Radiative $B \to K^* \gamma $ transition in QCD

We evaluate the branching ratios of the radiative decays $B \to K^* \gamma$, and $B \to K_1 \gamma$ in the framework of three-point function QCD sum rules. We find: $\Gamma(B \to K^* \gamma) / \Gamma(b \to s \gamma) = 0.17 \pm 0.05$ and $\Gamma(B \to K_1 \gamma) / \Gamma(b \to s \gamma) = 0.30 \pm 0.15$. We also study, in the infinite quark mass limit, the connection between the form factor of the radiative $B \to K^* \gamma$ transition and the weak hadronic form factors entering the semileptonic B-meson decays.