Hadronic Light-by-Light Contribution to the Muon g-2

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The anomalous magnetic moment of the muon — the muon g-2 — is serving as a precision test for the Standard Model (SM) of particle physics. However, at the moment this test does not seem to work out, which is a hint for physics beyond the SM. There is a discrepancy between the SM prediction and the experimental value of the muon g-2. Presently, this discrepancy is at the level of 4.2 standard deviations. Two dedicated experiments at Fermilab and J-PARC aim, respectively, to refine and independently confirm the experimental value in the coming years. To rigorously answer the question whether we observe New Physics in the muon g-2 experiments, the accuracy of the SM prediction must be improved to complement the anticipated precision of the new Fermilab experiment. This should be achieved in our Joint Research Project JRP.The accuracy of the SM prediction is limited by hadronic contributions. We distinguish the hadronic vacuum polarization (HVP) and light-by-light scattering (HLbL)  contributions. While the HVP is about 2 orders of magnitude larger than the HLbL, the theoretical uncertainty of the HVP is only a factor of 2 larger than the uncertainty of the HLbL. Due to the complicated non-perturbative nature of quantum chromodynamics (QCD), hadronic contributions are rather hard to calculate. In the absence of a simple QCD description, we employ data-driven dispersive evaluations and lattice QCD. Our main objective is to improve the prediction of the HLbL contribution. Firstly, we will consolidate our existing lattice QCD calculation of the HLbL contribution and reduce the statistical and the systematic errors from the present 15% accuracy level to 10% or better. The ultimate aim is a direct calculation with physical pion mass. Secondly, we will perform data-driven dispersive evaluations of the different single- and multi-meson channel contributions. Here, we employ new experimental data-sets from the BESIII and MAMI facilities, that we generate in Project TFF. The two independent predictions — from lattice QCD and phenomenology — could then be combined into a weighted average, as is done for the presently recommended HLbL value.Considering the HVP contribution, there is a tension of 2.1 standard deviations between the presently accepted data-driven estimate, using experimentally measured hadronic cross sections, and the  lattice QCD prediction by the BMW Collaboration. Clearly, an independent lattice QCD calculation with comparable overall precision is required to clarify the situation. Therefore, our other objective is to compute isospin-breaking corrections to the HVP contribution that arise from electromagnetic and strong interaction effects. These are required to control the overall uncertainty at the sub-percent level. For the QED corrections, we will again have two approaches: 1) direct lattice QCD calculation; 2) a Cottingham-type formula with lattice QCD results for the forward HLbL amplitudes, obtained in Project LBL, as input.