pith. machine review for the scientific record. sign in

arxiv: 2602.18075 · v2 · submitted 2026-02-20 · ✦ hep-ph

Recognition: 2 theorem links

· Lean Theorem

Hidden-charm uds\,cbar c pentaquarks as flavor eigenstates in a constituent quark model

M.C. Gordillo , J.M. Alcaraz-Pelegrina , J. Segovia
Authors on Pith no claims yet

Pith reviewed 2026-05-15 21:05 UTC · model grok-4.3

classification ✦ hep-ph
keywords pentaquarkshidden-charmSU(3) flavorconstituent quark modeldiffusion Monte CarloP_cs(4338)P_cs(4459)
0
0 comments X

The pith

Requiring SU(3) flavor eigenstates in udsc pentaquarks produces two masses matching the observed P_cs(4338) and P_cs(4459).

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

A non-relativistic constituent quark model solves the Schrödinger equation for udsc bar c pentaquarks using diffusion Monte Carlo. States fixed in parity, color, spin and isospin (I=0, J^P=1/2^-) yield only one mass matching experiment. Adding the condition that the wave function is an eigenvector of the SU(3) flavor operator gives two structures whose calculated masses align with those extracted from the J/ψΛ spectrum. The model also predicts two additional states that lie below the J/ψΛ threshold but above the η_cΛ threshold and thus would not be seen in the J/ψΛ channel. Without the flavor condition only a single structure fits the data.

Core claim

The paper establishes that imposing the condition that the total wavefunction of the udsc bar c pentaquark is an eigenvector of the SU(3) flavor operator, in addition to having well-defined parity, color, spin and isospin, yields two structures with masses compatible with the P_cs(4338) and P_cs(4459) observed in the J/ψΛ spectrum.

What carries the argument

Diffusion Monte Carlo solution of the five-body Schrödinger equation with the wavefunction constrained to be an SU(3) flavor eigenvector.

If this is right

  • Two pentaquark structures have masses matching the experimental P_cs(4338) and P_cs(4459).
  • Two states are predicted below the J/ψΛ threshold but above the η_cΛ threshold.
  • These additional states would not appear in the J/ψΛ decay channel.
  • Imposing only the I=0 condition produces a single structure compatible with the quantum numbers but with mass below the J/ψΛ threshold.

Where Pith is reading between the lines

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

  • The flavor eigenstate requirement may lead to specific selection rules in production and decay processes.
  • Search for the predicted lower-mass states in the η_cΛ invariant mass spectrum could test the model.
  • Similar flavor constraints might apply to other multiquark systems with strange and charm content.

Load-bearing premise

The assumption that the total wavefunction must be an eigenvector of the SU(3) flavor operator to explain the two observed pentaquarks.

What would settle it

Observation of only one resonance instead of two in the J/ψΛ spectrum near the predicted masses, or failure to detect the two additional states below the J/ψΛ threshold in the η_cΛ channel.

read the original abstract

We use a diffusion Monte Carlo (DMC) algorithm to solve the Schr\"odinger equation that describes $udsc\bar c$ pentaquarks within the framework of a non-relativistic constituent quark model. We considered only multiquark states with defined values of parity, color, spin and isospin, selected to be compatible with the experimentally favored assignment $J^P=1/2^-$ for one of the candidates, and assumed $I=0$. However, we found that, to explain the existence of the $P_{cs}(4338)$ and $P_{cs}(4459)$ pentaquarks, we need the total wavefunction to be also an eigenvector of the SU(3) {\em flavor} operator. When we impose that condition, we obtain two structures compatible with the masses extracted from the $J/\psi\Lambda$ spectrum. In addition, two states are predicted below the $J/\psi\Lambda$ threshold but above the $\eta_c\Lambda$ one that would not appear in that channel. If we only impose the $I=0$ condition, we obtain a {\em single} (not two) structure compatible with the experimental quantum numbers, with a mass below the $J/\psi\Lambda$ threshold.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript uses a diffusion Monte Carlo algorithm to solve the non-relativistic Schrödinger equation for udsc c-bar pentaquarks in a constituent quark model. States are restricted to J^P=1/2^-, I=0, and additionally required to be eigenvectors of the SU(3) flavor operator; this yields two structures whose masses match the observed P_cs(4338) and P_cs(4459) in the J/ψΛ spectrum. Imposing only I=0 produces a single state below the J/ψΛ threshold. Two further states are predicted below the J/ψΛ but above the η_cΛ threshold.

Significance. If the numerical masses are robust, the result suggests that an explicit SU(3) flavor constraint can select which pentaquark configurations appear in experiment despite explicit breaking in the Hamiltonian. The prediction of additional states below the J/ψΛ threshold but above η_cΛ provides a concrete, falsifiable signature for future searches. The approach also demonstrates the utility of DMC for multiquark systems with flavor constraints.

major comments (2)
  1. The central claim rests on imposing that the total wavefunction be an SU(3) flavor eigenvector in addition to I=0. However, the model Hamiltonian contains flavor-dependent constituent masses and potentials for u, d, s, c quarks, which explicitly break SU(3)_f so that [H, T^a] ≠ 0. No dynamical justification is given for why the eigenstates of this broken Hamiltonian must lie in a single SU(3) representation rather than allowing mixing; the constraint therefore appears to be an external selection rule rather than a consequence of the dynamics.
  2. The abstract and method description provide no information on the explicit form of the interquark potential, the number of DMC walkers, time-step size, convergence criteria, or statistical/systematic error estimates on the extracted masses. Without these, it is impossible to judge whether the reported distinction between the single I=0 state and the two flavor-eigenstate structures is numerically stable or within the quoted experimental mass windows.
minor comments (2)
  1. The abstract states that two states are predicted below the J/ψΛ threshold but above the η_cΛ one; their explicit quantum numbers (color, spin, flavor representation) and decay channels should be tabulated for clarity.
  2. Notation for the SU(3) flavor operator and the precise definition of 'flavor eigenstates' (which representation, which Casimir) should be stated explicitly in the text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and valuable comments on our manuscript. We address each major comment below and will revise the manuscript to improve clarity and completeness.

read point-by-point responses

  1. Referee: The central claim rests on imposing that the total wavefunction be an SU(3) flavor eigenvector in addition to I=0. However, the model Hamiltonian contains flavor-dependent constituent masses and potentials for u, d, s, c quarks, which explicitly break SU(3)_f so that [H, T^a] ≠ 0. No dynamical justification is given for why the eigenstates of this broken Hamiltonian must lie in a single SU(3) representation rather than allowing mixing; the constraint therefore appears to be an external selection rule rather than a consequence of the dynamics.

    Authors: We acknowledge that the Hamiltonian explicitly breaks SU(3) due to flavor-dependent masses and potentials, so the eigenstate constraint is not a dynamical consequence. It is imposed phenomenologically because SU(3) remains a useful approximate symmetry in the light-quark sector; this selection allows us to isolate configurations that simultaneously reproduce both observed P_cs states. We will add a dedicated paragraph in the introduction and discussion sections clarifying this motivation, noting the explicit breaking, and explaining that mixing is not explored in the present exploratory study. The additional predicted states below the J/ψΛ threshold remain a concrete, falsifiable outcome of the assumption. revision: partial

  2. Referee: The abstract and method description provide no information on the explicit form of the interquark potential, the number of DMC walkers, time-step size, convergence criteria, or statistical/systematic error estimates on the extracted masses. Without these, it is impossible to judge whether the reported distinction between the single I=0 state and the two flavor-eigenstate structures is numerically stable or within the quoted experimental mass windows.

    Authors: We agree that the technical implementation details were insufficient. In the revised manuscript we will expand the methods section to specify the explicit interquark potential (the standard form employed in our prior multiquark studies), the number of DMC walkers (several thousand), the time-step sizes used, the convergence criteria based on energy stabilization over imaginary time, and both statistical and systematic error estimates obtained by varying parameters and monitoring fluctuations. These additions will allow readers to assess the numerical robustness of the distinction between the I=0-only and flavor-eigenstate results. revision: yes

Circularity Check

0 steps flagged

No significant circularity: masses from independent DMC solution of Schrödinger equation under explicit constraints

full rationale

The derivation consists of numerically solving the five-body Schrödinger equation via diffusion Monte Carlo within a fixed constituent quark model Hamiltonian (with parameters taken from prior meson/baryon fits). The only load-bearing steps are (i) restricting to J^P=1/2^-, I=0 states and (ii) optionally requiring the wave function to be an eigenvector of the SU(3) flavor generators. Both are explicit external constraints imposed on the trial wave function before the Monte Carlo sampling; the resulting energies are genuine outputs of the stochastic integration and are not algebraically identical to any fitted quantity or to the experimental masses. No equation in the paper equates a computed mass to a parameter that was itself determined from the P_cs states, nor does any self-citation supply a uniqueness theorem that forces the SU(3) eigenstate condition. The model Hamiltonian explicitly breaks SU(3)_f through unequal constituent masses, but that is a statement about dynamical justification, not a circular reduction of the numerical result to its inputs. Hence the central claim—that two structures appear only after the extra flavor constraint—remains a non-trivial numerical finding rather than a tautology.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard assumptions of the non-relativistic constituent quark model and the numerical solution method, with parameters typically determined from prior data on mesons and baryons.

free parameters (1)
  • constituent quark masses and potential parameters
    Constituent quark models require parameters fitted to known hadron spectra to reproduce masses; exact values not specified in abstract.
axioms (2)
  • domain assumption Non-relativistic approximation for quark dynamics
    The Schrödinger equation is solved non-relativistically for the multiquark system.
  • domain assumption Constituent quark model with color and spin-dependent interactions
    Standard framework assumed for describing multiquark states with effective potentials.

pith-pipeline@v0.9.0 · 5547 in / 1679 out tokens · 112889 ms · 2026-05-15T21:05:09.744964+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

68 extracted references · 68 canonical work pages · 7 internal anchors

  1. [1]

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

    Aaij, R., et al. (LHCb), 2015. Observation ofJ/ψpResonances Consistent with Pentaquark States inΛ0 b →J/ψK −pDecays. Phys. Rev. Lett. 115, 072001. doi:10.1103/PhysRevLett.115.072001,arXiv:1507.03414

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.115.072001 2015

  2. [2]

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

    Aaij, R., et al. (LHCb), 2019. Observation of a narrow pentaquark state, Pc(4312)+, and of two-peak structure of thePc(4450)+. Phys. Rev. Lett. 122, 222001. doi:10.1103/PhysRevLett.122.222001,arXiv:1904.03947

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.122.222001 2019

  3. [3]

    EvidenceofaJ/ψΛstructureandobservation of excitedΞ− states in theΞ− b →J/ψΛK − decay

    Aaij, R., etal.(LHCb), 2021. EvidenceofaJ/ψΛstructureandobservation of excitedΞ− states in theΞ− b →J/ψΛK − decay. Sci. Bull. 66, 1278–1287. doi:10.1016/j.scib.2021.02.030,arXiv:2012.10380

    work page doi:10.1016/j.scib.2021.02.030 2021

  4. [4]

    (LHCb), 2023

    Aaij, R., et al. (LHCb), 2023. Observation of a J/ψΛResonance Consistent with a Strange Pentaquark Candidate in B-→J/ψΛp¯De- cays. Phys. Rev. Lett. 131, 031901. doi:10.1103/PhysRevLett.131.031901, arXiv:2210.10346

    work page doi:10.1103/physrevlett.131.031901 2023

  5. [5]

    Diffusion Monte Carlo cal- culations of fully heavy compact hexaquarks

    Alcaraz-Pelegrina, J.M., Gordillo, M.C., 2022. Diffusion Monte Carlo cal- culations of fully heavy compact hexaquarks. Phys. Rev. D 106, 114028. doi:10.1103/PhysRevD.106.114028,arXiv:2205.13886

    work page doi:10.1103/physrevd.106.114028 2022

  6. [6]

    The quark structure of hadrons

    Amsler, C., 2018. The quark structure of hadrons. Lecture Notes in Physics

    work page 2018

  7. [7]

    Investigation of the strange pen- taquark candidate PψsΛ(4338)0 recently observed by LHCb

    Azizi, K., Sarac, Y., Sundu, H., 2023. Investigation of the strange pen- taquark candidate PψsΛ(4338)0 recently observed by LHCb. Phys. Rev. D 108, 074010. doi:10.1103/PhysRevD.108.074010,arXiv:2304.00604

    work page doi:10.1103/physrevd.108.074010 2023

  8. [8]

    TheLHCbstatePψsΛ(4338)asatriangle singularity

    Burns, T.J., Swanson, E.S., 2023. TheLHCbstatePψsΛ(4338)asatriangle singularity. Phys. Lett. B 838, 137715. doi:10.1016/j.physletb.2023.137715, arXiv:2208.05106. 12

    work page doi:10.1016/j.physletb.2023.137715 2023

  9. [9]

    Hadronic molecules in B decays

    Chen, H.X., 2022. Hadronic molecules in B decays. Phys. Rev. D 105, 094003. doi:10.1103/PhysRevD.105.094003,arXiv:2103.08586

    work page doi:10.1103/physrevd.105.094003 2022

  10. [10]

    Establishing the first hidden-charm pentaquark with strangeness

    Chen, H.X., Chen, W., Liu, X., Liu, X.H., 2021. Establishing the first hidden-charm pentaquark with strangeness. Eur. Phys. J. C 81, 409. doi:10.1140/epjc/s10052-021-09196-4,arXiv:2011.01079

    work page doi:10.1140/epjc/s10052-021-09196-4 2021

  11. [11]

    A review of the open charm and open bottom systems

    Chen, H.X., Chen, W., Liu, X., Liu, Y.R., Zhu, S.L., 2017. A review of the open charm and open bottom systems. Rept. Prog. Phys. 80, 076201. doi:10.1088/1361-6633/aa6420,arXiv:1609.08928

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1361-6633/aa6420 2017

  12. [12]

    An up- dated review of the new hadron states

    Chen, H.X., Chen, W., Liu, X., Liu, Y.R., Zhu, S.L., 2023. An up- dated review of the new hadron states. Rept. Prog. Phys. 86, 026201. doi:10.1088/1361-6633/aca3b6,arXiv:2204.02649

    work page doi:10.1088/1361-6633/aca3b6 2023

  13. [13]

    The hidden-charm pentaquark and tetraquark states

    Chen, H.X., Chen, W., Liu, X., Zhu, S.L., 2016. The hidden- charm pentaquark and tetraquark states. Phys. Rept. 639, 1–121. doi:10.1016/j.physrep.2016.05.004,arXiv:1601.02092

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physrep.2016.05.004 2016

  14. [14]

    Production of exotic hadrons in pp and nuclear collisions

    Chen, J.H., Chen, J., Guo, F.K., Ma, Y.G., Shen, C.P., Shou, Q.Y., Shou, Q., Wang, Q., Wu, J.J., Zou, B.S., 2025. Production of exotic hadrons in pp and nuclear collisions. Nucl. Sci. Tech. 36, 55. doi:10.1007/s41365-025- 01664-w,arXiv:2411.18257

    work page doi:10.1007/s41365-025- 2025

  15. [15]

    Comparison between the PψN and PψsΛsystems

    Chen, K., Lin, Z.Y., Zhu, S.L., 2022. Comparison between the PψN and PψsΛsystems. Phys. Rev. D 106, 116017. doi:10.1103/PhysRevD.106.116017,arXiv:2211.05558

    work page doi:10.1103/physrevd.106.116017 2022

  16. [16]

    Can the newly reportedP cs(4459)be a strange hidden-charmΞ c ¯D∗ molecular pentaquark? Phys

    Chen, R., 2021. Can the newly reportedP cs(4459)be a strange hidden-charmΞ c ¯D∗ molecular pentaquark? Phys. Rev. D 103, 054007. doi:10.1103/PhysRevD.103.054007,arXiv:2011.07214

    work page doi:10.1103/physrevd.103.054007 2021

  17. [17]

    Mass behavior of hidden-charm open-strange pentaquarks inspired by the establishedPc molecular states

    Chen, R., Liu, X., 2022. Mass behavior of hidden-charm open-strange pentaquarks inspired by the establishedPc molecular states. Phys. Rev. D 105, 014029. doi:10.1103/PhysRevD.105.014029,arXiv:2201.07603

    work page doi:10.1103/physrevd.105.014029 2022

  18. [18]

    A survey of heavy–heavy hadronic molecules

    Dong, X.K., Guo, F.K., Zou, B.S., 2021a. A survey of heavy–heavy hadronic molecules. Commun. Theor. Phys. 73, 125201. doi:10.1088/1572- 9494/ac27a2,arXiv:2108.02673

    work page doi:10.1088/1572-

  19. [19]

    Explaining the Many Threshold Structures in the Heavy-Quark Hadron Spectrum

    Dong, X.K., Guo, F.K., Zou, B.S., 2021b. Explaining the Many Threshold Structures in the Heavy-Quark Hadron Spectrum. Phys. Rev. Lett. 126, 152001. doi:10.1103/PhysRevLett.126.152001,arXiv:2011.14517

    work page doi:10.1103/physrevlett.126.152001 2011

  20. [20]

    Revisiting the nature of the Pc pentaquarks

    Du, M.L., Baru, V., Guo, F.K., Hanhart, C., Meißner, U.G., Oller, J.A., Wang, Q., 2021. Revisiting the nature of the Pc pentaquarks. JHEP 08,

    work page 2021

  21. [21]

    doi:10.1007/JHEP08(2021)157,arXiv:2102.07159. 13

    work page doi:10.1007/jhep08(2021)157 2021

  22. [22]

    A new look at the Pcs states from a molecular per- spective

    Feijoo, A., Wang, W.F., Xiao, C.W., Wu, J.J., Oset, E., Nieves, J., Zou, B.S., 2023. A new look at the Pcs states from a molecular per- spective. Phys. Lett. B 839, 137760. doi:10.1016/j.physletb.2023.137760, arXiv:2212.12223

    work page doi:10.1016/j.physletb.2023.137760 2023

  23. [23]

    Lattice perspectives on doubly heavy tetraquarks

    Francis, A., 2025. Lattice perspectives on doubly heavy tetraquarks. Prog. Part. Nucl. Phys. 140, 104143. doi:10.1016/j.ppnp.2024.104143, arXiv:2502.04701

    work page doi:10.1016/j.ppnp.2024.104143 2025

  24. [24]

    A Schematic Model of Baryons and Mesons

    Gell-Mann, M., 1964. A Schematic Model of Baryons and Mesons. Phys. Lett. 8, 214–215. doi:10.1016/S0031-9163(64)92001-3

    work page doi:10.1016/s0031-9163(64)92001-3 1964

  25. [25]

    Rich structure of the hidden-charm pentaquarks near threshold regions

    Giachino, A., Hosaka, A., Santopinto, E., Takeuchi, S., Takizawa, M., Yamaguchi, Y., 2023. Rich structure of the hidden-charm pentaquarks near threshold regions. Phys. Rev. D 108, 074012. doi:10.1103/PhysRevD.108.074012,arXiv:2209.10413

    work page doi:10.1103/physrevd.108.074012 2023

  26. [26]

    Asymptotic mass limit of large fully heavy compact multiquarks

    Gordillo, M.C., Alcaraz-Pelegrina, J.M., 2023. Asymptotic mass limit of large fully heavy compact multiquarks. Phys. Rev. D 108, 054027. doi:10.1103/PhysRevD.108.054027,arXiv:2307.08408

    work page doi:10.1103/physrevd.108.054027 2023

  27. [27]

    Diffusion Monte Carlo calculations of fully-heavy multiquark bound states

    Gordillo, M.C., De Soto, F., Segovia, J., 2020. Diffusion Monte Carlo calculations of fully-heavy multiquark bound states. Phys. Rev. D 102, 114007. doi:10.1103/PhysRevD.102.114007,arXiv:2009.11889

    work page doi:10.1103/physrevd.102.114007 2020

  28. [28]

    Structure of the X(3872) as explained by a diffusion Monte Carlo calculation

    Gordillo, M.C., De Soto, F., Segovia, J., 2021. Structure of the X(3872) as explained by a diffusion Monte Carlo calculation. Phys. Rev. D 104, 054036. doi:10.1103/PhysRevD.104.054036,arXiv:2105.11976

    work page doi:10.1103/physrevd.104.054036 2021

  29. [29]

    X(3872)’s excitation and its connection with production at hadron colliders

    Gordillo, M.C., De Soto, F., Segovia, J., 2022. X(3872)’s excitation and its connection with production at hadron colliders. Phys. Rev. D 106, 094004. doi:10.1103/PhysRevD.106.094004,arXiv:2209.04221

    work page doi:10.1103/physrevd.106.094004 2022

  30. [30]

    Heavy multiquark systems as clusters of smaller units: A diffusion Monte Carlo calculation

    Gordillo, M.C., Segovia, J., 2024. Heavy multiquark systems as clusters of smaller units: A diffusion Monte Carlo calculation. Phys. Rev. D 109, 094032. doi:10.1103/PhysRevD.109.094032,arXiv:2403.15000

    work page doi:10.1103/physrevd.109.094032 2024

  31. [31]

    Diffusion Monte Carlo calculation of compact Tcs0 and Tcs¯0 tetraquarks

    Gordillo, M.C., Segovia, J., 2025. Diffusion Monte Carlo calculation of compact Tcs0 and Tcs¯0 tetraquarks. Phys. Lett. B 870, 139927. doi:10.1016/j.physletb.2025.139927,arXiv:2507.10346

    work page doi:10.1016/j.physletb.2025.139927 2025

  32. [32]

    Diffusion Monte Carlo calculation of fully heavy pentaquarks

    Gordillo, M.C., Segovia, J., Alcaraz-Pelegrina, J.M., 2024. Diffusion Monte Carlo calculation of fully heavy pentaquarks. Phys. Rev. D 110, 094024. doi:10.1103/PhysRevD.110.094024,arXiv:2409.04130

    work page doi:10.1103/physrevd.110.094024 2024

  33. [33]

    Hadronic molecules

    Guo, F.K., Hanhart, C., Meißner, U.G., Wang, Q., Zhao, Q., Zou, B.S., 2018. Hadronic molecules. Rev. Mod. Phys. 90, 015004. doi:10.1103/RevModPhys.90.015004,arXiv:1705.00141. 14

    work page doi:10.1103/revmodphys.90.015004 2018

  34. [34]

    Monte Carlo Methods in ab Initio Quantum Chemistry

    Hammond, B., Lester, W., Reynolds, P., 1994. Monte Carlo Methods in ab Initio Quantum Chemistry. World Scientific, Singapore

    work page 1994

  35. [35]

    Hadronic molecules and multiquark states arXiv:2504.06043

    Hanhart, C., 2025. Hadronic molecules and multiquark states arXiv:2504.06043

    work page arXiv 2025

  36. [36]

    Tetraquarks and Pentaquarks from Quark Model Perspective

    Huang, H., Deng, C., Liu, X., Tan, Y., Ping, J., 2023. Tetraquarks and Pentaquarks from Quark Model Perspective. Symmetry 15, 1298. doi:10.3390/sym15071298

    work page doi:10.3390/sym15071298 2023

  37. [37]

    A brief guide to exotic hadrons

    Hüsken, N., Norella, E.S., Polyakov, I., 2025. A brief guide to exotic hadrons. Mod. Phys. Lett. A 40, 2530002. doi:10.1142/S0217732325300022, arXiv:2410.06923

    work page doi:10.1142/s0217732325300022 2025

  38. [38]

    Exotic Hadrons at LHCb

    Johnson, D., Polyakov, I., Skwarnicki, T., Wang, M., 2024. Exotic Hadrons at LHCb. Ann. Rev. Nucl. Part. Sci. 74, 583–612. doi:10.1146/annurev- nucl-102422-040628,arXiv:2403.04051

    work page doi:10.1146/annurev- 2024

  39. [39]

    New strange pentaquarks

    Karliner, M., Rosner, J.L., 2022. New strange pentaquarks. Phys. Rev. D 106, 036024. doi:10.1103/PhysRevD.106.036024,arXiv:2207.07581

    work page doi:10.1103/physrevd.106.036024 2022

  40. [40]

    Theoryofthe(Heavy-Quark)ExoticHadrons: APrimer for the Flavor Community

    Lebed, R.F., 2023. Theoryofthe(Heavy-Quark)ExoticHadrons: APrimer for the Flavor Community. PoS FPCP2023, 028. doi:10.22323/1.445.0028, arXiv:2308.00781

    work page doi:10.22323/1.445.0028 2023

  41. [41]

    Hidden-charm pentaquark states in a mass splitting model

    Li, S.Y., Liu, Y.R., Man, Z.L., Si, Z.G., Wu, J., 2023. Hidden-charm pentaquark states in a mass splitting model. Phys. Rev. D 108, 056015. doi:10.1103/PhysRevD.108.056015,arXiv:2307.00539

    work page doi:10.1103/physrevd.108.056015 2023

  42. [42]

    Three ways to decipher the nature of exotic hadrons: Multiplets, three- body hadronic molecules, and correlation functions

    Liu, M.Z., Pan, Y.W., Liu, Z.W., Wu, T.W., Lu, J.X., Geng, L.S., 2025. Three ways to decipher the nature of exotic hadrons: Multiplets, three- body hadronic molecules, and correlation functions. Phys. Rept. 1108, 1–108. doi:10.1016/j.physrep.2024.12.001,arXiv:2404.06399

    work page doi:10.1016/j.physrep.2024.12.001 2025

  43. [43]

    Pentaquark and Tetraquark states

    Liu, Y.R., Chen, H.X., Chen, W., Liu, X., Zhu, S.L., 2019. Pen- taquark and Tetraquark states. Prog. Part. Nucl. Phys. 107, 237–320. doi:10.1016/j.ppnp.2019.04.003,arXiv:1903.11976

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.ppnp.2019.04.003 2019

  44. [44]

    Searching for a $P_{cs}(4200)$ state in the $\Lambda_b\to\phi\eta_c\Lambda$ reaction

    Lyu, W., Oset, E., 2026. Searching for apcs(4200)state in theλ b →ϕη cλ reactionarXiv:2601.20630

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  45. [45]

    Towards a theory of hadron resonances

    Mai, M., Meißner, U.G., Urbach, C., 2023. Towards a theory of hadron resonances. Phys. Rept. 1001, 1–66. doi:10.1016/j.physrep.2022.11.005, arXiv:2206.01477

    work page doi:10.1016/j.physrep.2022.11.005 2023

  46. [46]

    The pentaquark spectrum from Fermi statistics

    Maiani, L., Polosa, A.D., Riquer, V., 2023. The pentaquark spectrum from Fermi statistics. Eur. Phys. J. C 83, 378. doi:10.1140/epjc/s10052-023- 11492-0,arXiv:2303.04056. 15

    work page doi:10.1140/epjc/s10052-023- 2023

  47. [47]

    Double thresholds distort the line shapes of the PψsΛ(4338)0 resonance

    Meng, L., Wang, B., Zhu, S.L., 2023. Double thresholds distort the line shapes of the PψsΛ(4338)0 resonance. Phys. Rev. D 107, 014005. doi:10.1103/PhysRevD.107.014005,arXiv:2208.03883

    work page doi:10.1103/physrevd.107.014005 2023

  48. [48]

    Navas et al

    Navas, S., et al. (Particle Data Group), 2024. Review of particle physics. Phys. Rev. D 110, 030001. doi:10.1103/PhysRevD.110.030001

    work page doi:10.1103/physrevd.110.030001 2024

  49. [49]

    Coupling hadron-hadron thresh- olds within a chiral quark model approach

    Ortega, P.G., Entem, D.R., 2021. Coupling hadron-hadron thresh- olds within a chiral quark model approach. Symmetry 13, 279. doi:10.3390/sym13020279,arXiv:2012.10105

    work page doi:10.3390/sym13020279 2021

  50. [50]

    Strange hidden-charm PψsΛ(4459) and PψsΛ(4338) pentaquarks and additional PψsΛ, PψsΣand PψssN candidates in a quark model approach

    Ortega, P.G., Entem, D.R., Fernandez, F., 2023. Strange hidden-charm PψsΛ(4459) and PψsΛ(4338) pentaquarks and additional PψsΛ, PψsΣand PψssN candidates in a quark model approach. Phys. Lett. B 838, 137747. doi:10.1016/j.physletb.2023.137747,arXiv:2210.04465

    work page doi:10.1016/j.physletb.2023.137747 2023

  51. [51]

    Diquonia and potential models

    Semay, C., Silvestre-Brac, B., 1994. Diquonia and potential models. Z. Phys. C 61, 271–275. doi:10.1007/BF01413104

    work page doi:10.1007/bf01413104 1994

  52. [52]

    Hidden charm pentaquark states in a diquark model

    Shi, P.P., Huang, F., Wang, W.L., 2021. Hidden charm pentaquark states in a diquark model. Eur. Phys. J. A 57, 237. doi:10.1140/epja/s10050-021- 00542-4,arXiv:2107.08680

    work page doi:10.1140/epja/s10050-021- 2021

  53. [53]

    Spectrum and static properties of heavy baryons

    Silvestre-Brac, B., 1996. Spectrum and static properties of heavy baryons. Few Body Syst. 20, 1–25. doi:10.1007/s006010050028

    work page doi:10.1007/s006010050028 1996

  54. [54]

    Emergence of molecular-type character- istic spectrum of hidden-charm pentaquark with strangeness embod- ied in the PψsΛ(4338) and Pcs(4459)

    Wang, F.L., Liu, X., 2022. Emergence of molecular-type character- istic spectrum of hidden-charm pentaquark with strangeness embod- ied in the PψsΛ(4338) and Pcs(4459). Phys. Lett. B 835, 137583. doi:10.1016/j.physletb.2022.137583,arXiv:2207.10493

    work page doi:10.1016/j.physletb.2022.137583 2022

  55. [55]

    Colloquium: Hadron Production in Open-charm Meson Pair at $e^+e^-$ Collider

    Wang, X., Liu, X., Gao, Y., 2025. Hadron Production in Open-charm Meson Pair ate+e− ColliderarXiv:2502.15117

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  56. [56]

    Study of isospin eigenstates of the pen- taquark molecular states with strangeness

    Wang, X.W., Wang, Z.G., 2022. Study of isospin eigenstates of the pen- taquark molecular states with strangeness. Int. J. Mod. Phys. A 37, 2250189. doi:10.1142/S0217751X22501895,arXiv:2205.02530

    work page doi:10.1142/s0217751x22501895 2022

  57. [57]

    Analysis of Pcs(4338) and related pen- taquark molecular states via QCD sum rules*

    Wang, X.W., Wang, Z.G., 2023. Analysis of Pcs(4338) and related pen- taquark molecular states via QCD sum rules*. Chin. Phys. C 47, 013109. doi:10.1088/1674-1137/ac9aab,arXiv:2207.06060

    work page doi:10.1088/1674-1137/ac9aab 2023

  58. [58]

    Analysis of theP cs(4459)as the hidden-charm pen- taquark state with QCD sum rules

    Wang, Z.G., 2021. Analysis of theP cs(4459)as the hidden-charm pen- taquark state with QCD sum rules. Int. J. Mod. Phys. A 36, 2150071. doi:10.1142/S0217751X21500718,arXiv:2011.05102

    work page doi:10.1142/s0217751x21500718 2021

  59. [59]

    Review of the QCD sum rules for exotic states arXiv:2502.11351

    Wang, Z.G., 2025. Review of the QCD sum rules for exotic states arXiv:2502.11351. 16

    work page arXiv 2025

  60. [60]

    Molecular nature ofP cs(4459) and its heavy quark spin partners

    Xiao, C.W., Wu, J.J., Zou, B.S., 2021. Molecular nature ofP cs(4459) and its heavy quark spin partners. Phys. Rev. D 103, 054016. doi:10.1103/PhysRevD.103.054016,arXiv:2102.02607

    work page doi:10.1103/physrevd.103.054016 2021

  61. [61]

    Yan, M.J., Peng, F.Z., Sánchez Sánchez, M., Pavon Valderrama, M.,

    work page

  62. [62]

    PψsΛ(4338) pentaquark and its partners in the molecular pic- ture. Phys. Rev. D 107, 074025. doi:10.1103/PhysRevD.107.074025, arXiv:2207.11144

    work page doi:10.1103/physrevd.107.074025

  63. [63]

    Tetra- and penta-quark structures in the constituent quark model

    Yang, G., Ping, J., Segovia, J., 2020. Tetra- and penta-quark structures in the constituent quark model. Symmetry 12, 1869. doi:10.3390/sym12111869,arXiv:2009.00238

    work page doi:10.3390/sym12111869 2020

  64. [64]

    Molecular Pψpentaquarks from light-meson exchange saturation

    Yang, Z.Y., Peng, F.Z., Yan, M.J., Sánchez Sánchez, M., Pavon Valder- rama, M., 2025. Molecular Pψpentaquarks from light-meson exchange saturation. Phys. Rev. D 111, 014012. doi:10.1103/PhysRevD.111.014012, arXiv:2211.08211

    work page doi:10.1103/physrevd.111.014012 2025

  65. [65]

    PψsΛ(4459) and PψsΛ(4338) as molec- ular states in J/ψΛinvariant mass spectra

    Zhu, J.T., Kong, S.Y., He, J., 2023. PψsΛ(4459) and PψsΛ(4338) as molec- ular states in J/ψΛinvariant mass spectra. Phys. Rev. D 107, 034029. doi:10.1103/PhysRevD.107.034029,arXiv:2211.06232

    work page doi:10.1103/physrevd.107.034029 2023

  66. [66]

    Zhu, J.T., Song, L.Q., He, J., 2021.Pcs(4459)and other possible molecular states fromΞ (∗) c ¯D(∗) andΞ ′ c ¯D(∗) interactions. Phys. Rev. D 103, 074007. doi:10.1103/PhysRevD.103.074007,arXiv:2101.12441

    work page doi:10.1103/physrevd.103.074007 2021

  67. [67]

    Building up the spectrum of pentaquark states as hadronic molecules

    Zou, B.S., 2021. Building up the spectrum of pentaquark states as hadronic molecules. Sci. Bull. 66, 1258. doi:10.1016/j.scib.2021.04.023, arXiv:2103.15273

    work page doi:10.1016/j.scib.2021.04.023 2021

  68. [68]

    Developments in the Quark Theory of Hadrons

    Zweig, G., 1964. Developments in the Quark Theory of Hadrons. 17

    work page 1964