Calculation of Long-Distance Effects in Exclusive Weak Radiative Decays of B-Mesons

Abstract

We calculate the contribution of the weak annihilation to the $B\to \rho \gamma$ decay amplitude by means of QCD sum rules using the photon light-cone wave function. We find that this long-distance contribution amounts to about 10\% of the leading short-distance effect in $B^{-}\to {\rho }^{-}\gamma$. On the other hand, weak annihilation is the dominant source of the corresponding $D$ meson decays and according to our estimates, yields branching ratios of $O(10^{-4})$ for $D^0\to {\bar{K}}^{\ast 0}\gamma$, $O(10^{-5})$ for $D_s\to {\rho }^{+}\gamma$, and $O(10^{-6})$ for $D^{-}\to {\rho }^{-}\gamma$ and for $D^0\to {\rho }^0\gamma$.

Comments: 14 pages, Latex, two figures added as an uuencoded .ps file