Proof of factorization for B → Dπ

We prove that the matrix elements of four fermion operators mediating the decays B^¯0 → D⁺π⁻ and B⁻ → D⁰π⁻ factor into the product of a form factor describing the B → Dπ transition and a convolution of a short distance coefficient with the nonperturbative pion light-cone wave function. This is shown to all orders in α_s, with corrections suppressed by factors of 1/m_b, 1/m_c, and 1/E_π. It is not necessary to assume that the pion state is dominated by the qq^¯ Fock state.