  In this paper, we investigate the factorization hypothesis step by step for
the exclusive process $B \to \rho$ at next-to-leading order (NLO) with the
collinear factorization approach, 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. The full NLO
amplitudes can be factorized into two parts: the NLO $B$ and $\rho$ meson wave
functions containing the collinear divergence and the leading order (LO) finite
hard kernels. We give the general form of the nonlocal hadron matrix for the
NLO $B$ and $\rho$ meson wave functions and all results of factorization for
different twists' combinations.
