The complete-experiment problem in the truncated partial-wave analysis (PWA) of pseudoscalar meson photoproduction with suppressed t-channel exchanges is investigated. The focus is set to ambiguities of the group S observables with the unpolarized differential cross section, σ 0 , and the three single-spin observables, , T , and P . For this purpose, the approach and formalism already worked out by Omelaenko [Sov. J. Nucl. Phys. 34, 406 (1981)] is revisited in this work. A numerical study using multipoles of the PWA solution MAID2007 shows how only one additional double polarization observable can resolve all ambiguities. Therefore, the possibility emerges to perform a complete experiment with only five observables.

We compare the methods of amplitude reconstruction, for a complete experiment and a truncated partial wave analysis, applied to the photoproduction of pseudo-scalar mesons. The approach is pedagogical, showing in detail how the amplitude reconstruction (observables measured at a single energy and angle) is related to a truncated partial-wave analysis (observables measured at a single energy and a number of angles).

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The first measurement is reported of the double-polarization observable G in the photoproduction of neutral pions off protons, covering the photon energy range from 620 to 1120 MeV and the full solid angle. G describes the correlation between the photon polarization plane and the scattering plane for protons polarized along the direction of the incoming photon. The observable is highly sensitive to contributions from baryon resonances. The new results are compared to the predictions from SAID, MAID, and BnGa partial wave analyses. In spite of the long-lasting efforts to understand γp→pπ(0) as the simplest photoproduction reaction, surprisingly large differences between the new data and the latest predictions are observed which are traced to different contributions of the N(1535) resonance with spin parity J(P)=1/2(-) and N(1520) with J(P)=3/2(-). In the third resonance region, where N(1680) with J(P)=5/2(+) production dominates, the new data are reasonably close to the predictions.

New data on pion-photoproduction off the proton have been included in the partial wave analyses Bonn-Gatchina and SAID and in the dynamical coupled-channel approach Jülich-Bonn. All reproduce the recent new data well: the double polarization data for E, G, H, P and T in γp → π 0 p from ELSA, the beam asymmetry Σ for γp → π 0 p and π + n from Jefferson Laboratory, and the precise new differential cross section and beam asymmetry data Σ for γp → π 0 p from MAMI. The new fit results for the multipoles are compared with predictions not taking into account the new data. The mutual agreement is improved considerably but still far from being perfect.