QCD estimate of the long-distance effect in $B \to K^* \gamma$

Abstract

We suggest to use operator product expansion and QCD sum rule techniques to estimate the long-distance contribution to the amplitude of the exclusive rare decay $B\to K^* \gamma$. In contrast to a phenomenological description in terms of $\psi$ resonances converting into a photon, the virtual charm quark loop interacting with soft gluons is represented by a new quark-gluon-photon operator. The matrix element of this operator is calculated in the same approximation as the matrix element of the leading magnetic penguin operator. The overall correction is found to be small, not more than about 5%.