Next-to-leading order corrections to B → ρ transition in the kT factorization

In this paper, we investigate the factorization hypothesis step by step for the exclusive process B -> rho at next-to-leading order (NLO), and then we extend our results to the k(T) factorization frame. We show that the soft divergence from the specific NLO diagrams will cancel each other at the quark level, while the remaining collinear divergence can be absorbed into the NLO wave functions of the mesons involved. The full NLO amplitudes can be factorized into two parts: the B meson and the rho meson NLO wave functions containing the collinear divergence and the finite leading order hard kernels. We give the general expressions of the nonlocal hadron matrix for the NLO B meson and rho meson wave functions and the analytical results of factorization for the combinations of different twist parts.