QCD factorisation in exclusive semileptonic B decays : new applications and resummation of rapidity logarithms

Exclusive charmless decays of heavy B-mesons play an important role both in testing the Standard Model of particle physics as well as in searches for new physics. Due to the non-perturbative nature of the strong interactions, reliable predictions for hadronic decay rates are intrinsically difficult to estimate. Exploiting the simplifications of the strong interaction dynamics that arise in the heavy-quark limit, the "QCD factorisation approach" (QCDF) allows for a separation of perturbative and non-perturbative effects in these decays. In this thesis we present new applications of the QCDF approach and investigate cases where the factorisation is not yet understood. In a first project, we introduce a novel factorisation formula for form factors in semileptonic multi-body B → ππlν decays that is valid for large pion energies and a large dipion invariant mass. We present phenomenological implications in the form of approximate form factor relations, which can be used to interpolate between different phase-space regions. Theoretically, a careful consideration of endpoint-divergent moments is crucial in the confirmation of the factorisation formula. They either cancel in factorisable contributions or can be absorbed into simpler and more universal B → π form factors. For the B → π form factors themselves, a complete factorisation of scales is presently not understood as a consequence of ill-defined convolution integrals. We investigate these so-called "endpoint divergences" in a perturbative toy model, in which the hadronic states are approximated as non-relativistic bound states of two heavy quarks. The relativistic QCD dynamics is then calculable in perturbation theory, and by employing the method of regions the factorisation properties can be studied. Fairly new methods that go under the names rapidity renormalisation group and collinear anomaly have been successfully applied to handle endpoint divergences in collider physics observables. In this thesis we apply these techniques to heavy-to-light form factors at large hadronic recoil. As a first step on the way to establish an all-order factorisation theorem, we present an improved factorisation that contains a resummation of all leading logarithms within the perturbative model. Due to operator mixing, the structures that arise in the resummed expression are more complicated but also more interesting than in collider physics applications of these methods.