This thesis describes a set of connected studies regarding the phenomenology of supersymmetric models, based around the Minimal Supersymmetric Standard Model (MSSM) and its extensions.

The prospects of discovering supersymmetry at the Large Hadron Collider are re- analysed, in order to re-express coverage in terms of a fine-tuning parameter and to extend the analysis to scalar masses (m0) above 2 TeV. The discovery reach at high m0 is of interest because this region has been found to have a focus point, leading to relatively low fine-tuning, and because it remains uncertain how much of the region can be ruled out due to lack of radiative electroweak symmetry breaking. The best fine tuning reach is found in a mono-leptonic channel. All points in minimal supergravity (mSUGRA) with m0 < 4000 GeV, with a fine tuning measure up to 210 or 500 are covered by the search, depending upon whether the definition of fine-tuning excludes or includes the contribution from the top Yukawa coupling. Even for arbitrarily high m0 , mSUGRA c11n be discovered through gaugino events, provided the gaugino mass parameter M1; 2 < 460 GeV.

The MSSM can include two soft breaking terms which are often neglected: a non- analytic scalar trilinear coupling and a higgsino bilinear term. This is known as Non- Standard Supersymmetry Breaking (NSSB). A set of high-scale boundary conditions consistent with the reparameterisation invariance which the model possesses is obtained.

The three-family renormalisation group equations for the MSSM with these terms are presented. The ranges of the universal high-scale values of these couplings which lead to an acceptable TeV-scale theory are obtained, as is the supersymmetric particle spectrum at this scale. The effect of the new terms on fine-tuning is presented. SOFTSUSY, an existing program for calculating SUSY particle spectra, has been used, with as few modifications as possible to include NSSB terms.

A computer program for automatically determining the one-loop effective potential and one-loop mass matrices of a general supersymmetric model is described. The development of this software is discussed, and results for a variety of models are presented as evidence of its capabilities. These include studies of explicit CP and R-parity violation in the MSSM, where results are obtained that are both consistent with existing studies where expected, and include fuller analyses than previous work. In the study of CP violation, results for the scalar/pseudoscalar coupling ratio of fermions are consistent with previous studies, but the electric dipole moments are found to get large contributions from the light Higgs boson, which is no longer a CP eigenstate. This effect occurs only when the Higgs mass is in violation of LEP mass bounds.