**\(\eta\)-\(\eta'\) mixing in large-\(N_c\) chiral perturbation theory**We performed a calculation of the \(\eta\)-\(\eta'\) mixing in the framework of large-\(N_c\) chiral perturbation theory. A general expression for the \(\eta\)-\(\eta'\) mixing at next-to-next-to-leading order (NNLO) was derived, including higher-derivative terms up to fourth order in the four momentum, kinetic and mass terms. In addition, the axial-vector decay constants of the \(\eta\)-\(\eta'\) system were determined at NNLO. The numerical analysis of the results was performed successively at LO, NLO, and NNLO.

**Quantum corrections to the chiral anomaly in large-\(N_c\) chiral perturbation theory**We calculated the anomalous decays \(\eta^{(')}\to\gamma^{(\ast)}\gamma^{(\ast)}\) and \(\eta^{(')}\to\pi^+\pi^-\gamma^{(\ast)}\) at the one-loop level up to next-to-next-to-leading order (NNLO) in large-\(N_c\) chiral perturbation theory. Both the decays to real photons and the decays involving virtual photons, providing access to the substructure of the mesons, have been discussed. The results were numerically evaluated successively at LO, NLO, and NNLO. The appearing low-energy constants were determined through fits to the available experimental data. In the case of \(\eta^{(')}\to\gamma^{(\ast)}\gamma^{(\ast)}\) we investigated the decay widths to real photons, the widths of \(\eta^{(')}\to \gamma l^+l^-\), where \(l=e, \mu\), and the single-virtual transition form factors. The considered observables of the decays \(\eta^{(')}\to\pi^+\pi^-\gamma^{(\ast)}\) are the spectra of the decays involving a real photon, \(\eta^{(')}\to\pi^+\pi^-\gamma\), as well as the spectra of \(\eta^{(')}\to\pi^+\pi^-l^+l^-\), where \(l=e,\mu\), with respect to the invariant masses of the \(\pi^+\pi^-\) and \(l^+l^-\) systems.

*Photon-energy spectrum of \(\eta\to\pi^+\pi^-\gamma\) at LO (gray), NLO (blue)* *and NNLO (red). For the NLO and NNLO results the corresponding 1~\(\sigma\) error bands* *are shown. The experimental data are taken from P. Adlarson et al. [Wasa-at-COSY Collaboration],* *Phys.Lett.B 707, 243 (2012)*

**Meson decays \(VP\gamma\)**

We studied radiative transitions between the vector-meson nonet and the pseudoscalar nonet. Since the leading-order Lagrangian is not sufficient to describe all of the 12 physical reactions, we constructed the relevant chiral effective Lagrangians at next-to-leading order in a combined \(1/N_c\) and quark-mass expansion. The calculation includes both \(\phi\)-\(\omega\) and \(\eta\)-\(\eta'\) mixings. Although the inclusion of higher-order terms leads to an improved description of the experimental data, some discrepancies remain which could also hint towards an inconsistency among different data sets. When analyzing the Dalitz decays, we found that a simple vector-dominance assumption is not yet able to describe all of the available data.**Dalitz plot analysis of the decay \(\eta' \to \eta \pi^0 \pi^0\)**

We performed a Dalitz plot analysis of the decay \(\eta' \to \eta \pi^0\pi^0\) using about 124,000 signal decays collected with the Crystal Ball/TAPS setup and the Endpoint Tagger (EPT) in 2014. The A2 dataset analysed in this paper is the largest sample of \(\eta'\to\eta \pi^0\pi^0\) decays so far and results in the most precise to date determination of the parameters describing the matrix element for this decay.

The large dataset also allows, for the first time, the observation of a structure below the \(\pi^+\pi^-\) threshold, which is in good agreement with the cusp that was predicted based on the \(\pi\pi\) scattering length combination, \(a_0 - a_2\), extracted from \(K \to 3\pi\) decays. It is interesting to note that BESIII published an analysis of the same decay almost simultaneously. The BESIII analysis is based on \(1.3\times 10^9\) \(J/\psi\) events, yielding roughly half the \(\eta'\) statistics compared to the A2 dataset; the statistics of BESIII does not require the cusp to achieve a satisfactory fit to data. From spring 2019 on, BESIII will have \(10^{10}\) \(J/\psi\) on tape.**Measurement of the Dalitz plot distribution of \(\eta' \to \pi^0 \pi^0 \pi^0\)**

[PhD project of Martin Wolfes.] Using the EPT data set of A2, we attempt to reconstruct the decay \(\eta' \to \pi^0 \pi^0 \pi^0\), with the goal to perform a Dalitz plot analysis. Initial expectations based on the number of produced \(\eta'\), the branching fraction, and a signal Monte Carlo study indicated that a signal yield comparable to the BESIII sample of 1900 reconstructed \(\eta' \to \pi^0 \pi^0 \pi^0\) would be within reach.

However, performing the analysis we had to realise that a clean extraction of the signal decay is not possible due to the presence of a large, irreducible, background from \(3\pi^0\) production which does not proceed via a primary \(\eta'\). This analysis therefore turns out to be not feasible within the scope of a PhD thesis.

Instead, a measurement of the cross section \(\gamma p \to \Sigma^+ K^0\) with \(\Sigma^+ \to p \pi^0\) and \(K{^0_S} \to \pi^0\pi^0\) is being performed. The analysis sees about 52000 reconstructed signal decays; a measurement of the differential cross section in several bins of \(E_\gamma\) is therefore possible.**Measurement of the branching fraction \(\eta' \to \omega \gamma\)**

[This measurement is the PhD project of Andreas Neiser.] The plan is to measure the branching fraction of \(\eta' \to \omega \gamma \to \pi^0 \gamma\) relative to the abundant reference channel \(\eta' \to \gamma \gamma\). Signal yields of about 50,000 reference and 1300 signal decays are found in the full endpoint tagger data set. However, there is a systematic difference between data and simulation in the signal efficiency, so that the preliminary result for the branching fraction comes out significantly smaller than the PDG average. A publication using an alternative analysis chain is under preparation.**Measurement of the branching fraction \(\omega \to \eta \gamma\)**

[PhD project of Oliver Steffen.] The decay \(\omega \to \eta \gamma\) was planned to be measured using the decay \(\omega \to \pi^0 \gamma\) as a reference, using the approximately \(6\times 10^7\) \(\omega\) mesons produced in the EPT beam times. The reference channel is cleanly reconstructed with the expected rates, but identification of the signal decay is seriously hampered by the presence of a large background from the processes \(\gamma p \to \eta \pi^0 p\), in which one photon from the \(\pi^0\) is not detected. Additional backgrounds are also present, and the distribution of \(m(\eta \gamma)\) is not well described by simulation, making a determination of the signal yield very unreliable.

As an alternative result, the differential cross section for \(\omega\) photoproduction is measured in bins of the incident photon energy; this agrees within uncertainties with previous results.**Study of charmonium decays to three pions**We developed and applied a data selection for the channels \(J/\psi \rightarrow \pi^+\pi^-\pi^0\) and \(\psi^\prime \rightarrow \pi^+\pi^-\pi^0\) on the full BESIII data sets. Fits to these data using Veneziano amplitudes in close collaboration with A. Szczepaniak (Indiana University) were started and show a very good description of the \(J/\psi\) data; more work is needed for a thorough understanding of the \(\psi^\prime\) data.

**Dalitz plot analysis of \(D^0\to K^0_S K^+K^-\)**

We finalised the Dalitz plot analysis and measurement of the branching fraction of the decay \(D^0\to K^0_S K^+K^-\) using the full \(2.92\) fb\(^{-2}\) data sample taken at \(\sqrt{s}=3.773\) GeV. The branching fraction result is the most precise measurement to date. The uncertainty is dominated by systematic uncertainties and improves on the PDG average by a factor of 1.7. A journal publication is under internal review within BESIII; submission is expected in the first quarter of 2019.**Exotic Charmonium states**Since the beginning of the second funding period we performed the search for the two isospin singlet states \(\eta_c \eta\) in the reaction channel \(e^+e^{-} \rightarrow \eta_c\eta \pi\pi\) and \(J\psi \eta\) in the reaction channel \(e^+e^{-} \rightarrow J\psi\ \eta\eta\) with data of the BESIII experiment. The first step was the optimization of the extraction of events with the correct signature in the detector.

To extract the \(\eta_c \eta\) events we had to sum over 16 different \(\eta_c\) decay channels in order to get a reasonable amount of \(\eta_c\) candidates. Concerning the background contributions we were not able to describe the remaining background distribution with the recent models. We performed dedicated studies of the remaining background distributions to be sure there is no peaking background left. Therefore we are able to describe the remaining contribution in the data directly by fitting a combined model of a signal and a background function simultaneously to each of the 16 \(\eta_c\) decay channels. A very detailed study of the systematic uncertainties led to the calculation of the upper limits for the production of this reaction channel at the five large data sets at center of mass energies above 4.23 GeV. For this analysis the review process for the data analysis at BESIII is almost finished and the paper draft is already written. The internal review committee is going to release the analysis for collaboration wide review soon.

For the \(J\psi \eta\) case extensive studies were performed in order to subtract the background contributions. For some contributions, no cross section measurements exist, therefore a rough analysis was done for the missing channels in order to determine at least upper limit on their contributions. Only very few events survive for the five energy points above 4.23 GeV with large statistics datasets. Therefore we calculated the upper limits for each energy and took into account all systematic uncertainties. We expect the full analysis memo and the start of the review process in spring 2019.

In parallel we are preparing for the simultaneous fit planned for fitting various energies and reaction channels simultaneously. The first step was to provide clean and well understood event samples of the reaction channels \(e^+e^{-} \rightarrow (D \bar{D}^*)^+ \pi^{-}\) and \(e^+e^{-} \rightarrow (D \bar{D}^*)^0 \pi^{0}\) at 4.42 GeV. The selection for these channels is finished and the two independent analyses were cross-checked in detail and differences understood.

Whilst the reaction channel \(e^+e^{-} \rightarrow (D \bar{D}^*)^0 \pi^{0}\) can be extracted almost free of background events, the charged mode is more challenging to prepare due to a remaining background contribution in the order of 5 %. This number is however not too large in principle. If the kinematics of the background are well understood, it can be taken into account for the partial wave analysis. Unfortunately the remaining background channels were not yet studied, therefore no cross section measurement and no measurement of the angular distributions in these channels are available. A large fraction of time was spent in order to get these background channels under control.