the parameter space, especially a large λ, is ruled out by our constraints.
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