Asymptotics of QCD factorization in exclusive hadronic decays of B mesons

Using the renormalon calculus, we study the asymptotic behavior of die perturbative expansion of the hard-scattering kernels entering the QCD factorization formula for the nonleptonic weak decays (B) over bar (0) --> D(*)+ M-, where M is a light meson. In the "large-beta (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 Lambda (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(beta (n-1)(0) alpha (n)(s)) corrections to explore the numerical significance of higher-order perturbative and power corrections. We also derive explicit expressions for the O(beta (0) alpha (2)(s)) contributions to the kernels, and for the renormalon singularities corresponding to power corrections of order (Lambda (QCD)/m(b))(2). Finally, we study the limit m(c) --> 0 relevant to charmless hadronic decays such as B --> pi pi. (C) 2001 Elsevier Science B.V. All rights reserved.