Proof of factorization for B→Dπ -: art. no. 201806

We prove that the matrix elements of four fermion operators mediating the decays (B) over bar (0) --> D+ pi (-) and B- --> D(o)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 q (q) over bar Fock state.