The complete experiment problem of pseudoscalar meson photoproduction in a truncated partial wave analysis

Abstract

One of the remaining open challenges in Standard Model phenomenology is the formation of bound states of quarks in the strong coupling regime of Quantum Chromodynamics (QCD). This is true in particular for the excited states of baryons (qqq-states). There is still room for improvement of our understanding, which is seen once predictions from constituent quark models or lattice QCD are confronted with information on baryon resonances extracted from experiment.<br /> From the experimental side, one studies baryon resonances by impinging strong or electromagnetic probes coming from manufacturable beams (pions, photons, electrons, . . .) on target nucleons in order to produce excited states. Then, the decay products are studied in order to infer the resonances. Thus, generally many different reactions are important for baryon spectroscopy.<br /> The main currently accepted method to determine physical properties of resonances (masses, widths, quantum numbers, . . .) from data are so-called energy-dependent (ED) fits. Here, reaction-theoretic models construct the amplitude as a function of energy, and the model-parameters are (loosely speaking) varied in a fit. Then, the resulting amplitude is analytically continued into the complex energy plane to search for the resonance-poles. In almost all ED approaches, many reactions are analyzed at once in so-called coupled-channel fits.<br /> An alternative Ansatz consists of trying to extract maximal information on reaction-amplitudes from the data, without introducing any kind of model-assumptions. For reactions involving particles with spin, e.g. πN → πN , γN → πN , eN → e'πN , . . ., generally n complex spin amplitudes are necessary to model-independently constraint the full reaction T-matrix. Furthermore, the <em>data</em> for such reactions consist of n² measurable so-called polarization observables (or -asymmetries), which in general have to be measured in order to obtain information on amplitude-interferences. Thus, the question for an optimization of the measurement effort arises and one searches for so-called <em>complete experiments</em>. Those are minimal subsets of all measurable polarization observables sufficient in order to maximally constrain the underlying amplitudes. The complete experiment problem is most commonly treated as a purely mathematical problem, i.e. for idealized data with infinite precision.<br /> This thesis treats the problem of complete experiments for the photoproduction of a single pseudoscalar meson φ, with a recoil-baryon B in the final state: γN → φB. In this case, 4 complex amplitudes are accompanied by 16 polarization observables. The observables are again divided into the unpolarized differential cross section σ₀, 3 single-spin asymmetries and 12 double-polarization observables which are again subdivided into the classes of beam-target (BT), beam-recoil (BR) and target-recoil (TR) observables.<br /> In an earlier work, W.-T. Chiang and F. Tabakin deduced completeness-rules according to which 8<em> carefully selected observables</em> are sufficient in order to determine the 4 amplitudes up to one overall phase. However, these rules are again only valid for idealized data. One point which is troubling about the complete experiments according to Chiang and Tabakin is that they enforce the measurement of the double-polarization observables with recoil polarization (BR and TR), a task which is very hard to accomplish experimentally.<br /> The goal of this thesis was therefore to study the analogous problem, however not for extraction of the full spin amplitudes, but for the photoproduction partial waves ('multipoles') in a truncated partial wave analysis (TPWA) up to some maximal angular momentum cutoff l_max. The extraction of partial waves in such analyses proceeds on each energy-bin individually, thus one refers to them as single-energy (SE) fits. The work has been triggered initially by a paper from the author V. F. Grushin, which investigates similar questions for quite low truncation orders (l_max = 1). Here, a promising aspect of Grushin's work was that he has been able to infer (almost) unique multipole-solutions without using any double-polarization observables at all.<br /> The early concept for the thesis consisted of approaching the complete experiment problem for the TPWA from two sides. Those consist of the purely mathematical, or algebraic, side, which should then be complemented by numerical investigations on TPWAs. The present document collects the results of the project.<br /> A review and further development of an earlier work by A. S. Omelaenko, which discussed linear factor decompositions of the polynomial amplitude, partial wave zero's (akin to so-called Barrelet zero's) and discrete ambiguities in TPWAs, is shown. This approach allowed for an identification of candidates for complete sets in a TPWA, although it was not fully clear up to which l_max such candidates hold up.<br /> A welcome by-product of the formalization for the photoproduction TPWA performed in this work was the possibility of doing so-called <em>moment-analyses</em> on the angular distributions of the observables alone. A survey of such analyses for observables in π⁰-photoproduction is presented.<br /> Lastly, the completeness-rules postulated in the algebraic part of the thesis had to be checked using model-independent numerical methods for the extraction of multipoles. Complete sets in TPWAs are thus studied numerically for synthetic idealized model-data, pseudo-data with errors of variable size and then, finally, also for real data. The influence of errors on the precision of extracted multipoles, as well as on the stability of the fits in general, is studied using the bootstrap.