Non-leptonic B decays are with their rich phenomenology ideally suited to study
the quark flavour sector of the Standard Model (SM) of particle physics. They
have been measured extensively at collider experiments. On the theoretical side
their description is complicated due the appearance of strong interactions
ranging from short- to long-distance physics scales. QCD factorization (QCDF)
is a model-independent framework that disentangles such short-distance and
long-distance effects in the heavy-mass limit. It allows one to systematically
calculate transition amplitudes to leading power in Lambda(QCD)/m(b) in a
perturbative expansion in the strong coupling. QCDF has already been
successfully applied to non-leptonic two-body decays. In contrast, for
non-leptonic three-body decays no genuine QCD-based description has been
developed so far. In this work we consider two applications of QCDF.
First, we evaluate the perturbative vertex corrections to the colour-allowed
tree topology of the decay anti-B0 --> D+ pi- to next-to-next-to leading order
accuracy. The calculation is technically challenging and involves the reduction
of several thousand scalar two-loop two-scale integrals to master integrals
which have to be evaluated thereafter. For the reduction we apply the Laporta
algorithm and for evaluating the master integrals we use common methods
like differential equations and Mellin Barnes representations. In addition, we
apply a novel approach to obtain analytical results for all master integrals in
a canonical basis. As the decay anti-B0 --> D+ pi- is dominated by SM physics a
comparison of theoretically calculated observables with experimental data
allows us to estimate the size of the neglected power corrections that arise in
QCDF due to the finite mass of the b quark.
In the second part of the thesis we apply QCDF to non-leptonic three-body
decays such as B+ --> pi+ pi- pi+. As the kinematics of three-body decays is
not fixed in contrast to two-body decays, the final-state particles populate a
kinematic phase space (the Dalitz plot). We identify special kinematic
configurations as regions in the Dalitz plot. Adopting the well-established
factorization properties of non-leptonic two-body decays, we employ different
descriptions in the central region and in the edges of the Dalitz plot. In
contrast to the two-body case, this requires introducing generalized
non-perturbative quantities such as B --> pi pi form factor and two-pion
distribution amplitudes. We evaluate the transition amplitudes in the different
regions to leading power in Lambda(QCD)/m(b) and to leading order in the strong
coupling. Finally, we investigate the prospects of a matching of the
descriptions in both regions for a physical value of the b-quark mass.