We present a new approach to quantifying pole parameters of single-channel processes based on a Laurent expansion of partial-wave T-matrices in the vicinity of the real axis. Instead of using the conventional power-series description of the non-singular part of the Laurent expansion, we represent this part by a convergent series of Pietarinen functions. As the analytic structure of the non-singular part is usually very well known (physical cuts with branch points at inelastic thresholds, and unphysical cuts in the negative energy plane), we find that one Pietarinen series per cut represents the analytic structure fairly reliably. The number of terms in each Pietarinen series is determined by the quality of the fit. The method is tested in two ways: on a toy model constructed from two known poles, various background terms, and two physical cuts, and on several sets of realistic πN elastic energy-dependent partial-wave amplitudes (GWU/SAID -[1, 2], and Dubna-Mainz-Taipei - [3,4]). We show that the method is robust and confident using up to three Pietarinen series, and is particularly convenient in fits to amplitudes, such as single-energy solutions, coming more directly from experiment; cases where the analytic structure of the regular part is apriori unknown.

The isobar model EtaMAID has been updated with new and high precision data for η and η photoproduction on protons and neutrons from MAMI, ELSA, GRAAL and CLAS. The background is described in a recently developed Regge-cut model, and for the resonance part the whole list of nucleon resonances has been investigated with 21 N * states contributing to η photoproduction and 12 N * states contributing to η photoproduction. A new approach is discussed to avoid double counting in the overlap region of Regge and resonances. A comparison is done among four newly updated partial waves analyses for observables and partial waves. Finally, the possibility of a narrow resonance near W = 1900 MeV is discussed, that would be able to explain unexpected energy and angular dependence of observables in p(γ, η )p near η threshold.

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Data on the reaction γp → K + Λ from the CLAS experiments are used to derive the leading multipoles, E0+, M1−, E1+, and M1+, from the production threshold to 2180 MeV in 24 slices of the invariant mass. The four multipoles are determined without any constraints. The multipoles are fitted using a multichannel L + P model which allows us to search for singularities and to extract the positions of poles on the complex energy plane in an almost model-independent method. The multipoles are also used as additional constraints in an energy-dependent analysis of a large body of pion and photo-induced reactions within the Bonn-Gatchina (BnGa) partial wave analysis. The study confirms the existence of poles due to nucleon resonances with spin-parity J P = 1/2 − ; 1/2 + , and 3/2 + in the region at about 1.9 GeV."Three quarks for Muster Mark" [1]. This sentence inspired Gell-Mann [2] to call quarks the three constituents of nucleons, of protons or neutrons. As a three-body system, the nucleon is expected to exhibit a large number of excitation modes. The most comprehensive predictions of the resonance excitation spectrum stem from quark-model calculations [3]-[8]; this predicted spectrum is qualitatively confirmed by recent Lattice QCD calculations [9], even though the quark masses used lead to a pion mass of 396 MeV. The predicted resonances may decay into a large variety of different decay modes. The most easily accessible was, for a long time, the πN decay of nucleon excitations by studying π ± p elastic scattering and the π − p → π 0 n charge exchange reaction. A large amount of data were analyzed by the groups at Karlsruhe-Helsinki (KH) [10], Carnegie-Mellon (CM) [11] and at GWU [12]. Real and imaginary parts of partial waves amplitudes with defined spin and parity (J P ) were extracted in slices of the πN invariant mass, and resonant contributions were identified. However, only a small fraction of the predicted energy levels has been observed experimentally, and for some of them, the evidence for their existence is only fair or even poor [13,14].The small number of observed excitations of the nucleon, as compared to quark model calculations, led to a number of speculations: Are nucleon resonances quarkdiquark oscillations with quasi-stable diquarks [15][16][17][18][19]) ? Are resonances generated by meson-baryon interactions [20][21][22][23][24][25], and are quarks and gluons misleading as degrees of freedom to interpret the excitation spectrum ? Does the mass-degeneracy of high-mass baryon resonances with positive and negative-parity hadron resonances indicate the onset of a new regime in which chiral symmetry is restored [26][27][28] ? At low excitation energy, chiral symmetry is strongly violated as indicated by the large mass gap between the nucleon mass (with spinparity J P = 1/2 + ) and its chiral partner N (1535) with [36]. The resonances stem from energydependent fits to the data. The resonances and the background contributions in all partial waves need to be determined in a single step. New data on γp → K +...

Poles of partial wave scattering matrices in hadron spectroscopy have recently been established as a sole link between experiment and QCD theories and models. Karlsruhe-Helsinki (KH) partial wave analyses have been "above the line" in the Review of Particle Physics (RPP) for over three decades. The RPP compiles Breit-Wigner (BW) parameters from local BW fits, but give only a limited number of pole positions using speed plots (SP). In the KH method only Mandelstam analyticity is used as a theoretical constraint, so these partial wave solutions are as model independent as possible. They are a valuable source of information. It is unsatisfactory that BW parameters given in the RPP have been obtained from the KH80 solution, while pole parameters have been obtained from the KA84 version. To remedy this, we have used a newly developed Laurent + Pietarinen expansion method to obtain pole positions for all partial waves for KH80 and KA84 solutions. We show that differences from pole parameters are, with a few exceptions, negligible for most partial waves. We give a full set of pole parameters for both solutions.