Supersymmetry without a light Higgs boson

In this thesis I shall discuss a class of supersymmetric models characterized by a Higgs sector with a strongish self-coupling and a relatively heavy spectrum, with the mass of the lightest CP-even Higgs boson around 200-300 GeV. The effective field theory for these models is SUSY [1] that is to say the Next-To-Minimal Supersymmetric Standard Model with large coupling SH1H2 in the superpotential. I shall discuss in detail a model with scale-invariant superpotential, with particular focus on the dynamical origin of the term and its relation with the mass of the Higgs boson. I shall discuss the fine tuning of the model and various experimental constraints from LEP direct searches, precision data and direct DM searches. I shall argue that the model naturally accommodates the current limits and I shall discuss the main features of the signatures at the LHC. The material of this thesis comes mostly from two papers [2, 3]. Furthermore, during my PhD years in Pisa I have worked on other problems in collider phenomenology [4] and astro-particle physics [5]. As they do not have direct connection with supersymmetry and the Higgs boson they are not discussed in this thesis.