TH-PHD-2017-006

One of the main topics of interest in physics is the composition and structure of matter. Especially for hadrons, which are bound states of quarks and gluons such as the proton and neutron, the description is incomplete. Quantumchromodynamics (QCD), the theory of the strong interaction, is in accordance with most of the results from measurements. However QCD as well as derived effective theories or lattice-QCD calculations are unable to fully explain the rich hadron spectrum. The isoscalar part of the hadron spectrum is particularly interesting, because states with a large gluon content are expected in this sector. In order to validate or invalidate theories, the precise measurement of the states is crucial. The mass and width of states can be measured by energy scans. With the method of partial wave analysis one is able to extract additional information such as the spin and parity of the states. In this respect, the BESIII experiment at IHEP in Beijing and the future PANDA experiment at FAIR in Darmstadt, will contribute with valuable information.

A key parameter for such experiments is the luminosity, which is needed for energy scans and the measurement of absolute cross sections. In this thesis the implementation of the versatile LuminosityFit software package is presented. It is responsible for the determination of the luminosity from the reconstructed tracks of the PANDA luminosity detector with high stability and an accuracy of below 0.5 %. Essential for the small systematic uncertainty is the correction of influences from the accelerator beam and the target. In consequence a high accuracy for line shape measurements of resonances is ensured with the highly accurate luminosity determination.

Furthermore this thesis aims towards the extraction of the isoscalar mesons in the reaction J/ψ → π⁰π⁰γ. The presence of many wide and interfering states makes a correct theoretical description difficult. To address this matter the implementation of the helicity formalism for the general partial wave analysis framework ComPWA is presented in this thesis. The goal of ComPWA is to establish the comparability of various theoretical models and formulations. The study of the isoscalar mesons can benefit from the direct comparison of different theories. This implementation of the helicity formalism takes the novel approach by using an expert system. An exhaustive validation of the implementation is performed on the basis of the J/ψ → π⁰π⁰γ reaction. With the availability of the helicity formalism in ComPWA, partial wave analysis can be performed with this first general model, that serves as a reference for comparisons with other implementations.