Three-Scale Factorization Theorem and Effective Field Theory

Details Three-Scale Factorization Theorem and Effective Field Theory Three-Scale Factorization Theorem and Effective Field Theory

1996-07-02

arxiv.org/abs/hep-ph/9607214v1

Phys.Rev.D55:5577-5580,1997

Physics

High Energy Physics

High Energy Physics - Phenomenology

12 pages, LaTeX, 2 Postscript figures

Scientific paper

10.1103/PhysRevD.55.5577

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 $a_2/a_1$.

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