Using methods of effective field theory, factorized expressions for arbitraryB → X u l −ν decay distributions in the shape-function region of large hadronic energy and moderate hadronic invariant mass are derived. Large logarithms are resummed at next-to-leading order in renormalization-group improved perturbation theory. The operator product expansion is employed to relate moments of the renormalized shape function with HQET parameters such as m b ,Λ and λ 1 defined in a new physical subtraction scheme. An analytic expression for the asymptotic behavior of the shape function is obtained, which reveals that it is not positive definite. Explicit expressions are presented for the chargedlepton energy spectrum, the hadronic invariant mass distribution, and the spectrum in the hadronic light-cone momentum P + = E H − | P H |. A new method for a precision measurement of |V ub | is proposed, which combines good theoretical control with high efficiency and a powerful discrimination against charm background.

We provide a model-independent framework for the analysis of the radiative B-meson decays B → K * γ and B → ργ. In particular, we give a systematic discussion of the various contributions to these exclusive processes based on the heavy-quark limit of QCD. We propose a novel factorization formula for the consistent treatment of B → V γ matrix elements involving charm (or up-quark) loops, which contribute at leading power in Λ QCD /m B to the decay amplitude. Annihilation topologies are shown to be power suppressed. In some cases they are nevertheless calculable. The approach is similar to the framework of QCD factorization that has recently been formulated for two-body non-leptonic B decays. These results allow us, for the first time, to compute exclusive b → s(d)γ decays systematically beyond the leading logarithmic approximation. We present results for these decays complete to next-to-leading order in QCD and to leading order in the heavy-quark limit. Phenomenological implications for various observables of interest are discussed, including direct CP violation, and isospin and U-spin breaking effects.

Soft-collinear effective theory is used to prove factorization of the B → γlν decay amplitude at leading power in Λ/m b , including a demonstration of the absence of non-valence Fock states and of the finiteness of the convolution integral in the factorization formula. Large logarithms entering the hard-scattering kernel are resummed by performing a two-step perturbative matching onto the low-energy effective theory, and by solving evolution equations derived from the renormalization properties of the leading-order B-meson light-cone distribution amplitude. As a byproduct, the evolution equation for heavy-collinear current operators in soft-collinear effective theory is derived.

The contributions of subleading shape functions to inclusive decay distributions of B mesons are derived from a systematic two-step matching of QCD current correlators onto soft-collinear and heavy-quark effective theory. At tree-level, the results can be expressed in terms of forward matrix elements of bi-local light-cone operators. Fourquark operators, which arise at O(α s ), are included. Our results are in disagreement with some previous studies of subleading shape-function effects. A numerical analysis ofB → X u l −ν decay distributions suggests that power corrections are small, with the possible exception of the endpoint region of the charged-lepton energy spectrum.