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Bd \to \pi^- K^{(*)+} and Bs \to \pi^+(\rho^+) K^- decays with QCD factorization and flavor symmetry
High Energy Physics - Phenomenology · Submitted 24 Feb 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Therefore the ratio of these two branching ratios could be an interesting indicator of the role of charming penguins in charmless B decays.
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The abstract, sentence by sentence
The QCD factorization (QCDF) method usually contains infrared divergences which introduce large model dependence to its predictions on charmless B decays. The amplitudes of charmless B decays can be decomposed into "tree" and "penguin" parts which are conventionally defined, not from the topology of the dominant diagrams, but through their associated CKM factors V_{ub}^* V_{uq} and V_{tb}^* V_{tq}, respectively, with q=d,s. We find that for B_{d,s} \to \pi^+ K^- decays, the "tree" amplitude can be well estimated in QCDF with small errors, as the endpoint singularities have been canceled to a large extent. With this as the only input from QCDF and combined with flavor symmetry, the branching ratio of B_s \to \pi^+ K^- are estimated to be significantly larger than the CDF measurement. This contradiction could be solved if the form factor F^{B_s K} is smaller than the light cone sum rules estimation or the "tree" amplitude has been over estimated in QCDF. The latter possibility could happen if charming penguins are nonperturbative and not small, as argued in soft collinear effective theory. To differentiate between these two possibilities, we examine the similar B_s \to \rho^+ K^- decay with the same technique. It is found that a large part of the uncertainties are canceled in the ratio B(B_s \to \rho^+ K^-)/B(B_s \to \pi^+ K^-). It is predicted to be 2.5 \pm 0.2 in QCDF which is independent on the form factor. However if charming penguins are important, this ratio could be very different from the QCDF prediction. Therefore the ratio of these two branching ratios could be an interesting indicator of the role of charming penguins in charmless B decays.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The QCD factorization (QCDF) method usually contains infrared divergences which introduce large model dependence to its predictions on charmless B decays. | background 0.99 | 0.05 | 0.02 | asserted 0.98 |
| s1 | The amplitudes of charmless B decays can be decomposed into "tree" and "penguin" parts which are conventionally defined, not from the topology of the dominant diagrams, but through their associated CKM factors V_{ub}^* V_{uq} and V_{tb}^* V_{tq}, respectively, with q=d,s. | background 0.99 | 0.05 | 0.02 | asserted 1.00 |
| s2 | We find that for B_{d,s} \to \pi^+ K^- decays, the "tree" amplitude can be well estimated in QCDF with small errors, as the endpoint singularities have been canceled to a large extent. | result 0.99 | 0.92 | 0.08 | asserted 1.00 |
| s3 | With this as the only input from QCDF and combined with flavor symmetry, the branching ratio of B_s \to \pi^+ K^- are estimated to be significantly larger than the CDF measurement. | result 1.00 | 0.90 | 0.24 | asserted 0.91 |
| s4 | This contradiction could be solved if the form factor F^{B_s K} is smaller than the light cone sum rules estimation or the "tree" amplitude has been over estimated in QCDF. | interpretation 0.97 | 0.34 | 0.09 | hedged possibility 1.00 |
| s5 | The latter possibility could happen if charming penguins are nonperturbative and not small, as argued in soft collinear effective theory. | interpretation 0.79 | 0.06 | 0.04 | hedged possibility 1.00 |
| s6 | To differentiate between these two possibilities, we examine the similar B_s \to \rho^+ K^- decay with the same technique. | method 0.60 | 0.84 | 0.04 | asserted 0.95 |
| s7 | It is found that a large part of the uncertainties are canceled in the ratio B(B_s \to \rho^+ K^-)/B(B_s \to \pi^+ K^-). | result 0.93 | 0.92 | 0.09 | asserted 1.00 |
| s8 | It is predicted to be 2.5 \pm 0.2 in QCDF which is independent on the form factor. | result 1.00 | 0.87 | 0.21 | asserted 1.00 |
| s9 | However if charming penguins are important, this ratio could be very different from the QCDF prediction. | interpretation 0.88 | 0.24 | 0.11 | hedged possibility 1.00 |
| s10 | Therefore the ratio of these two branching ratios could be an interesting indicator of the role of charming penguins in charmless B decays. | interpretation 0.97 | 0.48 | 0.61 | hedged possibility 0.97 |
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The paper
Original abstract
The QCD factorization (QCDF) method usually contains infrared divergences which introduce large model dependence to its predictions on charmless B decays. The amplitudes of charmless B decays can be decomposed into "tree" and "penguin" parts which are conventionally defined, not from the topology of the dominant diagrams, but through their associated CKM factors V_{ub}^* V_{uq} and V_{tb}^* V_{tq}, respectively, with q=d,s. We find that for B_{d,s} \to \pi^+ K^- decays, the "tree" amplitude can be well estimated in QCDF with small errors, as the endpoint singularities have been canceled to a large extent. With this as the only input from QCDF and combined with flavor symmetry, the branching ratio of B_s \to \pi^+ K^- are estimated to be significantly larger than the CDF measurement. This contradiction could be solved if the form factor F^{B_s K} is smaller than the light cone sum rules estimation or the "tree" amplitude has been over estimated in QCDF. The latter possibility could happen if charming penguins are nonperturbative and not small, as argued in soft collinear effective theory. To differentiate between these two possibilities, we examine the similar B_s \to \rho^+ K^- decay with the same technique. It is found that a large part of the uncertainties are canceled in the ratio B(B_s \to \rho^+ K^-)/B(B_s \to \pi^+ K^-). It is predicted to be 2.5 \pm 0.2 in QCDF which is independent on the form factor. However if charming penguins are important, this ratio could be very different from the QCDF prediction. Therefore the ratio of these two branching ratios could be an interesting indicator of the role of charming penguins in charmless B decays.
Human review
How the literature uses it
3 arXiv papers cite this in 4 sentences
Papers citing it · 2 sentences without a confident label
Cites it as support 1 paper
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Especially, due to large theoretical uncertainty vanishing, the ratio $B(B̅_s→ρ^- K^+)/B(B̅_s→π^- K^+)$ is much more suitable to test SM and probe NP [ref] .
The Effects of a Family Non-universal Z' Boson in the \bar{B}_s->\pi K, \pi K*, \rho K Decays and B_d-\bar{B_d} mixing · Introduction · 0.99
Cites it as background 1 paper
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For this possible branching ratio mismatch, many efforts have been done within both SM and possible New Physics (NP) scenarios, for example Refs. [ref] .
The Effects of a Family Non-universal Z' Boson in the \bar{B}_s->\pi K, \pi K*, \rho K Decays and B_d-\bar{B_d} mixing · Introduction · 0.91
What it cites · 20 sentences without a confident label
Uses the method or tool of 1 paper
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In QCDF [ref] , [equation] where the weak annihilation contributions are contained in $β$ terms, while all the other parts are grouped into $α$ terms, including the vertex corrections and the hard spectator scattering contributions.
QCD factorization for B->PP and B->PV decays · $B_d,s →π^∓K^±$ decays · 0.89
Uses data or values from 5 papers
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With the CKM parameters taken from CKMfitter [ref] : [equation] , the determination of $|V_ub |F^Bπ=(9.1 ±0.7)×10^-4$ [ref] from the semi-leptonic $B →πℓν̅$ decay and $τ_B_d=1.525 ±0.009$ ps [ref] , we obtain [equation] with the uncertainties coming mainly from the variation of $|V_ub |F^Bπ$.
CP Violation and the CKM Matrix: Assessing the Impact of the Asymmetric B Factories · $B_d,s →π^∓K^±$ decays · 1.00
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With the CKM parameters taken from CKMfitter [ref] : [equation] , the determination of $|V_ub |F^Bπ=(9.1 ±0.7)×10^-4$ [ref] from the semi-leptonic $B →πℓν̅$ decay and $τ_B_d=1.525 ±0.009$ ps [ref] , we obtain [equation] with the uncertainties coming mainly from the variation of $|V_ub |F^Bπ$.
Averages of b-hadron and c-hadron Properties at the End of 2007 · $B_d,s →π^∓K^±$ decays · 1.00
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With the CKM parameters taken from CKMfitter [ref] : [equation] , the determination of $|V_ub |F^Bπ=(9.1 ±0.7)×10^-4$ [ref] from the semi-leptonic $B →πℓν̅$ decay and $τ_B_d=1.525 ±0.009$ ps [ref] , we obtain [equation] with the uncertainties coming mainly from the variation of $|V_ub |F^Bπ$.
|V_ub| from UTangles and B->pi l nu · $B_d,s →π^∓K^±$ decays · 1.00
Cites as support 1 paper
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As observed in [ref] , the flavor symmetry breaking effects in $B_d,s →π^∓K^±$ should be unusually small due to charge conjugation which is a strict symmetry for the strong phases from final state interactions.
Is observed direct CP violation in $B_d \to K^+ \pi^-$ due to new physics? Check standard model prediction of equal violation in $B_s \to K^- \pi^+$ · $B_d,s →π^∓K^±$ decays · 0.98
Cites as background 11 papers
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Consequently these charming penguin amplitudes[It was first proposed in [ref] that the charming penguins may play an important role in charmless B decays.] can only be determined by fitting to the data.
Charming Penguins in B decays · Introduction · 0.84
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Consequently these charming penguin amplitudes[It was first proposed in [ref] that the charming penguins may play an important role in charmless B decays.] can only be determined by fitting to the data.
Charming Penguins Strike Back · Introduction · 0.84
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For charmless B decays, there are three factorization approaches available in the market: QCDF [ref] , the perturbative QCD method (PQCD) [ref] and soft collinear effective theory (SCET) [ref] .
Branching Ratio and CP Violation of B to pi pi Decays in Perturbative QCD Approach · Introduction · 0.95
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