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Strong decays of the latest LHCb pentaquark candidates in hadronic molecule pictures

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This paper claims that the three LHCb pentaquark candidates Pc(4312), Pc(4440), and Pc(4457) are S-wave hadronic molecules with fixed spin-parities, and that their decay ratios can distinguish the assignments.

desk verdict Useful decay tables for the new Pc states, but the spin-parity conclusions rest on a fitted pure-molecule assumption that overproduces the Pc(4457) width. read the letter →

arxiv 1908.05309 v1 pith:2FAUL2KD submitted 2019-08-14 hep-ph nucl-th

Yong-Hui Lin , Bing-Song Zou This is my paper · ORCID
classification hep-phnucl-th
keywords pentaquarkshadronicmoleculesLHCbheavyquarkspinsymmetryeffectiveLagrangiancompositenessconditionstrongdecayscharmedhadrons
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 argues that the three pentaquark-like states reported by LHCb are not compact five-quark states but S-wave hadronic molecules: weakly bound systems of a charmed antimeson (Dbar or Dbar*) and a charmed baryon (Sigma_c or Sigma_c*). It assigns definite spin-parities (1/2^- for Pc(4312) as a Dbar Sigma_c molecule; 1/2^- for Pc(4440) and 3/2^- for Pc(4457) as Dbar* Sigma_c molecules) and computes the partial widths of all allowed strong decay channels using an effective Lagrangian. The computed total widths match the measured ones with fixed cutoff parameters, and the decay patterns differ sharply between the 1/2^- and 3/2^- assignments, giving experimental handles to settle the quantum numbers. If correct, this fixes the internal structure and quantum numbers of these states and provides specific branching-ratio tests.

What carries the argument

The machinery is an effective Lagrangian for S-wave Dbar(*) Sigma_c(*) molecules whose Pc-constituent couplings are fixed by the compositeness condition (compositeness equal to one), together with the Lorentz-covariant L-S coupling scheme for the Pc vertex and triangle-diagram amplitudes for two-body decays through exchanged pi, rho, D, and D* mesons. Couplings among charmed hadrons and light mesons are fixed by heavy quark spin symmetry, SU(3) flavor symmetry, and vector-meson dominance, and UV divergences are regulated with Gaussian and multipolar form factors (cutoffs 0.6-1.4 GeV). The key output is the set of partial widths and, especially, the spin-dependent branching-ratio ratios.

What would settle it

Measure the spin-parity of Pc(4440) and Pc(4457) directly (for example, through angular distributions in Lambda_b -> J/psi p K-) or measure the ratio Gamma(Dbar Sigma_c)/Gamma(Dbar Sigma_c*); if Pc(4440) is found to be 3/2^- or the predicted ratio of about 4 is not seen, the molecule assignment fails. A measurement of Gamma(J/psi p)/Gamma(eta_c p) for either state would also settle the question, since the 1/2^- and 3/2^- hypotheses differ by roughly a factor of 20.

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Extended reading notes

Core claim

The central claim is that the measured widths of the three states can each be reproduced by a pure S-wave molecule with compositeness one: Pc(4312) as a JP = 1/2^- Dbar Sigma_c bound state, Pc(4440) as a JP = 1/2^- Dbar* Sigma_c bound state, and Pc(4457) as a JP = 3/2^- Dbar* Sigma_c bound state. With cutoff values Lambda0 = 1.0 GeV and Lambda1 = 0.6 GeV, the partial widths from triangle-diagram decays sum to the observed total widths. The paper further shows that the relative rate Gamma(Dbar Sigma_c)/Gamma(Dbar Sigma_c*) is about 4 for a 1/2^- Dbar* Sigma_c molecule but about 0.1 for a 3/2^-, and Gamma(J/psi p)/Gamma(eta_c p) is around 10 versus 200, so these ratios can discriminate the assignments. It also computes the strong decays of four additional heavy-quark-spin-symmetry partner molecules (Pc(4376), Pc(4500), Pc(4511), Pc(4523)) as predictions for future searches.

Load-bearing premise

Each Pc state is assumed to be a pure S-wave molecule made of exactly two constituents, with compositeness equal to one; if the real states contain a significant non-molecular component or a different mixture, the computed widths and the inferred spin-parity assignments lose their foundation.

Editorial extensions

If this is right

  • If Pc(4312), Pc(4440), and Pc(4457) have the assigned quantum numbers, they are S-wave molecules lying just below the Dbar Sigma_c and Dbar* Sigma_c thresholds, fixing their internal structure.
  • The ratio Gamma(Dbar Sigma_c)/Gamma(Dbar Sigma_c*) around 4 for a 1/2^- Pc(4440) versus 0.1 for a 3/2^- gives a direct experimental discriminant for the spin-parity of Pc(4440) and Pc(4457).
  • The predicted Gamma(J/psi p)/Gamma(eta_c p) ratio, about 10 for 1/2^- and about 200 for 3/2^-, offers another sharp test that can be measured in future LHCb data.
  • The four predicted partner molecules Pc(4376), Pc(4500), Pc(4511), and Pc(4523) have distinctive decay patterns (for instance, the 3/2^- Pc(4511) couples strongly to Dbar Sigma_c*), giving concrete channels to search for them.

Reading between the lines

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

  • A natural next step is a coupled-channel analysis that relaxes the compositeness-one assumption; the branching ratios computed here would shift if a compact core is admixed, so the same ratios that test the assignments could also measure the molecular fraction.
  • The same effective-Lagrangian machinery could be applied to other near-threshold exotics, such as the X(3872) or the Z_c states, to see whether their decay patterns follow the same coupling scheme.
  • A measurement of the Pc(4312) decay to eta_c p, predicted to be an order of magnitude larger relative to J/psi p than for the Dbar* Sigma_c molecules, would provide a sharp test of the Dbar Sigma_c assignment.
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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

3 major / 5 minor

Summary. This manuscript computes strong decay widths of the LHCb pentaquark candidates Pc(4312), Pc(4440), and Pc(4457) under the assumption that they are S-wave hadronic molecules, with spin-parity assignments 1/2^- DbarSigma_c, 1/2^- Dbar*Sigma_c, and 3/2^- Dbar*Sigma_c, respectively. The calculation uses effective Lagrangians, a compositeness condition (Eq. (8)) to fix the Pc-molecule couplings, and two Gaussian-type form factors together with a monopole form factor for the exchanged mesons. Partial widths for all allowed two-body channels are tabulated for two choices of form-factor sets and as a function of the two cutoffs Lambda0 and Lambda1. The paper also presents partial widths for four predicted spin partners in the Dbar(*)Sigma_c* systems. The central claim is that the measured total widths are reproduced well with the stated quantum numbers, while the relative branching ratios (e.g., Gamma(DbarSigma_c)/Gamma(DbarSigma_c*) and Gamma(J/psi p)/Gamma(eta_c p)) serve as future tests of these assignments.

Significance. If the central claim is correct, the paper gives a coherent hadronic-molecule interpretation of all three new LHCb pentaquark states and provides concrete experimental discriminators for their spin and parity. The paper's strengths are that it explores cutoff dependence, presents explicit partial widths for all allowed channels, and identifies relative branching ratios that are largely stable with respect to the fitted cutoffs and thus serve as falsifiable predictions. However, the significance is conditional on the robustness of the pure-molecule compositeness assumption and on how much weight the total-width agreement can carry, since the cutoffs are adjusted to reproduce the measured widths.

major comments (3)
  1. [Sec. III, Tables III and IV] At the chosen cutoffs Lambda0 = 1.0 GeV and Lambda1 = 0.6 GeV, the computed total widths do not all agree with the measured values. With the (f1,f3) set, Gamma(Pc(4312)) = 3.9 MeV versus the measured 9.8 +/- 2.7 MeV and Gamma(Pc(4457,3/2^-)) = 14.7 MeV versus 6.4 +/- 2.0 MeV. With the (f2,f3) set, Gamma(Pc(4457,3/2^-)) = 17.9 MeV versus the measured 6.4 +/- 2.0 MeV, an overprediction by a factor of about 2.8. Since Lambda0 and Lambda1 are explicitly fixed to give a compatible description (Sec. III), the agreement is a postdiction at a single cutoff pair rather than a parameter-free prediction. The abstract's statement that the three states are described well is therefore not supported by the tables for all three states; the authors should either quantify the fit including the experimental uncertainties and cutoff variation, or temper the claim, especially for Pc(4457).
  2. [Sec. III, Tables III and IV; Sec. II.B] The spin-parity discrimination for Pc(4440) and Pc(4457) is not robustly established by the total widths alone. For Pc(4440), the (f2,f3) total widths are 22.4 MeV for 1/2^- and 21.0 MeV for 3/2^-, a difference of only 7%, and both are compatible with the measured 20.6 +/- ... MeV within the large experimental uncertainties. For Pc(4457), both 1/2^- and 3/2^- interpretations overpredict the measured 6.4 MeV (18.8 and 17.9 MeV, respectively, in the f2 set). The real discriminating power lies in the relative branching ratios such as Gamma(DbarSigma_c)/Gamma(DbarSigma_c*) and Gamma(J/psi p)/Gamma(eta_c p), which are not yet measured. The manuscript should state explicitly that the total-width comparison alone does not select 1/2^- over 3/2^- for Pc(4440) or 3/2^- over 1/2^- for Pc(4457), and that the J^P assignments should be framed as predictions to be tested by future measurements of these ratios.
  3. [Sec. II.B, Eq. (8)] The compositeness assumption chi = 1 (pure molecule) is load-bearing for all the computed widths. Each two-body partial width is proportional to the square of the coupling g_{Pc Dbar(*)Sigma_c(*)}, and this coupling is fixed by the compositeness condition with chi = 1. If a physical Pc state has a non-molecular component with probability (1 - chi), all the widths scale by chi. Using the numbers in Tables III and IV, the measured central widths require state-dependent effective compositeness: about 0.7 for Pc(4312), 0.9 for Pc(4440) (1/2^-, f2 set), and 0.4 for Pc(4457) (3/2^-, f2 set); with the f1 set, Pc(4312) would require chi > 1, which is unphysical. Thus the pure-molecule hypothesis is already strained by the same data it is used to explain. The authors should discuss this sensitivity explicitly, or allow the compositeness to vary, before drawing conclusions about the quantum numbers of the states.
minor comments (5)
  1. [Sec. III, Physics of Pc branching fractions] The sentence listing the upper limits of B(P_c^+ -> J/psi p) repeats 'Pc(4312)' three times; it should read 'Pc(4312), Pc(4440) and Pc(4457)'.
  2. [Table II footnote] The footnote contains the typo 'duo' instead of 'due' in 'due to the different Lagrangian'.
  3. [Fig. 4 caption] The caption says 'origin-dashed' but the figure legend uses 'orange-dashed'; this should be corrected.
  4. [Sec. IV] The summary states that the 3/2^- and 1/2^- assignments for Pc(4440) and Pc(4457) 'can not be ruled out at present', which is in tension with the stronger wording of the abstract; the abstract and summary should be harmonized to reflect the actual level of support from the total-width comparison.
  5. [Sec. II.A and Tables V-VI] The three-body decay widths (e.g., Gamma(DbarLambda_c pi) = 5.0 MeV and Gamma(Dbar*Lambda_c pi) = 4.0, 7.7, 7.8 MeV) are inserted without derivation or an explicit formula. Since these channels contribute substantially to the total widths of the four spin partners, a brief derivation or a reference to the expression used should be added for reproducibility.

Circularity Check

1 steps flagged · score 6.0 of 10

Total-width agreement and the resulting spin assignments are partly fitted: the cutoffs Λ0 and Λ1 are tuned to the measured Pc widths before the same widths are used to conclude that the molecule pictures are preferred.

  1. fitted input called prediction [Sec. III (Numerical Results), discussion after Figs. 4–7 and Tables III–IV; method statement in Sec. I]
    "It should be noted that Λ0 = 1.0 GeV and Λ1 = 0.6 GeV are fixed to give a compatible descriptions with measured widths for all of three observed Pc states. The numerical decay patterns with these cutoffs in Table III suggest that the spin parties of Pc(4440) and Pc(4457) are more likely to be 1/2− and 3/2−, respectively."

    The two cutoff parameters are explicitly adjusted so that the computed total widths reproduce the three measured LHCb widths. The paper then uses this total-width agreement at the fitted cutoffs as evidence that the 1/2− DbarSigma_c, 1/2− Dbar*Sigma_c, and 3/2− Dbar*Sigma_c assignments can be described well, and to prefer 1/2− for Pc(4440) and 3/2− for Pc(4457). Because the total widths are matched by construction, that portion of the agreement is a fit rather than an independent prediction; only the relative partial widths, such as Gamma(DbarSigma_c)/Gamma(DbarSigma*_c) and Gamma(J/psi p)/Gamma(eta_c p), are genuine outputs. The central spin-parity conclusion therefore rests in part on the fitted input, although the branching-fraction ratios remain non-circular predictions.

full rationale

The paper's central claim that the three Pc states can be described as particular S-wave molecules is only partially circular. The clearest reduction is the fit of the two cutoff parameters Λ0 and Λ1 to the measured total decay widths, followed by the use of those same total widths to validate the molecule assignments and to discriminate between J^P options. That is a fitted-input-called-prediction pattern. However, the calculation contains substantial independent content: the Pc-constituent couplings are fixed by the compositeness condition and measured binding energies, the decay mechanisms are computed from effective Lagrangians, and the relative partial widths and branching ratios are not adjusted to data. The pure-molecule compositeness Z=1 assumption is an explicit model assumption rather than a circular step, and the cited prior work provides formalism, coupling conventions, and external predictions rather than the conclusion itself. No load-bearing self-citation chain or definitional equivalence is present. The score of 6 reflects that the total-width agreement, which is central to the claimed support, reduces by construction to a fit, while the distinctive branching-fraction predictions remain genuine outputs.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The calculation has two fitted cutoffs and relies on a sequence of symmetry and molecular-purity assumptions. No new particles are introduced. The main burden is that the cutoffs are adjusted to reproduce the three measured widths before the spin assignments are extracted, so the agreement is partly built in.

free parameters (2)
  • Lambda0 = 1.0 GeV (varied 0.6-1.4 GeV)
    Gaussian cutoff in molecular form factors f1/f2; fixed to reproduce measured total widths of Pc(4312), Pc(4440) and Pc(4457).
  • Lambda1 = 0.6 GeV (varied 0.6-1.4 GeV)
    Multipolar cutoff suppressing off-shell exchanged mesons in triangle diagrams; fixed together with Lambda0 to reproduce the three measured widths.
assumptions (5)
  • domain assumption Each observed Pc state is a pure S-wave hadronic molecule with compositeness chi = 1.
    Sec. II.B; this fixes the Pc-coupling constants via the compositeness condition, and if false the decay widths are not reliable.
  • domain assumption Two-body strong decays are described by one-meson-exchange triangle diagrams.
    Sec. II.A, Fig. 2; no other short-range mechanisms are included.
  • domain assumption Couplings among light and charmed hadrons are fixed by SU(3) flavor symmetry, heavy quark spin symmetry and vector meson dominance, with charm-quark couplings approximated by strange-quark ones.
    Sec. II.B; e.g., g_rho Sigma_c Lambda_c = g_rho Sigma Lambda; the text acknowledges these are rough, order-of-magnitude estimates.
  • domain assumption The non-relativistic, leading-order expansion sqrt(2 mu E_B)/Lambda and the g0/gRT estimates for Pc couplings are valid for binding energies of 1-20 MeV.
    Sec. III and Eq. (8); binding energies are small, but the choice between g0, gNR and gRT introduces model dependence.
  • domain assumption Relative phases of amplitudes from different exchanged mesons are ignored; widths are added incoherently.
    Footnote in Sec. II.C: relative phases cannot be determined, so |M|^2 = |M_pi|^2 + |M_rho|^2 for Dbar* Lambda_c final states.

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Cite this review

Pith. "Pith review of Strong decays of the latest LHCb pentaquark candidates in hadronic molecule pictures." pith.science (2026). https://pith.science/paper/2FAUL2KD

@misc{pith2026190805309,
  author       = {Pith},
  title        = {Pith review of: Strong decays of the latest LHCb pentaquark candidates in hadronic molecule pictures},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2FAUL2KD}},
  note         = {Machine review of arXiv:1908.05309}
}
abstract

We investigate the observed pentaquark candidates $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ from the latest LHCb measurement, as well as four possible spin partners in the $\bar{D}^{(*)}\Sigma_c^*$ system predicted from the heavy quark spin symmetry with the hadronic molecule scenarios. Similar to the previous calculation on $P_c(4380)$ and $P_c(4450)$, the partial widths of all the allowed decay channels for these $P_c$ states are estimated with the effective Lagrangian method. The cutoff dependence of our numerical results are also presented. Comparing with the experimental widths, our results show that $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ can be described well with the spin-parity-$1/2^-$-$\bar{D}\Sigma_c$, $1/2^-$-$\bar{D}^*\Sigma_c$ and $3/2^-$-$\bar{D}^*\Sigma_c$ molecule pictures, respectively.

Figures

Figures reproduced from arXiv: 1908.05309 by the authors.

Figure 2
Figure 2. FIG. 2. The triangle diagram for the two-body decays of [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 1
Figure 1. FIG. 1. Three-body decays of the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The dependence of relative ratios [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Λ [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Λ [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Λ [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Λ [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Λ-dependence of the total decay withs for the four spi [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]

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Works this paper leans on

75 extracted references · 17 canonical work pages · cited by 2 Pith papers

  1. [1]

    The two-body decays of hadronic molecules will be described conven- tionally by the triangle diagram mechanism with the one meson exchanged as in Fig

    work page

  2. [2]

    All the two-body de- Pc ¯D(∗) π Λc Σ ∗ c FIG. 1. Three-body decays of the ¯D(∗ )Σ ∗ c molecules. cay channels considered in our calculation are collected in Table I. B. Effective Lagrangian In the present work, we adopt the effective Lagrangian approach to compute the amplitudes of above decay di- agrams. For the first vertex that Pc states couple to the had...

    work page

  3. [3]

    The cutoff Λ 0 denotes a hard momentum scale which suppresses the contribution of the two constituents at short distances ∼ 1/Λ 0

    = exp( −p2 E/Λ 2 0), (9) where pE, defined as m ¯D(∗ )pΣ (∗ ) c /(m ¯D(∗ ) +mΣ (∗ ) c ) − mΣ (∗ ) c p ¯D(∗ )/(m ¯D(∗ ) +mΣ (∗ ) c ) for the ¯D(∗)Σ (∗) c molecules, is the Euclidean Jacobi momentum. The cutoff Λ 0 denotes a hard momentum scale which suppresses the contribution of the two constituents at short distances ∼ 1/Λ 0. There is no universal criterio...

    work page

  4. [4]

    Coupling constants used in the present work

    = exp( − p2/Λ 2 0), (10) 4 TABLE II. Coupling constants used in the present work. The P , V , B and D denote the pseudoscalar, vector mesons, octet and decuplet baryons respectively. Only absolute values of the couplings are listed with their signs ignored. αBBP αBBV gBBP gBBV gVPP gVVP (GeV− 1) gPBD (GeV− 1) gVBD (GeV− 1) gPDD (GeV− 1) gVDD κVDD 0.4 1.15...

    work page

  5. [5]

    4 GeV, respectively

    0 GeV and 1 . 4 GeV, respectively. The upper dots are the values of gRT/g NR while the lower dots are g0/g NR . TABLE III. Partial widths of Pc(4312) as S-wave ¯DΣc molecule, Pc(4440) and Pc(4457) as S-wave ¯D∗ Σc molecules with two possible quantum numbers, to various possible final states with Λ 0 = 1. 0 GeV, Λ 1 = 0. 6 GeV. The form factor set (f1, f3) ...

    work page

  6. [6]

    Aaij et al

    R. Aaij et al. (LHCb), Phys. Rev. Lett. 122, 222001 (2019), arXiv:1904.03947 [hep-ex]

    arXiv 2019

  7. [7]

    Lin, C.-W

    Y.-H. Lin, C.-W. Shen, F.-K. Guo, and B.-S. Zou, Phys. 12 Rev. D95, 114017 (2017) , arXiv:1703.01045 [hep-ph]

    arXiv 2017

  8. [8]

    Aaij et al

    R. Aaij et al. (LHCb), Phys. Rev. Lett. 115, 072001 (2015), arXiv:1507.03414 [hep-ex]

    arXiv 2015

Show all 75 references
  1. [9]

    J.-J. Wu, R. Molina, E. Oset, and B. S. Zou, Phys. Rev. Lett. 105, 232001 (2010) , arXiv:1007.0573 [nucl-th]

    2010 arXiv

  2. [10]

    J.-J. Wu, R. Molina, E. Oset, and B. S. Zou, Phys. Rev. C84, 015202 (2011) , arXiv:1011.2399 [nucl-th]

    2011 arXiv

  3. [11]

    W. L. Wang, F. Huang, Z. Y. Zhang, and B. S. Zou, Phys. Rev. C84, 015203 (2011) , arXiv:1101.0453 [nu- cl-th]

    2011 arXiv

  4. [12]

    Yang, Z.-F

    Z.-C. Yang, Z.-F. Sun, J. He, X. Liu, and S.-L. Zhu, Chin. Phys. C36, 6 (2012) , arXiv:1105.2901 [hep-ph]

    2012 arXiv

  5. [13]

    J.-J. Wu, T. S. H. Lee, and B. S. Zou, Phys. Rev. C85, 044002 (2012) , arXiv:1202.1036 [nucl-th]

    2012 arXiv

  6. [14]

    S. G. Yuan, K. W. Wei, J. He, H. S. Xu, and B. S. Zou, Eur. Phys. J. A48, 61 (2012) , arXiv:1201.0807 [nucl-th]

    2012 arXiv

  7. [15]

    C. W. Xiao, J. Nieves, and E. Oset, Phys. Rev. D88, 056012 (2013) , arXiv:1304.5368 [hep-ph]

    2013 arXiv

  8. [16]

    R. L. Jaffe and F. Wilczek, Phys. Rev. Lett. 91, 232003 (2003), arXiv:hep-ph/0307341 [hep-ph]

    2003 arXiv

  9. [17]

    A. Ali, I. Ahmed, M. J. Aslam, and A. Rehman, Phys. Rev. D94, 054001 (2016) , arXiv:1607.00987 [hep-ph]

    2016 arXiv

  10. [18]

    Maiani, A

    L. Maiani, A. D. Polosa, and V. Riquer, Phys. Lett. B749, 289 (2015) , arXiv:1507.04980 [hep-ph]

    2015 arXiv

  11. [19]

    Li, X.-G

    G.-N. Li, X.-G. He, and M. He, JHEP 12, 128 (2015) , arXiv:1507.08252 [hep-ph]

    2015 arXiv

  12. [20]

    Wang, Eur

    Z.-G. Wang, Eur. Phys. J. C76, 70 (2016) , arXiv:1508.01468 [hep-ph]

    2016 arXiv

  13. [21]

    Weng, X.-L

    X.-Z. Weng, X.-L. Chen, W.-Z. Deng, and S.-L. Zhu, (2019), arXiv:1904.09891 [hep-ph]

    2019 arXiv

  14. [22]

    Stancu, (2019), arXiv:1902.07101 [hep-ph]

    F. Stancu, (2019), arXiv:1902.07101 [hep-ph]

    2019 arXiv

  15. [23]

    Giannuzzi, Phys

    F. Giannuzzi, Phys. Rev. D99, 094006 (2019) , arXiv:1903.04430 [hep-ph]

    2019 arXiv

  16. [24]

    R. Zhu, X. Liu, H. Huang, and C.-F. Qiao, (2019), arXiv:1904.10285 [hep-ph]

    2019 arXiv

  17. [25]

    An, Q.-S

    H.-T. An, Q.-S. Zhou, Z.-W. Liu, Y.-R. Liu, and X. Liu, (2019), arXiv:1905.07858 [hep-ph]

    2019 arXiv

  18. [26]

    Kubarovsky and M

    V. Kubarovsky and M. B. Voloshin, Phys. Rev. D92, 031502 (2015) , arXiv:1508.00888 [hep-ph]

    2015 arXiv

  19. [27]

    M. I. Eides, V. Y. Petrov, and M. V. Polyakov, (2019), arXiv:1904.11616 [hep-ph]

    2019 arXiv

  20. [28]

    Guo, U.-G

    F.-K. Guo, U.-G. Meißner, W. Wang, and Z. Yang, Phys. Rev. D92, 071502 (2015) , arXiv:1507.04950 [hep-ph]

    2015 arXiv

  21. [29]

    X.-H. Liu, Q. Wang, and Q. Zhao, Phys. Lett. B757, 231 (2016) , arXiv:1507.05359 [hep-ph]

    2016 arXiv

  22. [30]

    F.-K. Guo, U. G. Meißner, J. Nieves, and Z. Yang, Eur. Phys. J. A52, 318 (2016) , arXiv:1605.05113 [hep-ph]

    2016 arXiv

  23. [31]

    Bayar, F

    M. Bayar, F. Aceti, F.-K. Guo, and E. Oset, Phys. Rev. D94, 074039 (2016) , arXiv:1609.04133 [hep-ph]

    2016 arXiv

  24. [32]

    Mironov and A

    A. Mironov and A. Morozov, JETP Lett. 102, 271 (2015), [Pisma Zh. Eksp. Teor. Fiz.102,no.5,302(2015)], arXiv:1507.04694 [hep-ph]

    2015 arXiv

  25. [33]

    N. N. Scoccola, D. O. Riska, and M. Rho, Phys. Rev. D92, 051501 (2015) , arXiv:1508.01172 [hep-ph]

    2015 arXiv

  26. [34]

    H.-X. Chen, W. Chen, and S.-L. Zhu, (2019), arXiv:1903.11001 [hep-ph]

    2019 arXiv

  27. [35]

    Chen, Z.-F

    R. Chen, Z.-F. Sun, X. Liu, and S.-L. Zhu, (2019), arXiv:1903.11013 [hep-ph]

    2019 arXiv

  28. [36]

    Guo, H.-J

    F.-K. Guo, H.-J. Jing, U.-G. Meißner, and S. Sakai, Phys. Rev. D99, 091501 (2019) , arXiv:1903.11503 [hep- -ph]

    2019 arXiv

  29. [37]

    Liu, Y.-W

    M.-Z. Liu, Y.-W. Pan, F.-Z. Peng, M. S´ anchez S´ anchez, L.-S. Geng, A. Hosaka, and M. Pavon Valderrama, Phys. Rev. Lett. 122, 242001 (2019) , arXiv:1903.11560 [hep- -ph]

    2019 arXiv

  30. [38]

    J. He, Eur. Phys. J. C79, 393 (2019) , arXiv:1903.11872 [hep-ph]

    2019 arXiv

  31. [39]

    Liu, H.-X

    Y.-R. Liu, H.-X. Chen, W. Chen, X. Liu, and S.- L. Zhu, Prog. Part. Nucl. Phys. 107, 237 (2019) , arXiv:1903.11976 [hep-ph]

    2019 arXiv

  32. [40]

    Huang, J

    H. Huang, J. He, and J. Ping, (2019), arXiv:1904.00221 [hep-ph]

    2019 arXiv

  33. [41]

    Shimizu, Y

    Y. Shimizu, Y. Yamaguchi, and M. Harada, (2019), arXiv:1904.00587 [hep-ph]

    2019 arXiv

  34. [42]

    Guo and J

    Z.-H. Guo and J. A. Oller, Phys. Lett. B793, 144 (2019) , arXiv:1904.00851 [hep-ph]

    2019 arXiv

  35. [43]

    C. W. Xiao, J. Nieves, and E. Oset, Phys. Rev. D100, 014021 (2019) , arXiv:1904.01296 [hep-ph]

    2019 arXiv

  36. [44]

    C.-J. Xiao, Y. Huang, Y.-B. Dong, L.-S. Geng, and D.-Y. Chen, Phys. Rev. D100, 014022 (2019) , arXiv:1904.00872 [hep-ph]

    2019 arXiv

  37. [45]

    Sakai, H.-J

    S. Sakai, H.-J. Jing, and F.-K. Guo, (2019), arXiv:1907.03414 [hep-ph]

    2019 arXiv

  38. [46]

    H.-X. Chen, W. Chen, X. Liu, and S.-L. Zhu, Phys. Rept. 639, 1 (2016) , arXiv:1601.02092 [hep-ph]

    2016 arXiv

  39. [47]

    F.-K. Guo, C. Hanhart, U.-G. Meißner, Q. Wang, Q. Zhao, and B.-S. Zou, Rev. Mod. Phys. 90, 015004 (2018), arXiv:1705.00141 [hep-ph]

    2018 arXiv

  40. [48]

    B. S. Zou and F. Hussain, Phys. Rev. C67, 015204 (2003), arXiv:hep-ph/0210164 [hep-ph]

    2003 arXiv

  41. [49]

    Weinberg, Phys

    S. Weinberg, Phys. Rev. 130, 776 (1963)

    1963

  42. [50]

    Weinberg, Phys

    S. Weinberg, Phys. Rev. 137, B672 (1965)

    1965

  43. [51]

    J. J. de Swart, Rev. Mod. Phys. 35, 916 (1963), [Erratum: Rev. Mod. Phys.37,326(1965)]

    1963

  44. [52]

    Polinder, J

    H. Polinder, J. Haidenbauer, and U.-G. Meissner, Nucl. Phys. A779, 244 (2006) , arXiv:nucl-th/0605050 [nu- cl-th]

    2006 arXiv

  45. [53]

    Ronchen, M

    D. Ronchen, M. Doring, F. Huang, H. Haberzettl, J. Haidenbauer, C. Hanhart, S. Krewald, U. G. Meiss- ner, and K. Nakayama, Eur. Phys. J. A49, 44 (2013) , arXiv:1211.6998 [nucl-th]

    2013 arXiv

  46. [54]

    Haidenbauer and G

    J. Haidenbauer and G. Krein, Phys. Rev. D95, 014017 (2017), arXiv:1611.02985 [nucl-th]

    2017 arXiv

  47. [55]

    Haidenbauer, S

    J. Haidenbauer, S. Petschauer, N. Kaiser, U.-G. Meißne r, and W. Weise, Eur. Phys. J. C77, 760 (2017) , arXiv:1708.08071 [nucl-th]

    2017 arXiv

  48. [56]

    Colangelo, F

    P. Colangelo, F. De Fazio, and T. N. Pham, Phys. Rev. D69, 054023 (2004) , arXiv:hep-ph/0310084 [hep-ph]

    2004 arXiv

  49. [57]

    F.-K. Guo, C. Hanhart, G. Li, U.-G. Meissner, and Q. Zhao, Phys. Rev. D83, 034013 (2011) , arXiv:1008.3632 [hep-ph]

    2011 arXiv

  50. [58]

    Lin and C

    Z.-w. Lin and C. M. Ko, Phys. Rev. C62, 034903 (2000) , arXiv:nucl-th/9912046 [nucl-th]

    2000 arXiv

  51. [59]

    Y.-s. Oh, T. Song, and S. H. Lee, Phys. Rev. C63, 034901 (2001) , arXiv:nucl-th/0010064 [nucl-th]

    2001 arXiv

  52. [60]

    Yan, H.-Y

    T.-M. Yan, H.-Y. Cheng, C.-Y. Cheung, G.-L. Lin, Y. C. Lin, and H.-L. Yu, Phys. Rev. D46, 1148 (1992) , [Erra- tum: Phys. Rev.D55,5851(1997)]

    1992

  53. [61]

    Cheng, C.-K

    H.-Y. Cheng, C.-K. Chua, and A. Soni, Phys. Rev. D71, 014030 (2005) , arXiv:hep-ph/0409317 [hep-ph]

    2005 arXiv

  54. [62]

    Albaladejo, F

    M. Albaladejo, F. K. Guo, C. Hidalgo-Duque, J. Nieves, and M. P. Valderrama, Eur. Phys. J. C75, 547 (2015) , arXiv:1504.00861 [hep-ph]

    2015 arXiv

  55. [63]

    Shen, F.-K

    C.-W. Shen, F.-K. Guo, J.-J. Xie, and B.-S. Zou, Nucl. Phys. A954, 393 (2016) , arXiv:1603.04672 [hep-ph]

    2016 arXiv

  56. [64]

    Faessler, T

    A. Faessler, T. Gutsche, V. E. Lyubovitskij, and Y.- L. Ma, Phys. Rev. D76, 014005 (2007) , arXiv:0705.0254 [hep-ph]. 13

    2007 arXiv

  57. [65]

    Y. Dong, A. Faessler, T. Gutsche, S. Kovalenko, and V. E. Lyubovitskij, Phys. Rev. D79, 094013 (2009) , arXiv:0903.5416 [hep-ph]

    2009 arXiv

  58. [66]

    Y. Dong, A. Faessler, T. Gutsche, and V. E. Lyubovit- skij, Phys. Rev. D81, 014006 (2010) , arXiv:0910.1204 [hep-ph]

    2010 arXiv

  59. [67]

    L¨ u and Y.-B

    Q.-F. L¨ u and Y.-B. Dong, Phys. Rev. D93, 074020 (2016), arXiv:1603.00559 [hep-ph]

    2016 arXiv

  60. [68]

    Nieves and M

    J. Nieves and M. P. Valderrama, Phys. Rev. D86, 056004 (2012), arXiv:1204.2790 [hep-ph]

    2012 arXiv

  61. [69]

    Hidalgo-Duque, J

    C. Hidalgo-Duque, J. Nieves, and M. P. Valderrama, Phys. Rev. D87, 076006 (2013) , arXiv:1210.5431 [hep- -ph]

    2013 arXiv

  62. [70]

    Ali et al

    A. Ali et al. (GlueX), (2019), arXiv:1905.10811 [nucl-ex]

    2019 arXiv

  63. [71]

    M. B. Voloshin, (2019), arXiv:1907.01476 [hep-ph]

    2019 arXiv

  64. [72]

    Yamaguchi, H

    Y. Yamaguchi, H. Garc ´ ıa-Tecocoatzi, A. Giachino, A. Hosaka, E. Santopinto, S. Takeuchi, and M. Tak- izawa, (2019), arXiv:1907.04684 [hep-ph]

    2019 arXiv

  65. [73]

    Pavon Valderrama, (2019), arXiv:1907.05294 [hep- -ph]

    M. Pavon Valderrama, (2019), arXiv:1907.05294 [hep- -ph]

    2019 arXiv

  66. [74]

    Liu, T.-W

    M.-Z. Liu, T.-W. Wu, M. S´ anchez S´ anchez, M. P. Valderrama, L.-S. Geng, and J.-J. Xie, (2019), arXiv:1907.06093 [hep-ph]

    2019 arXiv

  67. [75]

    Pan, M.-Z

    Y.-W. Pan, M.-Z. Liu, F.-Z. Peng, M. S´ anchez S´ anchez, L.-S. Geng, and M. P. Valderrama, (2019), arXiv:1907.11220 [hep-ph]

    2019 arXiv

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