  We develop a perturbative QCD factorization theorem which is compatible with
effective field theory. The factorization involves three scales: an infrared
cutoff of order $\Lambda_{\rm QCD}$, a hard scale of order the $B$ meson mass,
and an ultraviolet cutoff of order the $W$ boson mass. Our approach is
renormalization group invariant and moderates the scale-dependence problem in
effective field theory. Applying this formalism to exclusive nonleptonic $B$
meson decays, we clarify the controversy over the Bauer-Stech-Wirbel parameters
$a_2/a_1$ for charm and bottom decays. It is found that the nonfactorizable
contribution plays an important role in the explanation of the sign and
magnitude of $a_2/a_1$.
