Pith. sign in

REVIEW 3 major objections 6 minor 5 cited by

The paper predicts that 1/2 to 3/2 weak decays occur only for Omega_c and Omega_b, with branching fractions up to about 22%.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Form factors and decay widths are computed for 1/2 to 3/2 weak transitions of Omega_c and Omega_b baryons, yielding branching-ratio predictions for semileptonic and nonleptonic modes.

T0 review reviewed 2026-08-05 challenge →

load-bearing objection Honest, standard LFQM computation of Omega_Q -> 3/2 weak decays with useful tables, but the hand-picked shape parameters and their 10% uncertainty are the entire error budget, so a sensitivity scan is needed before the numbers can be taken as robust. the 3 major comments →

arxiv 2508.13648 v1 pith:JF57ANRM submitted 2025-08-19 hep-ph hep-ex

Weak decays of singly heavy baryons: the $1/2\to3/2$ case

classification hep-ph hep-ex
keywords light-front quark modelthree-quark picturesingly heavy baryonsweak decaysOmega_cOmega_bsemileptonic decaysnonleptonic decays
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

This paper predicts the spin-1/2 to spin-3/2 weak decays of singly heavy baryons, showing that at leading QCD order only the Omega_c and Omega_b channels are allowed because antitriplet baryons' spin wavefunctions are orthogonal to spin-3/2 final states. Using a light-front quark model in which the three valence quarks are treated independently, it extracts the vector and axial-vector form factors at $q^2=0$ and then applies a single-pole $q^2$ dependence to compute semileptonic and nonleptonic widths. The headline numbers are branching fractions of about $6\%$ for $\Omega_c^0 \to \Omega^- e^+ \nu_e$ and $22\%$ for $\Omega_c^0 \to \Omega^- \rho^+$, plus a $3.6\%$ rate for $\Omega_b^- \to \Omega_c^{*0} e^- \bar{\nu}_e$. These are motivated estimates for channels that have not yet been established, and they agree with the spread of earlier model predictions while sitting below the current experimental central value of the $\Omega_c$ electron-to-pion ratio.

Core claim

On the paper's own terms, the discovery is that the $1/2 \to 3/2$ weak transitions of singly heavy baryons form a closed, computable set: the amplitudes from antitriplet initial states vanish by spin-wavefunction orthogonality at leading order in QCD, so the physics reduces to the four sextet channels $\Omega_c^0 \to \Xi^{*-}$, $\Omega_c^0 \to \Omega^-$, $\Omega_b^- \to \Xi^{*0}$, and $\Omega_b^- \to \Omega_c^{*0}$. In the three-quark picture of the light-front quark model, the transition matrix element is parameterized by eight form factors $f_i(q^2)$ and $g_i(q^2)$; the paper computes their $q^2=0$ values (for example $f_1(0) = -0.591 \pm 0.067$ and $g_4(0)=0.615 \pm 0.078$ for $\$Omega_c^{0}$

What carries the argument

The carrying object is the three-quark momentum wavefunction $\Phi(x_i,k_{i\perp}) = \sqrt{e_1e_2e_3/(x_1x_2x_3 M_0)}\,\varphi(\vec k_1,\beta_1)\,\varphi((\vec k_2-\vec k_3)/2,\beta_{23})$, a product of Gaussians whose widths are controlled by five shape parameters $\beta_{\{ss\}}$, $\beta_{q\{ss\}}$, $\beta_{s\{ss\}}$, $\beta_{c\{ss\}}$, $\beta_{b\{ss\}}$ given in Eq. (19). Overlap integrals of initial- and final-state wavefunctions of this form produce all eight form factors; flavor-space overlap factors set the relative normalizations of the four channels; the single-pole interpolation $F(q^2)=F(0)/(1-q^2/m_{\rm pole}^2)$ supplies the off-shell behavior; and helicity amplitudes built from

Load-bearing premise

The calculation stands on the five Gaussian width parameters of Eq. (19), which are picked by analogy with earlier quark-model values and assigned 'approximately 10%' uncertainties; if these hand-chosen widths are wrong, every form factor, width, and branching ratio shifts by an amount the quoted errors do not capture.

What would settle it

Measure the ratio $R_{e/\pi}=\mathcal{B}(\Omega_c^0\to\Omega^- e^+\nu_e)/\mathcal{B}(\Omega_c^0\to\Omega^-\pi^+)$ with errors below the current spread: the paper predicts $1.31\pm0.02$, while the most precise existing measurement centers near $1.98$. A single high-statistics measurement at the few-percent level would settle whether the form-factor normalization at $q^2=0$ is right; alternatively, observing $\Omega_c^0 \to \Xi^{*-}$ semileptonic decay at a rate very different from the predicted $1.77\times10^{-3}$ branching fraction would expose errors in the overlap factors or the single-pole

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • The $\Omega_c^0 \to \Omega^- \rho^+$ channel is predicted at a branching fraction near $22\%$, making it the most promising first discovery mode for a $1/2\to3/2$ weak baryon decay.
  • The predicted ratio $R_{e/\pi}\approx1.3$ is a sharp, measurable number; the gap between it and the current central value near $2$ is what a future run can resolve.
  • For the bottom sector, $\Omega_b^- \to \Omega_c^{*0} e^-\bar{\nu}_e$ has a $3.6\%$ branching fraction and a longitudinal-to-transverse polarization ratio $1.26\pm0.02$, so its angular distribution can probe the $g$-type form factors.
  • Because antitriplet-to-$3/2$ transitions vanish at leading order, any observed $\Lambda_c$ or $\Xi_c$ decay into a spin-$3/2$ baryon would indicate higher-order QCD or new dynamics rather than a standard weak transition.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The paper leaves nonfactorizable contributions out of the nonleptonic rates; a clean test of that approximation is the $\Omega_c^0\to\Omega^-\pi^+$ versus $\Omega_c^0\to\Omega^-\rho^+$ ratio, because the two modes share form factors but differ in final-state interactions.
  • The single-pole $q^2$ dependence is transferred from meson physics without a dedicated baryon check; a first-principles computation of these form factors at three or more momentum transfers would either validate the pole-mass choice or show that the shapes for $\Omega_b$ transitions need a modified interpolation.
  • The quoted errors come only from the 10% uncertainty on the five shape parameters, so if the interpolation logic behind Eq. (19) is off by more than that, the central values themselves are biased; the model's real discriminating power should be judged by comparison across independently fitted parameter sets.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper studies weak decays of singly heavy baryons into spin-3/2 final states, i.e. the 1/2 -> 3/2 transitions. The authors argue that antitriplet baryons cannot decay to spin-3/2 baryons at leading order because of spin-wavefunction orthogonality, so only Omega_c and Omega_b decays are treated. Using the three-quark light-front quark model, they extract q^2=0 form factors for Omega_c -> Xi*-, Omega_c -> Omega-, Omega_b -> Xi*0, and Omega_b -> Omega*_c, adopt a single-pole q^2 dependence, and compute semileptonic widths as well as nonleptonic widths from the factorizable W-emission diagram. Representative predictions are BR(Omega_c -> Omega^- e+ nu_e)=(6.03 +/- 1.34) x 10^-2 and BR(Omega_c -> Omega^- rho^+)=(2.21 +/- 0.48) x 10^-1. The results are compared with existing quark-model and phenomenological estimates, and the ratio R_{e/pi} is found to be smaller than the Belle measurement.

Significance. If the results hold, the paper provides a useful systematic survey of unmeasured weak-decay channels of Omega_c and Omega_b, including several channels not previously compiled in one framework. The paper is commendably transparent: it explicitly states that nonleptonic predictions omit non-factorizable contributions, it reports large propagated errors, and it tabulates form factors and many observables for later comparison. The overlap factors in Table I and the form-factor table are convenient references. The main value is as a model-based, falsifiable set of predictions; however, the numerical error bars should be viewed with caution because, as detailed below, they inherit an unquantified assumption about five shape parameters.

major comments (3)
  1. [Sec. III A, Eq. (19), Tables II-IV] The five shape parameters beta_{ss}=0.30, beta_{qss}=0.33, beta_{sss}=0.35, beta_{css}=0.51, beta_{bss}=0.68 GeV are fixed by qualitative interpolation ('It is reasonable that ...') and assigned 'approximately 10% uncertainties' with no quantitative justification. Since the Gaussian wavefunction Phi in Eq. (13) depends on these beta values, every entry in Table II, and consequently the widths in Tables III and IV, are controlled by this choice. A 20% shift in a beta value would rescale wavefunction overlaps by at least ~10-20%, and widths, which are quadratic in form factors, by potentially 30-50%. The quoted error bars therefore measure only the assumed 10%, not the actual model uncertainty. The authors should include a sensitivity scan over a wider, justified range of the beta_{ss} family, or determine the parameters from spectroscopy or other observables; otherwise the robustness of t
  2. [Sec. II B] The form-factor extraction is only described as three verbal steps after Eq. (16). No explicit projection formulas for f_i(q^2) and g_i(q^2) in terms of the overlap integrals are given. Since Table II is the load-bearing input to all phenomenological results, the reader cannot independently reproduce or verify the central derivation. The authors should present the explicit expressions (or provide a supplementary file with the integrals and the projection matrices) so that the extraction can be checked.
  3. [Sec. III B, Eq. (24)] The q^2 dependence is modeled by the single-pole formula F(q^2)=F(0)/(1-q^2/m_pole^2), with the only cited justification being meson-sector evidence in Ref. [28]. The same functional form is applied to 1/2 -> 3/2 baryon transitions without a dedicated test. The sensitivity of Tables III and IV to this prescription is not examined. I request a quantitative check, for example varying m_pole by +/-10% or comparing with a dipole form, and a statement of how much the widths change. This is important for the larger-q^2 channels such as Omega_b -> Omega*_c e nu.
minor comments (6)
  1. [Sec. II A] Typo: 'diquak' should be 'diquark' in the descriptions of Eqs. (9)-(11).
  2. [Introduction, Fig. 1] Typo: 'symmtry' should be 'symmetry' in both the introduction and the Fig. 1 caption.
  3. [Eq. (32)] The expression contains a garbled symbol '|− →P ′|' in the numerator; presumably this should be the three-momentum |\vec P'|. Please correct the typesetting.
  4. [Table V] The entry 'Alice [46]' should be 'ALICE [46]'.
  5. [Table II] For the Omega_b -> Xi*0 transition, f2(0)=0.000 +/- 0.000 exactly. A one-sentence explanation of this exact zero would help the reader.
  6. [Sec. III D] The nonleptonic predictions are explicitly limited to the factorizable W-emission diagram, which is appropriate. It would be useful to state in the abstract or conclusions that the nonleptonic branching fractions are 'factorizable-model estimates' rather than full predictions.

Circularity Check

0 steps flagged

No significant circularity: the 1/2→3/2 form factors and widths are genuine model outputs; the β parameters are transparent inputs, even though several are inherited from the authors' prior work.

full rationale

The derivation chain is: three-quark LFQM wavefunction (Sec. II) with quark masses (Eq. 17) and shape parameters from Refs. [4,34] plus the new β{ss} family chosen by heuristic mass/size ordering (Eq. 19) yields the q^2=0 form factors (Table II) through overlap integrals; these are converted to semileptonic and nonleptonic widths (Tables III–IV) via Eq. (24). None of the target 1/2→3/2 form factors, widths, or branching ratios is used to fit β{ss}, β{qss}, β{sss}, β{css}, or β{bss}; those parameters are fixed before the calculation, so the table entries are genuine model outputs rather than fitted quantities renamed as predictions. The 'approximately 10% uncertainties' on the shape parameters are assumed inputs, not derived from data, so the quoted error bars inherit an arbitrary assumption; this is a robustness/correctness concern, not a circular reduction. The self-citational elements (inherited β's from Refs. [4,34] and the single-pole ansatz referenced to Ref. [28]) are load-bearing model choices, but the central phenomenological predictions are compared with independent literature and Belle data and are not equivalent by construction to any input. No specific equation is shown to reduce to a previous result or to a fitted value of the target observable, so the paper does not exhibit self-definitional or fitted-input circularity.

Axiom & Free-Parameter Ledger

7 free parameters · 4 axioms · 0 invented entities

The central calculation is a parameter-carrying model computation. The eight form factors of Table II follow from the overlap integral of three-quark wavefunctions whose Gaussian widths are the five beta parameters of Eq. (19); three of these (beta{ss}, beta{qss}, beta{sss}) are new to this paper and are picked by hand, while beta{css} and beta{bss} are set to be 'slightly larger' than the authors' earlier values. Quark masses (Eq. 17) and the base beta's (Eq. 18) come from the authors' Refs. [4,34]. The 10% input uncertainty that produces all quoted errors is also an assumption. No new particles or forces are introduced.

free parameters (7)
  • Shape parameter beta{ss} = 0.30 GeV
    Chosen by hand in Eq. (19): 'slightly larger than beta{ud}=0.28 and much smaller than beta{cc}=0.40', not fitted to any 1/2 to 3/2 observable.
  • Shape parameter beta{qss} (q=u,d) = 0.33 GeV
    Hand-picked in Eq. (19); required to be larger than beta{ud} and smaller than beta{sss}.
  • Shape parameter beta{sss} = 0.35 GeV
    Hand-picked in Eq. (19) from beta{ss}, with no direct constraint from data.
  • Shape parameter beta{css} = 0.51 GeV
    Hand-picked in Eq. (19) as 'slightly larger than beta{c{ud}}=0.49'.
  • Shape parameter beta{bss} = 0.68 GeV
    Hand-picked in Eq. (19) as 'slightly larger than beta{b{ud}}=0.66'.
  • Constituent quark masses m_u=m_d, m_s, m_c, m_b = 0.25, 0.37, 1.4, 4.8 GeV
    Inputs of Eq. (17) inherited from the LFQM literature (Ref. [34]); fitted there to other hadron observables, not to 1/2 to 3/2 transitions.
  • Assumed 10% uncertainty on shape parameters = 10%
    Sec. III A: 'These shape parameters carry approximately 10% uncertainties, which will be used for error estimation'. The error bars in Tables II-IV derive entirely from this assumption.
axioms (4)
  • domain assumption Baryons are described by three on-shell constituent quarks with the Gaussian momentum wavefunction of Eq. (13) and the spin wavefunction Ansatze of Eqs. (9)-(11).
    The LFQM three-quark picture from Ref. [34]; none of this is derived within the paper.
  • domain assumption Antitriplet baryon to spin-3/2 baryon weak amplitudes vanish at leading order from spin-wavefunction orthogonality.
    Stated in the abstract and Sec. I to justify restricting to Omega_Q; no derivation or citation is given in this paper.
  • domain assumption Form factors follow a single-pole q2 dependence, Eq. (24), with meson masses as pole masses.
    Sec. III B; validity is deferred to Ref. [28] in the meson sector.
  • domain assumption Nonleptonic decays are dominated by the factorizable external W-emission diagram with Wilson coefficient a1.
    Sec. III D; the paper explicitly notes non-factorizable contributions are dropped and predictions are 'rough estimates'.

reviewed 2026-08-05 · how reviews work

0 comments
Cite this review

Pith. "Pith review of Weak decays of singly heavy baryons: the $1/2\to3/2$ case." pith.science (2026). https://pith.science/paper/JF57ANRM

@misc{pith2026250813648,
  author       = {Pith},
  title        = {Pith review of: Weak decays of singly heavy baryons: the $1/2\to3/2$ case},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JF57ANRM}},
  note         = {Machine review of arXiv:2508.13648}
}
Share X Bluesky LinkedIn Reddit HN
abstract

This work is devoted to investigating the $1/2\to3/2$ weak decays of singly heavy baryons. Due to the orthogonality between the spin wavefunctions of antitriplet baryons and spin-3/2 baryons, the weak decay amplitude for such processes vanishes at the leading order of QCD. Consequently, this study exclusively examines the weak decays of $\Omega_{Q}$. Using the light-front approach under the three-quark picture, we first extract the relevant form factors, and then apply them to investigate corresponding semileptonic and nonleptonic decays. Finally, we compare our phenomenological predictions with existing results in the literature. Our findings are expected to be helpful in experimentally establishing these decay channels.

Figures

Figures reproduced from arXiv: 2508.13648 by Fu-Wei Zhang, Zhen-Xing Zhao.

Figure 1
Figure 1. Figure 1: FIG. 1: SU(3) flavor symmtry arranges singly heavy baryons into a [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Analysis of the semileptonic decays $\Sigma_b\to\Sigma_cl\bar{\nu}_l$, $\Xi'_b\to\Xi'_cl\bar{\nu}_l$ and $\Omega_b\to\Omega_cl\bar{\nu}_l$ in QCD sum rules

    hep-ph 2026-02 conditional novelty 5.0

    QCD sum-rule calculations predict Σ_b→Σ_c, Ξ'_b→Ξ'_c and Ω_b→Ω_c semileptonic widths that differ by less than 13%, supporting approximate SU(3) flavor symmetry.

  2. A Phenomenological Study of Semileptonic $B^+$ and $B_s^0$ Decays into Axial-Vector Mesons $\big(D_1(2420),\, D_1^\prime(2430),\, D_{s1}(2460),\, \text{and } D_{s1}^\prime(2536)\big)$ within the Standard Model

    hep-ph 2026-05 unverdicted novelty 4.0

    Semileptonic B decays to mixed axial-vector mesons show branching ratios and polarization observables that vary strongly with the D1 mixing angle in the covariant light-front quark model.

  3. A Phenomenological Study of Semileptonic $B^+$ and $B_s^0$ Decays into Axial-Vector Mesons $\big(D_1(2420),\, D_1^\prime(2430),\, D_{s1}(2460),\, \text{and } D_{s1}^\prime(2536)\big)$ within the Standard Model

    hep-ph 2026-05 unverdicted novelty 4.0

    Semileptonic B to axial-vector meson decays are studied as functions of the mixing angle θ_D1 using covariant light-front quark model form factors, producing predictions for branching ratios, forward-backward asymmetr...

  4. Semileptonic and nonleptonic weak decays of bottom baryons $\Omega^{(*)}_{b}$

    hep-ph 2025-10 conditional novelty 4.0

    QCD sum-rule calculation predicts Ω_b^*→Ω_c and Ω_b→Ω_c^* semileptonic and nonleptonic decay widths, e.g. Γ(Ω_b^*→Ω_c eν)=(1.54+0.29−0.27)×10^-14 GeV.

  5. Analysis of the semileptonic decays $\Sigma_b\to\Sigma_cl\bar{\nu}_l$, $\Xi'_b\to\Xi'_cl\bar{\nu}_l$ and $\Omega_b\to\Omega_cl\bar{\nu}_l$ in QCD sum rules

    hep-ph 2026-02 unverdicted novelty 3.0

    Electroweak form factors for Σ_b→Σ_c, Ξ'_b→Ξ'_c and Ω_b→Ω_c transitions are computed in QCD sum rules, producing decay widths that approximately obey SU(3) flavor symmetry along with branching ratios and new-physics p...

Reference graph

Works this paper leans on

49 extracted references · 28 canonical work pages · cited by 3 Pith papers · 23 internal anchors

  1. [1]

    diquark picture

    Specifically, for charmed baryons, ¯3 is composed of Λ + c and Ξ+,0 c , while 6 is composed of Σ ++,+,0 c , Ξ′+,′0 c and Ω 0 c; for bottom baryons, ¯3 is composed of Λ 0 b and Ξ 0,− b , while 6 is composed of Σ +,0,− b , Ξ′0,′− b and Ω − b . Only the antitriplet heavy baryons and the sextet Ω Q predominantly undergo arXiv:2508.13648v1 [hep-ph] 19 Aug 2025 ...

  2. [2]

    Aaij et al

    R. Aaij et al. [LHCb], Nature 643, no.8074, 1223-1228 (2025) doi:10.1038/s41586-025-09119-3 [arXiv:2503.16954 [hep-ex]]

  3. [3]

    F. S. Yu and C. D. L¨ u, Sci. Bull. 70, 2035-2036 (2025) [arXiv:2504.15008 [hep-ph]]

  4. [4]

    J. P. Wang and F. S. Yu, Chin. Phys. C 48, no.10, 101002 (2024) doi:10.1088/1674-1137/ad75f4 [arXiv:2407.04110 [hep-ph]]

  5. [5]

    Z. X. Zhao, Chin. Phys. C 42, no.9, 093101 (2018) doi:10.1088/1674-1137/42/9/093101 [arXiv:1803.02292 [hep-ph]]

  6. [6]

    M. A. Ivanov, V. E. Lyubovitskij, J. G. Korner and P. Kroll, Phys . Rev. D 56, 348-364 (1997) doi:10.1103/PhysRevD.56.348 [arXiv:hep-ph/9612463 [hep-ph]]

  7. [7]

    H. Y. Cheng, Phys. Rev. D 56, 2799-2811 (1997) [erratum: Phys. Rev. D 99, no.7, 079901 (2019)] doi:10.1103/PhysRevD.56.2799 [arXiv:hep-ph/9612223 [hep-ph]]

  8. [8]

    Ebert, R

    D. Ebert, R. N. Faustov and V. O. Galkin, Phys. Rev. D 73, 094002 (2006) doi:10.1103/PhysRevD.73.094002 [arXiv:hep-ph/0604017 [hep-ph]]

  9. [9]

    H. W. Ke, N. Hao and X. Q. Li, J. Phys. G 46, no.11, 115003 (2019) doi:10.1088/1361-6471/ab29a7 [arXiv:1711.02518 [hep-ph]]

  10. [10]

    T. M. Aliev, S. Bilmis and M. Savci, Phys. Rev. D 106, no.7, 074022 (2022) doi:10.1103/PhysRevD.106.074022 [arXiv:2208.10365 [hep-ph]]

  11. [11]

    K. L. Wang, Q. F. L¨ u, J. J. Xie and X. H. Zhong, Phys. Rev. D 107, no.3, 034015 (2023) doi:10.1103/PhysRevD.107.034015 [arXiv:2203.04458 [hep-ph]]

  12. [12]

    C. W. Liu, Phys. Rev. D 109, no.3, 033004 (2024) doi:10.1103/PhysRevD.109.033004 [arXiv:2308 .07754 [hep-ph]]

  13. [13]

    F. Lu, H. W. Ke, X. H. Liu and Y. L. Shi, Eur. Phys. J. C 83, no.5, 412 (2023) doi:10.1140/epjc/s10052- 023-11572-1 [arXiv:2303.02946 [hep-ph]]

  14. [14]

    S. Zeng, F. Xu and Y. Gu, Eur. Phys. J. C 85, no.2, 184 (2025) doi:10.1140/epjc/s10052-025-13886-8 [arXiv:2406.02097 [hep-ph]]

  15. [15]

    Y. J. Shi and J. Zeng, Eur. Phys. J. C 85, no.6, 712 (2025) doi:10.1140/epjc/s10052-025-14436-y [arXiv:2503.18628 [hep-ph]]

  16. [16]

    Semileptonic Decays of Heavy Omega Baryons in a Quark Model

    M. Pervin, W. Roberts and S. Capstick, Phys. Rev. C 74, 025205 (2006) doi:10.1103/PhysRevC.74.025205 [arXiv:nucl-th/0603061 [nucl-th]]

  17. [17]

    H. Y. Cheng and C. K. Chua, Phys. Rev. D 69, 094007 (2004) [erratum: Phys. Rev. D 81, 059901 (2010)] doi:10.1103/PhysRevD.69.094007 [arXiv:hep-ph/0401141 [h ep-ph]]

  18. [18]

    H. W. Ke, X. Q. Li and Z. T. Wei, Phys. Rev. D 80, 074030 (2009) doi:10.1103/PhysRevD.80.074030 [arXiv:0907.5465 [hep-ph]]

  19. [19]

    H. W. Ke, X. Q. Li and Z. T. Wei, Eur. Phys. J. C 69, 133-138 (2010) doi:10.1140/epjc/s10052-010- 1383-6 [arXiv:0912.4094 [hep-ph]]. 12

  20. [20]

    H. Y. Cheng and C. K. Chua, Phys. Rev. D 81, 114006 (2010) [erratum: Phys. Rev. D 82, 059904 (2010)] doi:10.1103/PhysRevD.81.114006 [arXiv:0909.4627 [hep-ph]]

  21. [21]

    C. D. Lu, W. Wang and Z. T. Wei, Phys. Rev. D 76, 014013 (2007) doi:10.1103/PhysRevD.76.014013 [arXiv:hep-ph/0701265 [hep-ph]]

  22. [22]

    W. Enqi, R. H. Li and Z. X. Zhao, [arXiv:2504.15056 [hep-ph]]

  23. [23]

    W. Wang, Y. L. Shen and C. D. Lu, Eur. Phys. J. C 51, 841-847 (2007) doi:10.1140/epjc/s10052-007- 0334-3 [arXiv:0704.2493 [hep-ph]]

  24. [24]

    W. Wang, Y. L. Shen and C. D. Lu, Phys. Rev. D 79, 054012 (2009) doi:10.1103/PhysRevD.79.054012 [arXiv:0811.3748 [hep-ph]]

  25. [25]

    Wang and Y

    W. Wang and Y. L. Shen, Phys. Rev. D 78, 054002 (2008) doi:10.1103/PhysRevD.78.054002

  26. [26]

    X. X. Wang, W. Wang and C. D. Lu, Phys. Rev. D 79, 114018 (2009) doi:10.1103/PhysRevD.79.114018 [arXiv:0901.1934 [hep-ph]]

  27. [27]

    C. H. Chen, Y. L. Shen and W. Wang, Phys. Lett. B 686, 118-123 (2010) doi:10.1016/j.physletb.2010.02.056 [arXiv:0911.2875 [hep-ph]]

  28. [28]

    G. Li, F. l. Shao and W. Wang, Phys. Rev. D 82, 094031 (2010) doi:10.1103/PhysRevD.82.094031 [arXiv:1008.3696 [hep-ph]]

  29. [29]

    Y. J. Shi, W. Wang and Z. X. Zhao, Eur. Phys. J. C 76, no.10, 555 (2016) doi:10.1140/epjc/s10052- 016-4405-1 [arXiv:1607.00622 [hep-ph]]

  30. [30]

    H. Y. Cheng, C. K. Chua and C. W. Hwang, Phys. Rev. D 69, 074025 (2004) doi:10.1103/PhysRevD.69.074025 [arXiv:hep-ph/0310359 [hep-ph]]

  31. [31]

    Y. J. Shi and Z. P. Xing, Nucl. Phys. B 1000, 116486 (2024) doi:10.1016/j.nuclphysb.2024.116486 [arXiv:2307.02767 [hep-ph]]

  32. [32]

    Z. P. Xing and Z. X. Zhao, Phys. Rev. D 98, no.5, 056002 (2018) doi:10.1103/PhysRevD.98.056002 [arXiv:1807.03101 [hep-ph]]

  33. [33]

    Z. X. Zhao, Eur. Phys. J. C 78, no.9, 756 (2018) doi:10.1140/epjc/s10052-018-6213-2 [arXiv:18 05.10878 [hep-ph]]

  34. [34]

    Z. X. Zhao, F. W. Zhang and Q. Yang, Eur. Phys. J. C 85, no.1, 106 (2025) doi:10.1140/epjc/s10052- 025-13780-3 [arXiv:2204.00759 [hep-ph]]

  35. [35]

    Z. X. Zhao, F. W. Zhang, X. H. Hu and Y. J. Shi, Phys. Rev. D 107, no.11, 116025 (2023) doi:10.1103/PhysRevD.107.116025 [arXiv:2304.07698 [hep-ph]]

  36. [36]

    Y. P. Xing, X. Y. Sun and Z. X. Zhao, [arXiv:2410.06507 [hep-ph]]

  37. [37]

    Z. P. Xing, Y. J. Shi, J. Sun and Z. X. Zhao, [arXiv:2312.17568 [hep -ph]]

  38. [38]

    Wang and Z

    W. Wang and Z. P. Xing, Phys. Lett. B 834, 137402 (2022) doi:10.1016/j.physletb.2022.137402 [arXiv:2203.14446 [hep-ph]]

  39. [39]

    H. Liu, Z. P. Xing and C. Yang, Eur. Phys. J. C 83, no.2, 123 (2023) doi:10.1140/epjc/s10052-023- 11263-x [arXiv:2210.10529 [hep-ph]]

  40. [40]

    H. Liu, W. Wang and Z. P. Xing, Phys. Rev. D 108, no.3, 035008 (2023) doi:10.1103/PhysRevD.108.035008 [arXiv:2305.01168 [hep-ph]]

  41. [41]

    J. Zhu, Z. T. Wei and H. W. Ke, Phys. Rev. D 99, no.5, 054020 (2019) doi:10.1103/PhysRevD.99.054020 [arXiv:1803.01297 [hep-ph]]

  42. [42]

    W. Wang, F. S. Yu and Z. X. Zhao, Eur. Phys. J. C 77, no.11, 781 (2017) doi:10.1140/epjc/s10052- 017-5360-1 [arXiv:1707.02834 [hep-ph]]

  43. [43]

    Navas et al

    S. Navas et al. [Particle Data Group], Phys. Rev. D 110, no.3, 030001 (2024) 13 doi:10.1103/PhysRevD.110.030001

  44. [44]

    Carrasco, P

    N. Carrasco, P. Dimopoulos, R. Frezzotti, P. Lami, V. Lubicz, F . Nazzaro, E. Picca, L. Riggio, G. C. Rossi and F. Sanfilippo, et al. Phys. Rev. D 91, no.5, 054507 (2015) doi:10.1103/PhysRevD.91.054507 [arXiv:1411.7908 [hep-lat]]

  45. [45]

    A. J. Buras, [arXiv:hep-ph/9806471 [hep-ph]]

  46. [46]

    Y. K. Hsiao, L. Yang, C. C. Lih and S. Y. Tsai, Eur. Phys. J. C 80, no.11, 1066 (2020) doi:10.1140/epjc/s10052-020-08619-y [arXiv:2009.12752 [hep-ph ]]

  47. [47]
  48. [48]

    Y. B. Li et al. [Belle], Phys. Rev. D 105, no.9, L091101 (2022) doi:10.1103/PhysRevD.105.L091101 [arXiv:2112.10367 [hep-ex]]

  49. [49]

    Observation of the Decay Omega_C^0 --> Omega- e+ nu_e

    R. Ammar et al. [CLEO], Phys. Rev. Lett. 89, 171803 (2002) doi:10.1103/PhysRevLett.89.171803 [arXiv:hep-ex/0207078 [hep-ex]]

This paper was first reviewed by deepseek-v4-flash on August 5, 2026.