Semi-inclusive nonleptonic decays B\to D_s^{(*)} X

We calculate the total and differential decay rates for the semi-inclusive nonleptonic decays $B\to D_s^{(\ast )}{X}_q$ ($q=c$ or $u$) under the factorization hypothesis. The initial bound state effect is treated using the light-cone expansion and the heavy quark effective theory. We investigate the contribution of the penguin amplitude for the decay mode $B\to D_s^{(\ast )}{X}_c$ and find that it is small but non-negligible. The resulting decay rates for $B\to D_s^{()} X_c$agreewiththemeasurements\mathrm{.}Theuseofthedecaymode$B\to D_s^{()} X_u$todetermine$|V_{ub}|$ is discussed.