Determining pseudoscalar meson photo-production amplitudes from complete experiments

We review the development of the most general analytic form of the cross section, dependent upon the three polarization vectors of the beam, target and recoil baryon, including all single, double and triple-polarization terms involving 16 spin-dependent observables. We examine the different conventions that have been used by different authors, and we present expressions that allow the direct numerical calculation of any pseudoscalar meson photo-production observables with arbitrary spin projections from the Chew-Goldberger-Low-Nambu amplitudes. We use this numerical tool to clarify apparent sign differences that exist in the literature. We also present analytic expressions that determine the recoil baryon polarization, together with examples of their potential use with quasi-4pi detectors to deduce observables. As an illustration of the use of the consistent machinery presented in this review, we carry out a multipole analysis of the gamma p -> K^+ Lambda reaction and examine the impact of recently published polarization measurements. In fitting multipoles, we use a combined Monte Carlo sampling of the amplitude space, with gradient minimization, and find a shallow chi^2 valley pitted with a very large number of local minima. This results in broad bands of multipole solutions that are experimentally indistinguishable. While these bands have been noticeably narrowed by the inclusion of new polarization measurements, many of the multipoles remain very poorly determined, even in sign, despite the inclusion of data on 8 different observables. We have compared multipoles from recent PWA codes with our model-independent solution bands. The potential accuracy of amplitudes that could be extracted from measurements of all 16 polarization observables has been studied with mock data using the statistical variations that are expected from ongoing experiments.