The goal of this research is to explore the extent to which observations of supersymmetric particle production at an electron-photon collider will be able to refine the determination of critical parameters in the Minimal Supersymmetric Model (MSSM). In our thesis, the focus will be on the process e⁻ + γ → ν_e + [special characters omitted] + W⁻ + Z°, where the [special characters omitted] is the invisible lightest neutralino of MSSM. We propose to make detailed measurements of the rates for this final state for different helicity configurations of the collider e⁻ and γ. These rates will depend on the MSSM parameters tan β and μ through the couplings that enter into the various contributing Feynman diagrams. We presume that the masses of the various supersymmetric particles have already been measured using e⁺e⁻ collisions with accuracies obtained from previous studies. Since the mass measurement will then already have determined tan β and μ within certain levels of accuracy, the question we wish to address is whether the additional e⁻ + γ → ν_e + [special characters omitted] + W⁻ + Z° rate measurements can improve the accuracy of these determinations. Developed results show that the accuracy of the tan β and μ determinations will be slightly improved by using just this one process.

The smallness of the improvement, however, is mainly due to the fact that our results show that the level of the Standard Model backgrounds in relation to the above processes is quite severe. Extensive cuts are required in order to obtain a reasonable signal to background ratio. However, this study suggests that, if the many possible processes for supersymmetric particle production in e⁻ + γ collision are all examined at once, significant improvement of the tan β and μ determinations might result. However, because the extraction of the signal process from the backgrounds is such a difficult task even for the one process examined, we have not attempted to verify this as part of the present project.