Decay modesBd,s0¯→γD*0

Abstract

The various decay modes of the type $B\ensuremath{\rightarrow}\ensuremath{\gamma}{D}^{*}$ are dynamically different. In general, there are factorized contributions of pole and nonpole type, and pseudoscalar exchange contributions at meson level. The purpose of this paper is to point out that the decay modes $\overline{{B}_{d,s}^{0}}\ensuremath{\rightarrow}\ensuremath{\gamma}{D}^{*0}$ have small contributions from such mechanisms, in contrast to the decay modes $\overline{{B}_{d,s}^{0}}\ensuremath{\rightarrow}\ensuremath{\gamma}\overline{{D}^{*0}}$ and ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\gamma}{D}_{s,d}^{*\ensuremath{-}}$. On the other hand, there are nonfactorizable $1/{N}_{c}$ suppressed contributions from colored four quark operators obtained from Fierz transformations of the standard four quark operators. Such $1/{N}_{c}$ suppressed terms involving emission of soft gluons are calculated within a heavy-light chiral quark model, and they are found to dominate the amplitudes for the decay modes $\overline{{B}_{d,s}^{0}}\ensuremath{\rightarrow}\ensuremath{\gamma}{D}^{*0}$. We estimate the branching ratio for these modes in the low velocity regime, i.e. in the heavy quark limit, both for the $b$ and the $c$ quarks. In this limit we obtain a value $\ensuremath{\simeq}1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ for $\overline{{B}_{d}^{0}}\ensuremath{\rightarrow}\ensuremath{\gamma}{D}^{*0}$, and $\ensuremath{\simeq}6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ for $\overline{{B}_{s}^{0}}\ensuremath{\rightarrow}\ensuremath{\gamma}{D}^{*0}$. We expect substantial corrections to these numbers because the energy gap between the $b$- and $c$-quark masses are significantly bigger than 1 GeV. However, we expect that our estimates of the amplitudes for $\overline{{B}_{d,s}^{0}}\ensuremath{\rightarrow}\ensuremath{\gamma}{D}^{*0}$ give the right order of magnitude because other mechanisms are numerically suppressed in this special case.