S3: Accomplishments of the second funding period

The empirical knowledge about the nucleon excitation spectrum has significantly increased during the last decade. This progress is mainly based on a variety of meson photo- and electroproduction experiments at ELSA, JLAB, GRAAL and MAMI. However, some important questions still remain open. For example: given the present uncertainties in masses (pole positions), the possible existence of parity doublets cannot be clearly confirmed or rejected. Such doublets with the same mass and spin but opposite parity are neither predicted by quark models nor by lattice QCD. Furthermore, our knowledge about branching fractions to different decay or production modes is rather limited, and above 1900 MeV even the observed mass spectrum is incomplete.

The central goal of this project is the reconstruction of partial wave amplitudes and resonance properties from experimental data with minimal model dependence. To reach this goal, we are measuring different hadronic finals states in photoproduction experiments (MAMI, ELSA) and in charmonium decays (BESIII). In parallel, we are developing sophisticated tools for partial wave analyses and the determination of resonance parameters.

• Photoproduction experiments at MAMI and ELSA
Until the end of 2016, several experiments with polarized beam and polarized protons and deuterons were successfully performed within the A2 collaboration at MAMI. We have obtained high precision data sets for the $$\pi^0 N$$, $$\eta N$$, $$\eta' N$$, $$\omega N$$, $$\pi^0 \pi^0 N$$, and $$\pi^0 \eta N$$ final states in the energy range accessible with MAMI ($$W ≲ 1.9$$ GeV). Most of the analyses are completed and the data are published (see publication list). The helicity dependence of $$\pi^0$$ production off quasi-free protons and neutrons is presently studied as part of the PhD thesis of F. Cividini. This work will be completed in 2018. In parallel, the construction of a new focal plane detector for the tagging spectrometer was completed. This work was mainly done by Dr. P. Drexler who is partially paid by this project.
In order to extend the measurements to higher energies, the reliable dilution cryostat of the Mainz polarized target was combined with the renewed Crystal Barrel experiment at the ELSA accelerator. In spring 2017 this cryostat including the $$^3He$$ circulation system and the transverse holding coil was transported to ELSA and integrated into the existing Bonn polarized target set-up in close collaboration with the target groups in Dubna, Bonn and Bochum. Two runs with transversely polarized protons were successfully performed and a measurement with polarized deuterons has just started.
• Analysis of BESIII data
Within the last run period the BESIII experiment has multiplied its $$J/\psi$$ data set by a factor of 4 in order to reach 6 billion recorded $$J/\psi$$ events. And within the next months the number of 10 billion $$J/\psi$$ events will be reached. This unique $$J/\psi$$ data set gives the opportunity to extract certain decay channels still with a very large amount of events of the same final state. In comparison to the photo production reactions which were used for the production of nucleon resonances at MAMI, the decay of charmonia (e.g. $$J/\psi$$) offers a completely different environment for the production of baryon resonances. This gives additional constraints to the production mechanism of the resonances and therefore narrows the number of resonances which can be produced in this kind of decay channels. For some of the nucleon resonances also branching fractions to final state particles with strange quark content were observed.
For this reason we started the analysis of the two reaction channels $$J/\psi \rightarrow p\bar{p}\eta$$ and $$J/\psi \rightarrow K_S \Sigma^+ \bar{p}$$. In both cases the analysis started in 2018. Now, both PhD students (Sebastian Jäger and Leonard Wollenberg from Bochum) are familiar with the tools provided from the BESIII collaboration. The extraction of the $$p\bar{p}\eta$$ events is already rather advanced and the expected background level is well below 1 %. The extraction of events with $$K_S$$ and $$\Sigma^+$$ particles in the final state started 3 months ago.
• Partial wave analysis
In order to perform sophisticated partial wave analyses with the available manpower we founded a collaboration with groups in Tuzla (J. Stahov) and Zagreb (A. Svarc). Each step in the analyses is discussed during weekly meetings and annual workshops in Mainz which are funded by the CRC. Until now, we focused on the interpretation of the $$\gamma N\to\eta N$$ and $$\gamma N\to\eta' N$$ reactions using all available data and following a 3-fold strategy:

1. New $$\eta$$-MAID isobar models have been developed. They include explicit resonances on top of a non-resonant background, which consists of Born-terms and t-channel Regge exchanges. A detailed paper about the new $$\eta$$MAID model has been submitted for publication. This work is mainly performed by Dr. V. Kashevarov.
2. Isobar models as $$\eta$$MAID violate fixed-t dispersion relations, which can be derived from analyticity and crossing symmetry. In his PhD thesis, K. Nikonov developed modifications of the MAID model in order to fulfill fixed-t dispersion relations. The thesis was completed in August 2018 and a publication of the results is under preparation.
3. The least biased determination of multipole amplitudes is possible in so called single-energy or energy-independent analyses. Here, a truncated partial wave expansion of the measured angular distributions is performed at each individual energy bin without assuming any model for the energy-dependence. However, it can be shown that fully unconstrained single-energy analyses lead to ambiguities which cannot be resolved by experimental data alone. In order to avoid model constraints we have developed and applied a new method using fixed-t analyticity in an iterative fitting procedure at fixed-t and fixed energy. The analyses for $$\eta$$ production are completed and published.