A Investigation of Cp-Violation and Chiral Perturbation Theory Using Pion Dispersion Relations.

In this thesis, a new method of enhancing the set of pi-pi scattering data is developed. Each data point is stochastically "shaken", then a smoothed spline is fit to the data set and a dispersion integral over the spline is performed and recorded. This process is repeated many times and the distribution of results produces not only the mean but also the standard deviation of the desired function of the data. This method allows us to calculate accurately pi-pi scattering amplitudes and phase shifts which we use for interpolation in the important region near threshold. Using these amplitudes with known uncertainty, we calculate the phase of the CP violation parameter varepsilon^' and examine two types of Chiral Perturbation Theory. We demonstrate that the recently developed "Improved Chiral Perturbation Theory" exhibits superior consistency with experimental data.