Pith. sign in

REVIEW 3 minor 92 references

Three-body molecular states composed of $D^{(*)}$ and two nucleons

T0 review · 0 major / 3 minor · reviewed 2026-05-25 · grok-4.3

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

Pith's one-line read The DNN system forms a robust compact bound state in the 1/2(1-) channel over a broad range of cutoffs even when the DN subsystem is weakly bound or unbound.

desk verdict The paper finds cutoff-robust bound states in DNN (I=1/2, J^P=1^-) and a spin hierarchy in D*NN using HQS potentials plus realistic NN, solved via GEM and checked with complex scaling. read the letter →

arxiv 2602.19504 v3 pith:3RIPBK53 submitted 2026-02-23 hep-ph hep-exnucl-th

Si-Yi Chen , Fei-Yu Chen , Xu-Liang Chen , Lu Meng , Ning Li , Wei Chen This is my paper · ORCID
classification hep-phhep-exnucl-th
keywords charmedmesonnucleonthree-bodyboundstateheavyquarksymmetrymolecularGaussianexpansionmethodDNNsystem
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 investigates three-body molecular states of a D or D* meson with two nucleons by combining a realistic nucleon-nucleon interaction with a D(*)N potential fixed by heavy-quark symmetry. The three-body Schrödinger equation is solved using the Gaussian Expansion Method, and the spectrum is analyzed with the Complex Scaling Method to identify bound states and check for resonances. The central result is that DNN supports a stable, spatially compact bound state in the I(J^P)=1/2(1^-) channel across wide cutoff variations. For D*NN the spin-1 nature of the heavy meson produces a clear hierarchy of binding energies and sizes across 0^-, 1^-, and 2^- channels, all more compressed than the deuteron. These calculations supply quantitative predictions for possible charmed-meson-nuclear bound states.

What carries the argument

The three-body Schrödinger equation solved by the Gaussian Expansion Method after combining a realistic NN potential with a D(*)N potential constrained by heavy-quark symmetry, together with the Complex Scaling Method for locating resonances.

What would settle it

An experimental search that either detects or rules out a bound state with the predicted binding energy, isospin, and spin-parity in the DNN system at the expected mass would confirm or refute the result.

Watch

Extended reading notes

Core claim

The DNN system supports a robust and compact bound state in the I(J^P)=1/2(1^-) channel over a broad range of cutoff values, even when the corresponding DN subsystem is weakly bound or unbound. For D*NN the spin-1 nature of the heavy meson generates a clear spin hierarchy: deeply bound states appear in both 0^- and 2^- channels, while the 1^- channel exhibits a two-branch pattern with one strongly bound compact branch and one more weakly bound spatially extended branch. Root-mean-square radii show pronounced spatial compression relative to the deuteron, and no three-body resonances appear under complex scaling in the explored parameter space.

Load-bearing premise

The D(*)N interaction is correctly captured by heavy-quark symmetry when added to a realistic NN force.

Editorial extensions

If this is right

  • DNN remains bound even when the two-body DN subsystem is unbound or only weakly bound.
  • D*NN exhibits a spin-dependent hierarchy with compact states in 0^- and 2^- channels and a two-branch structure in the 1^- channel.
  • All predicted states have root-mean-square radii smaller than the deuteron, indicating cooperative compression from NN correlations and D(*)N forces.
  • No three-body resonances are found across the scanned cutoff range.

Reading between the lines

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

  • Similar compact states may exist when the D meson is replaced by a B meson, extending the same heavy-quark symmetry framework to bottom flavor.
  • The predicted mass and size ranges could guide dedicated searches in heavy-ion or electron-beam experiments that produce charmed mesons near threshold.
  • If the states are observed, their radii would test whether heavy-quark symmetry remains accurate inside a three-body nuclear environment.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

0 major / 3 minor

Summary. The manuscript investigates DNN and D*NN three-body systems in a hadronic molecular framework by combining a realistic NN interaction with D(*)N potentials constrained by heavy-quark symmetry. The three-body Schrödinger equation is solved using the Gaussian Expansion Method, and the analytic structure is analyzed via the Complex Scaling Method. The central claims are a robust, compact bound state in the DNN I(J^P)=1/2(1^-) channel persisting over a broad cutoff range even when the DN subsystem is weakly bound or unbound, a clear spin hierarchy for D*NN with deeply bound states in 0^- and 2^- channels plus a two-branch pattern in 1^-, pronounced spatial compression relative to the deuteron, and the absence of three-body resonances.

Significance. If the numerical results hold, this work supplies quantitative benchmarks for experimental searches of charmed-meson-nuclear bound states. It explicitly demonstrates the cooperative roles of realistic NN correlations, D(*)N interactions, and heavy-quark symmetry in forming compact heavy-flavor few-body states. The systematic survey over the single free parameter (cutoff) together with the use of the Complex Scaling Method to confirm the lack of resonances are positive methodological strengths that enhance the reliability of the bound-state claims.

minor comments (3)
  1. The abstract states that the DNN bound state persists 'over a broad range of cutoff values' but does not quote the explicit range or tabulate the binding energies versus cutoff; adding a compact table or figure panel would make the robustness claim immediately verifiable.
  2. Section describing the Gaussian Expansion Method implementation should include the basis size, number of channels retained, and explicit convergence tests with respect to the expansion parameters to allow independent reproduction of the three-body energies.
  3. The root-mean-square radii are compared to the deuteron scale, but the precise definition (e.g., matter radius versus charge radius) and the numerical extraction procedure from the GEM wave functions are not stated; a short clarifying sentence would remove ambiguity.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript, the recognition of its methodological strengths (including the cutoff survey and Complex Scaling Method analysis), and the recommendation for minor revision. No specific major comments were listed in the report.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; results are numerical outputs from standard QM solver

full rationale

The derivation consists of combining a realistic NN potential with a D(*)N potential (constrained by heavy-quark symmetry and regularized by cutoff) and solving the three-body Schrödinger equation via the Gaussian Expansion Method, followed by Complex Scaling Method analysis. The reported bound states and radii are direct numerical results of this procedure across a range of cutoffs; they do not reduce to the inputs by construction, nor does the paper rename fitted quantities as predictions or rely on load-bearing self-citations for uniqueness. The methodology is self-contained and externally falsifiable via the Schrödinger equation itself.

Assumptions & free parameters 1 free parameters · 2 assumptions · 0 invented entities

The central claim rests on the validity of the hadronic molecular framework, heavy-quark symmetry for the two-body potential, and the numerical accuracy of the Gaussian Expansion Method; the cutoff is the main adjustable parameter.

free parameters (1)
  • cutoff
    The D(*)N potential depends on a cutoff parameter, with results shown over a broad range of values.
assumptions (2)
  • domain assumption Heavy-quark symmetry constrains the D(*)N potential
    Used to build the two-body potential from known symmetry principles.
  • domain assumption Realistic nucleon-nucleon interaction is used as input
    Combined with the meson-nucleon potential in the three-body calculation.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Three-body molecular states composed of $D^{(*)}$ and two nucleons." pith.science (2026). https://pith.science/paper/3RIPBK53

@misc{pith2026260219504,
  author       = {Pith},
  title        = {Pith review of: Three-body molecular states composed of $D^(*)$ and two nucleons},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3RIPBK53}},
  note         = {Machine review of arXiv:2602.19504}
}
abstract

We study the three-body systems $DNN$ and $D^{*}NN$ within a hadronic molecular framework by combining a realistic nucleon-nucleon interaction with a $D^{(*)}N$ potential constrained by heavy-quark symmetry. The three-body Schr\"odinger equation is solved with the Gaussian Expansion Method, and the analytic structure of the spectrum is investigated using the Complex Scaling Method. We find that the $DNN$ system supports a robust and compact bound state in the $I(J^{P})=\tfrac{1}{2}(1^-)$ channel over a broad range of cutoff values, even when the corresponding $DN$ subsystem is weakly bound or unbound. For $D^{*}NN$, the spin-$1$ nature of the heavy meson and the associated spin-dependent forces generate a clear spin hierarchy: deeply bound states appear in both $0^-$ and $2^-$ channels, while the $1^-$ channel exhibits a characteristic two-branch pattern with a strongly bound compact branch and a more weakly bound, spatially extended branch. The root-mean-square radii indicate pronounced spatial compression compared with the deuteron scale, highlighting the cooperative roles of realistic $NN$ correlations, the $D^{(*)}N$ interactions, and heavy-quark symmetry in forming compact heavy-flavor few-body bound states. No three-body resonances under complex scaling are found in the explored parameter space. Our results provide quantitative benchmarks for future experimental searches for such charmed-meson-nuclear bound states.

Figures

Figures reproduced from arXiv: 2602.19504 by the authors.

Figure 1
Figure 1. FIG. 1. Feynman diagrams used to derive OBE potentials for the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Two sets of Jacobi coordinates corresponding to different [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Binding energies of the [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Root-mean-square (RMS) radii of the [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Binding energies of the three-body [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. RMS radii of the [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Pole trajectories of the [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

92 extracted references · 92 canonical work pages

  1. [1]

    S. K. Choiet al.(Belle), Observation of a narrow charmonium- like state in exclusiveB ± →K ±π+π−J/ψdecays, Phys. Rev. Lett.91, 262001 (2003), arXiv:hep-ex/0309032

    work page Pith review arXiv 2003

  2. [2]

    Observation of a charged charmoniumlike structure in e+e- to pi+pi-J/psi at \sqrt{s}=4.26 GeV

    M. Ablikimet al.(BESIII), Observation of a Charged Charmo- niumlike Structure ine +e− →π +π−J/ψat √s=4.26 GeV, Phys. Rev. Lett.110, 252001 (2013), arXiv:1303.5949 [hep-ex]

    work page Pith review arXiv 2013

  3. [3]

    Z. Q. Liuet al.(Belle), Study ofe +e−ßπ+π−J/ψand Ob- servation of a Charged Charmoniumlike State at Belle, Phys. Rev. Lett.110, 252002 (2013), [Erratum: Phys.Rev.Lett. 111, 019901 (2013)], arXiv:1304.0121 [hep-ex]

    work page Pith review arXiv 2013

  4. [4]

    Observation of $J/\psi p$ resonances consistent with pentaquark states in ${\Lambda_b^0\to J/\psi K^-p}$ decays

    R. Aaijet al.(LHCb), Observation ofJ/ψpResonances Con- sistent with Pentaquark States inΛ 0 b →J/ψK −pDecays, Phys. Rev. Lett.115, 072001 (2015), arXiv:1507.03414 [hep- ex]. 13 TABLE III. Numerical results for the three-bodyDN Nsystem and the corresponding two-body subsystems are obtained with the rescaled coupling constants fixed atR s =R β =R λ = 1. The...

    work page Pith review arXiv 2015

  5. [5]

    Observation of a narrow pentaquark state, $P_c(4312)^+$, and of two-peak structure of the $P_c(4450)^+$

    R. Aaijet al.(LHCb), Observation of a narrow pentaquark state, Pc(4312)+, and of two-peak structure of thePc(4450)+, Phys. Rev. Lett.122, 222001 (2019), arXiv:1904.03947 [hep-ex]

    work page Pith review arXiv 2019

  6. [6]

    Aaij et al

    R. Aaijet al.(LHCb), Study of the doubly charmed tetraquark T + cc, Nature Commun.13, 3351 (2022), arXiv:2109.01056 [hep-ex]

    work page arXiv 2022

  7. [7]

    Aaij et al

    R. Aaijet al.(LHCb), Observation of an exotic narrow doubly charmed tetraquark, Nature Phys.18, 751 (2022), arXiv:2109.01038 [hep-ex]

    work page arXiv 2022

  8. [8]

    E. S. Swanson, The New heavy mesons: A Status report, Phys. Rept.429, 243 (2006), arXiv:hep-ph/0601110

    work page Pith review arXiv 2006

Show all 92 references
  1. [9]

    M. B. V oloshin, Charmonium, Prog. Part. Nucl. Phys.61, 455 (2008), arXiv:0711.4556 [hep-ph]

    2008 arXiv

  2. [10]

    Brambillaet al., Heavy Quarkonium: Progress, Puz- zles, and Opportunities, Eur

    N. Brambillaet al., Heavy Quarkonium: Progress, Puz- zles, and Opportunities, Eur. Phys. J. C71, 1534 (2011), arXiv:1010.5827 [hep-ph]

    2011 arXiv

  3. [11]

    Brambillaet al., QCD and Strongly Coupled Gauge The- ories: Challenges and Perspectives, Eur

    N. Brambillaet al., QCD and Strongly Coupled Gauge The- ories: Challenges and Perspectives, Eur. Phys. J. C74, 2981 (2014), arXiv:1404.3723 [hep-ph]

    2014 arXiv

  4. [12]

    Hosaka, T

    A. Hosaka, T. Iijima, K. Miyabayashi, Y . Sakai, and S. Yasui, Exotic hadrons with heavy flavors: X, Y , Z, and related states, PTEP2016, 062C01 (2016), arXiv:1603.09229 [hep-ph]

    2016

  5. [13]

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

    2016 arXiv

  6. [14]

    Esposito, A

    A. Esposito, A. Pilloni, and A. D. Polosa, Multiquark Reso- nances, Phys. Rept.668, 1 (2017), arXiv:1611.07920 [hep-ph]

    2017 arXiv

  7. [15]

    R. F. Lebed, R. E. Mitchell, and E. S. Swanson, Heavy- Quark QCD Exotica, Prog. Part. Nucl. Phys.93, 143 (2017), arXiv:1610.04528 [hep-ph]

    2017 arXiv

  8. [16]

    A. Ali, J. S. Lange, and S. Stone, Exotics: Heavy Pen- taquarks and Tetraquarks, Prog. Part. Nucl. Phys.97, 123 (2017), arXiv:1706.00610 [hep-ph]

    2017 arXiv

  9. [17]

    F.-K. Guo, C. Hanhart, U.-G. Meißner, Q. Wang, Q. Zhao, and B.-S. Zou, Hadronic molecules, Rev. Mod. Phys.90, 015004 (2018), [Erratum: Rev.Mod.Phys. 94, 029901 (2022)], 14 arXiv:1705.00141 [hep-ph]

    2018 arXiv

  10. [18]

    S. L. Olsen, T. Skwarnicki, and D. Zieminska, Nonstandard heavy mesons and baryons: Experimental evidence, Rev. Mod. Phys.90, 015003 (2018), arXiv:1708.04012 [hep-ph]

    2018 arXiv

  11. [19]

    Liu, H.-X

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

    2019 arXiv

  12. [20]

    Brambilla, S

    N. Brambilla, S. Eidelman, C. Hanhart, A. Nefediev, C.-P. Shen, C. E. Thomas, A. Vairo, and C.-Z. Yuan, TheXY Z states: experimental and theoretical status and perspectives, Phys. Rept.873, 1 (2020), arXiv:1907.07583 [hep-ex]

    2020

  13. [21]

    L. Meng, B. Wang, G.-J. Wang, and S.-L. Zhu, Chiral perturba- tion theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules, Phys. Rept.1019, 2266 (2023), arXiv:2204.08716 [hep-ph]

    2023

  14. [22]

    H.-X. Chen, W. Chen, X. Liu, Y .-R. Liu, and S.-L. Zhu, An updated review of the new hadron states, Rept. Prog. Phys.86, 026201 (2023), arXiv:2204.02649 [hep-ph]

    2023

  15. [23]

    Liu, Y .-W

    M.-Z. Liu, Y .-W. Pan, Z.-W. Liu, T.-W. Wu, J.-X. Lu, and L.- S. Geng, Three ways to decipher the nature of exotic hadrons: Multiplets, three-body hadronic molecules, and correlation functions, Phys. Rept.1108, 1 (2025), arXiv:2404.06399 [hep- ph]

    2025

  16. [24]

    Wang, Review of the QCD sum rules for exotic states, Front

    Z.-G. Wang, Review of the QCD sum rules for exotic states, Front. Phys. (Beijing)21, 016300 (2026), arXiv:2502.11351 [hep-ph]

    2026

  17. [25]

    Van Der Leun and C

    C. Van Der Leun and C. Alderliesten, The deuteron binding energy, Nuclear Physics A380, 261 (1982)

    1982

  18. [26]

    Horiuchi, Y

    W. Horiuchi, Y . Suzuki, T. Uesaka, and M. Miwa, Total reac- tion cross section on a deuteron target and the eclipse effect of the constituent neutron and proton, Phys. Rev. C102, 054601 (2020), arXiv:2010.09956 [nucl-th]

    2020

  19. [27]

    Greenwood and W

    R. Greenwood and W. Black, The binding energy of the deuteron determined from measurement of the hydrogen neu- tron capture gamma-ray energy, Physics Letters21, 702 (1966)

    1966

  20. [28]

    V . G. J. Stoks, R. A. M. Klomp, C. P. F. Terheggen, and J. J. de Swart, Construction of high quality N N potential models, Phys. Rev. C49, 2950 (1994), arXiv:nucl-th/9406039

    1994 arXiv

  21. [29]

    R. B. Wiringa, V . G. J. Stoks, and R. Schiavilla, An Accurate nucleon-nucleon potential with charge independence breaking, Phys. Rev. C51, 38 (1995), arXiv:nucl-th/9408016

    1995 arXiv

  22. [30]

    T.-S. Park, K. Kubodera, D.-P. Min, and M. Rho, The Power of effective field theories in nuclei: The Deuteron, N N scatter- ing and electroweak processes, Nucl. Phys. A646, 83 (1999), arXiv:nucl-th/9807054

    1999 arXiv

  23. [31]

    Hassaneen, H

    K. Hassaneen, H. Abo-Elsebaa, E. Sultan, and H. Mansour, Nuclear binding energy and symmetry energy of nuclear mat- ter with modern nucleon–nucleon potentials, Annals of Physics 326, 566 (2011)

    2011

  24. [32]

    Krebs, Nuclear Currents in Chiral Effective Field Theory, Eur

    H. Krebs, Nuclear Currents in Chiral Effective Field Theory, Eur. Phys. J. A56, 234 (2020), arXiv:2008.00974 [nucl-th]

    2020

  25. [33]

    H. A. Bethe, The Meson Theory of Nuclear Forces. Part 2. The- ory of the Deuteron, Phys. Rev.57, 390 (1940)

    1940

  26. [34]

    Machleidt, The High precision, charge dependent Bonn nucleon-nucleon potential (CD-Bonn), Phys

    R. Machleidt, The High precision, charge dependent Bonn nucleon-nucleon potential (CD-Bonn), Phys. Rev. C63, 024001 (2001), arXiv:nucl-th/0006014

    2001 arXiv

  27. [35]

    S. R. Beane, E. Chang, W. Detmold, H. W. Lin, T. C. Luu, K. Orginos, A. Parreno, M. J. Savage, A. Torok, and A. Walker- Loud (NPLQCD), The Deuteron and Exotic Two-Body Bound States from Lattice QCD, Phys. Rev. D85, 054511 (2012), arXiv:1109.2889 [hep-lat]

    2012 arXiv

  28. [36]

    Epelbaum, H.-W

    E. Epelbaum, H.-W. Hammer, and U.-G. Meißner, Modern the- ory of nuclear forces, Reviews of Modern Physics81, 1773 (2009), arXiv:0811.1338 [nucl-th]

    2009 arXiv

  29. [37]

    Machleidt and D

    R. Machleidt and D. R. Entem, Chiral effective field theory and nuclear forces, Phys. Rept.503, 1 (2011), arXiv:1105.2919 [nucl-th]

    2011 arXiv

  30. [38]

    Epelbaum, H

    E. Epelbaum, H. Krebs, and P. Reinert, High-precision nuclear forces from chiral EFT: State-of-the-art, challenges and out- look, Front. in Phys.8, 98 (2020), arXiv:1911.11875 [nucl-th]

    2020

  31. [39]

    Krebs and E

    H. Krebs and E. Epelbaum, Toward consistent nuclear interac- tions from chiral Lagrangians. II. Symmetry preserving regu- larization, Phys. Rev. C110, 044004 (2024), arXiv:2312.13932 [nucl-th]

    2024

  32. [40]

    Krebs and E

    H. Krebs and E. Epelbaum, Toward consistent nuclear interac- tions from chiral Lagrangians. I. The path-integral approach, Phys. Rev. C110, 044003 (2024), 2311.10893 [nucl-th]

    2024

  33. [41]

    M. F. M. Lutz and E. E. Kolomeitsev, Baryon resonances from chiral coupled-channel dynamics, Nucl. Phys. A755, 29 (2005), arXiv:hep-ph/0501224

    2005 arXiv

  34. [42]

    Garcia-Recio, V

    C. Garcia-Recio, V . K. Magas, T. Mizutani, J. Nieves, A. Ramos, L. L. Salcedo, and L. Tolos, The s-wave charmed baryon resonances from a coupled-channel approach with heavy quark symmetry, Phys. Rev. D79, 054004 (2009), arXiv:0807.2969 [hep-ph]

    2009 arXiv

  35. [43]

    He, Y .-T

    J. He, Y .-T. Ye, Z.-F. Sun, and X. Liu, The observed charmed hadronΛ c(2940)+ and theD ∗Ninteraction, Phys. Rev. D82, 114029 (2010), arXiv:1008.1500 [hep-ph]

    2010 arXiv

  36. [44]

    Haidenbauer, G

    J. Haidenbauer, G. Krein, U.-G. Meissner, and L. Tolos, DN interaction from meson exchange, Eur. Phys. J. A47, 18 (2011), arXiv:1008.3794 [nucl-th]

    2011 arXiv

  37. [45]

    Sakai, F.-K

    S. Sakai, F.-K. Guo, and B. Kubis, Extraction of ND scat- tering lengths from theΛ b →π −pD0 decay and proper- ties of theΣ c(2800)+, Phys. Lett. B808, 135623 (2020), arXiv:2004.09824 [hep-ph]

    2020

  38. [46]

    Yasui and K

    S. Yasui and K. Sudoh, Exotic nuclei with open heavy fla- vor mesons, Phys. Rev. D80, 034008 (2009), arXiv:0906.1452 [hep-ph]

    2009 arXiv

  39. [47]

    Yamaguchi, S

    Y . Yamaguchi, S. Ohkoda, S. Yasui, and A. Hosaka, Exotic baryons from a heavy meson and a nucleon - Positive par- ity states -, Phys. Rev. D85, 054003 (2012), arXiv:1111.2691 [hep-ph]

    2012

  40. [48]

    Yamaguchi, S

    Y . Yamaguchi, S. Yasui, and A. Hosaka, Open charm and bot- tom meson-nucleon potentials `a la the nuclear force, Phys. Rev. D106, 094001 (2022), arXiv:2206.01921 [hep-ph]

    2022

  41. [49]

    L. Zhao, H. Huang, and J. Ping,N DandN Bsystems in quark delocalization color screening model, Eur. Phys. J. A53, 28 (2017), arXiv:1612.00350 [hep-ph]

    2017 arXiv

  42. [50]

    D. R. Entem, P. G. Ortega, and F. Fern ´andez, Hadronic molecules in the heavy baryon spectrum, AIP Conf. Proc.1701, 050003 (2016)

    2016

  43. [51]

    Zhang, D

    D. Zhang, D. Yang, X.-F. Wang, and K. Nakayama, PossibleS- waveN D (∗) andN ¯B(∗) bound states in a chiral quark model, (2019), arXiv:1903.01207 [nucl-th]

    2019 arXiv

  44. [52]

    B. Wang, L. Meng, and S.-L. Zhu,D (∗)Ninteraction and the structure ofΣ c(2800)andΛ c(2940)in chiral effective field theory, Phys. Rev. D101, 094035 (2020), arXiv:2003.05688 [hep-ph]

    2020

  45. [53]

    Shen, Y .-H

    C.-W. Shen, Y .-H. Lin, and H.-J. Jing, Towards the LHCb pentaquark modes in the single-charm sector, (2025), arXiv:2511.15649 [hep-ph]

    2025

  46. [54]

    Y . Dong, A. Faessler, T. Gutsche, and V . E. Lyubovitskij, Charmed baryon Sigmac(2800) as a ND hadronic molecule, Phys. Rev. D81, 074011 (2010), arXiv:1002.0218 [hep-ph]

    2010 arXiv

  47. [55]

    P. G. Ortega, D. R. Entem, and F. Fernandez, Quark model description of theΛ c(2940)+ as a molecularD ∗Nstate and the possible existence of theΛb(6248), Phys. Lett. B718, 1381 (2013), arXiv:1210.2633 [hep-ph]. 15

    2013 arXiv

  48. [56]

    Zhang,S-waveD (∗)Nmolecular states:Σ c(2800) andΛ c(2940)+?, Phys

    J.-R. Zhang,S-waveD (∗)Nmolecular states:Σ c(2800) andΛ c(2940)+?, Phys. Rev. D89, 096006 (2014), arXiv:1212.5325 [hep-ph]

    2014 arXiv

  49. [57]

    Aaijet al.(LHCb), Study of theD 0pamplitude inΛ 0 b → D0pπ− decays, JHEP05, 030, arXiv:1701.07873 [hep-ex]

    R. Aaijet al.(LHCb), Study of theD 0pamplitude inΛ 0 b → D0pπ− decays, JHEP05, 030, arXiv:1701.07873 [hep-ex]

    arXiv

  50. [58]

    Acharyaet al.(ALICE), First study of the two-body scatter- ing involving charm hadrons, Phys

    S. Acharyaet al.(ALICE), First study of the two-body scatter- ing involving charm hadrons, Phys. Rev. D106, 052010 (2022), arXiv:2201.05352 [nucl-ex]

    2022

  51. [59]

    Garcilazo, A

    H. Garcilazo, A. Valcarce, and T. F. Caram ´es, Three-body sys- tems with open flavor heavy mesons, Phys. Rev. D96, 074009 (2017)

    2017

  52. [60]

    Luo, T.-W

    S.-Q. Luo, T.-W. Wu, M.-Z. Liu, L.-S. Geng, and X. Liu, Triple- charm molecular states composed of D*D*D and D*D*D*, Phys. Rev. D105, 074033 (2022), arXiv:2111.15079 [hep-ph]

    2022

  53. [61]

    Fu, Y .-H

    H.-L. Fu, Y .-H. Lin, F.-K. Guo, H.-W. Hammer, U.-G. Meißner, A. Rusetsky, and X. Zhang, Exploring Efimov states in D ∗D∗D∗ and DD ∗D∗ three-body systems, JHEP07, 081, arXiv:2503.19709 [hep-ph]

  54. [62]

    Wu, M.-Z

    T.-W. Wu, M.-Z. Liu, and L.-S. Geng, Implication of the Existence of JPC=0– D¯sDK Bound State on the Nature of Ds0*(2317), and a New Configuration of Exotic State, Phys. Rev. Lett.135, 031902 (2025), arXiv:2501.11358 [hep-ph]

    2025

  55. [63]

    Dot ´e, M

    A. Dot ´e, M. Bayar, C. W. Xiao, T. Hyodo, M. Oka, and E. Oset, A narrow quasi-bound state of theDN Nsystem, Nucl. Phys. A914, 499 (2013)

    2013

  56. [64]

    Hiyama, Y

    E. Hiyama, Y . Kino, and M. Kamimura, Gaussian expansion method for few-body systems, Prog. Part. Nucl. Phys.51, 223 (2003)

    2003

  57. [65]

    Aguilar and J

    J. Aguilar and J. M. Combes, A class of analytic perturbations for one-body schroedinger hamiltonians, Commun. Math. Phys. 22, 269 (1971)

    1971

  58. [66]

    Balslev and J

    E. Balslev and J. M. Combes, Spectral properties of many- body schroedinger operators with dilatation-analytic interac- tions, Commun. Math. Phys.22, 280 (1971)

    1971

  59. [67]

    H.-X. Zhu, L. Meng, Y . Ma, N. Li, W. Chen, and S.- L. Zhu, Constraining the DDD* three-body bound state via the Zc(3900) pole, Phys. Rev. D111, 094022 (2025), arXiv:2412.12816 [hep-ph]

    2025

  60. [68]

    L.-Z. Wen, Y . Ma, L. Meng, and S.-L. Zhu,ϕnn,J/ψN N, and ηcnnsystems based on hal qcd interactions, Phys. Rev. D111, 114004 (2025), arXiv:2503.11938 [hep-ph]

    2025

  61. [69]

    Y .-K. Chen, L. Meng, J.-Z. Wang, and S.-L. Zhu, Existence of the DD * ¯K* and BB *K* three-body molecular states, (2026), arXiv:2602.12010 [hep-ph]

    2026

  62. [70]

    Y . Ma, L. Meng, L.-Z. Wen, and S.-L. Zhu, Trilepton and tetralepton bound and resonant states: The QED counter- part of multiquark states, Phys. Rev. D111, 073001 (2025), arXiv:2501.00871 [hep-ph]

    2025

  63. [71]

    Wen and S.-L

    L.-Z. Wen and S.-L. Zhu, Bound and Resonant States of Muonic Few-Body Coulomb Systems: Extended Stochas- tic Variational Approach, (2025), arXiv:2512.07323 [physics.atom-ph]

    2025

  64. [72]

    Chen, W.-L

    Y .-K. Chen, W.-L. Wu, L. Meng, and S.-L. Zhu, Unified de- scription of the Qsq¯q¯molecular bound states, molecular resonances, and compact tetraquark states in the quark poten- tial model, Phys. Rev. D109, 014010 (2024), arXiv:2310.14597 [hep-ph]

    2024

  65. [73]

    Ma, W.-L

    Y . Ma, W.-L. Wu, L. Meng, Y .-K. Chen, and S.-L. Zhu, Fully strange tetraquark resonant states as the cousins of X(6900), Phys. Rev. D110, 074026 (2024), arXiv:2408.00503 [hep-ph]

    2024

  66. [74]

    Meng, Y .-K

    L. Meng, Y .-K. Chen, Y . Ma, and S.-L. Zhu, Tetraquark bound states in constituent quark models: Benchmark test calcula- tions, Phys. Rev. D108, 114016 (2023), arXiv:2310.13354 [hep-ph]

    2023

  67. [75]

    Wu, Y .-K

    W.-L. Wu, Y .-K. Chen, L. Meng, and S.-L. Zhu, Benchmark calculations of fully heavy compact and molecular tetraquark states, Phys. Rev. D109, 054034 (2024), arXiv:2401.14899 [hep-ph]

    2024

  68. [76]

    W.-L. Wu, Y . Ma, Y .-K. Chen, L. Meng, and S.-L. Zhu, Fully heavy tetraquark resonant states with different flavors, Phys. Rev. D110, 034030 (2024), arXiv:2406.17824 [hep-ph]

    2024

  69. [77]

    W.-L. Wu, Y . Ma, Y .-K. Chen, L. Meng, and S.-L. Zhu, Doubly heavy tetraquark bound and resonant states, Phys. Rev. D110, 094041 (2024), arXiv:2409.03373 [hep-ph]

    2024

  70. [78]

    L. D. Faddeev, Scattering Theory for a Three-Particle System, Sov. Phys. JETP12, 1014 (1961)

    1961

  71. [79]

    Akaishi and T

    Y . Akaishi and T. Yamazaki, Nuclear ¯kbound states in light nuclei, Phys. Rev. C65, 044005 (2002)

    2002

  72. [80]

    N. V . Shevchenko, A. Gal, J. Mares, and J. Revai, anti-K NN quasi-bound state and the anti-K N interaction: Coupled- channel Faddeev calculations of the anti-K NN - pi Sigma N system, Phys. Rev. C76, 044004 (2007), arXiv:0706.4393 [nucl-th]

    2007 arXiv

  73. [81]

    A. Dote, T. Hyodo, and W. Weise, K- pp system with chiral SU(3) effective interaction, Nucl. Phys. A804, 197 (2008), arXiv:0802.0238 [nucl-th]

    2008 arXiv

  74. [82]

    Agnelloet al.(FINUDA), Evidence for a kaon-bound state K −ppproduced inK − absorption reactions at rest, Phys

    M. Agnelloet al.(FINUDA), Evidence for a kaon-bound state K −ppproduced inK − absorption reactions at rest, Phys. Rev. Lett.94, 212303 (2005)

    2005

  75. [83]

    Yamazakiet al., Indication of a deeply bound compact K-pp state formed in the pp ->p Lambda K+ reaction at 2.85 GeV, Phys

    T. Yamazakiet al., Indication of a deeply bound compact K-pp state formed in the pp ->p Lambda K+ reaction at 2.85 GeV, Phys. Rev. Lett.104, 132502 (2010), arXiv:1002.3526 [nucl- ex]

    2010 arXiv

  76. [84]

    Machleidt, K

    R. Machleidt, K. Holinde, and C. Elster, The Bonn Meson Ex- change Model for the Nucleon Nucleon Interaction, Phys. Rept. 149, 1 (1987)

    1987

  77. [85]

    R. L. Workmanet al.(Particle Data Group), Review of Particle Physics, PTEP2022, 083C01 (2022)

    2022

  78. [86]

    Casalbuoni, A

    R. Casalbuoni, A. Dandrea, N. Di Bartolomeo, R. Gatto, F. Feruglio, and G. Nardulli, Phenomenology of heavy meson chiral Lagrangians, Phys. Rept.281, 145 (1997), arXiv:hep- ph/9605342

    1997

  79. [87]

    A. F. Falk and M. E. Luke, Strong decays of excited heavy mesons in chiral perturbation theory, Phys. Lett. B292, 119 (1992), arXiv:hep-ph/9206241

    1992 arXiv

  80. [88]

    M. B. Wise, Chiral perturbation theory for hadrons containing a heavy quark, Phys. Rev. D45, R2188 (1992)

    1992

  81. [89]

    Li, Z.-F

    N. Li, Z.-F. Sun, X. Liu, and S.-L. Zhu, Coupled-channel anal- ysis of the possibleD (∗)D(∗), B (∗) B (∗) andD (∗)B (∗) molec- ular states, Phys. Rev. D88, 114008 (2013), arXiv:1211.5007 [hep-ph]

    2013 arXiv

  82. [90]

    Liu, Y .-R

    X. Liu, Y .-R. Liu, W.-Z. Deng, and S.-L. Zhu, Z+(4430) as a D(1)-prime D* (D(1) D*) molecular state, Phys. Rev. D77, 094015 (2008), arXiv:0803.1295 [hep-ph]

    2008 arXiv

  83. [91]

    H.-x. Zhu, L. Meng, Y . Ma, N. Li, W. Chen, and S.-L. Zhu, Coupling constants of one-boson-exchange interactions deter- mined by x(3872), tcc(3875) and zc(3900) poles, 10.5281/zen- odo.14464767 (2024)

    2024 doi

  84. [92]

    W. J. Romo, Inner product for resonant states and shell-model applications, Nuclear Physics A116, 617 (1968)

    1968

Pith tools

Reviewed May 25, 2026 · model on record in the stance chip above.