NLL Corrections for B-Meson Radiative Exclusive Decays

We calculate the next-to-leading corrections to the branching ratio of exclusive $B\to K^* \gamma$ decay. The renormalization scale dependence is reduced compared to the leading logarithmic result but there remains a dependence on a cutoff parameter of the hadronic model. The calculated corrections increase the predicted branching ratio by about 10%, but it remains in agreement with the experimental value.