Higher Order Qcd Corrections in Exclusive Charmless B Decays

We discuss exclusive charmless B decays within the Standard Model of particle physics. These decays play a central role in the on-going process to constrain the parameters of the CKM matrix and to clarify the nature of CP violation. In order to exploit the rich source of data that is currently being collected at the experiments, a systematic theoretical treatment of the complicated hadronic dynamics is strongly desired. QCD Factorization represents a model-independent framework to compute hadronic matrix elements from first principles. It is based on a power expansion in ΛQCD/mb and allows for the systematic implementation of perturbative corrections. In particular, we consider hadronic two-body decays as B → ππ and perform a conceptual analysis of heavy-to-light form factors which encode the strong interaction effects in semi-leptonic decays as B → πlν. Concerning the hadronic decays we compute NNLO QCD corrections which are particularly important with respect to strong interaction phases and hence direct CP asymmetries. On the technical level, we perform a 2-loop calculation which is based on an automatized reduction algorithm and apply sophisticated techniques for the calculation of loop-integrals. We indeed find that the considered quantities are well-defined as predicted by QCD Factorization, which is the result of a highly complicated subtraction procedure. We present results for the imaginary part of the topological tree amplitudes and observe that the considered corrections are substantial. The calculation of the real part of the amplitudes is far more complicated and we present a preliminary result which is based on certain simplifications. Our calculation is one part of the full NNLO analysis of nonleptonic B decays within QCD Factorization which is currently pursued by various groups. In our conceptual analysis of the QCD dynamics in heavy-to-light transitions we consider form factors between non-relativistic bound states which can be addressed in perturbation theory. We perform a NLO analysis of these form factors and discuss some open questions of the general factorization formula which is obtained from the heavy-quark expansion in QCD. These include the origin and resummation of large logarithms and the non-factorization of soft and collinear effects in the so-called soft-overlap contribution. We show that the latter can be calculated in our set-up and address the issue of endpoint singularities. As a byproduct of our analysis, we calculate leading-twist light-cone distribution amplitudes for non-relativistic bound states which can be applied for the description of Bc and ηc mesons.