Perturbative QCD and non-leptonic B decays

We develop a perturbative QCD factorization theorem for the non-leptonic heavy meson decays. The factorization involves three scales: an infrared cutoff of order Lambda(QCD), a hard scale of order the heavy meson mass, and an ultraviolet cutoff of order the W boson mass. Unlike the conventional Bauer-Stech-Wirbel factorization approximation, our factorization is scale independent. Applying this formalism, we clarify the controversy over the 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).