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

Abstract

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 α 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 m bΛ <μ<m b with Λ∼0.5 GeV. We evolve the operators and the relevant time-ordered products in SCET I to SCET II, which is appropriate for μ< m bΛ . 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 B ̄ →ππ in soft-collinear effective theory.