Comments on $\left|\frac{V_{ub}}{V_{cb}}\right|$ and $|V_{ub}|$ from Non-leptonic $B$ Decays within the Perturbative QCD Approach

TL;DR

This paper refines the extraction of CKM matrix element ratios from non-leptonic B decays using perturbative QCD, providing updated values and predictions for branching ratios with implications for future experiments.

Contribution

It applies the perturbative QCD approach to non-leptonic B decays to accurately calculate form factors and decay ratios, offering improved CKM element estimates and decay predictions.

Findings

|V_{ub}/V_{cb}| = 0.083 ± 0.007

Predicted branching ratio for B̄^0 → D_s^-ρ^+ is (2.7 ± 1.2)×10^{-5}

The approach favors a smaller |V_{ub}| consistent with exclusive measurements.

Abstract

We revisited the extracting $\left|V_{ub}/V_{cb}\right|$ and $|V_{ub}|$ through calculating the ratios ${\cal B}(B^0\to D_s^{(*)+}(\pi^-,\rho^-)/ {\cal B}(B^0\to D_s^{(*)+} D^{(*)-})$ 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. Within the updated distribution amplitudes and the latest experimental data, we get $\left|{V_{ub}}/{V_{cb}}\right|=0.083\pm0.007$, which favors a bit smaller $|V_{ub}|$ compared with the averaged PDG value, but agrees well the exclusively measured values. Furthermore, we predict the branching ratio of $\bar B^0 \to D_s^-\rho^+$ $\sim$ $(2.7\pm 1.2)\times 10^{-5}$, which could be measured in $B$ factories 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 $B_s$ system, primarily because both $\bar B_s^0 $ and $B_s^0$ can decay into the same final states $D_s^+K^-$ and $D_s^+D_s^-$.