We consider rare radiative B decays such as B -> K^* gamma or B -> rho gamma
in soft-collinear effective theory, and show that the decay amplitudes are
factorized to all orders in alpha_s and at leading order in Lambda/m_b.By
employing two-step matching, we classify the operators for radiative B decays
in powers of a small parameter lambda(~ \sqrt{Lambda/m_b}) and obtain the
relevant operators to order lambda 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 Lambda/m_b, and evolve the operators
in order to compute the decay amplitudes for rare radiative decays in
soft-collinear effective theory. We show explictly 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
alpha_s.Comment: v2: 31 pages, 11 figures. An appendix is added about the quark mass
effects on radiative B decay
