On the Decay Modes $\bar{B_{d,s}^0} \to \gamma D^{*0}$

The various decay modes of the type $B \to \gamma D^*$ are dynamically different. In general there are factorizable contributions, and there are pole diagrams and pseudoscalar exchange contributions at meson level. The purpose of this paper is to point out that the decay modes $\bar{B_{d,s}^0} \to \gamma D^{*0}$ have negligible contributions from such mechanisms, in contrast to the decay modes $\bar{B_{d,s}^0} \to \gamma \bar{D^{*0}}$ and $B^- \to \gamma D_{s,d}^{*-}$. However, for the decay modes $\bar{B_{d,s}^0} \to \gamma D^{*0}$ there are non-factorizable contributions due to emision of soft gluons, and such non-factorizable contributions are found to dominate the amplitudes for these latter decay modes. We estimate the branching ratio for these modes in the heavy quark limits, both for the $b$- and the $c$- quarks, and obtain a value $\simeq 1.6 \times 10^{-6}$ for $\bar{B_{d}^0} \to \gamma D^{*0}$, and $\simeq 8 \times 10^{-7}$ for $\bar{B_{s}^0} \to \gamma D^{*0}$. We expect large corrections to this limit because the energy gap between the $b$- and $c$- quark masses are significantly bigger than 1 GeV. However, we expect that our estimate for $\bar{B_{d,s}^0} \to \gamma D^{*0}$ gives the right order of magnitude for the {\em amplitudes}.