QCD factorization for hadronic B decays: Proofs and higher-order corrections

Several issues related to the QCD factorization approach to exclusive hadronic B decays are discussed. This includes a proof of factorization in B → K*γ using the soft-collinear effective theory, and an examination of higher-order corrections to QCD factorization for two-body decays into heavy-light states, such as B → Dπ, and light-light final states, such as B → Kπ,ππ.; The proof of factorization in B → K*γ is arguably the most complicated QCD factorization formula proven so far. It is shown that reparameterization invariance in the intermediate effective theory restricts the appearance of transverse momentum components and 3-particle Fock states to operators that can be absorbed into the QCD from factor. This proof also includes an extension of SCET to deal with two collinear directions.; The examination of higher-order corrections to QCD factorization has implications for using this technique to extract CP violating weal; phases from data taken at the B factories. The renormalon calculus is used to calculate the $b0a2s$ contributions to the hard scattering kernels, and also to analyze the strength of power corrections due to soft gluon exchange. It is shown that while power corrections are generally small, the higher-order perturbative contributions to the hard scattering kernels have much larger imaginary parts than those at next-to-leading order (NLO). This significantly enhances some CP asymmetries compared to the NLO results, which is an effect that would survive a two-loop calculation unless there were large multi-loop corrections not related to the $b0a2s$ terms of the perturbative expansion.