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There are nowadays strong experimental constraints on supersymmetric theoriesfrom the Higgs measurements as well as from the null results in Sparticlesearches. However, even the parameter spaces which are in agreement withexperimental data can be further constrained by using theoreticalconsiderations. Here, we discuss for the MSSM and NMSSM the impact ofperturbative unitarity as well as of the stability of the one-loop effectivepotential. We find in the case of the MSSM, that vacuum stability is always thestronger constraint. On the other side, the situation is more diverse in theNMSSM and one should always check both kind of constraints.

Theoretical Constraints on Supersymmetric Models: Perturbative Unitarity vs. Vacuum Stability