We develop a perturbative QCD factorization theorem which is compatible with effective field theory. The factorization involves three scales: an infrared cutoff of order ΛQCD, a hard scale of the order of the B meson mass, and an ultraviolet cutoff of the order of the W boson mass. Our approach is renormalization-group invariant and moderates the scale-dependent problem in effective field theory. Employing this formalism with nonfactorizable contributions included, we clarify the controversy over the BSW parameters a₂/a₁ for charm and bottom decays.
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Chang et al. (1997) studied this question.