Asymptotics of QCD factorization in exclusive hadronic decays of B mesons

Abstract

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 B ̄ 0 →D (∗)+M − , where M is a light meson. In the “large- β 0 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 Λ QCD/ m b 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( β 0 n−1 α s n ) corrections to explore the numerical significance of higher-order perturbative and power corrections. We also derive explicit expressions for the O(β 0 α s 2) contributions to the kernels, and for the renormalon singularities corresponding to power corrections of order ( Λ QCD/ m b ) 2. Finally, we study the limit m c →0 relevant to charmless hadronic decays such as B→ ππ.