Measurement of|Vub/Vcb|(and|Vub|)in exclusive nonleptonic decays within the generalized factorization scheme

Within the generalized factorization scheme, we study extracting $|V_{\mathrm{ub}}{/V}_{\mathrm{cb}}|$ by calculating the ratios $\mathcal{B}(B^0\to D_s^{\left(*\right)-}({\pi }^{+},{\rho }^{+}\left)\right)/\mathcal{B}(B^0\to D_s^{\left(*\right)-}{D}^{\left(*\right)+})$ including penguin effects. The ratios involving the $B^0\to D_s^{-}{D}^{+}$ mode have considerable penguin corrections $(\sim 15\%$ at the amplitude level), but those involving the $B^0\to D_s^{-}{D}^{*+}$ mode have relatively small penguin corrections. On the other hand, the $B^0\to D_s^{-}{D}^{+}$ mode has a smaller form-factor dependence. Therefore, these ratios complement each other in measuring $V_{\mathrm{ub}}{/V}_{\mathrm{cb}}.$ The theoretical uncertainty from the hadronic form factors in our method is at the level of 20%, which is comparable to the model dependence uncertainty of about 20% in the measurement of $|V_{\mathrm{ub}}{/V}_{\mathrm{cb}}|$ from the exclusive semileptonic B decays. Using the newest upper limit on $\overrightarrow{B}{D}_s\pi$ decay from CLEO, our method sets an upper limit $|V_{\mathrm{ub}}{/V}_{\mathrm{cb}}|<0.13\mathrm{}$ which is very close to the measured values from the semileptonic B decays.