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We discuss unitarity constraints on the dynamics of a system of three interacting particles. We show how the short-range interaction that describes three-body resonances can be separated from the long-range exchange processes, in particular the one-pion-exchange process. It is demonstrated that unitarity demands a specific functional form of the amplitude with a clear interpretation: the bare three-particle resonances are dressed by the initial- and final-state interaction, in a way that is consistent with the considered long-range forces. We postulate that the resonance kernel admits a factorization in the energy variables of the initial- and the final-state particles. The factorization assumption leads to an algebraic form for the unitarity equations, which is reminiscent of the well-known two-body-unitarity condition and approaches it in the limit of the narrow-resonance approximation., Comment: 15 pages, 1 figure

A measurement of the double-polarization observable E for the reaction $$\gamma p\rightarrow \pi ^0 p$$ γ p → π 0 p is reported. The data were taken with the CBELSA/TAPS experiment at the ELSA facility in Bonn using the Bonn frozen-spin butanol (C$$_4$$ 4 H$$_9$$ 9 OH) target, which provided longitudinally-polarized protons. Circularly-polarized photons were produced via bremsstrahlung of longitudinally-polarized electrons. The data cover the photon energy range from $$E_\gamma =600$$ E γ = 600 to 2310 MeV and nearly the complete angular range. The results are compared to and have been included in recent partial wave analyses.

This paper combines the graph-theoretical ideas behind Moravcsik's theorem with a completely analytic derivation of discrete phase-ambiguities, recently published by Nakayama. The result is a new graphical procedure for the derivation of certain types of complete sets of observables for an amplitude-extraction problem with $N$ helicity-amplitudes. The procedure is applied to pseudoscalar meson photoproduction ($N = 4$ amplitudes) and electroproduction ($N = 6$ amplitudes), yielding complete sets with minimal length of $2N$ observables. For the case of electroproduction, this is the first time an extensive list of minimal complete sets is published. Furthermore, the generalization of the proposed procedure to processes with a larger number of amplitudes, i.e. $N > 6$ amplitudes, is sketched. The generalized procedure is outlined for the next more complicated example of two-meson photoproduction ($N = 8$ amplitudes)., 31 pages, 14 figures, 4 tables; Version 4 has been accepted for publication in Phys. Rev. C

Amplitude- and truncated partial-wave analyses are combined into a single-channel method for extracting multipoles directly from measured data. In practice, we have created a two-step procedure which is fit to the same database: in the first step we perform an energy-independent amplitude analysis where continuity is achieved by constraining the amplitude phase, and the result of this first step is then taken as a constraint for the second step where a constrained, energy-independent, truncated partial-wave analysis is done. The method is tested on the world collection of data for $\ensuremath{\eta}$ photoproduction, and the obtained fit results are very good. The sensitivity to different possible choices of amplitude phase is investigated and it is demonstrated that the present database is insensitive to notable phase changes due to an incomplete database. New measurements are recommended to remedy the problem.

Data on the beam asymmetry Σ in the photoproduction of η mesons off protons are reported for tagged photon energies from 1130 to 1790 MeV (mass range from W=1748 MeV to W=2045 MeV). The data cover the full solid angle that allows for a precise moment analysis. For the first time, a strong cusp effect in a polarization observable has been observed that is an effect of a branch-point singularity at the pη^{'} threshold [E_{γ}=1447 MeV (W=1896 MeV)]. The latest BnGa partial wave analysis includes the new beam asymmetry data and yields a strong indication for the N(1895)1/2^{-} nucleon resonance, demonstrating the importance of including all singularities for a correct determination of partial waves and resonance parameters.

We revisit Moravcsik's theorem on the unique extraction of amplitudes from polarization observables, which has been originally published in 1985. The proof is (re-) written in a more formal and detailed way and the theorem is corrected for the special case of an odd number of amplitudes (this case was treated incorrectly in the original publication). Moravcsik's theorem, in the modified form, can be applied in principle to the extraction of an arbitrary number of $N$ helicity amplitudes. The uniqueness theorem is then applied to hadronic reactions involving particles with spin. The most basic example is Pion-Nucleon scattering ($N=2$), the first non-trivial example is pseudoscalar meson photoproduction ($N=4$) and the most technically involved case treated here is given by pseudoscalar meson electroproduction ($N=6$). The application of Moravcsik's theorem to electroproduction yields new results, which for the first time provide insights into the structure and content of complete sets for this particular process. The uniqueness-statements for the various reactions are compared and an attempt is made to recognize general patterns, which emerge under the application of the theorem., 35 pages, 12 figures; Version 2 has been accepted for publication in Phys. Rev. C

Data on the beam asymmetry Σ in the photoproduction of η mesons off protons are reported for tagged photon energies from 1130 to 1790 MeV (mass range from W=1748 MeV to W=2045 MeV). The data cover the full solid angle that allows for a precise moment analysis. For the first time, a strong cusp effect in a polarization observable has been observed that is an effect of a branch-point singularity at the pη^{'} threshold [E_{γ}=1447 MeV (W=1896 MeV)]. The latest BnGa partial wave analysis includes the new beam asymmetry data and yields a strong indication for the N(1895)1/2^{-} nucleon resonance, demonstrating the importance of including all singularities for a correct determination of partial waves and resonance parameters.

For photoproduction reactions with final states consisting of two pseudoscalar mesons and a spin-1/2 baryon, 8 complex amplitudes need to be determined uniquely. A modified version of Moravcsik's theorem is employed for these reactions, resulting in slightly over-complete sets of polarization observables that are able to determine the amplitudes uniquely. Further steps were taken to reduce the found sets to minimal complete sets. As a final result, multiple minimal complete sets without any remaining ambiguities are presented for the first time. These sets consist of $2N=16$ observables, containing only one triple polarization observable., Comment: updated supplementary material

A measurement of the double-polarization observable E for the reaction \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma p\rightarrow \pi ^0 p$$\end{document}γp→π0p is reported. The data were taken with the CBELSA/TAPS experiment at the ELSA facility in Bonn using the Bonn frozen-spin butanol (C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_4$$\end{document}4H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_9$$\end{document}9OH) target, which provided longitudinally-polarized protons. Circularly-polarized photons were produced via bremsstrahlung of longitudinally-polarized electrons. The data cover the photon energy range from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E_\gamma =600$$\end{document}Eγ=600 to 2310 MeV and nearly the complete angular range. The results are compared to and have been included in recent partial wave analyses.

Important insights into the excitation spectra of baryons are provided by measurements of polarization observables in reactions that involve particles with spin. The photoproduction of a single pseudoscalar meson constitutes an example-reaction that has been under intense investigation recently. We present the basic method of moment-analysis for pseudoscalar meson photoproduction, in which just the angular distributions are analyzed. Using this method, the total angular momentum quantum number of the dominant partial waves contributing in the data can be extracted quickly. Furthermore, the Legendre-coeffcients extracted from the angular distributions show interesting composition-patterns in terms of multipoles and allow for instructive comparisons to models. In this contribution, recent results for moment analyses of polarization data for the photoproduction of pions and eta-mesons are shown.

The production of $\eta^{\prime}$ mesons in coincidence with forward-going protons has been studied in photon-induced reactions on 12C and on a liquid hydrogen (LH2) target for incoming photon energies of 1.3-2.6 GeV at the electron accelerator ELSA. The $\eta^{\prime}$ mesons have been identified via the $\eta^{\prime} \rightarrow \pi^{0} \pi^{0}\eta \rightarrow 6 \gamma$ decay registered with the CBELSA/TAPS detector system. Coincident protons have been identified in the MiniTAPS BaF2 array at polar angles of $2^{\circ} \le \theta_{p} \le 11^{\circ}$ . Under these kinematic constraints the $\eta^{\prime}$ mesons are produced with relatively low kinetic energy ( $\approx 150$ MeV) since the coincident protons take over most of the momentum of the incident-photon beam. For the C-target this allows the determination of the real part of the $\eta^{\prime}$ -carbon potential at low meson momenta by comparing with collision model calculations of the $\eta^{\prime}$ kinetic energy distribution and excitation function. Fitting the latter data for $\eta^{\prime}$ mesons going backwards in the center-of-mass system yields a potential depth of $V = -(44 \pm 16(stat) \pm 15(syst))$ MeV, consistent with earlier determinations of the potential depth in inclusive measurements for average $\eta^{\prime}$ momenta of $\approx 1.1$ GeV/c. Within the experimental uncertainties, there is no indication of a momentum dependence of the $\eta^{\prime}$ -carbon potential. The LH2 data, taken as a reference to check the data analysis and the model calculations, provide differential and integral cross sections in good agreement with previous results for $\eta^{\prime}$ photoproduction off the free proton.

Important contributions to the study of the excitation spectra of baryons are provided by measurements of polarization observables in reactions that involve particles with spin. Pseudoscalar meson photoproduction poses an example-reaction that has been under intense investigation recently. The extraction of resonance-parameters from the polarization-data in so-called energy-dependent fits, often involving sophisticated reaction- theories and analyzing several reaction-channels at once, represents the state-of-the-art method to get to the spectrum. While yielding important scientific insights, the construction and handling of such models is very sophisticated. The analysis of partial waves at single energies in so-called energy-independent fits represents a simpler problem. However, due to mathematical ambiguities rising exponentially in number with the amount of non-zero partial waves, such analyses still require some experience. In order to obtain first insights into a newly measured polarization dataset, simpler alternatives are desirable. Here we present the very basic method of moment-analysis for pseudoscalar meson photoproduction, which proceeds by analyzing just the angular distributions. The order of the dominant partial waves contributing in the data can be extracted quickly using this method. Furthermore, the coefficients extracted from the angular distributions show interesting composition-patterns in terms of multipoles and allow for instructive comparisons to models. This work was supported by the Deutsche Forschungsgemeinschaft (SFB/TR16).

Unconstrained partial-wave amplitudes obtained at discrete energies from fits to complete sets of experimental data may not vary smoothly with energy, and are in principle non-unique. We demonstrate how this behavior can be ascribed to the continuum ambiguity. Starting from the spinless scattering case, we demonstrate how an unknown overall phase depending on energy and angle mixes the structures seen in the associated partial-wave amplitudes making the partial wave decomposition non-unique, and illustrate it on a simple toy model. We then apply these principles to pseudo-scalar meson photoproduction and show that the non-uniqueness effect can be removed through a phase rotation, allowing a consistent comparison with model amplitudes. The effect of this phase ambiguity is also considered for Legendre expansions of experimental observables. 5 pages, Comment: 5 pages, 6 figures

Unconstrained partial-wave amplitudes obtained at discrete energies from fits to complete sets of eight independent observables which are required to uniquely reconstruct reaction amplitudes do not vary smoothly with energy, and are in principle non-unique. We demonstrate how this behavior can be ascribed to the continuum ambiguity. Starting from the spinless scattering case, we demonstrate how an unknown overall phase depending on energy and angle mixes the structures seen in the associated partial-wave amplitudes making the partial wave decomposition non-unique, and illustrate it on a simple toy model. We then apply these principles to pseudo-scalar meson photoproduction and show that the non-uniqueness effect can be removed through a phase rotation generating "up-to-a-phase" unique set of SE partial wave amplitudes. Extracting pole positions from partial wave amplitudes is the next step. Up to now, there was no reliable way to extract pole parameters from SE partial waves, but a new and simple single-channel method (Laurent + Pietarinen expansion) applicable for continuous and discrete data has been recently developed. It is based on applying the Laurent decomposition of partial wave amplitude, and expanding the nonresonant background into a power series of a conformal-mapping, quickly converging power series obtaining the simplest analytic function with well-defined partial wave analytic properties which fits the input. The generalization of this method to multi- channel case is also developed and presented. Unifying both methods in succession, one constructs a model independent procedure to extract pole parameters directly from experimental data without referring to any theoretical model., This article belongs to the Topical Collection "NSTAR2017 - The International Workshop on the Physics of Excited Nucleons". arXiv admin note: substantial text overlap with arXiv:1706.03211

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).

We compare the methods of amplitude reconstruction, for a complete experiment and a truncated partial-wave analysis, applied to the electroproduction of pseudoscalar mesons. We give examples which show, 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). A connection is made to existing data., Comment: 17 pages, 2 figures

This work presents a simple method to determine the significant partial wave contributions to experimentally determined observables in pseudoscalar meson photoproduction. First, fits to angular distributions are presented and the maximum orbital angular momentum $\text{L}_{\mathrm{max}}$ needed to achieve a good fit is determined. Then, recent polarization measurements for $\gamma p \rightarrow \pi^{0} p$ from ELSA, GRAAL, JLab and MAMI are investigated according to the proposed method. This method allows us to project high-spin partial wave contributions to any observable as long as the measurement has the necessary statistical accuracy. We show, that high precision and large angular coverage in the polarization data are needed in order to be sensitive to high-spin resonance-states and thereby also for the finding of small resonance contributions. This task can be achieved via interference of these resonances with the well-known states. For the channel $\gamma p \rightarrow \pi^{0} p$, those are the $N(1680)\frac{5}{2}^{+}$ and $\Delta(1950)\frac{7}{2}^{+}$, contributing to the $F$-waves., Comment: 66 pages, 19 figures, 47 tables; Version 2 has been accepted for publication in Eur. Phys. J. A

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 Julich-Bonn. All reproduce the recent new data well: the double-polarization data for E, G, H, P and T in $\gamma p\rightarrow \pi^{0}p$ from ELSA, the beam asymmetry $ \Sigma$ for $\gamma p\rightarrow \pi^{0}p$ and $ \pi^{+}n$ from Jefferson Laboratory, and the precise new differential cross section and beam asymmetry data $\Sigma$ for $\gamma p\rightarrow \pi^{0}p$ 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.

The photoproduction of $\omega$ and $\eta^\prime$ mesons off carbon and niobium nuclei has been measured as a function of the meson momentum for incident photon energies of 1.2-2.9 GeV at the electron accelerator ELSA. The mesons have been identified via the $\omega \rightarrow \pi^0 \gamma \rightarrow 3 \gamma$ and $\eta^\prime\rightarrow \pi^0 \pi^0\eta \rightarrow 6 \gamma$ decays, respectively, registered with the CBELSA/TAPS detector system. From the measured meson momentum distributions the momentum dependence of the transparency ratio has been determined for both mesons. Within a Glauber analysis the in-medium $\omega$ and $\eta^\prime$ widths and the corresponding absorption cross sections have been deduced as a function of the meson momentum. The results are compared to recent theoretical predictions for the in-medium $\omega$ width and $\eta^\prime$-N absorption cross sections. The energy dependence of the imaginary part of the $\omega$- and $\eta^\prime$-nucleus optical potential has been extracted. The finer binning of the present data compared to the existing data allows a more reliable extrapolation towards the production threshold. The modulus of the imaginary part of the $\eta^\prime$ nucleus potential is found to be about three times smaller than recently determined values of the real part of the $\eta^\prime$-nucleus potential, which makes the $\eta^\prime$ meson a suitable candidate for the search for meson-nucleus bound states. For the $\omega$ meson, the modulus of the imaginary part near threshold is comparable to the modulus of the real part of the potential. As a consequence, only broad structures can be expected which makes the observation of $\omega$ mesic states very difficult experimentally., Comment: 10 pages, 8 figures

The excitation function and momentum distribution of {\eta}' mesons have been measured in photoproduction off 93^Nb in the energy range of 1.2-2.9 GeV. The experiment has been performed with the combined Crystal Barrel and MiniTAPS detector system, using tagged photon beams from the ELSA electron accelerator. Information on the sign and magnitude of the real part of the {\eta}'-Nb potential has been extracted from a comparison of the data with model calculations. An attractive potential of -(41 \pm 10(stat) \pm 15(syst)) MeV depth at normal nuclear matter density is deduced within model uncertainties. This value is consistent with the potential depth of -(37 \pm 10(stat) \pm 10(syst)) MeV obtained in an earlier measurement for a light nucleus (carbon). This relatively shallow {\eta}'-nucleus potential will make the search for {\eta}'-nucleus bound states more difficult., Comment: 9 pages, 6 figures

New data on the polarization observables T, P, and H for the reaction γp→pπ0 are reported. The results are extracted from azimuthal asymmetries when a transversely polarized butanol target and a linearly polarized photon beam are used. The data were taken at the Bonn electron stretcher accelerator ELSA using the CBELSA/TAPS detector. These and earlier data are used to perform a truncated energy-independent partial wave analysis in sliced-energy bins. This energy-independent analysis is compared to the results from energy-dependent partial wave analyses.

New data on the polarization observables T, P, and H for the reaction γp→pπ(0) are reported. The results are extracted from azimuthal asymmetries when a transversely polarized butanol target and a linearly polarized photon beam are used. The data were taken at the Bonn electron stretcher accelerator ELSA using the CBELSA/TAPS detector. These and earlier data are used to perform a truncated energy-independent partial wave analysis in sliced-energy bins. This energy-independent analysis is compared to the results from energy-dependent partial wave analyses.

The complete experiment problem in the truncated partial wave analysis 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, $\sigma_0$, and the three single-spin observables, $\Sigma$, $T$ and $P$. For this purpose, the approach and formalism already worked out by Omelaenko in 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., Comment: 33 pages, 5 figures, 2 tables; Version 2 has been accepted for publication in Phys. Rev. C

The problem of the Complete Experiment for photoproduction of pseudoscalar mesons is treated. First the issue is reviewed briefly in the context of full production spin amplitudes as well as a truncated partial wave analysis (TPWA). Complete sets of polarization observables are given for both cases. Then, a numerical procedure for single energy TPWA fits is presented and first results are shown.

The first measurement is reported of the double-polarization observable G in 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 {\gamma}p -> p{\pi} 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) 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., Comment: Submitted for publication in PRL