Pushing the precision in B physics

Semi- and non-leptonic decays of B mesons offer a powerful probe for the flavour sector in the Standard Model (SM). With ever increasing amounts of experimental data from particle colliders, the need for more precise, but also more utilizable and reliable theoretical predictions is growing. In this work, we study the inclusive semileptonic decays B -> X_c l nu and B -> X_u l nu$ and extract the CKM elements Vcb and Vub from them, respectively. In addition, we investigate the extent of CP violation in the non-leptonic decay B -> 3 pi.
The description of these three decays is complicated due to the appearance of short- and long-distance effects in the strong interactions. In order to disentangle the pieces that can be determined from a perturbative expansion and the genuinely non-perturbative ones, we make use of an Operator Product Expansion. We collect all state-of-the-art corrections to the expressions and summarize them into open-source software packages.
For the decay B -> X_c l nu$, we exploit the Reparameterization Invariance (RPI) of the Heavy Quark Effective Theory to reduce the number of non-perturbative matrix elements. Subsequently we use the recently measured moments of the lepton invariant mass to extract a new value for Vcb in the Heavy Quark Expansion.
In the decay B -> X_u l nu it is necessary to subtract the unwanted background of the decay into a charmonium final state. This restriction causes the appearance of non-local shape functions, which have to be modelled. We include all available information about the leading and subleading shape functions and determine a cluster of models to find a reasonable estimate for the model uncertainty. Furthermore we include all perturbative corrections up to alpha_s^2 to finally calculate partial rates with various kinematical cuts and extract Vub from them.
Unlike the aforementioned semileptonic decays, the non-leptonic decay B -> 3 pi shows pronounced features in the CP landscape that are difficult to explain with theoretical methods. In recent amplitude analyses, only resonance contributions were included to dynamically generate the strong phase. We suggest a new parameterization of charm-loop effects, which can cause intricate structures in the CP landscape, while at the same time being easy to implement in current analyses. We discuss the implications of this approach and how the underlying physics can be made more visible by changing to a suitable set of physical operators in the analysis.