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

费米实验室μ介子g-2实验的测量结果与理论预测之间的持续紧张关系表明了标准模型之外的新物理学的潜力。通过分析运行2和运行3数据，费米实验室测量的精度提高了两倍，并且一旦分析了收集的所有数据，预计将再次提高相同的因子。这种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。虽然其他贡献的预测可以在微扰理论的框架内计算，HVP的贡献必须从色散或晶格QCD方法计算。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贡献的色散计算。要考虑的新数据集包括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其他实验（包括CMD-2）所获得的结果之间存在相当大的差异。有必要确定最好的方法来把这些数据和先前的结果一起包括进来，因为它们似乎与先前的结果不相容。对于HVP对g-2的贡献，色散和格点QCD预测之间也存在着明显的矛盾。当用格点QCD进行HVP计算时，得到了与实验结果更一致的结果。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，可以对所谓的窗口观测值进行色散预测，并与格点QCD群的色散预测进行比较。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功能，如关系数据库，并使代码更容易访问。从一开始计算就将采用盲法程序，目的是避免最终结果产生偏差。随着项目的进展，规范中使用的统计方法将得到改进，目的是分配更准确的不确定性。系统的不确定性和相关性的作用也将受到审查。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。将制定协调紧张局势数据集的无偏见方法，并应用于解决悬而未决的潜在问题。此外，分析中辐射校正的处理也将得到改进，该项目不仅将产生HVP对g-2贡献的更新色散计算，还将产生其他精密观测值的更新值。这些结果可以与其他精密物理实验的结果（如μ介子的超精细分裂）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最终的费米实验室测量结果和格点QCD结果进行比较。因此，该项目将为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.