Proof of Factorization forB→Dπ

Abstract

We prove that the matrix elements of four fermion operators mediating the decays B macro (0)-->D(+)pi(-) and B--->D(0)pi(-) factor into the product of a form factor describing the B-->D transition and a convolution of a short distance coefficient with the nonperturbative pion light-cone wave function. This is shown to all orders in alpha(s), with corrections suppressed by factors of 1/m(b), 1/m(c), and 1/E(pi). It is not necessary to assume that the pion state is dominated by the qq macro Fock state.