We discuss exclusive radiative decays in QCD factorization within the Standard Model. In particular, we consider the decays B -> V gamma, with a vector meson K^* or rho in the final state, and the double radiative modes B_s⁰ -> gamma gamma and B_d⁰ gamma gamma. At quark level, all these decays are governed by the flavour-changing neutral-current b -> s gamma or b -> d gamma transitions, which appear at the one-loop level in the Standard Model. Such processes allow us to study CP violation and the interplay of strong and electroweak interactions, to determine parameters of the CKM matrix, and to search for New Physics. The exclusive decays are experimentally better accessible, but pose more problems for the theoretical analysis. The heavy-quark limit m_b >> Lambda_QCD, however, allows to systematically separate perturbatively calculable hard scattering kernels from nonperturbative form factors and universal light-cone distribution amplitudes. The main results of this work are the following:

• We apply QCD factorization methods based on the heavy-quark limit to the hadronic matrix elements of the exclusive radiative decays B -> V gamma and B -> gamma gamma. A power counting in Lambda_QCD/m_b implies a hierarchy among the possible transition mechanisms and allows to identify leading and subleading contributions. In particular, effects from quark loops are calculable in terms of perturbative hard-scattering functions and universal meson light-cone distribution amplitudes rather than being generic, uncalculable long-distance contributions. Our approach is model independent and similar in spirit to the treatment of hadronic matrix elements in two-body non-leptonic B decays formulated by Beneke, Buchalla, Neubert, and Sachrajda.
• For the B -> V gamma decays we evaluate the leading Lambda_QCD/m_b contributions complete to next-to-leading order in QCD. We adopt existing results for the hard-vertex corrections and calculate in addition hard-spectator corrections, including also QCD penguin operators.
• Weak annihilation topologies in B -> V gamma are shown to be power suppressed. We prove to one-loop order that they are nevertheless calculable within QCD factorization. Because they are numerically enhanced we include the O(alpha_s⁰) annihilation contributions of current-current and QCD-penguin operators in our analysis.
• The double radiative B -> gamma gamma decays are analyzed with leading-logarithmic accuracy. In the heavy quark limit the dominant contribution at leading power comes from a single diagram. The contributions from one-particle irreducible diagrams are power suppressed but still calculable within QCD factorization. We use these corrections, including QCD penguins, to estimate CP asymmetries in B -> gamma gamma and so-called long-distance contributions in B and D -> gamma gamma.
• We predict branching ratios, CP and isospin asymmetries, and estimate U-spin breaking effects for B -> K^* gamma and B -> rho gamma. For the B -> gamma gamma decays we give numerical results for branching ratios and CP asymmetries. Varying the individual input parameters we estimate the error of our predictions. The dominant uncertainty comes from the poorly known nonperturbative input parameters.