Pith. sign in

REVIEW 4 major objections 5 minor 57 references

Systematic Analysis of $B_s \to SP$ Decays in Perturbative QCD Approach

T0 review · 4 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A complete perturbative-QCD treatment of B_s decays to one scalar plus one pseudoscalar meson predicts rates in the 10^-7 to 10^-5 window and isolates two channels whose rates and CP asymmetries reveal the nature of light scalar mesons.

desk verdict Systematic PQCD survey of B_s to scalar+pseudoscalar decays with new predictions and useful scenario discriminators; main caveat is reliance on unprinted amplitudes from an earlier paper. read the letter →

arxiv 2502.04191 v1 pith:T7FJWWXR submitted 2025-02-06 hep-ph hep-ex

Zhi-Tian Zou , Zhao-Xu He , Ya-Xin Wang , Ying Li This is my paper · ORCID
classification hep-phhep-ex
keywords B_smesondecaysscalarmesonspseudoscalarperturbativeQCDdirectCPasymmetrybranchingfractionlight-conedistributionamplitudesf0(980)-sigmamixing
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish the first systematic treatment of all charmless $B_s$ decays to one scalar ($S$) and one pseudoscalar ($P$) meson in the perturbative QCD (PQCD) approach, assuming scalar mesons are ordinary quark-antiquark states. It claims branching fractions in the $10^{-7}$ to $10^{-5}$ range, within experimental reach, with a clean pattern: penguin-dominated channels have larger rates and small direct $CP$ asymmetries, while tree-dominated channels have smaller rates but can reach $CP$ asymmetries of tens of percent. The calculation is restricted to the two-quark description of light scalars because four-quark wave functions cannot yet be defined. Two modes, $B_s \to f_0(1370)\eta$ and $B_s \to a_0(1450)K$, are singled out as sensitive to which scalar-meson scenario is correct, and the $B_s \to f_0(980)(\sigma)P$ rates and asymmetries are mapped against the $f_0$-$\sigma$ mixing angle. If the predictions hold, these decays become practical probes of the internal structure of scalar mesons and of the PQCD factorization machinery.

What carries the argument

The engine of the calculation is the PQCD factorized amplitude obtained by convolving the Wilson coefficients, a perturbatively computed hard kernel, and the wave functions (light-cone distribution amplitudes) of the $B_s$, pseudoscalar, and scalar mesons in transverse-momentum space. The $k_T$ dependence generates Sudakov logarithms that suppress soft contributions, and threshold resummation produces a jet function that smears endpoint singularities. The paper improves earlier treatments by keeping terms proportional to $r^2$ with $r = m_s/m_{B_s}$ in inner quark-propagator denominators and by fixing the relative sign of vector decay constants between a scalar meson and its antiparticle. Amplitudes for $B_s \to SP$ are obtained from the $B_s \to SV$ amplitudes by the appropriate substitutions for decay constants and distribution amplitudes, which is why the previously computed $SV$ set can be recycled.

What would settle it

Measure the branching fraction of $B_s \to f_0(1370)\eta$ in a high-statistics $B_s$ sample: the two-quark scenario predicts about $1.25\times10^{-6}$, while the alternative assignment predicts $14.3\times10^{-6}$, an 11-fold gap; a result clearly outside both, or a direct $CP$ asymmetry for $B_s \to a_0(1450)K$ that is neither a few percent nor of order 70--90%, would falsify the two-quark PQCD treatment as presented.

Watch

Extended reading notes

Core claim

The central claim is that, within the two-quark model, PQCD reproduces existing data for $B_s \to K_0^*(1430)K$ decays within uncertainties, updates earlier PQCD results, and produces a systematic pattern for the full $B_s \to SP$ family. Branching fractions for penguin-dominated modes are generally larger than for tree-dominated ones, but the direct $CP$ asymmetries reverse this ordering. Examples include a direct $CP$ asymmetry near 95% (scenario 1) and 83% (scenario 2) for the tree-dominated decay $B_s \to \bar K_0^*(1430)\pi^0$. The paper identifies $B_s \to f_0(1370)\eta$ as the sharpest rate discriminator, with branching fraction about $1.25\times10^{-6}$ in scenario 1 versus $14.3\times10^{-6}$ in scenario 2, and $B_s \to a_0(1450)K$ as the sharpest $CP$ discriminator, with asymmetries around 3% and $-7\%$ in scenario 1 and 72% and 94% in scenario 2. It also finds that $B_s \to \sigma\eta'$ and related modes can, once measured, decide between the acute and obtuse ranges of the $f_0(980)$-$\sigma$ mixing angle.

Load-bearing premise

The load-bearing premise is that the light scalar mesons ($a_0(980)$, $f_0(980)$, $\sigma$, $\kappa$) are ordinary quark-antiquark states, so their wave functions, decay constants, and distribution amplitudes are the ones used here; if they are four-quark states, every prediction involving them loses its input.

Editorial extensions

If this is right

  • The predicted $B_s \to f_0(1370)\eta$ branching fraction is about $1.25\times10^{-6}$ in scenario 1 but $14.3\times10^{-6}$ in scenario 2, so a single rate measurement can distinguish the two scalar-meson assignments.
  • The direct $CP$ asymmetries of $B_s \to a_0^+(1450)K^-$ and $B_s \to a_0(1450)\bar K^0$ are predicted at about 3% and $-7\%$ in scenario 1 versus 72% and 94% in scenario 2, making them sharp $CP$-based discriminators.
  • The ratio $R = \mathcal{B}(B_s \to a_0^+(980)K^-)/\mathcal{B}(B_s \to a_0^0(980)\bar K^0)$ is predicted to be about $1/2$, matching the analogous $B_s \to VS$ ratio and providing a consistency test of the PQCD framework.
  • For $B_s \to f_0(980)/\sigma P$ decays, both branching fractions and $CP$ asymmetries depend strongly on the $f_0$-$\sigma$ mixing angle, with the $\eta'$ modes showing the largest difference between the two accepted angle ranges.
  • The PQCD central values for $B_s \to K_0^*(1430)K$ lie above the QCDF predictions but agree with the LHCb measurements within the present large uncertainties.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The ordering 'penguin-dominated = larger rate, tree-dominated = larger $CP$ asymmetry' is likely more robust than any single number, because $CP$ asymmetries as ratios cancel many wave-function uncertainties; tests should target the ordering, not just individual central values.
  • If a precise measurement of $B_s \to f_0(1370)\eta$ lands between the two predictions, that would point beyond either pure quark model, e.g., to $q\bar q$--four-quark mixing or to non-factorizable effects absent from the present two-quark PQCD treatment.
  • Because the $SP$ amplitudes are obtained by substitution from $SV$ amplitudes, the technical improvements introduced here (the $r^2$ terms and sign conventions) can be carried over to other decays with scalars in the final state, such as $B \to SP$ and $B_c \to SP$, without recalculating the hard kernels from scratch.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper presents a PQCD study of charmless B_s -> SP decays (S scalar, P pseudoscalar) within the two-quark model of scalar mesons. The amplitudes are obtained from the B_s -> SV amplitudes of Ref. [30] through a substitution rule, with two advertised modifications: retaining r^2 terms (r = m_s/m_{B_s}) in inner quark propagator denominators and implementing the sign relation f_S = -f_{\bar S}. The authors compute branching fractions and direct CP asymmetries for light scalars (a0(980), kappa, sigma, f0(980)) in scenario 1, and for heavier scalars (a0(1450), K0*(1430), f0(1370), f0(1500)) in scenarios 1 and 2. They find branching fractions in the range 10^-7 to 10^-5, larger branching fractions for penguin-dominated modes, and larger CP asymmetries for tree-dominated modes. They also identify B_s -> f0(1370) eta and B_s -> a0(1450) K as scenario-sensitive channels, study the f0(980)-sigma mixing-angle dependence, and compare with LHCb data and earlier PQCD/QCDF results.

Significance. If the underlying expressions are correct, this would be a useful systematic set of PQCD predictions for a class of B_s decays that has received limited attention, including several first-time predictions and explicit scenario discriminators for the structure of scalar mesons. The paper does not fit any observable to data: all decay constants, Gegenbauer moments, shape parameters, CKM elements, and mixing angles are external inputs, and LHCb results are used only as consistency checks. The two-quark restriction for light scalars is disclosed, and the four-quark limitation is a model choice rather than an internal inconsistency. The main weakness is that the central numerical results are not independently reproducible from the manuscript, because the amplitudes are not shown and the advertised modifications are not written down.

major comments (4)
  1. [Sec. 2, Eq. (17)] The entire numerical program rests on amplitudes that are not shown. Section 2 states "we do not repeat the decay amplitudes in this work" and obtains the B_s -> SP amplitudes by the substitution in Eq. (17) from the B_s -> SV amplitudes of Ref. [30]. The two advertised modifications--retaining r^2 terms in the inner quark propagator denominators and implementing the sign relation f_S = -f_{\bar S}--are exactly the sign- and power-sensitive changes that must be displayed before the hard-scattering emission cancellation/amplification statement in Section 3 can be checked. As written, every entry in Tables 1-4 depends on unverifiable expressions, and the numerical predictions are not reproducible from the paper alone. Please provide an appendix with the explicit hard-scattering and annihilation amplitudes for B_s -> SP, with the r^2 terms and the scalar decay-constant sign conventions made manifest, or show the substituted amplitudes from Ref. [30] explicitly.
  2. [Sec. 3, Tables 3-4 and Eq. (27)] The claim that B_s -> f0(1370) eta and B_s -> a0(1450) K discriminate the two scalar scenarios depends on the assigned two-quark inputs: f_S, \bar f_S, B_1, and B_3 for each scalar meson in each scenario. These values are not tabulated; the reader is referred to Ref. [21]. Because the scenario dependence enters precisely through these parameters, the discrimination claim cannot be assessed without a table stating the numerical values used for f0(1370), f0(1500), a0(1450), and K0*(1430) in scenarios 1 and 2. Please include such an input table.
  3. [Sec. 2, Eqs. (13)-(16); Tables 1-4] Many of the predictions involve eta or eta' channels, including the key channel B_s -> f0(1370) eta in Eq. (27), yet the paper does not state the eta-eta' mixing scheme, the eta/eta' decay constants and Gegenbauer moments, or the chiral masses m_P^0 used in the pseudoscalar wave functions. Equations (14)-(16) list only pi and K moments. Since the eta and eta' branching fractions and CP asymmetries are strongly affected by these choices, the numerical results for those modes are not reproducible. Please specify all eta/eta' inputs explicitly, or cite the adopted values and mixing scheme precisely.
  4. [Abstract and Sec. 1] The abstract promises an analysis with two distinct structural scenarios, but the Introduction restricts all light-scalar predictions to the two-quark model because four-quark wave functions "cannot be defined till now." As a result, Tables 1 and 2 provide only scenario-1 results for a0(980), kappa, sigma, and f0(980), and the two-scenario comparison is made only for heavier scalar mesons. This is a substantial, self-imposed limitation of the claimed "systematic analysis." The abstract and the stated scope should be amended to say explicitly that predictions for light scalars are made only in the two-quark scenario.
minor comments (5)
  1. [Fig. 1 caption] The caption contains the typo "POCD"; it should read "PQCD".
  2. [Sec. 4, Summary] The phrase "suppressed by |VtdVtd|" is incorrect; it should be |V_td V_tb^*| or |V_tb V_td| as appropriate for the penguin contribution.
  3. [Tables 3-4] Several entries are corrupted or misaligned, for example "24.67.1+5.7+0.7" in the B_s -> K0*(1430)^\pm K^\mp row and the former-results columns that carry four or five separate uncertainties. The tables should be regenerated, and the ordering of the three uncertainty sources (wave-function, scale, CKM) should be stated in the captions.
  4. [Eq. (18)] The ratio test uses notation from Ref. [30] without defining how B_s -> a0^0(980) K^0 in Table 1 is related to B_s -> a0^0(980) \bar K^0 in Eq. (18); please clarify the charge-conjugate final states and whether a CP-averaged or mode-specific branching fraction is used.
  5. [Eq. (27)] The equation is malformed: the scenario-1 entry is missing a closing parenthesis and a multiplication sign before 10^-6, reading "(1.25 + ... -0.08 x 10^-6" instead of the intended "(1.25 + ... -0.08) x 10^-6".

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the self-cited amplitude substitution in Eq. (17) is a reuse of a prior calculation, not a reduction of outputs to inputs.

full rationale

No circular step can be identified. The branching fractions and direct CP asymmetries in Tables 1-4 are computed from the PQCD convolution in Eq. (1) using wave functions, decay constants, Gegenbauer moments, and CKM/Wilson inputs taken from independent sources (Refs. [19, 21] and standard literature); none of the target observables is fitted. LHCb measurements enter only after the calculation as a consistency check (Eqs. 21-24). The main self-citation is Ref. [30], a prior paper by overlapping authors (Zou and Li), from which the B_s -> SP amplitudes are obtained by the substitution rule in Eq. (17). This is load-bearing for reproducibility, and the paper explicitly states "we do not repeat the decay amplitudes in this work" (Sec. 2), so the tables are not independently checkable from the text alone. That is a completeness and transparency limitation, not circularity: the imported amplitudes are an independent previous calculation, not the same quantities as the predicted observables, and they are not fitted to those observables. The advertised r^2 and vector-decay-constant sign improvements are likewise asserted rather than exhibited, but this concerns verifiability, not equivalence-by-construction. The restriction to the two-quark model for light scalars is a disclosed model assumption. Overall, no prediction reduces to its input by definition, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The paper's central claim rests on the PQCD factorization framework and on a large set of input parameters (decay constants, Gegenbauer moments, shape parameters, mixing angles) taken from earlier analyses, several of which are from the same research group. No new entities are introduced. The two scalar scenarios are borrowed from prior literature, and the main simplifying choices are the asymptotic twist-3 LCDAs and the use of amplitudes from Ref. [30] via Eq. (17).

free parameters (7)
  • B_s LCDA shape parameter omega = 0.5 +/- 0.05 GeV
    Controls the x and b dependence of the B_s wave function in Eq. (3); taken from prior analyses (Refs. [41-44]).
  • B_s decay constant f_Bs = 0.23 +/- 0.02 GeV
    Normalizes the B_s wave function via Eq. (4); taken from earlier determinations.
  • Scalar meson Gegenbauer moments B1, B3 = Values from Ref. [21], not quoted in this paper
    Set the twist-2 LCDA of scalar mesons in Eq. (11); obtained from QCD sum rules in Ref. [19], with values listed in Ref. [21].
  • Pseudoscalar Gegenbauer moments a_i = a2_pi=0.44, a4_pi=0.25, a1_K=0.17, etc.
    Determine the pion and kaon LCDA shapes in Eqs. (14)-(16); taken from previous phenomenological fits.
  • Scalar decay constants f_S and fbar_S = Values from Ref. [21]
    Enter the scalar wave function normalization and the LCDA expansion; differ by scalar meson and scenario.
  • f0(980)-sigma mixing angle theta = Two ranges: 25-40 degrees and 140-165 degrees
    Parameter in Eqs. (19)-(20); the paper scans over these two ranges to predict the dependence of branching fractions and CP asymmetries.
  • QCD scale Lambda_QCD = 0.25 +/- 0.05 GeV
    Used in running couplings; varied to estimate higher-order uncertainty.
assumptions (6)
  • domain assumption PQCD factorization with kT factorization is valid for two-body B_s hadronic decays.
    The entire calculation assumes this factorization, as stated around Eq. (1) in Sec. 2.
  • domain assumption The B_s to SP amplitudes are obtained from B_s to SV amplitudes via the substitutions in Eq. (17).
    The paper does not derive SP amplitudes directly; it relies on the mapping from Ref. [30].
  • domain assumption Light scalar mesons can be approximated as two-quark states for PQCD predictions.
    The paper states in Sec. 1 that predictions for light scalars are made only in the 2-quark model because four-quark wave functions are not known.
  • domain assumption Twist-3 LCDAs of scalar mesons take the asymptotic forms in Eq. (12).
    Used for simplicity, despite the existence of more detailed QCD sum rule results (Refs. [48,49]).
  • domain assumption The f0(980)-sigma mixing relations in Eqs. (19)-(20) hold with the quoted mixing angle ranges.
    Basis for the theta-dependent predictions in Table 2 and Figs. 2 and 3; the angle ranges are taken from experimental analyses.
  • standard math The Standard Model weak effective Hamiltonian and Wilson coefficients are assumed.
    The paper uses the standard four-quark operator basis without rederiving it.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Systematic Analysis of $B_s \to SP$ Decays in Perturbative QCD Approach." pith.science (2026). https://pith.science/paper/T7FJWWXR

@misc{pith2026250204191,
  author       = {Pith},
  title        = {Pith review of: Systematic Analysis of $B_s \to SP$ Decays in Perturbative QCD Approach},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/T7FJWWXR}},
  note         = {Machine review of arXiv:2502.04191}
}
abstract

Within the perturbative QCD (PQCD) framework, we present a systematic investigation of charmless $B_s \to SP$ decays, where $S$ and $P$ denote scalar and pseudoscalar mesons, respectively. By employing two distinct structural scenarios for scalar mesons, we calculate the branching fractions and direct $CP$ asymmetries for these processes. Our results reveal branching fractions ranging from $10^{-7}$ to $10^{-5}$, values that are well within the measurable range of current experiments. A striking contrast emerges between penguin- and tree-dominated decays: while penguin-dominated processes yield larger branching fractions, tree-dominated decays exhibit significantly enhanced direct $CP$ asymmetries. In particular, the decays $B_s \to f_0(1370) \eta$ and $B_s \to a_0(1450) K$ demonstrate marked sensitivity to the choice of scalar meson scenario, offering critical constraints for identifying the optimal model once experimental data are available. Furthermore, we calculate the branching fractions of $B_s \to f_0(980)(\sigma)P$ decays in two distinct ranges of the mixing angle of $f_0(980)-\sigma$. The dependencies of both branching fractions and $CP$ asymmetries on this mixing angle are rigorously analyzed, establishing a framework essential for determining its value with future experimental results. These findings provide a robust theoretical foundation for advancing the understanding of nonleptonic $B_s$decays in QCD-based formalisms, as well as the nature of scalar mesons.

Figures

Figures reproduced from arXiv: 2502.04191 by the authors.

Figure 1
Figure 1. Leading order Feynman diagrams contributing to the [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. The branching fractions of the Bs → f0(980)[σ]P decays versus the f0(980) − σ mixing angle θ. B(Bs → K∗0 0 (1430)K 0 /K ∗0 0 (1430)K0 ) = (33.0 ± 2.5 ± 0.9 ± 9.1 ± 3.5) × 10−6 . (22) 13 [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. The direct CP asymmetries of the Bs → f0(980)[σ]P decays versus the f0(980) − σ mixing angle θ. In this work, we calculate the branching fractions for these decays using PQCD approach for the first time. Under two different scenarios, our results are given as follows: B(Bs → K∗± 0 (1430)K∓) = ( (43.6 +15.7+10.8+3.5 −12.5−8.7−1.1 ) × 10−6 scenario 1, (54.9 +22.9+14.1+2.0 −19.1−10.6−2.3 ) × 10−6 scenario 2; (23) 14 [… view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

57 extracted references · 40 canonical work pages

  1. [30]

    Charmless $B_s\to V S$ Decays in PQCD Approach

    Z.-W. Liu, Z.-T. Zou, Y. Li, X. Liu, and J. Wang, Charmless Bs →VS decays in PQCD approach, Eur. Phys. J. C 82 (2022), no. 1 59, [ arXiv:2111.04235]

    work page Pith review arXiv 2022

  2. [21]

    Revisiting charmless hadronic B decays to scalar mesons

    H.-Y. Cheng, C.-K. Chua, K.-C. Yang, and Z.-Q. Zhang, Revisiting charmless hadronic B decays to scalar mesons , Phys. Rev. D 87 (2013), no. 11 114001, [ arXiv:1303.4403]

    work page Pith review arXiv 2013

  3. [1]

    Dalitz analysis of the three-body charmless decays B+=>K+Pi+Pi- and B+=>K+K+K-

    Belle Collaboration, A. Garmash et al., Dalitz analysis of the three-body charmless decaysB+ →K +π +π − and B+ →K +K +K −, Phys. Rev. D 71 (2005) 092003, [ hep-ex/0412066]

    work page Pith review arXiv 2005

  4. [2]

    Search for Direct CP Violation in Three-Body Charmless B+- => K+-pi+-pi-+ Decay

    Belle Collaboration, K. Abe, Search for direct CP violation in three-body charmless B± →K ±π ±π ∓ decay, [ hep-ex/0509001]

    work page Pith review arXiv

  5. [3]

    Dalitz Analysis of B->K+pi+pi- and B->K+K+pi-

    Belle Collaboration, A. Bondar, Dalitz analysis of B+ →K +π +π − and B+ →K +K +K −, in 32nd International Conference on High Energy Physics , pp. 1125–1128, 11, 2004. hep-ex/0411004

    work page Pith review arXiv 2004

  6. [4]

    Study of $B^0 \to \eta K^+ \pi^-$ and $\eta \pi^+ \pi^-$

    Belle Collaboration, K. Abe et al., Study of B0 →ηK +π − and ηπ +π −, [hep-ex/0509003]

    work page Pith review arXiv

  7. [5]

    Search for B-Meson Decays to Two-Body Final States with a0(980) Mesons

    BaBar Collaboration, B. Aubert et al., Search for B-meson decays to two-body final states with a0(980) mesons, Phys. Rev. D 70 (2004) 111102, [ hep-ex/0407013]

    work page Pith review arXiv 2004

  8. [6]

    Measurements of Neutral B Decay Branching Fractions to K0S pi+ pi- Final States and the Charge Asymmetry of B0 --> K*+ pi-

    BaBar Collaboration, B. Aubert et al., Measurements of neutral B decay branching fractions to K 0 Sπ +π − final states and the charge asymmetry of B0 →K ∗+π −, Phys. Rev. D 73 (2006) 031101, [ hep-ex/0508013]

    work page Pith review arXiv 2006

Show all 57 references
  1. [7]

    Aubert et al., Measurements of the branching fraction and CP-violation asymmetries in B0 →f 0(980)K 0 S, Phys

    BaBar Collaboration, B. Aubert et al., Measurements of the branching fraction and CP-violation asymmetries in B0 →f 0(980)K 0 S, Phys. Rev. Lett. 94 (2005) 041802, [hep-ex/0406040]

    2005 arXiv

  2. [8]

    Aubert et al., Observation of B0 meson decays to a+ 1 (1260)π −, in 32nd International Conference on High Energy Physics , 8, 2004

    BaBar Collaboration, B. Aubert et al., Observation of B0 meson decays to a+ 1 (1260)π −, in 32nd International Conference on High Energy Physics , 8, 2004. hep-ex/0408021

    2004 arXiv

  3. [9]

    Aubert et al., B0 →K +π −π 0 Dalitz plot analysis , in 32nd International Conference on High Energy Physics , 8, 2004

    BaBar Collaboration, B. Aubert et al., B0 →K +π −π 0 Dalitz plot analysis , in 32nd International Conference on High Energy Physics , 8, 2004. hep-ex/0408073

    2004 arXiv

  4. [10]

    Aubert et al., Dalitz-plot analysis of the decays B± →K ±π ∓π ±, Phys

    BaBar Collaboration, B. Aubert et al., Dalitz-plot analysis of the decays B± →K ±π ∓π ±, Phys. Rev. D 72 (2005) 072003, [ hep-ex/0507004]. [Erratum: Phys.Rev.D 74, 099903 (2006)]

    2005 arXiv

  5. [11]

    Aubert et al., Amplitude analysis of B± →π ±π ∓π ± and B± →K ±π ∓π ±, in 32nd International Conference on High Energy Physics , 8, 2004

    BaBar Collaboration, B. Aubert et al., Amplitude analysis of B± →π ±π ∓π ± and B± →K ±π ∓π ±, in 32nd International Conference on High Energy Physics , 8, 2004. hep-ex/0408032. 17

    2004 arXiv

  6. [12]

    Aubert et al., An amplitude analysis of the decay B± →π ±π ±π ∓, Phys

    BaBar Collaboration, B. Aubert et al., An amplitude analysis of the decay B± →π ±π ±π ∓, Phys. Rev. D 72 (2005) 052002, [ hep-ex/0507025]

    2005 arXiv

  7. [13]

    Aaij et al., Measurement of the Bs effective lifetime in the J/ψf 0(980) final state , Phys

    LHCb Collaboration, R. Aaij et al., Measurement of the Bs effective lifetime in the J/ψf 0(980) final state , Phys. Rev. Lett. 109 (2012) 152002, [ arXiv:1207.0878]

    2012 arXiv

  8. [14]

    Aaij et al., Dalitz plot analysis of B0 s → ¯D0K −π + decays, Phys

    LHCb Collaboration, R. Aaij et al., Dalitz plot analysis of B0 s → ¯D0K −π + decays, Phys. Rev. D 90 (2014), no. 7 072003, [ arXiv:1407.7712]

    2014 arXiv

  9. [15]

    Aaij et al., Search for the decay B0 s →D 0 f0(980), JHEP 08 (2015) 005, [ arXiv:1505.01654]

    LHCb Collaboration, R. Aaij et al., Search for the decay B0 s →D 0 f0(980), JHEP 08 (2015) 005, [ arXiv:1505.01654]

    2015 arXiv

  10. [16]

    Aaij et al., Amplitude analysis of B0 s →K 0 SK ±π ∓ decays, JHEP 06 (2019) 114, [ arXiv:1902.07955]

    LHCb Collaboration, R. Aaij et al., Amplitude analysis of B0 s →K 0 SK ±π ∓ decays, JHEP 06 (2019) 114, [ arXiv:1902.07955]

    2019 arXiv

  11. [17]

    Navas et al., Review of particle physics , Phys

    Particle Data Group Collaboration, S. Navas et al., Review of particle physics , Phys. Rev. D 110 (2024), no. 3 030001

    2024

  12. [18]

    Banerjee et al., Averages of b-hadron,c-hadron, and τ-lepton properties as of 2023 , [ arXiv:2411.18639]

    Heavy Flavor Averaging Group (HFLA V) Collaboration, S. Banerjee et al., Averages of b-hadron,c-hadron, and τ-lepton properties as of 2023 , [ arXiv:2411.18639]

    2023 arXiv

  13. [19]

    Cheng, C.-K

    H.-Y. Cheng, C.-K. Chua, and K.-C. Yang, Charmless hadronic B decays involving scalar mesons: Implications to the nature of light scalar mesons , Phys. Rev. D 73 (2006) 014017, [ hep-ph/0508104]

    2006 arXiv

  14. [20]

    Cheng, C.-K

    H.-Y. Cheng, C.-K. Chua, and K.-C. Yang, Charmless B decays to a scalar meson and a vector meson , Phys. Rev. D 77 (2008) 014034, [ arXiv:0705.3079]

    2008 arXiv

  15. [22]

    Cheng and C.-K

    H.-Y. Cheng and C.-K. Chua, On Charmless B →Khη(′) Decays with Kh =K,K ∗,K ∗ 0 (1430),K ∗ 2 (1430), Phys. Rev. D 82 (2010) 034014, [ arXiv:1005.1968]

    2010 arXiv

  16. [23]

    Li, X.-J

    Y. Li, X.-J. Fan, J. Hua, and E.-L. Wang, Implications of Family Nonuniversal Z ′ Model on B →K ∗ 0π Decays, Phys. Rev. D 85 (2012) 074010, [ arXiv:1111.7153]

    2012 arXiv

  17. [24]

    L. Chen, M. Zhao, L. Wang, Y. Kang, Q. Chang, and J. Sun, Study of the nonleptonic charmless B →SS decays with the QCD factorization approach , Eur. Phys. J. C 83 (2023), no. 12 1142, [ arXiv:2306.06492]

    2023 arXiv

  18. [25]

    Wang, Y.-L

    W. Wang, Y.-L. Shen, Y. Li, and C.-D. Lu, Study of scalar mesons f0(980) and f0(1500) fromB →f0(980)K and B →f0(1500)K Decays, Phys. Rev. D 74 (2006) 114010, [hep-ph/0609082]

    2006 arXiv

  19. [26]

    Y.-L. Shen, W. Wang, J. Zhu, and C.-D. Lu, Study of K ∗ 0 (1430) and a0(980) from B →K ∗ 0 (1430)π and B →a0(980)K Decays, Eur. Phys. J. C 50 (2007) 877–887, [hep-ph/0610380]. 18

    2007 arXiv

  20. [27]

    Z.-T. Zou, Y. Li, and X. Liu, Study of Bc →DS decays in the perturbative QCD approach, Phys. Rev. D 97 (2018), no. 5 053005, [ arXiv:1712.02239]

    2018 arXiv

  21. [28]

    Z.-T. Zou, Y. Li, and X. Liu, Cabibbo-Kobayashi-Maskawa-favoredB decays to a scalar meson and a D meson, Eur. Phys. J. C 77 (2017), no. 12 870, [ arXiv:1704.03967]

    2017 arXiv

  22. [29]

    Z.-T. Zou, Y. Li, and X. liu, Two-body charmed Bs decays involving a light scalar meson , Phys. Rev. D 95 (2017), no. 1 016011, [ arXiv:1609.06444]

    2017 arXiv

  23. [31]

    Zhang, S.-Y

    Z.-Q. Zhang, S.-Y. Wang, and X.-K. Ma, Insight into f0(980) through the B(s) charmed decays, Phys. Rev. D 93 (2016), no. 5 054034, [ arXiv:1601.04137]

    2016 arXiv

  24. [32]

    Zhang, S.-J

    Z.-Q. Zhang, S.-J. Wang, and L.-Y. Zhang, Branching ratio and CP asymmetry of Bs →K ∗ 0 (1430)η(′) decays in the PQCD approach , Chin. Phys. C 37 (2013) 043103

    2013

  25. [33]

    Zhang, Branching ratio and CP asymmetry of Bs →K ∗ 0 (1430)π decays in the PQCD approach, EPL 97 (2012), no

    Z.-Q. Zhang, Branching ratio and CP asymmetry of Bs →K ∗ 0 (1430)π decays in the PQCD approach, EPL 97 (2012), no. 1 11001, [ arXiv:1203.5928]

    2012 arXiv

  26. [34]

    Zhang, Study of scalar meson f0(980) and K ∗ 0 (1430) fromB →f0(980)ρ(ω,φ ) and B →K ∗ 0 (1430)ρ(ω ) Decays, Phys

    Z.-Q. Zhang, Study of scalar meson f0(980) and K ∗ 0 (1430) fromB →f0(980)ρ(ω,φ ) and B →K ∗ 0 (1430)ρ(ω ) Decays, Phys. Rev. D 82 (2010) 034036, [ arXiv:1006.5772]

    2010 arXiv

  27. [35]

    Liu, Z.-Q

    X. Liu, Z.-Q. Zhang, and Z.-J. Xiao, B →K ∗ 0 (1430)η′ decays in the pQCD approach , Chin. Phys. C 34 (2010) 157–164, [ arXiv:0904.1955]

    2010 arXiv

  28. [36]

    Mathur, A

    N. Mathur, A. Alexandru, Y. Chen, S. J. Dong, T. Draper, I. H orvath, F. X. Lee, K. F. Liu, S. Tamhankar, and J. B. Zhang, Scalar Mesons a0(1450) and σ(600) from Lattice QCD, Phys. Rev. D 76 (2007) 114505, [ hep-ph/0607110]

    2007 arXiv

  29. [37]

    Prelovsek, T

    S. Prelovsek, T. Draper, C. B. Lang, M. Limmer, K.-F. Liu, N. Ma thur, and D. Mohler, Lattice study of light scalar tetraquarks with I = 0, 2, 1/ 2, 3/ 2: Are σ and κ tetraquarks?, Phys. Rev. D 82 (2010) 094507, [ arXiv:1005.0948]

    2010 arXiv

  30. [38]

    Alexandrou, J

    C. Alexandrou, J. O. Daldrop, M. Dalla Brida, M. Gravina, L. Scor zato, C. Urbach, and M. Wagner, Lattice investigation of the scalar mesons a0(980) and κ using four-quark operators, JHEP 04 (2013) 137, [ arXiv:1212.1418]

    2013 arXiv

  31. [39]

    Li and B

    H.-n. Li and B. Tseng, Nonfactorizable soft gluons in nonleptonic heavy meson dec ays, Phys. Rev. D 57 (1998) 443–451, [ hep-ph/9706441]

    1998 arXiv

  32. [40]

    Li, Threshold resummation for exclusive B meson decays , Phys

    H.-n. Li, Threshold resummation for exclusive B meson decays , Phys. Rev. D 66 (2002) 094010, [ hep-ph/0102013]

    2002 arXiv

  33. [41]

    A. Ali, G. Kramer, Y. Li, C.-D. Lu, Y.-L. Shen, W. Wang, and Y.-M. W ang, Charmless non-leptonic Bs decays to PP , PV and VV final states in the pQCD approach , Phys. Rev. D 76 (2007) 074018, [ hep-ph/0703162]. 19

    2007 arXiv

  34. [42]

    Z.-T. Zou, A. Ali, C.-D. Lu, X. Liu, and Y. Li, Improved Estimates of The B(s) →VV Decays in Perturbative QCD Approach , Phys. Rev. D 91 (2015) 054033, [arXiv:1501.00784]

    2015 arXiv

  35. [43]

    Qin, Z.-T

    Q. Qin, Z.-T. Zou, X. Yu, H.-n. Li, and C.-D. L¨ u, Perturbative QCD study of Bs decays to a pseudoscalar meson and a tensor meson , Phys. Lett. B 732 (2014) 36–40, [arXiv:1401.1028]

    2014 arXiv

  36. [44]

    Li, C.-D

    Y. Li, C.-D. Lu, Z.-J. Xiao, and X.-Q. Yu, Branching ratio and CP asymmetry of Bs →π +π − decays in the perturbative QCD approach , Phys. Rev. D 70 (2004) 034009, [hep-ph/0404028]

    2004 arXiv

  37. [45]

    Li and Y.-M

    H.-n. Li and Y.-M. Wang, Non-dipolar Wilson links for transverse-momentum-depend ent wave functions , JHEP 06 (2015) 013, [ arXiv:1410.7274]

    2015 arXiv

  38. [46]

    Qin, Y.-L

    Q. Qin, Y.-L. Shen, C. Wang, and Y.-M. Wang, Deciphering the Long-Distance Penguin Contribution to Bd,s →γγ Decays, Phys. Rev. Lett. 131 (2023), no. 9 091902, [arXiv:2207.02691]

    2023 arXiv

  39. [47]

    Wang, Y.-M

    W. Wang, Y.-M. Wang, J. Xu, and S. Zhao, B-meson light-cone distribution amplitude from Euclidean quantities , Phys. Rev. D 102 (2020), no. 1 011502, [ arXiv:1908.09933]

    2020 arXiv

  40. [48]

    Han, X.-G

    H.-Y. Han, X.-G. Wu, H.-B. Fu, Q.-L. Zhang, and T. Zhong, Twist-3 Distribution Amplitudes of Scalar Mesons within the QCD Sum Rules and Its A pplication to the B →S Transition Form Factors, Eur. Phys. J. A 49 (2013) 78, [ arXiv:1301.3978]

    2013 arXiv

  41. [49]

    Lu, Y.-M

    C.-D. Lu, Y.-M. Wang, and H. Zou, Twist-3 distribution amplitudes of scalar mesons from QCD sum rules , Phys. Rev. D 75 (2007) 056001, [ hep-ph/0612210]

    2007 arXiv

  42. [50]

    Lu and M.-Z

    C.-D. Lu and M.-Z. Yang, B →πρ, πω decays in perturbative QCD approach , Eur. Phys. J. C 23 (2002) 275–287, [ hep-ph/0011238]

    2002 arXiv

  43. [51]

    F. E. Close and N. A. Tornqvist, Scalar mesons above and below 1-GeV , J. Phys. G 28 (2002) R249–R267, [ hep-ph/0204205]

    2002 arXiv

  44. [52]

    R. L. Jaffe, Multi-Quark Hadrons. 1. The Phenomenology of (2 Quark 2 anti -Quark) Mesons, Phys. Rev. D 15 (1977) 267

    1977

  45. [53]

    R. L. Jaffe, Multi-Quark Hadrons. 2. Methods , Phys. Rev. D 15 (1977) 281

    1977

  46. [54]

    M. G. Alford and R. L. Jaffe, Insight into the scalar mesons from a lattice calculation , Nucl. Phys. B 578 (2000) 367–382, [ hep-lat/0001023]

    2000 arXiv

  47. [55]

    A. V. Anisovich, V. V. Anisovich, and V. A. Nikonov, Radiative decays of basic scalar, vector and tensor mesons and the determination of the P wave q ¯q multiplet, Eur. Phys. J. A 12 (2001) 103–115, [ hep-ph/0108186]. 20

    2001 arXiv

  48. [56]

    Gokalp, Y

    A. Gokalp, Y. Sarac, and O. Yilmaz, An Analysis of f0-sigma mixing in light cone QCD sum rules , Phys. Lett. B 609 (2005) 291–297, [ hep-ph/0410380]

    2005 arXiv

  49. [57]

    L. Chen, M. Zhao, Y. Zhang, and Q. Chang, Study of Bu,d,s →K ∗ 0 (1430)P and K ∗ 0 (1430)V decays within QCD factorization , Phys. Rev. D 105 (2022), no. 1 016002, [arXiv:2112.00915]. 21

    2022 arXiv

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.