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REVIEW 3 major objections 5 minor 121 references

Investigation of full heavy $ QQQQ'\bar{Q}$ pentaquark candidates

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Using the QCD sum-rule method, this paper predicts the masses and current couplings of two fully heavy pentaquarks, $cccb\bar{c}$ and $bbbc\bar{b}$, with spin-parity $1/2^-$, finding masses near 11.38 GeV and 20.99 GeV.

desk verdict Solid but unremarkable QCD sum rule extension: believable masses that match earlier predictions, undercut by omitted spectral densities and missing pole-dominance quantification. read the letter →

arxiv 2502.09409 v1 pith:4HF7L3S5 submitted 2025-02-13 hep-ph hep-exhep-lat

K. Azizi , Y. Sarac , H. Sundu This is my paper · ORCID
classification hep-phhep-exhep-lat
keywords pentaquarkQCDsumrulesfullyheavyhadronexoticmasspredictioncurrentcouplingquarkspectroscopy
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 asks whether pentaquarks made entirely of heavy quarks—specifically $cccb\bar{c}$ (four charm quarks plus a bottom antiquark) and $bbbc\bar{b}$ (four bottom quarks plus a charm antiquark)—can be described as $J^P = 1/2^-$ bound states. Using QCD sum rules, it predicts ground-state masses of $m_{P_{(4cb)}} = 11388.30 \pm 107.79$ MeV and $m_{P_{(4bc)}} = 20998.30 \pm 121.52$ MeV (from the $\not p$ Lorentz structure), with consistent values from the identity structure. It also reports the corresponding current couplings, which are the essential inputs for computing the states' decay widths. These predictions give experimental searches concrete mass targets for two very heavy pentaquark candidates.

What carries the argument

The calculation is built on the QCD sum-rule framework, in which the two-point correlation function of the interpolating current is evaluated once in terms of hadronic degrees of freedom and once by an operator product expansion (OPE) in QCD. The interpolating current in Eq. (2) is chosen to carry the desired $J^P = 1/2^-$ quantum numbers and the quark content $QQQQ'\bar Q$, with the color factor $\epsilon_{ijk}$ ensuring a color-singlet combination. The OPE side uses the heavy-quark propagator of Eq. (4), which contains the perturbative term, the gluon-field-strength correction, and the quark-gluon condensate contribution. After Fourier transformation, Borel transformation, and continuum subtraction through quark-hadron duality (encoded in the threshold $s_0$), the QCD side reduces to the sum rule (5). Matching the coefficients of the $\not p$ and $\mathbb{1}$ structures with the hadronic side (10) yields the two sum rules (11) and (12), from which the mass and current coupling are obtained through Eqs. (13) and (14).

What would settle it

A lattice QCD calculation of the two-point correlator for the same quantum numbers and quark content, which does not rely on single-pole dominance, would either confirm a bound state near the predicted masses or show that the extracted ground state is a two-meson threshold; similarly, a search in the invariant mass distributions of the relevant heavy-quark final states would settle whether narrow resonances appear at roughly 11.38 GeV and 20.99 GeV.

Watch

Extended reading notes

Core claim

The paper's central claim is that the QCD sum-rule computation based on the interpolating current $J_{P_{(4QQ')}} = [\epsilon_{ijk} Q_i^T C \gamma_\mu Q_j \, \gamma_5 \gamma^\mu Q'_k][\bar{Q}_l i\gamma_5 Q_l]$ determines the masses and current couplings of the $J^P = 1/2^-$ pentaquarks with quark content $cccb\bar{c}$ ($P_{(4cb)}$) and $bbbc\bar{b}$ ($P_{(4bc)}$). From the coefficients of the two Lorentz structures $\not p$ and $\mathbb{1}$, the masses are $m_{P_{(4cb)}} = 11388.30 \pm 107.79$ MeV and $11368.30 \pm 112.68$ MeV, and $m_{P_{(4bc)}} = 20998.30 \pm 121.52$ MeV and $20990.50 \pm 125.87$ MeV, respectively. The corresponding current couplings are $\lambda_{P_{(4cb)}} = 3.68 \pm 0.73$ GeV$^6$ and $2.96 \pm 0.59$ GeV$^6$, and $\lambda_{P_{(4bc)}} = (1.99 \pm 0.30)\times 10^2$ GeV$^6$ and $(1.54 \pm 0.24)\times 10^2$ GeV$^6$. The two Lorentz structures yield mutually consistent results within the quoted uncertainties.

Load-bearing premise

The extraction assumes that the interpolating current couples predominantly to the intended single-pentaquark ground state, rather than to a multi-hadron scattering state or a different resonance with the same quantum numbers, so that the Borel window isolates one pole.

Editorial extensions

If this is right

  • If the $P_{(4cb)}$ and $P_{(4bc)}$ states exist, their masses give direct search targets of roughly 11.38 GeV and 20.99 GeV.
  • The reported current couplings set the normalization of the hadronic matrix element, making them the necessary input for decay-width computations for these pentaquarks.
  • The consistency between the $\not p$ and $\mathbb{1}$ structure determinations supports the interpretation of the extracted poles as genuine $J^P = 1/2^-$ resonances rather than artifacts of a single projection.
  • The new masses sit between the higher prediction of one earlier study and the lower prediction of another, so a future measurement would help select among the existing theoretical descriptions.

Reading between the lines

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

  • Because the paper stops at masses and couplings, a natural extension is to compute the dominant decay channels with the extracted residues; the very large mass of the $bbbc\bar{b}$ state suggests it could be narrow and therefore a promising discovery channel.
  • The current couplings differ by about a factor of 50 between the two states; checking whether this ratio follows a simple power of the heavy-quark masses would provide a clean test of heavy-quark symmetry in fully heavy systems.
  • An independent lattice QCD determination of the same correlator would test the sum rule's pole-dominance assumption and clarify whether the predicted masses correspond to genuine bound states or to attractive thresholds.
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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. The manuscript studies candidate pentaquark states with quark contents cccb\bar{c} and bbbc\bar{b} and spin-parity J^P=1/2^- using QCD sum rules. The authors construct a single interpolating current, compute the operator product expansion (OPE) side, match it to the hadronic dispersion relation, and extract masses and current couplings from two Lorentz structures. They report m_P(4cb)=11388.30±107.79 MeV and 11368.30±112.68 MeV from the slashed-p and identity structures, respectively, and m_P(4bc)=20998.30±121.52 MeV and 20990.50±125.87 MeV, together with the corresponding current couplings in Table II. The paper compares these results with earlier model predictions and finds consistency with one of them.

Significance. If the extracted masses are reliable, the paper provides potentially useful predictions for future experimental searches of fully heavy pentaquarks. The calculation is a standard application of the QCD sum rule method, with the positive internal check that the two Lorentz structures yield mutually consistent masses. However, the central claim is not fully supported as presented: the OPE spectral densities are not shown, and the standard pole-dominance and OPE-convergence criteria are asserted but not quantified. These omissions leave open the possibility that the quoted masses are continuum averages rather than properties of the intended 1/2^- pentaquark ground state. The significance of the paper is therefore conditional on the authors supplying the missing validation.

major comments (3)
  1. [Section II, Eq. (5)] The spectral densities ρ_i(s) that enter Eq. (5) are not presented; the text states on page 3 that the final expressions are too lengthy to be given explicitly. Since these densities are the only input to the mass formula (13) and to the coupling formula (14), the central numerical results in Table II cannot be reproduced or independently checked from the manuscript. The authors should either present the full expressions or make them available in an appendix or as a supplementary file.
  2. [Section III, Borel windows] In the paragraph following Eq. (16), the paper claims that the Borel windows in Eqs. (17) and (18) are fixed by OPE convergence, pole dominance, and stability, but no quantitative measures are reported. The standard criteria—for instance, the pole contribution fraction defined as the ratio of the ground-state pole term to the total Borel-transformed correlator, and the relative size of the leading condensate contributions to the perturbative term—should be displayed as functions of M^2 for both states and both Lorentz structures. Without such checks, Eq. (13) may be returning a continuum average rather than the mass of the 1/2^- pentaquark, especially given that the quark threshold (4m_Q + m_Q') lies well below the extracted masses for both states.
  3. [Section III, threshold parameter] The continuum threshold ranges in Eqs. (15) and (16) are chosen by reference to the energy of the first excited state, but no estimate of that excitation energy is provided. The paper should quantify the sensitivity of the extracted masses to the s0 window, for example by showing the variation over a broader s0 range and by stating explicitly how much of the quoted uncertainty in Table II originates from the s0 variation. The stability plots in Figures 1–4 are necessary but not sufficient to validate the chosen windows.
minor comments (5)
  1. [Notation, Eqs. (11)–(14)] The notation for the second Lorentz structure is inconsistent: the abstract calls it \mathbb{1} (the identity matrix), while the body uses "/BD" (for example in Eqs. (11)–(14) and throughout Section III). Please standardize the notation.
  2. [Section II, Eq. (2)] The interpolating current is stated to have J^P = 1/2^-, but no derivation of its quantum numbers is given. A brief justification of the spin-parity assignment would help the reader understand why this current is appropriate for the states under study.
  3. [General] There are several typographical errors, such as "vice-verse" on page 2, which should be "vice versa". A careful proofreading pass is recommended.
  4. [Section III, Table II] The error budget in Table II is said to include input-parameter and auxiliary-window uncertainties, but no explicit statement is made about systematic errors from the truncation of the OPE or from the pole-dominance approximation. Even a brief limitation statement would be helpful.
  5. [Concluding remarks] The comparison with earlier predictions in the concluding remarks is brief and qualitative. A small table summarizing the results of Refs. [107–109] alongside the present results would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the masses are extracted from an OPE sum rule with external inputs, and the central limitation is missing spectral-density transparency, not circular reasoning.

full rationale

The derivation chain is self-contained. The masses in Table II are obtained from Eq. (13), the logarithmic derivative of the Borel-transformed OPE spectral density, with inputs limited to PDG quark masses, the standard gluon condensate, and the auxiliary parameters s0 and M2 chosen by the usual pole-dominance, OPE-convergence, and stability criteria. None of these inputs encode the final mass values, and there are no experimental masses for cccb-cbar or bbbc-bbar pentaquarks to fit, so the quoted results are genuine sum-rule outputs rather than fitted values. The interpolating current in Eq. (2) is an ansatz, but the paper does not define it in terms of the extracted mass and does not smuggle it in via self-citation; it is constructed explicitly and tested through the sum rule. Self-citations (e.g., Refs. 16, 18, 32, 65, 66, 115) appear only as contextual literature references and are not load-bearing; the method itself is anchored in the external foundational papers Refs. 116-118 and the external gluon-condensate input Ref. 119. The paper does state that the final spectral densities are too lengthy to present explicitly (Section II) and that pole dominance is imposed by standard guidelines without reporting quantitative pole fractions (Section III); this is a reproducibility and validation limitation, not circularity, because the masses still follow from the stated OPE computation. External comparisons with Refs. 107-109 provide independent context. Therefore no circular step is present.

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

The central result rests on the standard QCD sum rule assumptions about current-state overlap, quark-hadron duality, and OPE truncation, plus the free auxiliary parameters s0 and M^2. No new fundamental entities are introduced; the pentaquarks are predicted composite states composed of known quarks.

free parameters (2)
  • continuum threshold s0 = 135.0-140.0 GeV^2 for P(4cb), 470.0-480.0 GeV^2 for P(4bc)
    Chosen by considering the energy of the first likely excited state and tuned so the results are stable. The final mass values depend on this choice, so it is a free parameter of the sum rule extraction.
  • Borel parameter M^2 = 12.0-16.0 GeV^2 for P(4cb), 22.0-26.0 GeV^2 for P(4bc)
    Chosen to satisfy OPE convergence, pole dominance, and stability. The quoted mass uncertainties include the variation of M^2 across the chosen window.
assumptions (5)
  • domain assumption The interpolating current in Eq. (2) has nonzero overlap with a physical J^P=1/2^- pentaquark state.
    This is the standard QCD sum rule assumption that the chosen current excites the target state from the vacuum. No demonstration is given that the current is not dominated by an alternative five-quark channel.
  • domain assumption Quark-hadron duality: the hadronic spectral density can be replaced by the OPE result above the continuum threshold s0.
    Invoked in Section II around Eq. (5) for continuum subtraction. This is an uncontrolled approximation in strongly coupled QCD and is load-bearing for the extracted masses.
  • domain assumption The operator product expansion is truncated at the gluon condensate term, with higher-dimensional condensates and quark condensate terms neglected.
    The heavy quark propagator in Eq. (4) explicitly includes only perturbative, one-gluon, and gluon condensate terms. The validity of this truncation for a system of five heavy quarks is not quantified.
  • domain assumption The chosen auxiliary parameter windows (s0, M^2) satisfy OPE convergence and pole dominance.
    Stated in Section III, but no numerical pole contribution or convergence tables are provided, so the reader cannot verify that the working windows isolate the ground state.
  • domain assumption The QCD sum rule machinery, including the Borel transform and dispersion relation, is valid for these hypothetical states.
    The method is standard for hadron spectroscopy, but applying it to a state with five heavy quarks and a high-mass threshold is an extension that inherits the method's systematic uncertainties.

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Pith. "Pith review of Investigation of full heavy $ QQQQ'\bar{Q}$ pentaquark candidates." pith.science (2026). https://pith.science/paper/4HF7L3S5

@misc{pith2026250209409,
  author       = {Pith},
  title        = {Pith review of: Investigation of full heavy $ QQQQ'\barQ$ pentaquark candidates},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4HF7L3S5}},
  note         = {Machine review of arXiv:2502.09409}
}
abstract

Recent breakthroughs in research and experimentation have led to the identification of numerous exotic states in particle physics. Each new discovery not only sparks excitement for future findings but also fuels interest in uncovering additional unknown states. Motivated by this perspective and the recent identification of both standard and exotic hadrons with an increasing number of heavy quarks, this study conducts a spectroscopic analysis of possible pentaquark candidates with spin-parity $\frac{1}{2}^-$, and quark content of $cccb\bar{c}$ and $bbbc\bar{b}$. The masses of these states are calculated by considering the relevant Lorentz structures, including $\slashed{p}$ and $\mathbbm{1}$, yielding the following results, respectively: for the $P_{(4cb)}$ state, $m_{P_{(4cb)}} = 11388.30 \pm 107.79$~MeV and $m_{P_{(4cb)}} = 11368.30 \pm 112.68$~MeV, and for the $P_{(4bc)}$ state, $m_{P_{(4bc)}} = 20998.30 \pm 121.52$~MeV and $m_{P_{(4bc)}} = 20990.50 \pm 125.87$~MeV. Additionally, the current coupling constants of these states to the vacuum, which are essential for analyzing their potential decay modes, are also provided in this study.

Figures

Figures reproduced from arXiv: 2502.09409 by the authors.

Figure 1
Figure 1. FIG. 1. (a) The dependence of the mass of the [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) The dependence of the mass of the [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) The dependence of the residue or current coupling [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a) The dependence of the current coupling constant [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

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Works this paper leans on

121 extracted references · 25 canonical work pages

  1. [109]

    H. T. An, S. Q. Luo, Z. W. Liu and X. Liu, Phys. Rev. D 105, no.7, 074032 (2022) [arXiv:2203.03448 [hep-ph]]

    arXiv 2022

  2. [1]

    S. K. Choi et al. [Belle Collaboration], Phys. Rev. Lett. 91, 262001 (2003) [hep-ex/0309032]

    arXiv 2003

  3. [2]

    P. A. Zyla et al. [Particle Data Group], PTEP 2020, no.8, 083C01 (2020)

    2020

  4. [3]

    Aaij et al

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

    arXiv 2015

  5. [4]

    Aaij et al

    R. Aaij et al. [LHCb], Phys. Rev. Lett. 117, no.8, 082003 (2016) [arXiv:1606.06999 [hep-ex]]

    arXiv 2016

  6. [5]

    Aaij et al

    R. Aaij et al. [LHCb], Phys. Rev. Lett. 122, no.22, 222001 (2019) [arXiv:1904.03947 [hep-ex]]

    arXiv 2019

  7. [6]

    Aaij et al

    R. Aaij et al. [LHCb], Nature Commun. 13, no.1, 3351 (2022) [arXiv:2109.01056 [hep-ex]]

    arXiv 2022

  8. [7]

    Aaij et al

    R. Aaij et al. [LHCb], Nature Phys. 18, no.7, 751-754 (2022) [arXiv:2109.01038 [hep-ex]]

    arXiv 2022

Show all 121 references
  1. [8]

    Aaij et al

    R. Aaij et al. [LHCb], Phys. Rev. Lett. 128, no.6, 062001 (2022) [arXiv:2108.04720 [hep-ex]]

    2022

  2. [9]

    Aaij et al

    R. Aaij et al. [LHCb], Sci. Bull. 66, 1278-1287 (2021) [arXiv:2012.10380 [hep-ex]]

    2021

  3. [10]

    Aaij et al

    R. Aaij et al. [LHCb], Phys. Rev. Lett. 131, no.3, 031901 (2023) [arXiv:2210.10346 [hep-ex]]

    2023 arXiv

  4. [11]

    Navas et al

    S. Navas et al. [Particle Data Group], Phys. Rev. D 110, no.3, 030001 (2024)

    2024

  5. [12]

    H. X. Chen, W. Chen, X. Liu, T. G. Steele and S. L. Zhu, Phys. Rev. Lett. 115, no. 17, 172001 (2015) [arXiv:1507.03717 [hep-ph]]

    2015 arXiv

  6. [13]

    R. Chen, X. Liu, X. Q. Li and S. L. Zhu, Phys. Rev. Lett. 115, no. 13, 132002 (2015) [arXiv:1507.03704 [hep-ph]]

    2015 arXiv

  7. [14]

    He, Phys

    J. He, Phys. Lett. B 753, 547 (2016) [arXiv:1507.05200 [hep-ph]]

    2016 arXiv

  8. [15]

    L. Roca, J. Nieves and E. Oset, Phys. Rev. D 92, no. 9, 094003 (2015) [arXiv:1507.04249 [hep-ph]]

    2015 arXiv

  9. [16]

    Azizi, Y

    K. Azizi, Y. Sarac and H. Sundu, Phys. Rev. D 95, no. 9, 094016 (2017) [arXiv:1612.07479 [hep-ph]]

    2017 arXiv

  10. [17]

    U. G. Meißner and J. A. Oller, Phys. Lett. B 751, 59 (2015) [arXiv:1507.07478 [hep-ph]]

    2015 arXiv

  11. [18]

    Azizi, Y

    K. Azizi, Y. Sarac and H. Sundu, Phys. Lett. B 782, 694-701 (2018) [arXiv:1802.01384 [hep-ph]]

    2018 arXiv

  12. [19]

    H. X. Chen, Chin. Phys. C 46, no.9, 093105 (2022) [arXiv:2011.07187 [hep-ph]]

    2022 arXiv

  13. [20]

    H. S. Li, F. Guo, Y. D. Lei and F. Gao, [arXiv:2401.14767 [hep-ph]]

    arXiv

  14. [21]

    H. S. Li, [arXiv:2401.14759 [hep-ph]] . 8 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ p/ ● s0=140.0 GeV 2 ▼ s0=137.5 GeV 2 ■ s0=135.0 GeV 2 12 13 14 15 16 0 2 4 6 8 M2 (GeV2) λP4 cb (GeV6) ● ● ● ● ● ● ● ● ● ● ● ● ● ● ...

    arXiv

  15. [22]

    B. Wang, K. Chen, L. Meng and S. L. Zhu, [arXiv:2312.13591 [hep-ph]]

    arXiv

  16. [23]

    H. X. Chen, W. Chen, X. Liu and X. H. Liu, Eur. Phys. J. C 81, no.5, 409 (2021) [arXiv:2011.01079 [hep-ph]]

    2021 arXiv

  17. [24]

    F. Z. Peng, M. J. Yan, M. S´ anchez S´ anchez and M. P. Valde rrama, Eur. Phys. J. C 81, no.7, 666 (2021) [arXiv:2011.01915 [hep-ph]]

    2021 arXiv

  18. [25]

    Chen, Phys

    R. Chen, Phys. Rev. D 103, no.5, 054007 (2021) [arXiv:2011.07214 [hep-ph]]

    2021 arXiv

  19. [26]

    Z. G. Wang and X. Wang, Chin. Phys. C 44, 103102 (2020) [arXiv:1907.04582 [hep-ph]]

    2020 arXiv

  20. [27]

    Z. G. Wang and Q. Xin, Chin. Phys. C 45, no.12, 123105 (2021) [arXiv:2103.08239 [hep-ph]]

    2021 arXiv

  21. [28]

    Z. G. Wang, Int. J. Mod. Phys. A 34, no.19, 1950097 (2019) [arXiv:1806.10384 [hep-ph]]

    2019 arXiv

  22. [29]

    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, no.24, 242001 (2019) [arXiv:1903.11560 [hep-ph]]

    2019 arXiv

  23. [30]

    M. L. Du, V. Baru, F. K. Guo, C. Hanhart, U. G. Meißner, J. A . Oller and Q. Wang, JHEP 08, 157 (2021) [arXiv:2102.07159 [hep-ph]]

    2021 arXiv

  24. [31]

    M. Z. Liu, Y. W. Pan and L. S. Geng, [arXiv:2407.17318 [hep-ph]]

    arXiv

  25. [32]

    Azizi, Y

    K. Azizi, Y. Sarac and H. Sundu, Chin. Phys. C 45, no.5, 053103 (2021) [arXiv:2011.05828 [hep-ph]]

    2021 arXiv

  26. [33]

    R. F. Lebed, Phys. Lett. B 749, 454 (2015) [arXiv:1507.05867 [hep-ph]]

    2015 arXiv

  27. [34]

    Maiani, A

    L. Maiani, A. D. Polosa and V. Riquer, Phys. Lett. B 749, 289 (2015) [arXiv:1507.04980 [hep-ph]]

    2015 arXiv

  28. [35]

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

    2015 arXiv

  29. [36]

    Z. G. Wang and T. Huang, Eur. Phys. J. C 76, no. 1, 43 (2016) [arXiv:1508.04189 [hep-ph]]

    2016 arXiv

  30. [37]

    V. V. Anisovich, M. A. Matveev, J. Nyiri, A. V. Sarantsev and A. N. Semenova, arXiv:1507.07652 [hep-ph]

    arXiv

  31. [38]

    Z. G. Wang, Nucl. Phys. B 913, 163-208 (2016) [arXiv:1512.04763 [hep-ph]]

    2016 arXiv

  32. [39]

    Z. G. Wang, Eur. Phys. J. C 76, no. 2, 70 (2016) [arXiv:1508.01468 [hep-ph]]

    2016 arXiv

  33. [40]

    Ghosh, A

    R. Ghosh, A. Bhattacharya and B. Chakrabarti, Phys. Part. Nucl. Lett. 14, no.4, 550-552 (2017) [arXiv:1508.00356 [hep-ph]]

    2017 arXiv

  34. [41]

    Z. G. Wang, Eur. Phys. J. C 76, no.3, 142 (2016) [arXiv:1509.06436 [hep-ph]] . 9 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ p/ ● s0=480 GeV 2 ▼ s0=475 GeV 2 ■ s0=470 GeV 2 22 23 24 25 26 50 100 150 200 250 300 M2 (GeV2...

    2016 arXiv

  35. [42]

    J. X. Zhang, Z. G. Wang and Z. Y. Di, Acta Phys. Polon. B 48, 2013 (2017) [arXiv:1711.10728 [hep-ph]]

    2017 arXiv

  36. [43]

    Z. G. Wang, H. J. Wang and Q. Xin, Chin. Phys. C 45, 063104 (2021) [arXiv:2005.00535 [hep-ph]]

    2021 arXiv

  37. [44]

    A. Ali, I. Ahmed, M. J. Aslam, A. Parkhomenko and A. Rehma n, PoS ICHEP2020, 527 (2021) [arXiv:2012.07760 [hep-ph]]

    2021 arXiv

  38. [45]

    G. J. Wang, R. Chen, L. Ma, X. Liu and S. L. Zhu, Phys. Rev. D 94, no. 9, 094018 (2016) [arXiv:1605.01337 [hep-ph]]

    2016 arXiv

  39. [46]

    Z. G. Wang, Int. J. Mod. Phys. A 36, no.10, 2150071 (2021) [arXiv:2011.05102 [hep-ph]]

    2021 arXiv

  40. [47]

    Z. G. Wang, Int. J. Mod. Phys. A 35, no.01, 2050003 (2020) [arXiv:1905.02892 [hep-ph]]

    2020 arXiv

  41. [48]

    Zhu and C

    R. Zhu and C. F. Qiao, Phys. Lett. B 756, 259 (2016) [arXiv:1510.08693 [hep-ph]]

    2016 arXiv

  42. [49]

    N. N. Scoccola, D. O. Riska and M. Rho, Phys. Rev. D 92, no.5, 051501 (2015) [arXiv:1508.01172 [hep-ph]]

    2015 arXiv

  43. [50]

    Liu and I

    Y. Liu and I. Zahed, Phys. Rev. D 95, no.11, 116012 (2017) [arXiv:1704.03412 [hep-ph]]

    2017 arXiv

  44. [51]

    F. K. Guo, U. G. Meißner, W. Wang and Z. Yang, Phys. Rev. D 92, no.7, 071502 (2015) [arXiv:1507.04950 [hep-ph]]

    2015 arXiv

  45. [52]

    Mikhasenko, arXiv:1507.06552 [hep-ph]

    M. Mikhasenko, arXiv:1507.06552 [hep-ph]

    arXiv

  46. [53]

    F. K. Guo, U. G. Meißner, J. Nieves and Z. Yang, Eur. Phys. J. A 52, no.10, 318 (2016) [arXiv:1605.05113 [hep-ph]]

    2016 arXiv

  47. [54]

    Bayar, F

    M. Bayar, F. Aceti, F. K. Guo and E. Oset, Phys. Rev. D 94, no.7, 074039 (2016) [arXiv:1609.04133 [hep-ph]]

    2016 arXiv

  48. [55]

    D. A. O. Co and D. L. B. Sombillo, [arXiv:2411.14044 [hep-ph]]

    arXiv

  49. [56]

    X. H. Liu, Q. Wang and Q. Zhao, Phys. Lett. B 757, 231-236 (2016) [arXiv:1507.05359 [hep-ph]]

    2016 arXiv

  50. [57]

    X. Liu, H. Huang and J. Ping, Phys. Rev. C 102 (2020) no.2, 025204 [arXiv:2005.09646 [hep-ph]]

    2020 arXiv

  51. [58]

    Feijoo, V

    A. Feijoo, V. K. Magas, A. Ramos and E. Oset, Eur. Phys. J. C 76, no.8, 446 (2016) [arXiv:1512.08152 [hep-ph]]

    2016 arXiv

  52. [59]

    H. X. Chen, L. S. Geng, W. H. Liang, E. Oset, E. Wang and J. J . Xie, Phys. Rev. C 93, no.6, 065203 (2016) [arXiv:1510.01803 [hep-ph]]

    2016 arXiv

  53. [60]

    J. X. Lu, E. Wang, J. J. Xie, L. S. Geng and E. Oset, Phys. Rev. D 93, 094009 (2016) [arXiv:1601.00075 [hep-ph]]

    2016 arXiv

  54. [61]

    Y. Irie, M. Oka and S. Yasui, Phys. Rev. D 97, no.3, 034006 (2018) [arXiv:1707.04544 [hep-ph]]

    2018 arXiv

  55. [62]

    Zhang, B

    Q. Zhang, B. R. He and J. L. Ping, [arXiv:2006.01042 [hep-ph]]

    2006 arXiv

  56. [63]

    R. Chen, J. He and X. Liu, Chin. Phys. C 41, no.10, 103105 (2017) [arXiv:1609.03235 [hep-ph]] . 10

    2017 arXiv

  57. [64]

    Gutsche and V

    T. Gutsche and V. E. Lyubovitskij, Phys. Rev. D 100, no.9, 094031 (2019) [arXiv:1910.03984 [hep-ph]]

    2019 arXiv

  58. [65]

    Azizi, Y

    K. Azizi, Y. Sarac and H. Sundu, Phys. Rev. D 98, no.5, 054002 (2018) [arXiv:1805.06734 [hep-ph]]

    2018 arXiv

  59. [66]

    Azizi, Y

    K. Azizi, Y. Sarac and H. Sundu, Phys. Rev. D 96, no.9, 094030 (2017) [arXiv:1707.01248 [hep-ph]]

    2017 arXiv

  60. [67]

    X. Cao, F. K. Guo, Y. T. Liang, J. J. Wu, J. J. Xie, Y. P. Xie, Z. Yang and B. S. Zou, Phys. Rev. D 101, no.7, 074010 (2020) [arXiv:1912.12054 [hep-ph]]

    2020 arXiv

  61. [68]

    J. R. Zhang, Phys. Rev. D 103, no.7, 074016 (2021) [arXiv:2011.04594 [hep-ph]]

    2021 arXiv

  62. [69]

    Y. P. Xie and V. P. Goncalves, Phys. Lett. B 814, 136121 (2021) [arXiv:2012.07501 [hep-ph]]

    2021 arXiv

  63. [70]

    Feijoo and I

    A. Feijoo and I. Vida˜ na, [arXiv:2411.18248 [hep-ph]]

    arXiv

  64. [71]

    Z. Y. Wang, C. W. Xiao, Z. F. Sun and X. Liu, Phys. Rev. D 110, no.7, 076014 (2024) [arXiv:2407.13319 [hep-ph]]

    2024 arXiv

  65. [72]

    X. Liu, Y. Tan, X. Chen, D. Chen, H. Huang and J. Ping, Phys. Rev. D 110, no.7, 074001 (2024) [arXiv:2407.05598 [hep-ph]]

    2024 arXiv

  66. [73]

    E. Oset, L. Roca and M. Whitehead, Phys. Rev. D 110, no.3, 034016 (2024) [arXiv:2406.16504 [hep-ph]]

    2024 arXiv

  67. [74]

    J. Song, M. Y. Duan, L. Roca and E. Oset, Eur. Phys. J. C 84, no.10, 1055 (2024) [arXiv:2406.14895 [hep-ph]]

    2024 arXiv

  68. [75]

    Z. Y. Yang, Q. Wang and W. Chen, Phys. Rev. D 110, no.5, 056022 (2024) [arXiv:2405.09067 [hep-ph]]

    2024 arXiv

  69. [76]

    X. W. Wang and Z. G. Wang, Int. J. Mod. Phys. A 39, no.17n18, 2450067 (2024) [arXiv:2405.00281 [hep-ph]]

    2024 arXiv

  70. [77]

    E. Y. Paryev, [arXiv:2007.01172 [nucl-th]]

    2007 arXiv

  71. [78]

    F. L. Wang, R. Chen and X. Liu, Phys. Rev. D 103, no.3, 034014 (2021) [arXiv:2011.14296 [hep-ph]]

    2021 arXiv

  72. [79]

    F. B. Duan, Q. N. Wang, Z. Y. Yang, X. L. Chen and W. Chen, Phys. Rev. D 109, no.9, 094018 (2024) [arXiv:2401.10078 [hep-ph]]

    2024 arXiv

  73. [80]

    S. Y. Kong, J. T. Zhu, S. Chen and J. He, [arXiv:2402.02703 [hep-ph]]

    arXiv

  74. [81]

    Sharma and A

    A. Sharma and A. Upadhyay, [arXiv:2401.02146 [hep-ph]]

    arXiv

  75. [82]

    W. X. Zhang, C. L. Liu and D. Jia, [arXiv:2312.12770 [hep-ph]]

    arXiv

  76. [83]

    Y. Yan, H. Huang, X. Zhu and J. Ping, [arXiv:2312.04977 [hep-ph]]

    arXiv

  77. [84]

    X. Liu, Y. Tan, X. Chen, D. Chen, H. Huang and J. Ping, [arXiv:2312.04390 [hep-ph]]

    arXiv

  78. [85]

    Z. Y. Wang, C. W. Xiao, Z. F. Sun and X. Liu, [arXiv:2311.17736 [hep-ph]]

    arXiv

  79. [86]

    F. L. Wang and X. Liu, Phys. Rev. D 109, no.1, 1 (2024) [arXiv:2311.13968 [hep-ph]]

    2024 arXiv

  80. [87]

    G. Yang, J. Ping and J. Segovia, [arXiv:2311.01044 [hep-ph]]

    arXiv

  81. [88]

    X. Liu, Y. Tan, X. Chen, D. Chen, H. Huang and J. Ping, Phys. Rev. D 108, no.9, 094008 (2023)

    2023

  82. [89]

    E. Y. Paryev, Nucl. Phys. A 1042, 122792 (2024) [arXiv:2310.04123 [hep-ph]]

    2024 arXiv

  83. [90]

    J. X. Lin, H. X. Chen, W. H. Liang, W. Y. Liu and D. Zhou, Eur. Phys. J. A 60, no.1, 15 (2024) [arXiv:2308.01007 [hep-ph]]

    2024 arXiv

  84. [91]

    Q. Xin, X. S. Yang and Z. G. Wang, Int. J. Mod. Phys. A 38, no.22n23, 2350123 (2023) [arXiv:2307.08926 [hep-ph]]

    2023 arXiv

  85. [92]

    Chen and Q

    R. Chen and Q. Huang, Phys. Rev. D 108, no.5, 054011 (2023) [arXiv:2307.04168 [hep-ph]]

    2023 arXiv

  86. [93]

    X. Zhu, Y. Wu, H. Huang, J. Ping and Y. Yang, Universe 9, no.6, 265 (2023)

    2023

  87. [94]

    Y. Yan, Y. Wu, H. Huang, J. Ping and X. Zhu, Eur. Phys. J. C 83, no.7, 610 (2023) [arXiv:2305.16609 [hep-ph]]

    2023 arXiv

  88. [95]

    Sharma and A

    A. Sharma and A. Upadhyay, Eur. Phys. J. A 60, no.11, 231 (2024) [arXiv:2405.11479 [hep-ph]]

    2024 arXiv

  89. [96]

    C. L. Liu, W. X. Zhang and D. Jia, Chin. Phys. C 48, no.10, 103110 (2024) [arXiv:2403.13456 [hep-ph]]

    2024 arXiv

  90. [97]

    L. Roca, J. Song and E. Oset, Phys. Rev. D 109, no.9, 094005 (2024) [arXiv:2403.08732 [hep-ph]]

    2024 arXiv

  91. [98]

    Aaij et al

    R. Aaij et al. [LHCb], Phys. Rev. Lett. 119, no.11, 112001 (2017) [arXiv:1707.01621 [hep-ex]]

    2017 arXiv

  92. [99]

    Aaij et al

    R. Aaij et al. [LHCb], Phys. Rev. Lett. 121, no.16, 162002 (2018) [arXiv:1807.01919 [hep-ex]]

    2018 arXiv

  93. [100]

    Aaij et al

    R. Aaij et al. [LHCb], Sci. Bull. 65, no.23, 1983-1993 (2020) [arXiv:2006.16957 [hep-ex]]

    2020

  94. [101]

    Bouhova-Thacker [ATLAS], PoS ICHEP2022, 806 (2022)

    E. Bouhova-Thacker [ATLAS], PoS ICHEP2022, 806 (2022)

    2022

  95. [102]

    Zhang et al

    J. Zhang et al. [CMS], PoS ICHEP2022, 775 [arXiv:2212.00504 [hep-ex]]

    arXiv

  96. [103]

    Hayrapetyan et al

    A. Hayrapetyan et al. [CMS], [arXiv:2306.07164 [hep-ex]]

    arXiv

  97. [104]

    Aad et al

    G. Aad et al. [ATLAS], Phys. Rev. Lett. 131, no.15, 151902 (2023) [arXiv:2304.08962 [hep-ex]]

    2023 arXiv

  98. [105]

    Z. G. Wang, Nucl. Phys. B 973, 115579 (2021) [arXiv:2104.12090 [hep-ph]]

    2021 arXiv

  99. [106]

    Y. Yan, Y. Wu, X. Hu, H. Huang and J. Ping, Phys. Rev. D 105, no.1, 014027 (2022) [arXiv:2110.10853 [hep-ph]]

    2022 arXiv

  100. [107]

    W. X. Zhang, H. T. An and D. Jia, Eur. Phys. J. C 83, no.8, 727 (2023) [arXiv:2304.14876 [hep-ph]]

    2023 arXiv

  101. [108]

    H. T. An, K. Chen, Z. W. Liu and X. Liu, Phys. Rev. D 103, no.7, 074006 (2021) [arXiv:2012.12459 [hep-ph]]

    2021 arXiv

  102. [110]

    G. Yang, J. Ping and J. Segovia, Phys. Rev. D 106, no.1, 014005 (2022) [arXiv:2205.11548 [hep-ph]]

    2022 arXiv

  103. [111]

    Z. B. Liang, F. X. Liu and X. H. Zhong, [arXiv:2402.17974 [hep-ph]]

    arXiv

  104. [112]

    30 ± 121

    68 MeV, and for the P(4bc) state, mP(4bc) = 20998 . 30 ± 121. 52 MeV and mP(4bc) = 20990 . 50 ±

  105. [113]

    Upadhyay, [arXiv:2410.00633 [hep-ph]]

    Rashmi and A. Upadhyay, [arXiv:2410.00633 [hep-ph]]

    arXiv

  106. [114]

    Alonso-Valero, D

    A. Alonso-Valero, D. Berzal-Rozal´ en, F. J. Llanes-E strada, M. C. Pardo and C. Peset, [arXiv:2410.05066 [hep-ph]]

    arXiv

  107. [115]

    Azizi, Y

    K. Azizi, Y. Sarac and H. Sundu, Eur. Phys. J. C 84, no.7, 695 (2024) [arXiv:2402.19440 [hep-ph]]

    2024 arXiv

  108. [116]

    M. C. Gordillo and J. Segovia, Phys. Rev. D 109, no.9, 094032 (2024) [arXiv:2403.15000 [hep-ph]]

    2024 arXiv

  109. [117]

    M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, Nucl. Phys. B 147, 448 (1979)

    1979

  110. [118]

    M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, Nucl. Phys. B 147, 385 (1979)

    1979

  111. [119]

    V. M. Belyaev and B. L. Ioffe, Sov. Phys. JETP 57, 716 (1983) [Zh. Eksp. Teor. Fiz. 84, 1236 (1983)]

    1983

  112. [120]

    B. L. Ioffe, Nucl. Phys. B 188, 317 (1981) Erratum: [Nucl. Phys. B 191, 591 (1981)]

    1981

  113. [125]

    Additionally, the current coupling constants of the se states to the vacuum, which are essential for analyzing their potential decay modes, are al so provided in this study

    87 MeV. Additionally, the current coupling constants of the se states to the vacuum, which are essential for analyzing their potential decay modes, are al so provided in this study. I. INTRODUCTION Starting from the first time that the quark model was introduced, hadrons with u...

    2003

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