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

介子的反常磁矩--介子g-2--是粒子物理标准模型(SM)的精确度检验。然而，目前这项测试似乎没有奏效，这是对SM之外的物理学的一个暗示。介子g-2的SM预测值与实验值之间存在一定的偏差。目前，这一差异在4.2标准差的水平。费米实验室和J-PARC分别进行了两个专门的实验，目的是在未来几年提炼和独立确认实验值。为了严格回答我们在Muon g-2实验中是否观察到新物理的问题，必须提高SM预测的精度，以补充新费米实验室实验的预期精度。这应该在我们的联合研究项目JRP.中实现。SM预测的准确性受到强子贡献的限制。我们区分了强子真空偏振(HVP)和光散射(HLbL)的贡献。虽然HVP大约比HLbL大两个数量级，但HVP的理论不确定度仅比HLbL的不确定度大2倍。由于量子色动力学(QCD)的复杂的非微扰性质，强子的贡献很难计算。在缺乏简单的QCD描述的情况下，我们使用了数据驱动的离散评估和格子QCD。我们的主要目标是提高对HLbL贡献的预测。首先，我们将巩固我们现有的HLbL贡献的格子QCD计算，并将统计和系统误差从目前的15%精度水平降低到10%或更高。最终的目的是用物理的介子质量直接计算。其次，我们将对不同的单介子和多介子通道的贡献进行数据驱动的色散评估。在这里，我们使用来自BESIII和Mami设施的新实验数据集，这些数据集是我们在TFF项目中生成的。两个独立的预测--来自格子QCD和现象学--然后可以组合成加权平均，就像对目前推荐的HLbL值所做的那样。考虑到HVP的贡献，目前被接受的使用实验测量的强子截面的数据驱动估计与宝马合作的格子QCD预测之间存在2.1标准偏差。显然，需要一个具有相当整体精度的独立格子QCD计算来澄清这种情况。因此，我们的另一个目标是计算由电磁和强相互作用效应引起的HVP贡献的同位旋破缺修正。这些措施是将总体不确定性控制在低于百分比的水平所必需的。对于QED修正，我们将有两种方法：1)直接格子QCD计算；2)以在Project LBL中获得的HLbL正向振幅的格子QCD结果为输入的Cottingham型公式。

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.