Inclusive Decays of B Mesons into D_s and $D_s^{\ast }$ at $O({\alpha }_s)$ Including $D_s^{\ast }$ Polarization Effects

The dominant contribution to the inclusive decays of $B$ mesons into the charm-strangeness mesons $D_s$ and $D_s^{\ast }$ is expected to be given by the partonic process $b\to c+(D_s^{-},D_s^{\ast -})$. We determine the nonperturbative $O(1\mathrm{/}{m}_b^2)$ and the $O({\alpha }_s)$ radiative corrections to $b \to c+(D_s^-,D_s^{\ast -})$andtherebytotheinclusivedecays$ \bar{B} \to X_c+(D_s^-,D_s^{\ast -})$. The new feature of our calculation is that we separately determine the nonperturbative and the $O({\alpha }_s)$ corrections to the longitudinal ($L$) and transverse ($T$) pieces of the spin 1 $D_s^{\ast -}$ meson. The longitudinal/transverse composition of the $D_s^{\ast -}$ can be probed through its two principal decay modes $D_s^{\ast -}\to D_s^{-}+\gamma$ and $D_s^{\ast -}\to D_s^{-}+{\pi }^0$ for which we write down the angular decay distributions.