# M1: Accomplishments of the second funding period

• Dispersive formalism for hadronic light-by-light scattering
Besides the single pseudo-scalar channels, the production of two pseudo-scalar mesons are the next important contribution entering the hadronic light-by-light correction to $$(g-2)_\mu$$. To quantify this channel, we have performed a theoretical study of the $$\gamma\gamma \to \pi\eta$$ process from the threshold up to 1.4 GeV in the $$\pi\eta$$ invariant mass. For the s-wave $$a_0(980)$$ resonance state a dispersive formalism was adopted using a coupled-channel Omne`s representation, while the d-wave $$a_2(1320)$$ state was described as a Breit-Wigner resonance. An analytic continuation to the $$a_0(980)$$ pole position allows us to extract its two-photon decay width as $$\Gamma_{a_0\to\gamma\gamma}=0.27(4)$$ keV. The results have been submitted for publication.
• Light-by-light sum rules and its application to charmonium states
1. The light-quark meson contributions to three exact light-by-light scattering sum rules have been evaluated in light of new data by the Belle Collaboration for the transition form factors of the tensor meson $$f_2(1270)$$ and scalar meson $$f_0(980)$$. We confirm a previous finding that the $$\eta, \eta^\prime$$ and $$f_2(1270)$$ contributions saturate one of these sum rules up to photon virtualities around 1 GeV$$^2$$. At larger virtualities, our sum rule analysis shows an important contribution of the $$F_2(1565)$$ meson and provides a first empirical extraction of its helicity-2 transition form factor. Two further sum rules allow us to predict the helicity-0 and helicity-1 transition form factors of the $$f_2(1270)$$ meson. Furthermore, our analysis also provides an update for the scalar and tensor meson hadronic light-by-light contributions to $$(g-2)_mu$$. The results have been published.
2. The forward light-by-light scattering sum rules have also been applied to charmonium states. We have shown that these sum rules imply a cancellation between charmonium bound state contributions, which are mostly known from the $$\gamma\gamma$$ decay widths of these states, and continuum contributions above $$D \bar D$$ threshold, for which we provided a duality estimate. Two of these sum rules allow to predict the yet unmeasured $$\gamma^\ast\gamma$$ coupling, with one longitudinal and one transverse photon, of the $$\chi_{c1}(1P)$$ state as: $$\tilde \Gamma_{\gamma \gamma} \simeq \left( 1.6 \pm 0.30 \right) \; \mathrm{keV}$$, or equivalently $$\tilde \Gamma_{\gamma \gamma} / \Gamma_{tot} \simeq \left(1.9 \pm 0.4 \right) \times 10^{-3}$$. This prediction can be tested at present high-luminosity e+e− colliders. The results have been published.
• Spacelike meson TFF program at BES III
The analysis of the two hadronic reactions $$\gamma^\ast\gamma\to\pi^0$$ and $$\gamma^\ast\gamma\to\pi^+\pi^-$$ are in an advanced state. The $$Q^2$$ range covered in the analyses exceeds significantly towards smaller values as motivated by the hadronic light-by-light contribution to $$(g − 2)_\mu$$. Furthermore, in the two-pion channel for the first time the $$M_{\pi\pi}$$ mass range down to threshold can be investigated. The analysis of the neutral two-pion channel has started. A feasibility study for the reaction with two virtualities $$\gamma^\ast\gamma^\ast\to\pi^0$$ has been carried out.
• Timelike meson TFF program at BES III
The timelike TFF measurement at high momentum transfer of the η and η′ are within internal review within the BES III collaboration. The analysis of a measurement of the $$\pi^0$$ TFF is currently carried out within a master thesis.
• Timelike meson TFF program at A2/MAMI
Although originally foreseen as a feasibility study, the analysis of the timelike TFF using the $$\pi^0$$ Dalitz decay, could be published. As a consequence, a new high statistics measurement of this reaction was proposed at the MAMI PAC. Furthermore, a high statistics measurement of the $$\omega$$ and $$\eta$$ TFFs have been published within a common paper. The result of the $$\omega$$ TFF happens to be in agreement with theoretical models, which is not the case for the previous NA60 analysis.
• Hardware Project: Design study of a Zero Degree Detector (ZDD) for BESIII
Within a master thesis the readout of LYSO crystals with SiPM detectors has successfully been studied. In addition, investigations of the temperature behavior and the response to external light of LYSO crystals have been carried out. The background environment of the ZDD detector has been studied with large scale Monte Carlo simulations.