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

Abstract

We have studied extracting $|\text{vub}/\text{vcb}|$ by calculating the ratios $\mathcal{B}({\bar{B}}^0\to D_s^{(\ast )-}({\pi }^{+},{\rho }^{+}))/\mathcal{B}({\bar{B}}^0\to D_s^{(\ast )-}{D}^{(\ast )+})$ 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 ${\bar{B}}^0\to D_s^{-}{D}^{\ast +}$ 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 $\text{vub}/\text{vcb}$. 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 $|\text{vub}/\text{vcb}|$ from the exclusive semileptonic B decays. Using the newest upper limit on $B\to D_s\pi$ decay from CLEO, our method sets an upper limit $|\text{vub}/\text{vcb}|<0.13$ which is very close to the measured values from the semileptonic B decays. We also discuss the possible breaking of factorization assumption.

Comments: 15 pages, LaTeX