Precision Measurements in Supersymmetry [Thesis]

Supersymmetry is a promising framework in which to explore extensions of the standard model. To date, most studies of supersymmetry at future colliders have been concerned with particle searches. However, if candidates for supersymmetric particles are found, precision measurements of their properties will then be of paramount importance. The prospects for such measurements and their implications are the subject of this thesis. If charginos are produced at the LEP II collider, they are likely to be one of the few available supersymmetric signals for many years. We consider the possibility of determining fundamental supersymmetry parameters in such a scenario. The study is complicated by the dependence of observables on a large number of these parameters. We propose a straightforward procedure for disentangling these dependences and demonstrate its effectiveness by presenting a number of case studies at representative points in parameter space. For significant regions of parameter space, we find that it is possible to find strong bounds on the mass of the electron sneutrino, to test the assumption of gaugino mass unification, and to examine the viability of the lightest supersymmetric particle as a dark matter candidate. In addition to determining the properties of supersymmetric particles, precision measurements may also be used to establish that newly-discovered particles are, in fact, supersymmetric. Supersymmetry predicts quantitative relations among the couplings and masses of superparticles. We discuss tests of such relations at a future $e^+e^-$ linear collider, using measurements that exploit the availability of polarizable beams. Stringent tests of supersymmetry from chargino production are demonstrated in two representative cases, and sfermion and neutralino processes are also discussed.