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

We consider nonleptonic B decays into two light mesons at leading order in soft-collinear effective theory, and show that the decay amplitudes are factorized to all orders in alpha_s. The operators for nonleptonic B decays in the full theory are first matched to the operators in SCET_I, which is the effective theory appropriate for sqrt{m_b Lambda} <mu <m_b with Lambda~0.5 GeV. We evolve the operators and the relevant time-ordered products in SCET_I to SCET_II, which is appropriate for mu < sqrt{m_b Lambda}. Using the gauge-invariant operators in SCET_II, we compute nonleptonic B decays in SCET, including the nonfactorizable spectator contributions and spectator contributions to the heavy-to-light form factor. As an application, we present the decay amplitudes for B ->pi,pi in soft-collinear effective theory.