Higher Order Corrections to Nonleptonic and Rare Decays

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Nonleptonic exclusive decays of heavy mesons play a decisive role in quantifying the amount of CP violation, the most subtle phenomenon of flavour physics. In order to be competitive with precise measurements from current and future collider facilities, precision predictions from the theory side are indispensable for our understanding of the quark sector of the Standard Model (SM) and potentially even for finding hints for new physics. The aim of this project is to combine effective theory methods with the analysis of decay topologies and flavor symmetry relations and to increase the precision of the predicted amplitudes of two and three-body nonleptonic decays of bottomed (B) and charmed (D) mesons. For the two-body decays the emphasis is on achieving a quantitatively new level of accuracy. To this end we follow two approaches. On the one hand corrections to factorization theorems will be calculated in the effective theory framework, notably QCD factorization elaborated within Soft-Collinear Effective Theory. Besides higher-order perturbative (multi-loop) corrections, we will focus on contributions that are power-suppressed with respect to the inverse of the heavy quark mass. On the other hand we will make use of flavour symmetries and their breaking. By means of group-theoretical parameterizations of flavor symmetries we will derive amplitude relations which will be used for a model-independent description of the observables in these decays. One of the major goals is to quantify the final-state rescattering phases in two-body nonleptonic B-decays. Three-body decays offer ideal opportunities to search for CP violation in differential distributions. Therefore, the main effort will be aimed at phenomenological models for the Dalitz-distributions of the final states. Besides the more formal aspects such as the validity of factorization theorems at higher orders of the perturbative expansion, we will also perform dedicated phenomenological analyses which update and improve the theory predictions for nonleptonic B- and D-decays into light – in the case of B-mesons also into heavy – final states. In doing so, we will use updated and improved input parameters as well as reliable estimates for the universal hadronic matrix elements, derived from nonperturbative methods such as QCD sum rules and light-cone sum rules. Compared to nonleptonic B-decays, D-decays provide an important complementary test of CP violation within the SM. Since the mass of the charm quark is smaller than the mass of the bottom quark, and hence is further away from the heavy-mass limit, the theoretical description of D-meson decays is expected to be shaped by enhanced power corrections, which have to be carefully investigated and quantified.