Partial wave analysis of eta meson photoproduction using fixed-t dispersion relations
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Abstract
The photoproduction of eta mesons is a powerful source of information about the excitation spectrum of protons and neutrons. There are several methods to extract partial wave or multipole amplitudes from experimentally measured polarized and unpolarized differential cross sections. In so called isobar models the scattering amplitude is parameterized with two parts: resonances and non-resonant background. Such a model, EtaMAID, has been developed in Mainz 15 years ago when first precision data for unpolarized cross sections and beam asymmetries were measured. In the meantime, a signifcant amount of new data, in particular with polarized beams and targets, are available. Within this thesis, the EtaMaid model was updated and used to fit all available new data.
However, a drawback of all isobar models is the fact that they violate analyticity and crossing
symmetry which are important properties of scattering amplitudes. Therefore, in this thesis
fixed-t dispersion relations were applied as a constraint to the EtaMAID model in order to
obtain solutions which do fulfil analyticity and crossing symmetry. By fitting all modern
experimental data resonance parameters are obtained in an improved and less model dependent
way. Parameters like masses, widths, branching rations, and photocouplings for 14 nucleon
resonances were determined and are compared to results of the pure isobar model and to
existing averages from the PDG.
The thesis is organized as following: After a short introduction, baryon spectroscopy is discussed
in Chapter 2 with special focus to quark models and lattice QCD. In Chapter 3 the
general formalism of eta photoproduction on protons is introduced. In particular, the relations
between observables, invariant amplitudes, CGLN amplitudes and multipoles is described. Finally,
the connection to the contributing resonances is provided. In Chapter 4 the partial wave
content of recently measured polarization observables is studied in terms of a Legendre polynomial
expansion. In Chapter 5 different models, in particular the EtaMAID isobar model,
are discussed. Fixed-t dispersion relations and their application in eta photoproduction are explained in Chapter 6. The results of various fits with different background models are discussed
in Chapter 7. The thesis ends with a summary and conclusions.