Stability constraints in triplet extension of the MSSM

I will discuss the existence of unbounded-from-below (UFB) directions in the scalar potential of a triplet extension of the Minimal Supersymmetric Standard Model and the restrictions on the parameter space of the model by avoiding these directions. The model was introduced mainly to enhance the tree level Higgs boson mass. Two important consequence of lifting the UFB directions are that the lightest Higgs boson decay rate to diphoton  generally features larger deviations from the MSSM and fine-tuning is on an average higher compared to what it would be without imposing stability constraints.