New solutions in supergravity: A phenomenological study at the LHC

Supersymmetry and supergravity extend the standard model by introducing a new symmetry between fermions and bosons. Experimental data imply that supergravity must be broken. Among several mechanisms of supersymmetry breaking, gravity mediated supersymmetry breaking is central in this thesis. These mechanisms have the main feature to generate the so-called soft SUSY breaking terms. Recently, new solutions have been identified, leading to the usual soft breaking terms together with additional hard breaking terms. These new solutions are characterized by a new singlet chiral superfield with a non-standard behaviour. Along the line of these new solutions, two models with two singlet fields were identified: one leading to hard breaking terms called S2MSSM and one with only soft breaking terms called N2MSSM. In the S2MSSM, we study the effects of the hard breaking terms on the Higgs boson mass through radiative corrections. A comparison between the N2MSSM and the NMSSM through the fine-tuning of the electroweak scale is investigated. We also perform an analysis of a long-lived stop squark signature at the LHC in the MSSM with Gauge Mediated Supersymmetry Breaking.