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

μ子的反常磁矩-μ子g-2 -是粒子物理学标准模型（SM）的精确测试。然而，目前这个测试似乎没有成功，这是对SM之外的物理学的一个暗示。有一个SM的预测和μ子g-2的实验值之间的差异。目前，这一差异为4.2个标准差。费米实验室和J-PARC的两个专门实验分别旨在在未来几年内完善和独立确认实验价值。为了严格回答我们是否在μ子g-2实验中观察到新物理学的问题，必须提高SM预测的准确性，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。我们区分强子真空极化（HVP）和光的光散射（HLbL）的贡献。虽然HVP比HLbL大约大2个数量级，但HVP的理论不确定性仅比HLbL的不确定性大2倍。由于量子色动力学（QCD）复杂的非微扰性质，强子贡献的计算相当困难。在缺乏简单QCD描述的情况下，我们采用数据驱动的色散估计和格点QCD。我们的主要目标是提高HLbL贡献的预测。首先，我们将巩固我们现有的格点QCD计算的HLbL的贡献，并减少统计和系统误差从目前的15%的精度水平到10%或更好。最终目标是直接计算物理π介子质量。其次，我们将进行不同的单介子和多介子通道贡献的数据驱动的色散评估。在这里，我们采用新的实验数据集从BESIII和MAMI设施，我们在项目TFF中产生。这两个独立的预测-从格点QCD和唯象-然后可以合并成一个加权平均值，就像目前推荐的HLbL值一样。考虑到HVP的贡献，目前接受的数据驱动的估计，使用实验测量的强子截面，和宝马合作组织的格点QCD预测之间存在2.1个标准差的张力。显然，需要具有可比总体精度的独立格点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对HVP贡献的同位旋破缺修正。这些都是需要控制在低于百分之水平的总体不确定性。对于QED修正，我们将再次有两种方法：1）直接格点QCD计算; 2）一个Cottingham型公式，用LBL项目中获得的前向HLbL振幅的格点QCD结果作为输入。

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.