Theoretical constraints on supersymmetric models: Perturbative unitarity vs. vacuum stability

There are nowadays strong experimental constraints on supersymmetric theories from the Higgs measurements as well as from the null results in Sparticle searches. However, even the parameter spaces which are in agreement with experimental data can be further constrained by using theoretical considerations. Here, we discuss for the MSSM and NMSSM the impact of perturbative unitarity as well as of the stability of the one-loop effective potential. We find in the case of the MSSM, that vacuum stability is always the stronger constraint. On the other side, the situation is more diverse in the NMSSM and one should always check both kind of constraints.