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Comments on $\left|\frac{V_{ub}}{V_{cb}}\right|$ and $|V_{ub}|$ from Non-leptonic $B$ Decays within the Perturbative QCD Approach
High Energy Physics - Phenomenology · Submitted 14 Jul 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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 $D_s^+D_s^-$.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | contribution 0.85 | 0.89 | 0.09 | asserted 0.98 |
| s1 | Utilizing this approach, we could calculate the form factors effectively as well as non-factorizable and annihilation contributions. | method 0.96 | 0.60 | 0.03 | hedged possibility 0.99 |
| s2 | 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. | result 0.99 | 0.96 | 0.82 | asserted 0.96 |
| s3 | 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. | result 0.97 | 0.93 | 0.08 | hedged possibility 0.86 |
| s4 | In our calculation, the major uncertainty is due to our poor knowledge of heavy meson wave functions. | limitation 1.00 | 0.88 | 0.04 | asserted 1.00 |
| s5 | 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 $D_s^+D_s^-$. | limitation 0.98 | 0.57 | 0.04 | asserted 0.88 |
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The paper
Original 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 $D_s^+D_s^-$.
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How the literature uses it
2 arXiv papers cite this in 3 sentences
Papers citing it · 2 sentences without a confident label
Uses its method or tool 1 paper
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One can use the $→$ result to calculate the CKM matrix element $|V_ub|$ following the prescription laid out in Ref. [ref] .
Measurements of Branching Fractions for B0 --> Ds+pi- and B0-bar --> Ds+K- · Introduction · 0.94
What it cites · 23 sentences without a confident label
Uses the method or tool of 1 paper
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Following Ref. [ref] , we define the ratios and estimate the values as, [equation] where $p_c^X$ is the c.m. momentum of the decay particle $X$.
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^{(*)+} · Introduction · 0.98
Uses data or values from 7 papers
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In Table. 1, we also list the branching ratios calculated within the PQCD approach with the parameter values [ref] , $i.e.$ $|V_ub|=0. 00359$, $|V_cb|=0. 041$ and $|V_cs|=0.973$.
Model-independent constraints on Delta F=2 operators and the scale of New Physics · Introduction · 1.00
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In Table. 1, we also list the branching ratios calculated within the PQCD approach with the parameter values [ref] , $i.e.$ $|V_ub|=0. 00359$, $|V_cb|=0. 041$ and $|V_cs|=0.973$.
CP Violation and the CKM Matrix: Assessing the Impact of the Asymmetric B Factories · Introduction · 1.00
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For the light mesons $π$ and $ρ$, the distribution amplitudes are well studied within the light-cone QCD sum rules, and we will use the latest versions [ref] .
Higher-Twist Distribution Amplitudes of the K Meson in QCD · Introduction · 0.92
Compares with 1 paper
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It should be also noted that our result of $B̅^0 →D_s^- π^+$ is smaller than that from Ref. [ref] , mainly because the different light meson distribution amplitudes are used.
The CKM suppressed $B(B_s) \to \bar D_{(s)}P,\bar D_{(s)}V,\bar D_{(s)}^*P, \bar D_{(s)}^*V$ decays in perturbative QCD approach · Introduction · 0.99
Cites as background 7 papers
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In the past ten years, many efforts have been promoted to estimate the non-factorizabale contributions quantitatively, such as the QCD fatorization approach (QCDF) [ref] , the perturbative QCD approach (PQCD) [ref] and the soft collinear effective theory (SCET) [ref] .
QCD Factorization for $B\to\pi\pi$ Decays: Strong Phases and CP Violation in the Heavy Quark Limit · Introduction · 0.88
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In the past ten years, many efforts have been promoted to estimate the non-factorizabale contributions quantitatively, such as the QCD fatorization approach (QCDF) [ref] , the perturbative QCD approach (PQCD) [ref] and the soft collinear effective theory (SCET) [ref] .
Fat penguins and imaginary penguins in perturbative QCD · Introduction · 0.88
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In the past ten years, many efforts have been promoted to estimate the non-factorizabale contributions quantitatively, such as the QCD fatorization approach (QCDF) [ref] , the perturbative QCD approach (PQCD) [ref] and the soft collinear effective theory (SCET) [ref] .
Penguin Enhancement and $B\to K\pi$ decays in perturbative QCD · Introduction · 0.88
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