# M1: γγ physics and meson structure

### Goals

Project M1 aims to quantify the hadronic light-by-light (HLbL) contribution to the anomalous magnetic moment of the muon $$a_\mu$$, as well as study the quark structure of pseudo-scalar, scalar, axial-vector, and tensor mesons. There is a strong interplay between theory and experiment in this project. The experimental part involves the measurement of (spacelike) photon-photon fusion processes at BESIII, the measurement of timelike meson transition form factors (TFFs) in $$e^+e^-$$ annihilation at BESIII, and the Dalitz decays of $$\pi^0, \eta, \eta^\prime$$ mesons measured at A2/MAMI. The theoretical part focusses on dispersion techniques necessary to interpret the meson TFFs, the production of multi-meson states from photon-photon fusion processes or meson Dalitz decays, in order to quantify their contribution to $$a_\mu$$.

The highlights in the third funding period will be:

1. Dispersive formalism for hadronic light-by-light scattering
To further support the experimental program at BESIII, the coupled-channel dispersive formalisms will be extended to the virtual unequal mass $$\gamma^\ast \gamma \to \pi^0 \eta$$ process, as well as to the double virtual case $$\gamma^\ast \gamma^\ast \to \pi \pi, K \bar K, \pi \eta$$. Subsequently, this input will be incorporated into the dispersive formalisms to estimate the HLbL contribution to$$a_\mu$$.
2. Light-by-light sum rules and its application to charmonium states
We plan to extend the light-by-light sum rules to the radiative decays of quarkonium states. Such analysis allows for exact relations between the $$X \to \gamma Y$$ and $$Y \to \gamma X$$ radiative decays for $$Y = 1^{--}$$ quarkonium states, and provide an estimate of the strength originating from the contribution of states beyond $$q \bar q$$.
3. Lattice QCD calculations of the HLbL forward amplitudes
The direct lattice QCD program for the HLbL contribution to $$a_\mu$$ is described in Project P1. In project M1 we plan a second-generation computation of the HLbL forward scattering amplitudes on the lattice, and will confront them with the improved  dispersive input from the $$\pi \pi$$ and $$\pi \eta$$ channels.
4. Spacelike meson TFF program
We plan to analyze the $$\gamma^*\gamma \to \pi^0 \pi^0$$ and $$\gamma^*\gamma \to \pi^0 \eta$$ channels as well as the $$f_1$$(1285) resonance. With the increased BESIII data set, which will be available in the 3rd FP, it is also possible to increase the sensitivity for the double-tag measurement of the neutral pion transition form factor, which will allow to distinguish between different hadronic models.
5. Timelike meson TFF program
The BESIII analysis on the timelike $$\pi^0, \eta, \eta^\prime$$ FFs will be brought to publication. Also, a publication on the high statistics A2/MAMI measurement of the timelike pion TFF using the pion Dalitz decay, for which the data was collected in 2018, is foreseen.
6. Hardware Project: Construction of a crystal Zero Degree Detector (cZDD) for BESIII
The installation of a cZDD tagger at BESIII is foreseen for the first half of the third funding period, and will open the avenue for photon and electron tagging at very small polar angles.