Measurement of |V_{ub}/V_{cb}| (and |V_{ub}|) in Exclusive Nonleptonic Decays, \bar{B}^0 --> D_s^{(*)-}(π^+,ρ^+) and \bar{B}^0 --> D_s^{(*)-}D^{(*)+}

Abstract

We have studied extracting $|\vub/\vcb|$ by calculating the ratios ${\cal B}(\bar{B}^0\to D_s^{(*)-}(π^+,ρ^+))/{\cal B}(\bar{B}^0\to D_s^{(*)-}D^{(*)+})$ including penguin effects within the factorization assumption. The ratios involving $\bar{B}^0\to D_s^-D^{+}$ mode have considerable penguin corrections ($\sim 15%$ at the amplitude level), but those involving $\bar{B}^0\to D_s^-D^{*+}$ mode have relatively small penguin corrections. On the other hand, the $\bar{B}^0\to D_s^-D^{+}$ mode has smaller form-factor dependance. Therefore, these ratios complement each other in measuring $\vub/\vcb$. The theoretical uncertainty from the hadronic form factors in our method is at the level of 15%, which is comparable to the model-dependence uncertainty of about 20% in the measurement of $| \vub/\vcb |$ from the exclusive semileptonic B decays. Using the newest upper limit on $B\to D_s π$ decay from CLEO, our method sets an upper limit $| \vub/\vcb | < 0.13$ which is very close to the measured values from the semileptonic B decays. We also discuss the possible breaking of factorization assumption.