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REVIEW 4 major objections 6 minor 1 cited by

Two-body Hidden Charm Decays of $D$ Wave Charmonia

T0 review · 4 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The paper predicts that psi2(3823) decays to J/psi eta with a partial width near 30 keV, about 10% of its radiative width.

desk verdict A competent meson-loop calculation with a testable ψ2(3823)→J/ψη width, but the η-η' mixing angle sign is stated inconsistently and needs fixing. read the letter →

arxiv 2501.16124 v1 pith:7OD4C6VR submitted 2025-01-27 hep-ph

Xiao-Yu Qi , Qi Wu , Xing-Dao Guo , Dian-Yong Chen This is my paper · ORCID
classification hep-ph
keywords D-wavecharmoniahiddencharmdecaymesonloopmechanismpsi(3770)psi2(3823)psi3(3842)J/psietaeta_comega
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

This paper predicts the two-body hidden-charm decay rates of the spin-triplet D-wave charmonia using the meson loop mechanism. A single form-factor parameter $\alpha_\Lambda$ is fixed by reproducing the measured branching fraction of $\psi(3770)\to J/\psi\eta$, and the same parameter then yields $\Gamma[\psi_2(3823)\to J/\psi\eta]=(29.64^{+4.01}_{-4.63})$ keV. The corresponding ratio to $\psi_2(3823)\to\gamma\chi_{c1}$ is about 10%, below the current experimental upper limit and consistent with existing Belle and LHCb data. Because $\psi_2(3823)$ cannot decay to $D\bar D$, these hidden-charm channels are among its only strong decay modes, so the prediction gives a concrete target for BESIII, Belle II, and LHCb.

What carries the argument

The machinery is the meson loop mechanism: the initial charmonium fluctuates into an $S$-wave charmed-meson pair ($D\bar D$, $D\bar D^*$, $D^*\bar D^*$) that rescatters into $J/\psi\eta$ or $\eta_c\omega$. The amplitudes are built from heavy-quark effective Lagrangians — the superfield $R$ for $S$-wave charmonia, the spin multiplet $J^{\mu\lambda}$ for $D$-wave charmonia, and the $H$ superfields for charmed mesons — so all couplings are fixed by symmetry up to the gauge couplings $g_1$ and $g_2$. Loop convergence and off-shell effects are controlled by the monopole form factor $F=(m_q^2-\Lambda^2)/(q^2-\Lambda^2)$ with $\Lambda=m+\alpha_\Lambda\Lambda_{\mathrm{QCD}}$; the single free parameter $\alpha_\Lambda$ is the load-bearing dial.

What would settle it

Measure the ratio $\mathcal{B}[\psi_2(3823)\to J/\psi\eta]/\mathcal{B}[\psi_2(3823)\to\gamma\chi_{c1}]$ with the next generation of charmonium data; a central value outside roughly $5\%$–$15\%$, or an absolute $\psi_2(3823)\to J/\psi\eta$ width far from $30$ keV, would falsify the $\alpha_\Lambda$ transfer assumption.

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Extended reading notes

Core claim

The paper's central claim is that one meson-loop amplitude, regulated by a monopole form factor with a single fitted parameter, describes the hidden-charm decays of all three $D$-wave charmonia spin triplets. The fitted range $\alpha_\Lambda=(1.11^{+0.04}_{-0.05})$ reproduces $\mathcal{B}[\psi(3770)\to J/\psi\eta]=(8.7\pm1.2)\times10^{-4}$, and from it the paper obtains $\mathcal{B}[\psi(3770)\to\eta_c\omega]=(6.03^{+0.82}_{-0.92})\times10^{-5}$, $\Gamma[\psi_2(3823)\to J/\psi\eta]=(29.64^{+4.01}_{-4.63})$ keV, and $\Gamma[\psi_2(3823)\to\eta_c\omega]=(0.38^{+0.05}_{-0.06})$ keV. The ratio $\Gamma[\psi_2(3823)\to\eta_c\omega]/\Gamma[\psi_2(3823)\to J/\psi\eta]=0.127$ is essentially parameter-independent. For $\psi_3(3842)$, the widths are only $7.54$ eV and $1.12$ eV because its hidden-charm final states couple through an $F$ wave, so the paper concludes that hidden charm is negligible for that state.

Load-bearing premise

The prediction stands or falls on the assumption that the form-factor parameter $\alpha_\Lambda$ fitted to $\psi(3770)\to J/\psi\eta$ applies unchanged to $\psi_2(3823)$ and $\psi_3(3842)$ because the three $D$-wave states are similar; if the dressed meson-loop coupling or off-shell behavior differs with spin, the 30 keV width and the eV-scale $\psi_3(3842)$ widths would shift.

Editorial extensions

If this is right

  • The $\psi_2(3823)\to J/\psi\eta$ partial width is $(29.64^{+4.01}_{-4.63})$ keV, making it the dominant hidden-charm strong decay of $\psi_2(3823)$.
  • The ratio of this width to $\psi_2(3823)\to\gamma\chi_{c1}$ is about 10%, below the BESIII upper limit of 0.14 and consistent with the Belle and LHCb cascade measurements.
  • The $\psi_2(3823)\to\eta_c\omega$ mode is predicted at $(0.38^{+0.05}_{-0.06})$ keV, with a parameter-independent ratio of $0.127$ to $J/\psi\eta$.
  • $\psi(3770)\to\eta_c\omega$ has branching fraction $(6.03^{+0.82}_{-0.92})\times10^{-5}$, about an order of magnitude below $\psi(3770)\to J/\psi\eta$.
  • $\psi_3(3842)$ hidden-charm widths are only $7.54$ eV and $1.12$ eV, so hidden charm does not contribute meaningfully to its total width.

Reading between the lines

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

  • If the predicted 30 keV width is correct, the hidden-charm channels exhaust only a small part of $\psi_2(3823)$'s $<2.9$ MeV width, so its total width should be dominated by radiative transitions; a future width measurement would calibrate the E1-transition scale.
  • The same fitted parameter predicts $\psi(3770)\to\eta_c\omega$ at $6\times10^{-5}$; measuring that mode would provide a direct test of whether $\alpha_\Lambda$ truly transfers across spin states.
  • The framework leaves the $F$-wave coupling $\psi_3(3842)D\bar D$ out because it vanishes at leading order, so a sizable $\psi_3(3842)\to D\bar D$ contribution from on-shell loops could be the next place to look.
  • Extending the same calculation to the spin-singlet $\eta_{c2}$ partner would fill in the missing piece of the $D$-wave multiplet's hidden-charm decays.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The manuscript studies two-body hidden-charm decays of the D-wave charmonia ψ(3770), ψ2(3823), and ψ3(3842) in a hadronic meson-loop model. The model parameter αΛ is fixed by reproducing the measured branching fraction of ψ(3770)→J/ψη, and the same parameter range is then used to predict the partial widths of ψ(3770)→ηcω, ψ2(3823)→J/ψη/ηcω, and ψ3(3842)→J/ψη/ηcω. The central result is Γ[ψ2(3823)→J/ψη] = (29.64^{+4.01}_{-4.63}) keV, which corresponds to about a 10% ratio of ψ2(3823)→J/ψη to ψ2(3823)→γχc1 and is proposed as a testable observable for BESIII, Belle II, and LHCb.

Significance. If the predictions are reliable, the paper provides a useful quantitative estimate for a channel that is directly accessible to ongoing experiments, particularly the ψ2(3823)→J/ψη width and its ratio to the radiative width. The work is concrete and falsifiable, and the authors are explicit about the model, the amplitudes, and the parameter determination. The main strengths are the complete one-loop expressions and the use of an experimentally determined branching fraction to fix the cutoff parameter. However, the central numerical prediction depends sensitively on an η-η' mixing sign convention that is stated inconsistently, and the ψ3 predictions omit a vertex whose contribution the authors themselves acknowledge can be sizable. These issues must be resolved before the numerical results can be used as quantitative predictions.

major comments (4)
  1. [Section II, after Eq. (11); Section III.B] The η-η' mixing angle is stated inconsistently. The text says θ ranges from −10° to −20°, citing Refs. [46,47], but then sets θ = 19.1°, citing Refs. [48,49]. Because α(θ) = (cosθ − √2 sinθ)/√6 is linear in the amplitudes, α ≈ 0.58 at θ = −19.1° but α ≈ 0.20 at θ = +19.1°. Since αΛ is fitted to Br(ψ(3770)→J/ψη), a change in the sign convention shifts αΛ and does not simply rescale the predicted ψ2(3823)→J/ψη width, because the loop integrals have an αΛ dependence through the form factor. The authors must specify the mixing convention used for Refs. [48,49], repeat the fit with a consistent sign, and show how the headline value and its uncertainty change.
  2. [Eq. (19), Abstract, and Section IV] The quoted uncertainty of the central prediction is internally inconsistent: the abstract gives Γ[ψ2(3823)→J/ψη] = (29.64^{+4.01}_{-4.63}) keV, Eq. (19) gives (29.64^{+4.01}_{-4.43}) keV, and the summary gives (29.64^{+4.10}_{-4.43}) keV. Since the paper presents the asymmetric error as part of its quantitative claim, the authors should reconcile these numbers and explain how the error is propagated from the αΛ range, including whether the upper/lower asymmetry arises from the non-linear dependence of the loop integrals.
  3. [Section III.B, last paragraph; Appendix A, Eqs. (A3)-(A4)] The ψ3(3842)→J/ψη predictions omit the ψ3(3842)D Dbar vertex because it vanishes at leading order in the heavy-quark expansion, but the authors explicitly acknowledge that 'the meson loops relevant to ψ3(3842)D Dbar may have sizable contributions since the D Dbar in the meson loops could be on-shell.' Given that the predicted ψ3(3842) partial widths are only 7.54 eV and 1.12 eV, an omitted on-shell contribution is not negligible and could change the result by orders of magnitude. The authors should either estimate this contribution, or present the ψ3 predictions with a clear caveat that they are not complete quantitative predictions.
  4. [Section III.B] The extrapolation of αΛ from ψ(3770) to ψ2(3823) and ψ3(3842) is justified only by the statement 'Considering the similarity of the of the D-wave charmonia'. The initial states have different masses, different spin structures, and different allowed charmed-meson channels, so the off-shell form factor and the effective coupling strength need not be identical. Since the central ψ2 prediction depends on this transferability, the authors should provide a quantitative check, for example by showing the sensitivity of Γ[ψ2→J/ψη] to a state-dependent αΛ variation or by comparing the loop integrals for different J states.
minor comments (6)
  1. [Section II, Eq. (11)] The mixing angle θ appears with two different sign conventions in Refs. [46,47] and [48,49]. Please define the convention explicitly in the text so that the numerical value θ = 19.1° is unambiguous.
  2. [Section I and Section III.B] The measured branching fraction of ψ(3770)→J/ψη is quoted as (8.7±1.0±0.8)×10^-4 in the Introduction and as (8.7±1.2)×10^-4 in Section III.B. Please use one consistent experimental value with the full uncertainty breakdown.
  3. [Fig. 4 caption] The caption says 'lift panel' where 'left panel' is intended.
  4. [Section III.B] The sentence 'Considering the similarity of the of the D-wave charmonia' has a grammatical error and should be rewritten.
  5. [Eq. (8)] Several terms in the effective Lagrangian have index contractions that are hard to verify, for example the expressions involving pνϵα(p) and terms with pα1νgβμ−pβ2νgμα. Please check that all Lorentz indices are contracted consistently, since the reader needs to reproduce the amplitudes independently.
  6. [Section III.B, ψ3 discussion] The phrase 'which are much small comparing to widths' should read 'which are much smaller than the widths'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the one-parameter fit to Br(ψ(3770)→J/ψη) is an input, and the ψ2/ψ3 and ηcω widths are computed from distinct loop amplitudes rather than being the fitted observable itself.

full rationale

The paper fixes the monopole form-factor parameter αΛ by reproducing the measured Br(ψ(3770)→J/ψη) (Sec. III.B, Fig. 4, αΛ=(1.11+0.04/−0.05)), then computes the widths Γ[ψ2(3823)→J/ψη], Γ[ψ2(3823)→ηcω], Γ[ψ3(3842)→J/ψη] and Γ[ψ3(3842)→ηcω] from the separate amplitudes in Eqs. (12), (A1)–(A4), and (B1)–(B6). These amplitudes involve different D-wave charmonium couplings (gψ2, gψ3 in Eq. (17)) and different loop integrals, so the predictions are not equal to the fitted input by construction. The D-wave coupling constant g2=1.39 is taken from the authors' earlier work [54] but is itself fixed by the external ψ(3770)→D Dbar width [15], an independent benchmark outside the predicted hidden-charm channels; the heavy-quark multiplet framework is standard (Refs. [34–36]), so the self-citation is not load-bearing. The quoted sign inconsistency for the η–η′ mixing angle (θ given as −10° to −20° and then set to 19.1°) and the admitted neglect of ψ3D Dbar meson loops are real consistency/completeness caveats, but they do not make any predicted quantity equivalent to the fitted data. No step in the derivation reduces by definition to the input observable, so there is no significant circularity.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The calculation depends on two fitted numbers (alpha_Lambda and g2), a chosen form factor shape, and a set of heavy-quark and chiral-symmetry assumptions. The g2 coupling is taken from the authors' own earlier work. No new particles or interactions are introduced.

free parameters (3)
  • alpha_Lambda (form factor parameter) = 1.11 (+0.04/-0.05)
    Monopole form factor Lambda = m + alpha_Lambda * Lambda_QCD with Lambda_QCD = 220 MeV; fitted so that Br(psi(3770) to J/psi eta) matches (8.7 +/- 1.2) x 10^-4 (Section III.B, Fig. 4).
  • g2 (D-wave charmonium to charmed meson coupling) = 1.39
    Taken from Ref [54] by three of the present authors, obtained by the partial width of psi(3770) to D Dbar (Section III.A).
  • eta-eta' mixing angle theta = 19.1 degrees (text likely intended -19.1)
    Set to 'theta = 19.1 deg' with Refs [48,49], despite the text quoting a range of -10 to -20 degrees. The sign inconsistency affects the eta coupling strengths in the loops.
assumptions (5)
  • domain assumption Heavy quark limit effective Lagrangian describes charmed meson and charmonia couplings
    Used to construct all vertices in Section II, Eqs. (3)-(9).
  • domain assumption Meson loops provide the dominant long-distance contribution to OZI-suppressed hidden charm decays
    Section II, following Refs [19-21]; this is the phenomenological basis of the calculation.
  • domain assumption Only S-wave charmed mesons contribute to the loops
    Section II: masses of D-wave charmonia are far below S-wave plus P-wave charmed meson thresholds, so P-wave meson loops are neglected.
  • ad hoc to paper A monopole form factor Lambda = m + alpha_Lambda Lambda_QCD regularizes the loop integrals
    Section II, Eq. (13). The form factor shape is chosen, not derived, and alpha_Lambda is fitted to data.
  • ad hoc to paper The psi3(3842)-D Dbar vertex vanishes at leading order and can be omitted
    Section IV admits this omission; the authors note that on-shell D Dbar pairs may make the contribution sizable.

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Cite this review

Pith. "Pith review of Two-body Hidden Charm Decays of $D$ Wave Charmonia." pith.science (2026). https://pith.science/paper/7OD4C6VR

@misc{pith2026250116124,
  author       = {Pith},
  title        = {Pith review of: Two-body Hidden Charm Decays of $D$ Wave Charmonia},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7OD4C6VR}},
  note         = {Machine review of arXiv:2501.16124}
}
abstract

The experimental observations of $\psi_2(3823)$ and $\psi_3(3842)$ make $D$ wave charmonia family abundant. In the present work, we investigate the hidden charm decay processes of spin triplets of the $D$-wave charmonia with the meson loop mechanism. The model parameter $\alpha_\Lambda$ is determined by reproducing the branching fraction of $\psi(3770)\to J/\psi \eta$. With this range of model parameter values, the branching fractions (partial widths) of $\psi(3770) \to \eta_c \omega$, $\psi_2(3823)/\psi_3(3842) \to J/\psi \eta$, $\psi_2(3823)/\psi_3(3842) \to \eta_c \omega$ are estimated. Our estimations find that the partial width of $\psi_2(3823) \to J/\psi \eta$ is $\left(29.64^{+4.01}_{-4.63}\right)\ \mathrm{keV}$, and the partial width ratio of $\psi_2(3823) \to J/\psi \eta$ relative to $\psi_2(3823)\to \gamma \chi_{c1}$ is about $10\%$, which could be tested by further precise measurements from the BESIII, Belle II and LHCb Collaborations.

Figures

Figures reproduced from arXiv: 2501.16124 by the authors.

Figure 1
Figure 1. FIG. 1: Diagrams contributing to [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: The same as Fig [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: The same as Fig [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4: (Color online) The branching fractions of [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 6
Figure 6. Figure 6: In the considered αΛ range determined by ψ(3770) → J/ψη, the partial widths of the hidden charm decay processes of ψ3(3842) are estimated to be, Γ[ψ3(3842) → J/ψη] =  7.54+0.91 −1.05 eV, Γ[ψ3(3842) → ηcω] = (1.12+0.14 −0.17) eV, (21) which are much small comparing to…
Figure 7
Figure 7. Figure 7: FIG. 7: Diagrams contributing to [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: Diagrams contributing to [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9: Diagrams contributing to [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]

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Reference graph

Works this paper leans on

57 extracted references · 30 canonical work pages · cited by 1 Pith paper

  1. [1]

    J. E. Augustin et al. [SLAC-SP-017], Phys. Rev. Lett. 33 (1974), 1406-1408 doi:10.1103/PhysRevLett.33.1406

    doi:10.1103/physrevlett.33.1406 1974

  2. [2]

    J. J. Aubert et al. [E598], Phys. Rev. Lett.33 (1974), 1404-1406 11 doi:10.1103/PhysRevLett.33.1404

    doi:10.1103/physrevlett.33.1404 1974

  3. [3]

    Eichten, K

    E. Eichten, K. Gottfried, T. Kinoshita, J. B. Kogut, K. D. Lane and T. M. Yan, Phys. Rev. Lett. 34 (1975), 369-372 [erratum: Phys. Rev. Lett. 36 (1976), 1276] doi:10.1103/PhysRevLett.34.369

    doi:10.1103/physrevlett.34.369 1975

  4. [4]

    Eichten, K

    E. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane and T. M. Yan, Phys. Rev. Lett. 36 (1976), 500 doi:10.1103/PhysRevLett.36.500

    work page doi:10.1103/physrevlett.36.500 1976

  5. [5]

    K. D. Lane and E. Eichten, Phys. Rev. Lett. 37 (1976), 477 [erratum: Phys. Rev. Lett. 37 (1976), 1105] doi:10.1103/PhysRevLett.37.477

    work page doi:10.1103/physrevlett.37.477 1976

  6. [6]

    P. A. Rapidis, B. Gobbi, D. Luke, A. Barbaro-Galtieri, J. Dor- fan, R. Ely, G. J. Feldman, J. M. Feller, A. Fong and G. Hanson, et al. Phys. Rev. Lett. 39 (1977), 526 [erratum: Phys. Rev. Lett. 39 (1977), 974] doi:10.1103/PhysRevLett.39.526

    doi:10.1103/physrevlett.39.526 1977

  7. [7]

    Antoniazzi et al

    L. Antoniazzi et al. [E705], Phys. Rev. D50 (1994), 4258-4264 doi:10.1103/PhysRevD.50.4258

    work page doi:10.1103/physrevd.50.4258 1994

  8. [8]

    Bhardwaj et al

    V . Bhardwaj et al. [Belle], Phys. Rev. Lett. 111 (2013) no.3, 032001 doi:10.1103 /PhysRevLett.111.032001 [arXiv:1304.3975 [hep-ex]]

    arXiv 2013

Show all 57 references
  1. [9]

    Godfrey and N

    S. Godfrey and N. Isgur, Phys. Rev. D 32 (1985), 189-231 doi:10.1103/PhysRevD.32.189

    1985 doi

  2. [11]

    Ablikim et al

    M. Ablikim et al. [BESIII], Phys. Rev. Lett. 115 (2015) no.1, 011803 doi:10.1103 /PhysRevLett.115.011803 [arXiv:1503.08203 [hep-ex]]

    2015 arXiv

  3. [12]

    Ablikim et al

    M. Ablikim et al. [BESIII], Phys. Rev. Lett. 129 (2022) no.10, 102003 doi:10.1103 /PhysRevLett.129.102003 [arXiv:2203.05815 [hep-ex]]

    2022

  4. [13]

    Ablikim et al

    M. Ablikim et al. [BESIII], JHEP 02 (2023), 171 doi:10.1007/JHEP02(2023)171 [arXiv:2209.14744 [hep-ex]]

    2023

  5. [14]

    Aaij et al

    R. Aaij et al. [LHCb], JHEP 08 (2020), 123 doi:10.1007/JHEP08(2020)123 [arXiv:2005.13422 [hep-ex]]

    2020

  6. [15]

    Navas et al

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

    2024 doi

  7. [16]

    Ablikim et al

    M. Ablikim et al. [BES], Phys. Rev. Lett. 97 (2006), 121801 doi:10.1103/PhysRevLett.97.121801 [arXiv:hep-ex /0605107 [hep-ex]]

    2006 doi

  8. [17]

    Ablikim et al

    M. Ablikim et al. [BES], Phys. Lett. B 641 (2006), 145-155 doi:10.1016/j.physletb.2006.08.049 [arXiv:hep-ex /0605105 [hep-ex]]

    2006 doi

  9. [18]

    Ablikim et al

    M. Ablikim et al. [BES], Phys. Lett. B 659 (2008), 74-79 doi:10.1016/j.physletb.2007.11.078

    2008 doi

  10. [19]

    Y . J. Zhang, G. Li and Q. Zhao, Phys. Rev. Lett. 102 (2009), 172001 doi:10.1103 /PhysRevLett.102.172001 [arXiv:0902.1300 [hep-ph]]

    2009 arXiv

  11. [20]

    X. Liu, B. Zhang and X. Q. Li, Phys. Lett. B 675 (2009), 441-445 doi:10.1016/j.physletb.2009.04.047 [arXiv:0902.0480 [hep-ph]]

    2009 arXiv

  12. [21]

    G. Li, X. h. Liu, Q. Wang and Q. Zhao, Phys. Rev. D 88, no.1, 014010 (2013) doi:10.1103 /PhysRevD.88.014010 [arXiv:1302.1745 [hep-ph]]

    2013 arXiv

  13. [22]

    F. K. Guo, C. Hanhart and U. G. Meissner, Phys. Rev. Lett.103 (2009), 082003 [erratum: Phys. Rev. Lett. 104 (2010), 109901] doi:10.1103/PhysRevLett.103.082003 [arXiv:0907.0521 [hep- ph]]

    2009 arXiv

  14. [23]

    F. K. Guo, C. Hanhart, G. Li, U. G. Meissner and Q. Zhao, Phys. Rev. D 83 (2011), 034013 doi:10.1103 /PhysRevD.83.034013 [arXiv:1008.3632 [hep-ph]]

    2011 arXiv

  15. [24]

    Li and Q

    G. Li and Q. Zhao, Phys. Lett. B 670 (2008), 55- 60 doi:10.1016/j.physletb.2008.10.033 [arXiv:0709.4639 [hep- ph]]

    2008 arXiv

  16. [25]

    X. G. He, X. Q. Li, X. Liu and X. Q. Zeng, Eur. Phys. J. C 51 (2007), 883-889 doi:10.1140 /epjc/s10052-007-0347-y [arXiv:hep-ph/0606015 [hep-ph]]

    2007 arXiv

  17. [26]

    D. Y . Chen, J. He, X. Q. Li and X. Liu, Phys. Rev. D81 (2010), 074006 doi:10.1103 /PhysRevD.81.074006 [arXiv:0912.4860 [hep-ph]]

    2010 arXiv

  18. [27]

    Liu, Phys

    X. Liu, Phys. Lett. B 680 (2009), 137-140 doi:10.1016/j.physletb.2009.08.049 [arXiv:0904.0136 [hep- ph]]

    2009 arXiv

  19. [28]

    D. Y . Chen, Y . B. Dong and X. Liu, Eur. Phys. J. C 70 (2010), 177-182 doi:10.1140 /epjc/s10052-010-1449-5 [arXiv:1005.0066 [hep-ph]]

    2010 arXiv

  20. [29]

    D. Y . Chen, J. He, X. Q. Li and X. Liu, Phys. Rev. D84 (2011), 074006 doi:10.1103 /PhysRevD.84.074006 [arXiv:1105.1672 [hep-ph]]

    2011 arXiv

  21. [30]

    D. Y . Chen, X. Liu and X. Q. Li, Eur. Phys. J. C71 (2011), 1808 doi:10.1140/epjc/s10052-011-1808-x [arXiv:1109.1406 [hep- ph]]

    2011 arXiv

  22. [31]

    D. Y . Chen, X. Liu and T. Matsuki, Phys. Rev. D87 (2013) no.5, 054006 doi:10.1103 /PhysRevD.87.054006 [arXiv:1209.0064 [hep-ph]]

    2013 arXiv

  23. [32]

    D. Y . Chen, X. Liu and T. Matsuki, Phys. Rev. D87 (2013) no.9, 094010 doi:10.1103 /PhysRevD.87.094010 [arXiv:1304.0372 [hep-ph]]

    2013 arXiv

  24. [33]

    D. Y . Chen, X. Liu and T. Matsuki, PTEP 2015 (2015) no.4, 043B05 doi:10.1093/ptep/ptv038 [arXiv:1311.6274 [hep-ph]]

    2015 arXiv

  25. [34]

    Mannel, Rept

    T. Mannel, Rept. Prog. Phys. 60 (1997), 1113-1172 doi:10.1088/0034-4885/60/10/003

    1997 doi

  26. [35]

    Brambilla, A

    N. Brambilla, A. Pineda, J. Soto and A. Vairo, Rev. Mod. Phys. 77 (2005), 1423 doi:10.1103/RevModPhys.77.1423 [arXiv:hep-ph/0410047 [hep-ph]]

    2005 arXiv

  27. [36]

    Colangelo, F

    P. Colangelo, F. De Fazio and T. N. Pham, Phys. Rev. D 69 (2004), 054023 doi:10.1103/PhysRevD.69.054023 [arXiv:hep- ph/0310084 [hep-ph]]

    2004

  28. [37]

    A. F. Falk and M. E. Luke, Phys. Lett. B 292 (1992), 119-127 doi:10.1016/0370-2693(92)90618-E [arXiv:hep-ph /9206241 [hep-ph]]

    1992 doi

  29. [38]

    D. Y . Chen, X. Liu and T. Matsuki, Phys. Rev. D91 (2015) no.9, 094023 doi:10.1103 /PhysRevD.91.094023 [arXiv:1411.5136 [hep-ph]]

    2015 arXiv

  30. [39]

    T. M. Yan, H. Y . Cheng, C. Y . Cheung, G. L. Lin, Y . C. Lin and H. L. Yu, Phys. Rev. D 46 (1992), 1148-1164 [erratum: Phys. Rev. D 55 (1997), 5851] doi:10.1103/PhysRevD.46.1148

    1992 doi

  31. [40]

    H. Y . Cheng, C. Y . Cheung, G. L. Lin, Y . C. Lin, T. M. Yan and H. L. Yu, Phys. Rev. D 47 (1993), 1030-1042 doi:10.1103/PhysRevD.47.1030 [arXiv:hep-ph/9209262 [hep- ph]]

    1993 arXiv

  32. [41]

    M. B. Wise, Phys. Rev. D 45 (1992) no.7, R2188 doi:10.1103/PhysRevD.45.R2188

    1992 doi

  33. [42]

    Casalbuoni, A

    R. Casalbuoni, A. Deandrea, N. Di Bartolomeo, R. Gatto, F. Feruglio and G. Nardulli, Phys. Rept. 281 (1997), 145-238 doi:10.1016/S0370-1573(96)00027-0 [arXiv:hep-ph /9605342 [hep-ph]]

    1997 doi

  34. [43]

    Casalbuoni, A

    R. Casalbuoni, A. Deandrea, N. Di Bartolomeo, R. Gatto, F. Feruglio and G. Nardulli, Phys. Lett. B 292 (1992), 371-376 doi:10.1016/0370-2693(92)91189-G [arXiv:hep-ph /9209248 [hep-ph]]

    1992 doi

  35. [44]

    Casalbuoni, A

    R. Casalbuoni, A. Deandrea, N. Di Bartolomeo, R. Gatto, F. Feruglio and G. Nardulli, Phys. Lett. B 299 (1993), 139-150 doi:10.1016/0370-2693(93)90895-O [arXiv:hep-ph /9211248 [hep-ph]]

    1993 doi

  36. [45]

    F. J. Gilman and R. Kau ffman, Phys. Rev. D 36 (1987), 2761 [erratum: Phys. Rev. D 37 (1988), 3348] doi:10.1103/PhysRevD.37.3348 12

    1987 doi

  37. [46]

    Feldmann, Int

    T. Feldmann, Int. J. Mod. Phys. A 15 (2000), 159- 207 doi:10.1142/S0217751X00000082 [arXiv:hep-ph/9907491 [hep-ph]]

    2000 arXiv

  38. [47]

    X. H. Mo, Phys. Rev. D 109 (2024) no.3, 036036 doi:10.1103/PhysRevD.109.036036 [arXiv:2401.01381 [hep- ph]]

    2024 arXiv

  39. [48]

    Co ffman et al

    D. Co ffman et al. [MARK-III], Phys. Rev. D 38 (1988), 2695 [erratum: Phys. Rev. D 40 (1989), 3788] doi:10.1103/PhysRevD.38.2695

    1988 doi

  40. [49]

    Jousset et al

    J. Jousset et al. [DM2], Phys. Rev. D 41 (1990), 1389 doi:10.1103/PhysRevD.41.1389

    1990 doi

  41. [50]

    N. A. Tornqvist, Nuovo Cim. A 107 (1994), 2471-2476 doi:10.1007/BF02734018 [arXiv:hep-ph/9310225 [hep-ph]]

    1994 arXiv

  42. [51]

    N. A. Tornqvist, Z. Phys. C 61 (1994), 525-537 doi:10.1007/BF01413192 [arXiv:hep-ph/9310247 [hep-ph]]

    1994 arXiv

  43. [52]

    M. P. Locher, Y . Lu and B. S. Zou, Z. Phys. A347 (1994), 281- 284 doi:10.1007 /BF01289796 [arXiv:nucl-th /9311021 [nucl- th]]

    1994

  44. [53]

    X. Q. Li, D. V . Bugg and B. S. Zou, Phys. Rev. D 55 (1997), 1421-1424 doi:10.1103/PhysRevD.55.1421

    1997 doi

  45. [54]

    X. Y . Qi, Q. Wu and D. Y . Chen, Eur. Phys. J. C 83 (2023) no.11, 1006 doi:10.1140 /epjc/s10052-023-12151-0 [arXiv:2302.10050 [hep-ph]]

    2023 arXiv

  46. [55]

    Ablikim et al

    M. Ablikim et al. [BESIII], Phys. Rev. D 103 (2021) no.9, L091102 doi:10.1103 /PhysRevD.103.L091102 [arXiv:2102.10845 [hep-ex]]

    2021

  47. [56]

    Aaij et al

    R. Aaij et al. [LHCb], JHEP 04, 046 (2022) doi:10.1007/JHEP04(2022)046 [arXiv:2202.04045 [hep-ex]]

    2022

  48. [57]

    Barnes, S

    T. Barnes, S. Godfrey and E. S. Swanson, Phys. Rev. D 72 (2005), 054026 doi:10.1103/PhysRevD.72.054026 [arXiv:hep- ph/0505002 [hep-ph]]

    2005

  49. [58]

    B. Q. Li and K. T. Chao, Phys. Rev. D 79 (2009), 094004 doi:10.1103 /PhysRevD.79.094004 [arXiv:0903.5506 [hep-ph]]

    2009 arXiv

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