University of Tuzla, Faculty of Natural Sciences and Mathematics, Urfeta Vejzagića 4, 75000 Tuzla, Bosnia and Herzegovina European University ”Kallos”, Maršala Tita 2A-2B, 75000 Tuzla, Bosnia and Herzegovina Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, D-55099 Mainz,Germany P. N. Lebedev Physical Institute, 119991 Moscow, Russia Rudjer Bošković Institute, Bijenička cesta 54, P.O. Box 180, 10002 Zagreb, Croatia Tesla Biotech, Mandlova 7, 10002 Zagreb, Croatia (Dated: July 15, 2021)

We investigate the formation of resonances in the P33 partial wave with the emphasis on possible emergence of dynamically generated quasi-bound states as a consequence of a strong $p$-wave pion attractive interaction in this partial wave, as well as their possible interaction with the genuine quark excited states. By using the Laurent-Pietarinen expansion we follow the evolution of the $S$-matrix poles in the complex energy plane as a function of the interaction strength. Already without introducing a genuine quark resonant state, two physically interesting resonances emerge with pole masses around 1200 MeV and 1400 MeV, with the dominant $\pi N$ and $\pi\Delta$ component, respectively. The added genuine resonant state in the $(1s)^3$ quark configuration mixes with the lower dynamically generated resonance forming the physical $\Delta(1232)$ resonance, and pushes the second dynamical resonance to around 1500 MeV, which allows it to be identified with the $\Delta(1600)$ resonance. Adding a second resonant state with one quark promoted to the $2s$ orbit generates another pole whose evolution remains well separated from the lower two poles. We calculate the helicity amplitudes at the pole and suggest that their $Q^2$ dependence could be a decisive test to discriminate between different models of the $\Delta(1600)$ resonance.

High precision data of the $\gamma p \to \pi^0 p$ reaction from its threshold up to $W=2$~GeV have been used in order to perform a single-energy partial wave analysis with minimal model dependence. Continuity in energy was achieved by imposing constraints from fixed-$t$ analyticity in an iterative procedure. Reaction models were only used as starting point in the very first iteration. We demonstrate that with this procedure partial wave amplitudes can be obtained which show only a minimal dependence on the initial model assumptions.

It has recently been proven that the invariance of observables with respect to angle dependent phase rotations of reaction amplitudes mixes multipoles changing also their relative strength [1]. All contemporary partial wave analyses (PWA) in $\eta$ photoproduction on protons, either energy dependent (ED) [2-5] or single energy (SE) [6] do not take this effect into consideration. It is commonly accepted that there exist quite some similarity in the $E0+$ multipole for all PWA, but notable differences in this, but also in remaining partial waves still remain. In this paper we demonstrate that once this phase rotations are properly taken into account, all contemporary ED and SE partial wave analysis become almost identical for the dominant $E0+$ multipole, and the agreement among all other multipoles becomes much better. We also show that the the measured observables are almost equally well reproduced for all PWA, and the remaining differences among multipoles can be attributed solely to the difference of predictions for unmeasured observables. So, new measurements are needed.

In view of the recent results of lattice QCD simulation in the P11 partial wave that has found no clear signal for the three-quark Roper state we investigate a different mechanism for the formation of the Roper resonance in a coupled channel approach including the πN , π∆ and σN channels. We fix the pion-baryon vertices in the underlying quark model while the s-wave sigma-baryon interaction is introduced phenomenologically with the coupling strength, the mass and the width of the σ meson as free parameters. The Laurent-Pietarinen expansion is used to extract the information about the S-matrix pole. The Lippmann-Schwinger equation for the K matrix with a separable kernel is solved to all orders. For sufficiently strong σNN coupling the kernel becomes singular and a quasi-bound state emerges at around 1.4 GeV, dominated by the σN component and reflecting itself in a pole of the S-matrix. The alternative mechanism involving a (1s)2s quark resonant state is added to the model and the interplay of the dynamically generated state and the three-quark resonant state is studied. It turns out that for the mass of the three-quark resonant state above 1.6 GeV the mass of the resonance is determined solely by the dynamically generated state, nonetheless, the inclusion of the three-quark resonant state is imperative to reproduce the experimental width and the modulus of the resonance pole.

Partial wave amplitudes of meson photoproduction reactions are an important source of information in baryon spectroscopy. We investigate a new approach in single-energy partial wave analyses of these reactions. Instead of using a constraint to theoretical models in order to achieve solutions which are continuous in energy, we enforce the analyticity of the amplitudes at fixed values of the Mandelstam variable $t$. We present an iterative procedure with successive fixed-$t$ amplitude analyses which constrain the single-energy partial wave analyses and apply this method to the $\gamma p \to \eta p$ reaction. We use pseudo data, generated by the EtaMAID model, to test the method and to analyze ambiguities. Finally, we present an analytically constrained partial wave analysis using experimental data for four polarization observables recently measured at MAMI and GRAAL in the energy range from threshold to $\sqrt{s}=1.85$ GeV.

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,

Electromagnetic resonance properties are uniquely defined at the pole and do not depend on the separation of the resonance from background or the decay channel. Photon-nucleon branching ratios are nowadays often quoted at the pole, and we generalize the considerations to the case of virtual photons. We derive and compare relations for nucleon to baryon transition form factors both for the Breit-Wigner and the pole positions. Using the MAID2007 and SAID SM08 partial wave analyses of pion electroproduction data, we compare the ${G}_{M}, {G}_{E}$, and ${G}_{C}$ form factors for the $\mathrm{\ensuremath{\Delta}}(1232)$ resonance excitation at the Breit-Wigner resonance and pole positions up to ${Q}^{2}=5\phantom{\rule{0.16em}{0ex}}{\mathrm{GeV}}^{2}$. We also explore the $E/M$ and $S/M$ ratios as functions of ${Q}^{2}$. For pole and residue extraction, we apply the Laurent + Pietarinen method.

The pole structure of the current GW/SAID partial-wave analysis of elastic $\pi N$ scattering and $\eta N$ production data is studied. Pole positions and residues are extracted from both the energy-dependent and single-energy fits, using two different methods. For the energy-dependent fits, both contour integration and a Laurent+Pietarinen approach are used. In the case of single-energy fits, the Laurent+Pietarinen approach is used. Errors are estimated and the two sets of results are compared to other recent and older fits to data.

Weappliedanewapproachtodeterminethepolepositionsandresiduesfrompionphotoproductionmultipoles. The method is based on a Laurent expansion of the partial-wave T matrices, with a Pietarinen series representing the regular part of energy-dependent and single-energy photoproduction solutions. The method is applied to multipole fits generated by the MAID and George Washington University SAID (GWU-SAID) groups. We show that the number and properties of poles extracted from photoproduction data correspond very well to results from πN elastic data and values cited by the Particle Data Group (PDG). The photoproduction residues provide new information for the electromagnetic current at the pole position, which are independent of background parametrizations, which is not the case for the Breit-Wigner representation. Finally, we present the photodecay amplitudes from the current MAID and SAID solutions at the pole for all four-star nucleon resonances below W = 2 GeV.