CP Violation Studies in Cascade Decay Sequence

This thesis studies CP violation in the decay of the Ξ− hyperon, also known as the cascade baryon, which decays in the sequence Ξ− → Λπ− → pπ−π−. A difference between the angular distribution of this decay sequence and the angular distribution of the charge conjugate decay sequence ͞Ξ+ →͞Λπ+ → ͞pπ+π+, after taking into account the inversion of the momenta due to the parity operation, is indicative of CP violation. The decay sequence is described by three asymmetry parameters: αΞ, αΛ and φΞ, while the charge conjugate decay's sequence is described by: ͞αΞ, ͞αΛ and ͞φΞ. A measure of CP violation is given by the CP violating observables: AΞ, AΛ and ΦΞ. The aim of this thesis is to study how the normalised statistical uncertainties in the asymmetry parameters and in the CP violating observables depend on the magnitude of the polarisation vector (polarisation) of the cascade and the anticascade. This was done by simulating 1.0×107 Ξ− → Λπ− → pπ−π− and ͞Ξ+ →͞Λπ+ → ͞pπ+π+ decays for different values of polarisation of the cascades using Monte Carlo, and then utilising maximum likelihood estimation and error propagation to estimate the uncertainties in the parameters and in the observables. It was shown using the methods of this thesis that the normalised statistical uncertainties in the asymmetry parameters and the CP violating observables decreased whenever the polarisation was increased, although with diminishing returns. In the region of 10% − 50% polarisation, the decrease in the uncertainties was substantial. An increase from 10% to 50% polarisation lowered all of the uncertainties by 76% − 80%. In the region of 50% − 100% polarisation, the decrease in the uncertainties was slightly less. An increase from 50% to 100% polarisation lowered the uncertainties in αΞ, ͞αΞ and AΞ by roughly 33%, in αΛ, ͞αΛ and AΛ by roughly 40%, and in φΞ, ͞φΞ and ΦΞ it went down by 53%. It was also shown that, if one were to produce 60% polarised cascades and use the method of this thesis, it would require a sample of 1.1×1011 − 1.3×1011 Ξ− → Λπ− → pπ−π− and ͞Ξ+ →͞Λπ+ → ͞pπ+π+ decays to reach the precision in the observables of the order given by the Standard Model. However, if one wished to match the uncertainty given by the most recent and best measurement of the observables, using 60% polarised cascades, one would only need a sample of 5.7×104 − 8.6×104 for each decay sequence