  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.
