Non-leptonic B decays into two light mesons in soft-collinear effective theory

We consider non-leptonic B decays into two light mesons at leading order in soft-collinear effective theory, and show that the decay amplitudes are factorized at next-to-leading order in _s. The operators for non-leptonic B decays in the full theory are first matched to the operators in SCET_I, which is the effective theory appropriate for with Λ0.5 GeV. We evolve the operators and the relevant time-ordered products in SCET_I to SCET_II, which is appropriate for . Using the gauge-invariant operators in SCET_II, we compute non-leptonic B decays in SCET, including the non-factorizable spectator contributions and spectator contributions to the heavy-to-light form factor. As an application, we present the decay amplitudes for in soft-collinear effective theory.