Asymptotics of QCD factorization in exclusive hadronic decays of B mesons Original Research Article

Using the renormalon calculus, we study the asymptotic behavior of the perturbative expansion of the hard-scattering kernels entering the QCD factorization formula for the nonleptonic weak decays B̄ 0→D(∗)+M−, where M is a light meson. In the “large-β0 limit”, the kernels are infrared finite and free of endpoint singularities to all orders of perturbation theory. The leading infrared renormalon singularity corresponding to a power correction of order ΛQCD/mb vanishes if the light meson has a symmetric light-cone distribution amplitude. We calculate the Borel transforms and the corresponding momentum distribution functions of the hard-scattering kernels, and resum the series of O(β0n−1αsn) corrections to explore the numerical significance of higher-order perturbative and power corrections. We also derive explicit expressions for the O(β0 αs2) contributions to the kernels, and for the renormalon singularities corresponding to power corrections of order (ΛQCD/mb)2. Finally, we study the limit mc→0 relevant to charmless hadronic decays such as B→ππ.