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Abstract
The phenomenology of several classes of supersymmetric models are considered, including general weak scale models, supergravity-motivated models, models with a light gravitino, and gauge-mediated models. In supergravity-motivated models, the trilepton signal from chargino-neutralino production at the Tevatron is computed with an estimation of the signal and background after cuts. Several effects related to the branching ratio of $\tilde N\sb2\to\tilde N\sb1\ell\sp+\ell\sp-$ are identified that could suppress the rate to an undetectable level. The two photon signal of the lightest Higgs boson in supersymmetry at LHC is computed, and again several effects that could suppress or enhance the signal are identified. In general weak scale models, an unusual $ee\gamma\gamma+\not E\sb{T}$ event at the Tevatron is considered as a signal of supersymmetry assuming the dominant decay $\tilde N\sb2\to\tilde N\sb1\gamma,$ and the consequences are extensively discussed. In models with a light gravitino, a discussion of the importance of the gravitino interactions when the gravitino is light is given, and the decay widths of the next-to-lightest supersymmetric particle into the gravitino and a particle are computed. If $\tilde N\sb1\to\tilde G\gamma$ is dominant and the decay occurs close the interaction vertex, then an excellent signal of this model is inclusive $\gamma\gamma$ plus missing energy (plus anything else). In gauge-mediated models, the phenomenology is divided into four main categories associated with which sparticles dominantly decay into the gravitino, and the collider signals are discussed. In addition, the three-body decay $\tilde\ell\sb{R}\to\ell\tau\tilde\tau\sb1$ is identified as a generic process that occurs when the $\tilde\tau\sb1$ is the next-to-lightest sparticle and $\tilde N\sb1$ is heavy; the width is calculated, and the decay length is shown to be possibly macroscopic. Finally, connections between the weak scale and much higher scales are considered. The supertrace of the weak scale model is discussed and its renormalization group evolution is calculated, illustrating one quantity that is possibly important for phenomenology. The nearly renormalization group invariant quantity $M/\alpha$ is then considered, and it is shown to be rather robust when extrapolated to much higher scales, although a series of effects can disrupt the evolution. These effects are typically at the few to tens of percent level, but some could give much larger corrections. Simultaneously, the ratio is sensitive to such effects, although disentangling the various contributions is likely to be a formidable task.
