Bayesian data analysis in baryon spectroscopy

The strong interaction within a nucleon has been the focus of much theoretical and experimental work in nuclear and particle physics. Theorists have been improving lattice QCD calculations and developing quark models that define the inter-quark interactions, and experimentalists have spent years gathering data to support and improve these models. Finding nucleon resonance states provides essential information for the development of these theories and improves our understanding of the excited nucleon spectrum. There are a variety of quark models that have been proposed which each predict a unique resonance spectrum. Currently, these models predict resonances that have not been observed experimentally. It is important to experimentally determine which of these resonances exist. Historically, many of the existing measurements came as a result of nucleon-pion scattering experiments. It has been suggested, however, that some resonances may couple more strongly to other reaction channels, such as the KΛ strangeness reaction channel analysed here. Pseudoscalar meson photoproduction experiments can be used to analyse such a reaction channel. In these experiments, a photon beam is incident on a stationary nucleon target and the reaction products are detected. The polarisation of the recoiling particle can often be determined or measured. In the KΛ channel, the recoiling baryon is a Λ whose polarisation can be obtained without the use of any additional hardware through the self-analysing properties of the hyperon. These experiments can be completely described by four complex amplitudes, which can be accessed experimentally through sixteen polarisation observables. The polarisation observables are bilinear combinations of the amplitudes and as such have nontrivial correlations. They are dependent on the polarisations of the beam, target and recoiling particle. By selecting different polarisations of the beam or target, or by using a combination of polarisations, different observables can be measured. The amplitudes can be obtained once a sufficient selection of observables is determined. Currently, analyses of pseudoscalar meson photoproduction data is done using a binned fitting method. The use of binned fitting inevitably leads to some information from the data being lost. In this thesis, a new analysis method is presented, based on Bayesian statistics. The aim of such an approach is to maximise the information yield from data. An event-by-event likelihood function reduces the information lost through histogram binning. It is shown that the use of a prior distribution in amplitude space can preserve the correlations between observables, also increasing the information yield. It is found that such an analysis programme leads to a significant extraction of information from existing data. It is also found that datasets from different experiments could be concatenated and analysed together using the programme presented in this work, and successfully extract observables. Information on observables to which the experiment is not directly sensitive can be found and visualised graphically. The development of this analysis programme is detailed in this thesis. Previously analysed data from two experiments are analysed using this analysis method, and the results are compared to those obtained in the past. It is shown that this Bayesian approach produces results that are consistent with accepted results and provides information on observables that are not directly measurable by a particular experiment. The data from two experiments is combined and analysed together, and it is shown that the results of the combined analysis are consistent with those obtained through separate analyses.