Precision Heavy Quark Expansion

为了对标准模型(SM)的Cabibbo-Kobayashi-Maskawa机构进行严格的测试，必须有可靠的理论工具来计算必要的强子矩阵元。在精度水平上控制这些矩阵元素使得植根于量子色动力学(QCD)的方法不可或缺。特别是，不能使用模型依赖的方法，因为模型引入了不可控的系统不确定性。幸运的是，有多种基于QCD的方法可用，它们使我们可以避免使用模型。在这些基于QCD的方法中，基于重质量展开的方法起着突出的作用。它们被表述为有效场论，其中可观测量按重夸克质量的反幂展开，主导项是无限重夸克质量的极限。最重要的是，重夸克膨胀的每一级本身都有一个强耦合常数的微扰展开。根据可观测性和运动学的不同，必须使用略有不同的重夸克展开。在过去的二十年里，重夸克膨胀方法得到了广泛的发展，其中一些方法已经非常成熟。这个项目的主要目标是进一步发展基于重夸克展开的方法，更好地理解它们的理论基础，并在这些展开中进行更高阶的计算。这既包括微扰方面，也包括非微扰方面。在微扰方面，我们将通过计算未知的高阶来改进重夸克膨胀的预测，这涉及到单圈或双圈费曼图的计算。在非微扰方面，这需要从数据或QCD求和规则估计中输入次导数阶的强子矩阵元。

In order to perform a stringent test of the Cabibbo-Kobayashi-Maskawa mechanism of the Standard Model (SM) one has to have reliable theoretical tools to compute the necessary hadronic matrix elements. Controlling these matrix elements at the precision level makes methods rooted in Quantum Chromodynamics (QCD) indispensable. In particular, model dependent methods cannot be employed, since models introduce uncontrollable systematic uncertainties. Fortunately there is a variety of QCD-based methods available which - at least to leading order - allows us to avoid the use of models. Among these QCD-based methods the approaches based on the heavy mass expansion play a prominent role. They are formulated as Effective Field Theories, where the observable quantities are expanded in inverse powers of the heavy-quark mass, and the leading term is the limit of infinite heavy-quark mass. On top of this, each individual order of the heavy quark expansion has itself a perturbative expansion in powers of the strong coupling constant. Depending on the observable and the kinematics, slightly different Heavy Quark Expansions have to be employed. The heavy-quark expansion methods have been developed extensively over the past twenty years and some of them are in a very mature state. The main objective of this project is to further develop the methods based on heavy quark expansion, to better understand their theoretical foundation and to perform calculations of higher orders in these expansions. This will include both the perturbative as well as the nonperturbative aspects. On the perturbative side we shall improve the predictions of the heavy quark expansion by computing yet unknown higher orders, which involves the calculation of one- or two loop Feyman diagrams. On the nonperturbative side this requires at subleading order the input of hadronic matrix elements from either data or from QCD sum rule estimates.