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Abstract.A new generation of complete experiments is focused on a high precision extraction of pseudoscalar meson photo-production amplitudes. Here, 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 ChewGoldberger-Low-Nambu (CGLN) amplitudes. We use this numerical tool to clarify apparent sign differences that exist in the literature, in particular with the definitions of six double-polarization observables. We also present analytic expressions that determine the recoil baryon polarization, together with examples of their potential use with quasi-4π 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 γp → K + Λ reaction and examine the impact of recently published polarization measurements. When combining data from different experiments, we utilize the Fierz identities to fit a consistent set of scales. In fitting multipoles, we use a combined Monte Carlo sampling of the amplitude space, with gradient minimization, and find a shallow χ 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, and found that such comparisons provide useful consistency tests which clarify model interpretations. 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. We conclude that, while a mathematical solution to the problem of determining an amplitude free of ambiguities may require 8 observables, as has been pointed out in the literature, experiments with realistically achievable uncertainties will require a significantly larger number.

A proton spin-polarizability characterizing backward Compton scattering has been extracted from a dispersion analysis of data between 33 and 309 MeV. This backward spinpolarizability, δ π =[27.1 ± 2.2(stat+sys) +2.8/-2.4(model)] × 10 -4 fm 4 , differs significantly from theoretical estimates and indicates a new contribution from the non-perturbative spinstructure of the proton. This δ π value removes an apparent inconsistency in the difference of charge polarizabilities extracted from data above π-threshold. Our global result, α β − = [10.11 ±1.74(stat+sys) +1.22/-0.86(model)] × 10 -4 fm 3 , agrees with the previous world average of data below 155 MeV. Our value for α β + =[13.23 ±0.86(stat+sys) +0.20/-0.49 (model)] × 10 -4 fm 3 is consistent with a recent re-evaluation of the Baldin sum rule.

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