Comments on [absolute value of ] from non-leptonic B decays within the perturbative QCD approach

We revisited the extracting [absolute value of ([V.sub.ub]/[V.sub.cb])] and [absolute value of ([V.sub.ub])] through calculating the ratios B([B.sup.0] [D.sup.(*)+.sub.s]) ([[pi].sup.-], [[rho].sup.-])/ B([B.sup.0] [right arrow] [D.sup.(*)+.sub.s] [D.sup.(*)-]) in the perturbative QCD approach, which is regarded as an effective theory in dealing with non-leptonic charmed B decays. Utilizing this approach, we could calculate the form factors effectively as well as non-factorizable and annihilation contributions. With the updated distribution amplitudes and the latest experimental data, we get [absolute value of ([V.sub.ub]/[V.sub.cb])] = 0.083 [+ or -] 0.007, which favors a bit smaller [absolute value of ([V.sub.ub])] compared with the averaged PDG value, but agrees well the exclusively measured values. Furthermore, we predict the branching ratio of [[bar.B].sup.0] [D.sup.-.sub.s][[rho].sup.+] ~ (2.7 [+ or -] 1.2) x [10.sup.-5], which could be measured in B factories in the near future. In our calculation, the major uncertainty is due to our poor knowledge of heavy meson wave functions. We also comment that it is not trivial to generalize this approach to the [B.sub.s] system, primarily because both [[bar.B].sup.0.sub.s] and [B.sup.0.sub.s] can decay into the same final states [D.sup.+.sub.s] [K.sup.-] and [D.sup.+.sub.s] [D.sup.-.sub.s].