Hadronic Vacuum Polarisation Contributions to g-2 and other precision observables

费米实验室μ子g-2实验的测量结果与理论预测之间的持续紧张表明，标准模型之外的新物理学可能存在。通过对Run 2和Run 3数据的分析，费米实验室测量的精度提高了两倍，一旦分析完所有收集的数据，预计将再次提高同样的精度。实验精度的提高需要伴随着理论精度的相应提高。理论预测的最大不确定性来源来自强子真空极化（HVP）的贡献。虽然对预测的其他贡献可以在微扰理论的框架内计算，但HVP的贡献必须从色散或晶格QCD方法中计算。本博士的主要重点是通过开发改进的方法和包括以前没有的新数据集来改进HVP贡献的分散计算。在新的数据集中，需要考虑的是用CMD-3实验收集的n+n-数据。这些结果与以前在同一设施进行的包括CMD-2在内的其他实验所获得的结果存在相当大的差异。有必要确定将这些数据与先前似乎不相容的结果结合起来的最佳方法。对于HVP对g-2的贡献，色散和晶格QCD预测之间也存在明显的张力。采用点阵QCD进行HVP计算，得到了与实验结果更为吻合的结果。这种紧张关系的根源尚不清楚，也是许多调查的根源。作为该项目的一部分，可以对所谓的窗口可观测物进行色散预测，并将其与晶格QCD群进行比较。该项目的第一阶段将是将用于计算HVP贡献的KNT程序更新为更现代的语言。这将允许使用强大的现代软件特性，如关系数据库，并使代码更易于访问。盲法程序也将从一开始实施到计算中；这些都是为了避免对最终结果产生偏差而引入的。随着项目的进展，代码中使用的统计方法将被改进，目的是分配更准确的不确定性。系统不确定性和相关性的作用也将被仔细研究。新的数据集将被引入分析，进一步提高测量的精度和准确性。将开发调和紧张数据集的公正方法，并将其应用于解决突出的潜在问题。此外，分析中辐射校正的处理将得到改进。该项目不仅将产生对g-2的HVP贡献的最新色散计算，而且还将产生其他精确观测值的最新值。这些结果可以与其他精密物理实验的结果（如μ子的超精细分裂）进行比较，或者，在计算QCD耦合运行的情况下，用作进一步测量的输入。更新后的计算结果将与费米实验室的最终测量结果和晶格QCD的结果进行比较。因此，这个项目将对标准模型的重大测试和寻找新物理学做出潜在的重要贡献。

Sustained tension between the measured results of the Muon g-2 experiment at Fermilab and the theoretical prediction suggests a potential for new physics beyond the Standard Model. The precision of the Fermilab measurement has been improved by a factor of two by analysis of Run 2 and Run 3 data, and is expected to improve by the same factor again once all of the data collected has been analysed. This improvement in experimental accuracy needs to be accompanied by a comparable improvement in theoretical accuracy.The largest source of uncertainty on the theoretical prediction comes from the Hadronic Vacuum Polarisation (HVP) contribution. While other contributions to the prediction can be calculated within the framework of perturbation theory, the HVP contribution must be calculated from dispersive or lattice QCD methods. The primary focus of this PhD is to refine the dispersive calculation of the HVP contribution, by means of developing improved methodology and including new data sets not previously available.Among the new data sets to be considered is the n+n- data collected with the CMD-3 experiment. There is a considerable discrepancy between these results and those obtained previously by other experiments including CMD-2, which ran at the same facility. It will be necessary to determine the best way to include these data alongside prior results with which they seem incompatible.There also exists a notable tension between the dispersive and lattice QCD predictions for the HVP contribution to g-2. When lattice QCD is used to perform the HVP calculation, a result more consistent with the experimental result is obtained. The source of this tension is as yet unknown, and is the source of much investigation. As part of this project, dispersive predictions of so-called window observables can be made and compared to those of lattice QCD groups.The first stage of this project will be to update the program used for the KNT calculation of the HVP contribution into a more modern language. This will allow use of powerful modern software features such as relational databases and make the code more accessible. Blinding procedures will also be implemented into the calculation from the start; these are introduced with the aim of avoiding biasing the final result.As the project progresses, the statistical methods used in the code will be refined with the aim of assigning more accurate uncertainties. The role of systematic uncertainties and correlations will also be scrutinised. New data sets will be introduced into the analysis, further increasing the precision and accuracy of the measurement. Unbiased methods of reconciling data sets in tension will be developed and applied to address outstanding potential issues. Furthermore, the handling of radiative corrections in the analysis will be improved.The project will yield not only an updated dispersive calculation of the HVP contribution to g-2, but also updated values for other precision observables. These can be compared to the results of other precision physics experiments (such as the hyperfine splitting of muonium), or, in the case of the calculation of the running of the QCD coupling, used as inputs for further measurements. The results of the updated calculation will be compared to the final Fermilab measurement and results from lattice QCD. This project therefore will make a potentially important contribution to a major test of the Standard Model and the search for new physics.