Precision Heavy Quark Expansion

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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.