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)

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.

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.