Rare radiative exclusive B decays in soft-collinear effective theory

We consider rare radiative B decays such as B̄→K*γ or B→ργ in soft-collinear effective theory (SCET) and show that the decay amplitudes are factorized to all orders in α_s and at leading order in Λ_QCD/m_b. By employing two-step matching, we classify the operators for radiative B decays in powers of a small parameter λ(∼ √Λ_QCD/m_b) and obtain the relevant operators to order λ in SCET_I. These operators are constructed with or without spectator quarks including the four-quark operators contributing to annihilation and W-exchange channels. And we employ SCET_II where the small parameter becomes of order Λ_QCD./m_b, and evolve the operators in order to compute the decay amplitudes for rare radiative decays in soft-collinear effective theory. We show explicitly that the contributions from the annihilation channels and the W-exchange channels vanish at leading order in SCET. We present the factorized result for the decay amplitudes in rare radiative B decays at leading order in SCET and at next-to-leading order in α_s.