Charmless B-decays in Soft-Collinear Effective Theory

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B-meson decays into light hadrons play a central role in testing the Cabibbo-Kobayashi-Maskawa mechanism of quark flavour mixing and CP violation. Within the Standard Model (SM), charmless B-decays are mediated by rare b -» u quark transitions or by loop-induced b -» d/s decays that are sensitive to effects from new heavy particles beyond the SM. The phenomenology of charmless B-decays is extremely rich, ranging from semiieptonic B -> X_u I nu to nonleptonic 8 -> K pi and radiative B -> X_s gamma decays. Most of the chamnless B-decays will be scrutinized at the Large Hadron Collider and the super-flavour factory Belle II in the next few years. A meaningful interpretation of the experimental data requires to control the underlying hadronic matrix elements in QCD. The heavy quark expansion (HQE) as well as its field-theoretical incarnation in terms of effective field theories (EFTs) provide a systematic framework to compute the hadronic matrix elements in a twofold expansion in l/m_b and alpha_s(m_b). At leading power in the HQE the hadronic matrix elements factorize into perturbative coefficient functions and process-independent hadronic parameters. The factorization is particularly involved for decays with energetic particles in the final state. The energetic degrees of freedom prevent a local operator product expansion, and one Is left with convolutions of hard-scattering kernels with nonlocal hadronic matrix elements. The relevant EFT is called Soft-Collinear Effective Theory (SCET) and one distinguishes between two different versions depending on the physical context. SCET-1 is the appropriate EFT for inclusive B-decays. The factorization of the differential decay rates in the endpoint region is well established. SCET-1 also provides the means to resum logarithmic corrections to all orders in perturbation theory based on renormalization group (RG) techniques. The theoretical understanding of exclusive B-decays within SCET-2 is currently incomplete. The problem is related to the separation of the various long-distance modes which result in endpoint-divergent convolution integrals. At present, one typically tries to circumvent this problem by absorbing the endpoint-sensitive contributions into hadronic parameters. While such a procedure limits the application of the EFT techniques, a better understanding of the endpoint dynamics is desirable. The project aims at improving the SCET techniques in various respects. First, the factorization of exclusive B-decay rates will be revisited. In the last few years, there has been considerable progress in understanding SCET-2 factorization theorems for collider physics observables. The new techniques go under the names 'collinear anomaly' and 'rapidity RG', and the project aims at transfemng these techniques to B-physics applications. In addition, RG properties of nonperturbative input parameters will be investigated and new factorization theorems for decays into multi-body final states will be derived.