Branching ratio and direct CP-violating rate asymmetry of the rare decays $B \to K^\ast γ$ and $B \to ργ$

We calculate CP-violating rate asymmetries in the rare radiative decays $B^\pm\rightarrow K^{\ast\pm} \gamma$ and $B^\pm\rightarrow \rho^\pm \gamma$. They arise because of the interference between leading-order penguin amplitudes and one-gluon corrections with absorptive phases, and provide unambiguous evidence for direct CP violation. Complementing earlier studies, we also investigate gluon exchange with the `spectator' quark. The bound state effects in the exclusive matrix elements are taken into account by a covariant model, which yields a branching ratio $BR(B\rightarrow K^\ast \gamma) = (4-5)\times 10^{-5}$ in good agreement with the observed value. The bound state effects increase the CP asymmetry, which is of order $1 \%$ in the channel $B\rightarrow K^\ast \gamma$ and $15 \%$ for $B \to \rho \gamma$.