Precision Physics in Finite and Infinite Volume

粒子物理的标准模型(SM)在它的许多预测中都取得了巨大的成功，但在某些情况下，它似乎与实验测量结果相吻合。这些差异可能是迄今未知的物理学线索，因此发现模型中的所有缺陷是非常重要的。在这个为期两年的项目中，我将及时和雄心勃勃地进行精确度测试所需的低能量SM计算，这些计算可以在未来指导寻找新的模型。这个项目分为两个方面。第一个集中在味道物理学上，夸克相互作用导致电荷-宇称破坏，这是一种与宇宙的物质-反物质不对称有关的现象。在这里，我将研究有限体积时空中的介子衰变，包括电磁修正。主要的焦点将是如何将这些介子衰变的有限体积晶格结果解析地转换为物理预测。一个关键的中间步骤将是理解包括电磁修正在内的介子-介子散射，这本身对于从晶格中提取散射参数也是有意义的。第二个焦点领域涉及已发现可能与实验不符的介子磁矩。这里的主要焦点将是分析计算，以减少SM预测的误差。在一个子项目中，我们将推导出强子真空偏振的主要依赖于结构的有限体积效应，以允许将来从所讨论的量的晶格QCD+QED进行改进的精度测试。在另一个子项目中，我们将借助算符乘积展开得到电弱对Muon磁矩贡献的短距离约束。这些短距离约束将减少电流对弱电贡献的不确定性。

The Standard Model (SM) of particle physics has had great success in its many predictions, but in certain cases there appears to betension with experimental measurements. These discrepancies could be hints of physics hitherto unknown, so it is of greatimportance to discover all flaws in the model. In this two-year project I will do timely and ambitious low-energy SM calculationsneeded for precision tests that in the future can guide in the search for a new model.This project is divided in two areas. The first focusses on flavour physics where quark interactions lead tocharge-parity violation, a phenomenon connected to the matter-antimatter asymmetry of the Universe. I willhere study kaon decays in a finite-volume spacetime, including electromagnetic corrections. The major focus point will be how toanalytically convert finite-volume lattice results for these kaon decays to physical predictions. A key intermediate step will be theunderstanding of pion-pion scattering including electromagnetic corrections, which on its own also is of interest for extraction ofscattering parameters from the lattice.The second focus area concerns the muon magnetic moment for which a possible discrepancy with experiments has beendiscovered. The main focus here will be on analytical calculations to reduce the error on the SM prediction. In one sub-project we willderive the leading structure-dependent finite-volume effects for the hadronic vacuum polarisation allowing for future improvedprecision tests from lattice QCD+QED of the quantity in question. In the other sub-project we will derive short-distance constraints onthe electroweak contribution to the muon magnetic moment with the help of the operator product expansion. These short-distanceconstraints will reduce the current uncertainty on the electroweak contribution.