Three-Scale Factorization Theorem and Effective Field Theory

Abstract

We develop a perturbative QCD factorization theorem which is compatible with effective field theory. The factorization involves three scales: an infrared cutoff of order ${\Lambda }_{\mathrm{QCD}}$, 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 $a_2/a_1$.

12 pages, LaTeX, 2 Postscript figures

References in corpus (1)

• Internal W-emmission and W-exchange Contributions to {\bf B}\to {{\bf D}^{(*)} Decays

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