Pith. sign in

REVIEW 3 major objections 9 minor 98 references

Bag model IDs T_cs(2900) as compact tetraquark, not molecule

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · glm-5.2

2026-07-08 23:48 UTC pith:NX6UJKP6

load-bearing objection MIT bag model with radius-dependent CEI applied to singly heavy tetraquarks; compactness criterion is quantitatively fragile for the headline state the 3 major comments →

arxiv 2607.05793 v1 pith:NX6UJKP6 submitted 2026-07-07 hep-ph

Compactness, mass spectra, and strong stability of singly heavy tetraquarks

Wen-Nian Liu , Kai-Kai Zhang , Duo-Jie jia , Fu-Quan Dou This is my paper
classification hep-ph PACS 12.39.Ba12.39.Jh
keywords heavysystemscompactmassradiussinglyspectrastrong
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper argues that the experimentally observed T_c̄s0(2900) — a resonance seen in D_sπ decays with a mass near 2908 MeV and a broad width of 136 MeV — is a compact singly heavy tetraquark rather than a loosely bound molecular state. The authors extend the MIT bag model by introducing a chromoelectric interaction (CEI) term that scales with the inverse bag radius, parameterized from heavy-meson spectroscopy and extended to four-quark systems via color factors. Using the bag confinement energy E_CON as a compactness criterion, they compute mass spectra and S-wave decay properties for five families of singly heavy tetraquarks (with charm and bottom quarks, various light-quark and strange-quark configurations). A specific state, T_ncs̄n̄(0+, 2.925), emerges with negative confinement energy (E_CON = -36 MeV), a bag radius below the critical limit R_c = 5.615 GeV^-1, and a large D_sπ decay factor (k·|c_i|² = 211 MeV), all consistent with the experimental mass, width, and decay channel of T_c̄s0(2900). The paper further predicts that high-spin states in the singly charmed sector generally fail to form compact structures (positive E_CON), while the bottom sector is more robustly compact due to the heavier quark suppressing the bag radius.

Core claim

The central discovery is that the state T_ncs̄n̄(0+, 2.925) satisfies three simultaneous criteria — negative bag confinement energy, sub-critical bag radius, and a large D_sπ decay factor — that together identify it as a compact tetraquark candidate matching the experimentally observed T_c̄s0(2900). The paper also establishes that compactness in singly charmed tetraquarks is inherently precarious: the bag radius sits near the confinement limit R_c ≈ 1.12 fm (matching the lattice QCD string-breaking distance), so only specific flavor-spin combinations remain bound, while the bottom sector is more reliably compact.

What carries the argument

The MIT bag model mass formula M(R) = Σω_i + (4/3)πR³B - Z_0/R + H_CMI + H_CEI, where H_CEI is the newly proposed chromoelectric interaction term H_CEI = -Σ⟨λ_i·λ_j⟩(3B̄_M R̄_M)/(16R). The confinement energy E_CON = (4/3)πR³B - Z_0/R serves as the compactness criterion: when E_CON < 0 and R < R_c, the state can form a compact single-bag configuration. The color-singlet weight |c_i|² in the 8_c⊗8_c / 1_c⊗1_c representation determines the S-wave decay factor k·|c_i|², which estimates partial widths.

Load-bearing premise

The CEI parameterization assumes that short-range binding energies extracted from five heavy mesons can be linearly scaled to arbitrary multiquark systems using color factors and a 1/R dependence, without independent validation that the same interaction applies when additional light quarks and different color structures are present.

What would settle it

If the predicted T_ncs̄n̄(0+, 2.925) state is excluded as a compact tetraquark — for instance, if future measurements show the D_sπ channel is dynamically suppressed relative to D*K*, or if the mass or quantum numbers disagree with refined experimental determinations of T_c̄s0(2900) — the central identification would fail. Additionally, if the CEI scaling from mesons to tetraquarks produces masses inconsistent with newly discovered tetraquark states across the five flavor families, the parameterization itself would be questioned.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The D_sπ decay channel of T_c̄s0(2900) is naturally explained as an OZI-superallowed process if the state is compact, whereas a D*K* molecular interpretation would suppress this channel — providing a discriminating observable.
  • Several predicted narrow compact states (e.g., T_ncs̄n̄(0+, 2.472), T_sc̄s̄n̄(0+, 2.699), T_sb̄s̄s̄(1+, 6.523)) with threshold-suppressed decay factors are identified as targets for future experimental searches.
  • The confinement-limit criterion predicts that all J^P = 2+ singly charmed tetraquark states are non-compact, which could be tested by searching for or excluding high-spin resonances in the relevant channels.
  • The bottom tetraquark sector is predicted to host more robustly compact states than the charm sector, suggesting that future experimental programs at higher energy thresholds may find cleaner compact tetraquark signals there.

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

3 major / 9 minor

Summary. The paper proposes a Coulomb-like chromoelectric interaction (CEI) term, parameterized by the bag radius R, within the MIT bag model framework. The CEI parameters are fitted to heavy meson spectra and then scaled to multiquark systems via color factors and a 1/R dependence. The authors use this unified variational framework to compute mass spectra of singly, doubly, and fully heavy baryons (validating against lattice QCD and experiment), and then systematically investigate the mass spectra, compactness, and S-wave strong decay properties of various singly heavy tetraquark systems (nQn̄n̄, nQs̄n̄, Qsn̄n̄, sQs̄n̄, sQs̄s̄). The central phenomenological claim is that the state T_ncs̄n̄(0+, 2.925) is a compact tetraquark candidate, identified with the experimentally observed T_c̄s0^a(2900), supported by a negative confinement energy E_CON = -36 MeV and a large D_sπ decay factor (k·|c_i|² = 211 MeV).

Significance. The paper provides a systematic and comprehensive survey of singly heavy tetraquark spectra within a well-defined model framework. The unified variational treatment of the CEI (Eq. 14) is a reasonable methodological step that connects meson and baryon spectroscopy within the bag model. The baryon mass predictions in Table II agree with lattice QCD within ~30-80 MeV, which is typical for bag model accuracy and provides a useful calibration. The identification of specific compact tetraquark candidates with falsifiable mass and decay predictions, particularly the connection to T_c̄s0^a(2900), is of current phenomenological interest. The compactness criterion based on E_CON provides a transparent, if approximate, diagnostic.

major comments (3)
  1. §III.B, Table VII: The central compactness claim for T_ncs̄n̄(0+, 2.925) rests on E_CON = -36 MeV with R₀ = 5.456 GeV⁻¹, which is only ~3% below the critical radius R_c = 5.615 GeV⁻¹. This margin is smaller than the model's own demonstrated systematic uncertainties: Table II shows baryon mass deviations of 30-80 MeV from lattice QCD, and the CEI binding energies B̄_M in Table I range from -48 to -261 MeV across the five fitted mesons. Since R₀ is determined variationally from the full mass formula including the CEI, a modest shift in the CEI strength or the CMI coupling α_s(R) could push R₀ past R_c and flip E_CON positive. The paper provides no sensitivity analysis or error estimates on R₀ or E_CON. This quantitative fragility should be addressed, at minimum by varying the CEI parameters within their fitted range and showing that the compactness classification is stable.
  2. §III.B, Eq. (20) and Table VIII: The decay-width argument for T_ncs̄n̄(0+, 2.925) compares k·|c_i|² = 211 MeV to the experimental width Γ = 136 MeV, but these are dimensionally and physically different quantities. Eq. (20) shows Γ_i = γ_i α k|c_i|², where α and γ_i are unknown. The text states that k·|c_i|² is 'comparable in magnitude' to Γ, but without knowing α and γ_i, this comparison is not a quantitative prediction. The paper should clarify that this is at most a qualitative consistency check (large k·|c_i|² suggests a large width) rather than evidence that the model reproduces the observed width. The current phrasing in §III.B and §IV overstates the strength of this argument.
  3. §II.B, Eq. (14): The CEI Hamiltonian H_CEI = -Σ⟨λ_i·λ_j⟩(3B̄_M R̄_M)/(16R) uses average values B̄_M and R̄_M extracted from five heavy mesons (Table I). The extrapolation to tetraquark systems with different color structures and additional light quarks is the key model assumption. While the color-factor scaling is standard, the use of a single averaged (B̄_M, R̄_M) pair for all quark pairs in the tetraquark—including light-light and heavy-light pairs—deserves justification. In the meson fit, B̄_M varies by a factor of ~5 across the five mesons. How sensitive are the tetraquark masses and radii to this averaging? A brief discussion or a check using pair-specific values would strengthen the robustness of the predictions.
minor comments (9)
  1. Abstract: The sentence beginning 'for the compact singly charmed systems,and for these systems' has formatting issues (missing space, capitalization). Similar issues appear throughout (e.g., 'tetrquark' in the abstract, 'usefull discussings' in Acknowledgments).
  2. Table I caption: The caption mentions 'heavy-flavor vector mesons' but the table also includes scalar meson values B_M. The caption should mention both.
  3. Table I: The entry B̄_M = 204 for B*_c appears to be missing a minus sign; all other entries are negative. Please verify.
  4. §II.B, Eq. (13): The fit parameters are given as a = -41, b = 30, c = -165, but no units are specified. Given that 1/μ has dimensions of length (GeV⁻¹), the units of a, b, c should be stated.
  5. Figure 1: The figure caption is minimal. It would benefit from specifying what the red and blue curves (if any) represent, and what the fit function is.
  6. §II.C: The statement that E_CON < 0 is 'necessary but not sufficient' for compactness is important and well-stated. It might be worth explicitly noting which of the identified compact candidates also have masses below or near thresholds, as this affects their experimental observability.
  7. Tables V-XIII: The eigenvector coefficients are listed without specifying the basis ordering in the table captions. The reader must cross-reference Table XIV and Appendix A, which is cumbersome. A brief note in each table caption specifying the basis vector ordering would help.
  8. §III.B: The state T_ncs̄n̄(0+, 2.925) is discussed as a candidate for T_c̄s0^a(2900), but the isospin of the calculated state is not explicitly stated in this section. Table VII does not list isospin. Please clarify the isospin assignment.
  9. References: Several references appear to be from 2025-2026 (e.g., Refs. [11], [12], [54]). If these are genuinely published, the citations are fine; if they are preprints, this should be noted.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for a careful and constructive report. The referee raises three substantive points regarding (1) the quantitative fragility of the compactness claim for T_ncs̄n̄(0+, 2.925), (2) the overstatement of the decay-width argument, and (3) the justification for using averaged CEI parameters across all quark pairs. We agree with all three points and will revise the manuscript accordingly. Details are given below.

read point-by-point responses

  1. Referee: §III.B, Table VII: The central compactness claim for T_ncs̄n̄(0+, 2.925) rests on E_CON = -36 MeV with R₀ = 5.456 GeV⁻¹, only ~3% below R_c = 5.615 GeV⁻¹. This margin is smaller than the model's demonstrated systematic uncertainties. No sensitivity analysis or error estimates on R₀ or E_CON are provided.

    Authors: The referee is correct. The margin between R₀ = 5.456 GeV⁻¹ and R_c = 5.615 GeV⁻¹ is indeed small (~2.8%), and it is smaller than the systematic uncertainties demonstrated by the baryon mass deviations in Table II (30–80 MeV) and the spread of CEI binding energies B̄_M in Table I (−48 to −261 MeV). We acknowledge that without a sensitivity analysis, the compactness classification of this state is not robustly established. In the revised manuscript, we will perform a sensitivity analysis by varying the CEI strength parameter (B̄_M) within the range spanned by the five fitted mesons and by varying α_s(R) within its scale uncertainty, and we will report the resulting shifts in R₀ and E_CON for the T_ncs̄n̄(0+, 2.925) state. We will also add an explicit caveat in §III.B and §IV stating that the compactness classification for this state is marginal and model-dependent, and that E_CON = −36 MeV should be interpreted as indicative rather than definitive. If the sensitivity analysis shows that the sign of E_CON can flip under reasonable parameter variations, we will state this explicitly and downgrade the claim accordingly. revision: yes

  2. Referee: §III.B, Eq. (20) and Table VIII: The decay-width argument compares k·|c_i|² = 211 MeV to Γ = 136 MeV, but these are dimensionally and physically different quantities. The comparison is not a quantitative prediction. The current phrasing overstates the strength of the argument.

    Authors: The referee is correct. The quantity k·|c_i|² is not the decay width; it is one factor entering the width formula Γ_i = γ_i α k |c_i|², where γ_i and α are unknown. Comparing k·|c_i|² = 211 MeV directly to Γ = 136 MeV is not a quantitative prediction. In the revised manuscript, we will rephrase the discussion in §III.B and §IV to explicitly state that this comparison is at most a qualitative consistency check: a large value of k·|c_i|² indicates that the state has a significant color-singlet component and sufficient phase space, which is consistent with—but does not quantitatively reproduce—the observed large width. We will remove language suggesting that k·|c_i|² is 'comparable in magnitude' to Γ as evidence of agreement, and replace it with a statement that the large k·|c_i|² value is qualitatively consistent with a broad resonance, without claiming quantitative agreement. revision: yes

  3. Referee: §II.B, Eq. (14): The CEI Hamiltonian uses average values B̄_M and R̄_M extracted from five heavy mesons. The use of a single averaged (B̄_M, R̄_M) pair for all quark pairs—including light-light and heavy-light pairs—deserves justification. B̄_M varies by a factor of ~5 across the five mesons. How sensitive are the tetraquark masses and radii to this averaging?

    Authors: The referee raises a valid concern. The use of a single averaged (B̄_M, R̄_M) pair for all quark pairs in the tetraquark is a simplifying model assumption. In the meson fit, B̄_M indeed varies significantly (from −48 MeV for D*_s to −261 MeV for Υ), reflecting the dependence of the CEI on the reduced mass of the quark pair. Applying the same averaged value to light-light, heavy-light, and heavy-heavy pairs in the tetraquark is not rigorously justified. In the revised manuscript, we will: (1) add a discussion in §II.B acknowledging this limitation and explaining that the averaging is motivated by the desire for a unified variational treatment with a minimal number of free parameters, and (2) perform a check by using pair-specific B_M values selected according to the reduced mass of each quark pair (using the fitted relation B(1/μ) in Eq. 13) and comparing the resulting tetraquark masses and radii with those obtained from the averaged approach. This will quantify the sensitivity of the predictions to the averaging procedure. We note that the light-light CEI is set to zero in the current framework (as stated after Eq. 15), so the averaging primarily affects heavy-light pairs, which somewhat limits the scope of the uncertainty. We will report the results of this check and discuss their implications for the robustness of the compactness predictions. revision: partial

Circularity Check

0 steps flagged

No significant circularity found; self-citations provide framework but predictions are not forced by construction.

full rationale

The paper's central derivation chain is: (1) fit CEI parameters (B̄_M, R̄_M) from heavy meson masses using the first three terms of Eq. (1) [Table I]; (2) propose a radius-dependent CEI Hamiltonian H_CEI = -Σ⟨λ_i·λ_j⟩(3B̄_M R̄_M)/(16R) [Eq. 14] that scales the fitted meson binding energies to arbitrary multiquark systems via color factors and 1/R; (3) verify on baryons against lattice QCD [Table II]; (4) apply to tetraquarks to predict masses, confinement energies, and decay factors. The self-citations (Refs [56, 57, 63, 64, 74]) are by overlapping authors and provide the bag-model framework with CMI/CEI and the compactness criterion, but the current paper explicitly modifies the CEI form ('We therefore depart from the conventional practice of treating the binding energies as input parameters'). The tetraquark predictions are not tautological reductions of the meson fits: the color factors differ (Table III vs. the meson -3/16), the number of quarks differs, and the variational radius R_0 is determined self-consistently for each tetraquark system. The identification of T_ncs̄n̄(0+, 2.925) with T_c̄s0^a(2900) is a post-diction (the experimental mass was known), but post-diction is a concern about predictive power, not circularity. The decay-width argument (k·|c_i|² = 211 MeV vs. Γ = 136 MeV) is qualitative since α and γ_i in Eq. 20 are unknown, but this is a weakness in the argument, not a circular reduction. No step was found where a prediction equals its input by construction. The self-citations raise the score slightly above zero because the compactness criterion and CEI framework originate from the authors' own prior work, but these are model assumptions (externally falsifiable against lattice QCD and experiment) rather than circular definitions. Score 2 reflects minor self-citation load that is not tautological.

Axiom & Free-Parameter Ledger

10 free parameters · 4 axioms · 0 invented entities

The paper introduces no new particles or forces. The CEI parameterization is a phenomenological ansatz, not a new physical entity. All free parameters are fitted to existing data.

free parameters (10)
  • B^{1/4} = 0.145 GeV
    MIT bag model vacuum energy parameter, fitted to light hadron masses and radii (Eq. 12).
  • Z_0 = 1.83
    Casimir energy parameter, fitted to light hadron data (Eq. 12).
  • m_n (u,d quark mass) = 0 GeV
    Light quark mass input, standard bag model choice (Eq. 12).
  • m_s = 0.279 GeV
    Strange quark mass input (Eq. 12).
  • m_c = 1.641 GeV
    Charm quark mass input (Eq. 12).
  • m_b = 5.093 GeV
    Bottom quark mass input (Eq. 12).
  • a (CEI fit) = -41
    Fitted parameter in B(1/μ) = a(1/μ)² + b(1/μ) + c, from 5 heavy meson data points (Eq. 13).
  • b (CEI fit) = 30
    Fitted parameter in CEI parameterization (Eq. 13).
  • c (CEI fit) = -165
    Fitted parameter in CEI parameterization (Eq. 13).
  • α_s(R) parameters = 0.296, 0.281
    Running coupling constants in CMI (Eq. 8), fitted parameters.
axioms (4)
  • domain assumption Spherical cavity approximation: quarks are confined in a spherically symmetric bag with linear boundary condition.
    Sec. IIA, Eq. (3). Standard MIT bag model assumption.
  • ad hoc to paper The CEI binding energy extracted from mesons can be scaled to multiquark systems via color factors and 1/R dependence.
    Sec. IIB, Eq. (14). The coefficient -3/16 comes from meson color factor; extrapolation to tetraquarks is assumed but not independently derived.
  • domain assumption E_CON < 0 is a necessary but not sufficient condition for compact tetraquark formation.
    Sec. IIC. The paper uses this as the primary compactness criterion, acknowledging it is not sufficient.
  • domain assumption Similarity relations for decay kinematic factors (Eqs. 22-25) hold across different final states.
    Sec. III. Assumes α is scale-dependent but common for identical flavor configurations.

pith-pipeline@v1.1.0-glm · 37059 in / 3174 out tokens · 555803 ms · 2026-07-08T23:48:22.370022+00:00 · methodology

0 comments
read the original abstract

We propose a Coulomb-like parameterization in terms of bag radius of the short-range chromo-electric interaction between heavy quarks and strange quarks within the framework of the MIT bag model for hadrons including multiquark systems and re-examine mass spectra of doubly and fully heavy baryons self-consistently and variationally. Building upon this, we apply this approach to systematically investigate the mass spectra and $S$-wave strong decay stability of singly heavy tetraquark systems, including $nQ\bar{n}\bar{n}$, $nQ\bar{s}\bar{n}$, $Qs\bar{n}\bar{n}$, $sQ\bar{s}\bar{n}$, and $sQ\bar{s}\bar{s}$ (with $Q=c,b$). Choosing the bag confinement energy as a compactness criterion, the bag radius is shown to be close to the confinement uplimit of the radius, $R_c = 5.615\,\text{GeV}^{-1}$, for the compact singly charmed systems,and for these systems some high-spin states are unlikely to form compact structures, while several others do exhibit potential for compactnessNotably, computation indicates that the state $T_{nc\bar{s}\bar{n}}(0^+,2.925)$ emerges as a compact tetraquark with relatively large strong decay width, a plausible candidate of the observed tetrquark $T_{c\bar{s}0}^{a}(2900)$.

Figures

Figures reproduced from arXiv: 2607.05793 by Duo-Jie Jia, Fu-Quan Dou, Kai-Kai Zhang, Wen-Nian Liu.

Figure 1
Figure 1. Figure 1: FIG. 1: Red and blue points represent the binding energies [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

discussion (0)

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

Reference graph

Works this paper leans on

98 extracted references · 98 canonical work pages · 46 internal anchors

  1. [1]

    The Hamiltonian of the CMI can be expressed as [ 63, 64, 66] HCMI = − ∑ i< j (λi ·λj)(σi ·σj)Ci j

    can be solved self-consistently through iteration. The Hamiltonian of the CMI can be expressed as [ 63, 64, 66] HCMI = − ∑ i< j (λi ·λj)(σi ·σj)Ci j. (4) here, i, j denote the indices for quarks or antiquarks, and λ and σrepresent the Gell-Mann matrices and Pauli matrices, respectively. Their expressions in terms of Casimir operat ors correspond to the co...

    work page

  2. [2]

    (1) for a unified variational solution

    can be substituted into the mass formula Eq. (1) for a unified variational solution. Based on the unified variational form of Eq. ( 1), we present in Table II the mass corrections for singly strange and doubly heavy baryons, which are within ±30 MeV [ 63], and further predict the masses of fully heavy baryons. Our results are compared with those of the rela...

    work page

  3. [3]

    −” indicates that the mass is below the threshold, and “ ∗

    278 and 2. 948 GeV , whereas the I¯n¯n = 1 states span 2 . 578 to 3. 015 GeV . For the bottom sector, the corresponding ranges are 5. 750–6. 325 GeV and 6. 007–6. 325 GeV , respectively. All computed masses exceed the lowest meson-meson thresholds (J p = 0+(B/ Dπ), 1 +(B∗/ D∗π), and 2 +(B∗/ D∗ω)), indicating that these tetraquarks are above the strong-dec...

    work page

  4. [4]

    547 GeV . All computed states lie above their respective 9 TABLE VII: For the nQ ¯s¯n system, the color-magnetic eigenstates, bag radius R0, confinement energy ECON, mass Mbag, and the threshold difference with respect to two-meson thresholds are given respe ctively. JPC Eigenvector R0 (GeV−1) ECON (MeV) Mbag (GeV) δm = M −MT hreshold (MeV) nc ¯s¯n 0+ 0.599...

    work page 2007

  5. [5]

    In the charm sector, the Tcs ¯n¯n(0, 2+, 3

    460 GeV in the bottom sector. In the charm sector, the Tcs ¯n¯n(0, 2+, 3. 050) state has a positive confinement energy (ECON = 10 MeV), indicating that this high-spin state is un- likely to form a compact structure. For the I = 1 charm states, the masses are about 200 MeV higher than their I = 0 counterparts, and their compactness potential is cor- respond...

    work page

  6. [6]

    The 0+ states range from 6

    684 GeV . The 0+ states range from 6. 153 to 6. 684 GeV , with ECON values between −36 and −149 MeV; the 1 + states span

    work page

  7. [7]

    −” indicates that the mass is below the threshold, and “ ∗

    217–6. 659 GeV with ECON from −31 to −127 MeV; and the two 2 + states at 6. 577 and 6. 601 GeV have ECON = −25 and −26 MeV , respectively. All states in the bottom sector have negative confinement energies, owing to the suppression of the bag radius by the heavier b quark. This implies that the 11 TABLE VIII: The table lists the |ci j|2 ·k (in GeV) values ...

    work page

  8. [8]

    −” indicates that the mass is below the threshold, and “ ∗

    441 GeV . The 0+ states are found at 3 . 097 and 3. 441 GeV , with ECON = −22 and 3 MeV , respectively; the latter has a positive confinement energy and is therefore disfavored as a compact candidate. The 1 + multiplet consists of three states 13 TABLE X: The table lists the |ci j|2 ·k (in GeV) values for the Qs ¯n¯n system; the numbers in parentheses can ...

    work page

  9. [9]

    −” indicates that the mass is below the threshold, and “ ∗

    792 GeV . All states have negative confinement energies ex- cept the 2 + state at 6. 716 GeV , which has ECON = −18 MeV . The 0 + states at 6 . 501 and 6 . 792 GeV have ECON = −118 and −41 MeV , respectively; the 1 + states at 6 . 523, 6. 690, and 6. 769 GeV have ECON = −108, −73, and −52 MeV . In particular, T sb ¯s ¯s(1+, 6. 523) has a confinement energy ...

    work page

  10. [10]

    Gell-Mann, Phys

    M. Gell-Mann, Phys. Lett. 8, 214 (1964)

    work page 1964

  11. [11]

    Zweig, CERN-TH-401 (1964)

    G. Zweig, CERN-TH-401 (1964)

    work page 1964

  12. [12]

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

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  13. [13]

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

    M. Ablikim et al. (BESIII), Phys. Rev. Lett. 110, 252001 (2013) , arXiv:1303.5949 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  14. [14]

    Aaij et al

    R. Aaij et al. (LHCb), Nature Commun. 13, 3351 (2022) , arXiv:2109.01056 [hep-ex]

    work page arXiv 2022

  15. [15]

    R. e. a. Aaij (LHCb Collaboration), Phys. Rev. Lett. 115, 072001 (2015)

    work page 2015

  16. [16]

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

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

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  17. [17]

    Aaij et al

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

    work page arXiv 2021

  18. [18]

    Aaij et al

    R. Aaij et al. (LHCb), Phys. Rev. Lett. 128, 062001 (2022) , arXiv:2108.04720 [hep-ex]

    work page arXiv 2022

  19. [19]

    Observation of a $J/\psi\Lambda$ resonance consistent with a strange pentaquark candidate in $B^-\to J/\psi\Lambda\bar{p}$ decays

    R. Aaij et al. (LHCb), Phys. Rev. Lett. 131, 031901 (2023) , arXiv:2210.10346 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  20. [20]

    Cheng, Z.-Y

    J.-B. Cheng, Z.-Y . Lin, J.-Z. Wang, and S.-L. Zhu, Phys. Rev. D 113, 096001 (2026) , arXiv:2601.20740 [hep-ph]

    work page arXiv 2026

  21. [21]

    Shen, Z.-W

    Y .-B. Shen, Z.-W. Liu, M.-Z. Liu, R.-X. Shi, C.-W. Xiao, W.- H. Liang, and L.-S. Geng, Phys. Rev. D 113, 074034 (2026) , arXiv:2512.24247 [hep-ph]

    work page arXiv 2026

  22. [22]

    Liu, Y .-W

    M.-Z. Liu, Y .-W. Pan, Z.-W. Liu, T.-W. Wu, J.-X. Lu, and L.-S. Geng, Physics Reports 1108, 1 (2025) , three ways to decipher the nature of exotic hadrons: Multiplets, three-body hadro nic molecules, and correlation functions

    work page 2025

  23. [23]

    H.-X. Chen, W. Chen, X. Liu, and S.-L. Zhu, Physics Reports 639, 1 (2016) , the hidden-charm pentaquark and tetraquark states

    work page 2016

  24. [24]

    Brambilla, S

    N. Brambilla, S. Eidelman, C. Hanhart, A. Nefediev, C.- P . Shen, C. E. Thomas, A. V airo, and C.-Z. Y uan, Physics Reports 873, 1 (2020) , the XYZ states: experimental and theoretical status and perspectives

    work page 2020

  25. [25]

    F.-K. Guo, C. Hanhart, U.-G. Meißner, Q. Wang, Q. Zhao, a nd B.-S. Zou, Rev. Mod. Phys. 90, 015004 (2018)

    work page 2018

  26. [26]

    Masses of fully heavy tetraquarks $QQ \bar Q \bar Q$ in an extended relativized quark model

    Q.-F. L¨ u, D.-Y . Chen, and Y .-B. Dong, Eur. Phys. J. C 80, 871 (2020) , arXiv:2006.14445 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  27. [27]

    Spectroscopy of all charm tetraquark states

    R. Tiwari, D. P . Rathaud, and A. K. Rai, Indian J. Phys. 97, 943 (2023) , arXiv:2108.04017 [hep-ph] 19

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  28. [28]

    Higher mass spectra of the fully-charmed and fully-bottom tetraquarks

    F.-X. Liu, M.-S. Liu, X.-H. Zhong, and Q. Zhao, Phys. Rev. D 104, 116029 (2021) , arXiv:2110.09052 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  29. [29]

    Interpretation of structure in the di-$J/\psi$ spectrum

    M. Karliner and J. L. Rosner, Phys. Rev. D 102, 114039 (2020) , arXiv:2009.04429 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  30. [30]

    R. N. Faustov, V . O. Galkin, and E. M. Savchenko, Phys. Rev. D 102, 114030 (2020) , arXiv:2009.13237 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  31. [31]

    H.-X. Chen, W. Chen, X. Liu, Y .-R. Liu, and S.-L. Zhu, Rept. Prog. Phys. 86, 026201 (2023) , arXiv:2204.02649 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  32. [32]

    Pentaquark and Tetraquark states

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

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  33. [33]

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

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  34. [34]

    Strange pentaquarks and excited $\Xi$ hyperons in $\Xi_b^- \to J/\psi \Lambda K^-$ final states

    M. Karliner and J. L. Rosner, Sci. Bull. 66, 1257 (2021) , arXiv:2104.15077 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  35. [35]

    B. Wang, L. Meng, and S.-L. Zhu, Phys. Rev. D 101, 034018 (2020) , arXiv:1912.12592 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  36. [36]

    Building up the spectrum of pentaquark states as hadronic molecules

    B.-S. Zou, Sci. Bull. 66, 1258 (2021) , arXiv:2103.15273 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  37. [37]

    Compact hidden charm pentaquark states and QCD isomers

    C.-R. Deng, Phys. Rev. D 105, 116021 (2022) , arXiv:2202.13570 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  38. [38]

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

    M.-Z. Liu, Y .-W. Pan, Z.-W. Liu, T.-W. Wu, J.-X. Lu, and L.-S. Geng, Phys. Rept. 1108, 1 (2025) , arXiv:2404.06399 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  39. [39]

    Aaij et al

    R. Aaij et al. (LHCb), Phys. Rev. Lett. 131, 041902 (2023) , arXiv:2212.02716 [hep-ex]

    work page arXiv 2023

  40. [40]

    Aaij et al

    R. Aaij et al. (LHCb), Phys. Rev. D 108, 012017 (2023) , arXiv:2212.02717 [hep-ex]

    work page arXiv 2023

  41. [41]

    Aaij et al

    R. Aaij et al. (LHCb), Phys. Rev. Lett. 133, 131902 (2024) , arXiv:2406.03156 [hep-ex]

    work page arXiv 2024

  42. [42]

    Aaij et al

    R. Aaij et al. (LHCb), Phys. Rev. Lett. 134, 101901 (2025) , arXiv:2411.19781 [hep-ex]

    work page arXiv 2025

  43. [43]

    X.-S. Yang, Q. Xin, and Z.-G. Wang, International Journal of Modern Physics A 38, 2350056 (2023) , https://doi.org/10.1142/S0217751X23500562

    work page doi:10.1142/s0217751x23500562 2023

  44. [44]

    D.-K. Lian, W. Chen, H.-X. Chen, L.-Y . Dai, and T. G. Stee le, Eur. Phys. J. C 84, 1 (2024) , arXiv:2302.01167 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  45. [45]

    Chen, H.-X

    W. Chen, H.-X. Chen, X. Liu, T. G. Steele, and S.-L. Zhu, Phys. Rev. D 95, 114005 (2017)

    work page 2017

  46. [46]

    Possibility of $T_{c\bar{s}}(2900)$ as the resonance-like structure induced by threshold effects

    Y .-H. Ge, X.-H. Liu, and H.-W. Ke, Eur. Phys. J. C 82, 955 (2022) , arXiv:2207.09900 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  47. [47]

    Triangle singularity as the origin of $X_0(2900)$ and $X_1(2900)$ observed in $B^+\to D^+ D^- K^+$

    X.-H. Liu, M.-J. Yan, H.-W. Ke, G. Li, and J.-J. Xie, Eur. Phys. J. C 80, 1178 (2020) , arXiv:2008.07190 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  48. [48]

    B. Wang, K. Chen, L. Meng, and S.-L. Zhu, Phys. Rev. D 109, 034027 (2024)

    work page 2024

  49. [49]

    X.-G. He, W. Wang, and R. Zhu, Eur. Phys. J. C 80, 1026 (2020) , arXiv:2008.07145 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  50. [50]

    Karliner and J

    M. Karliner and J. L. Rosner, Phys. Rev. D 102, 094016 (2020)

    work page 2020

  51. [51]

    G. Yang, J. Ping, and J. Segovia, Phys. Rev. D 103, 074011 (2021)

    work page 2021

  52. [52]

    T. Guo, J. Li, J. Zhao, and L. He, Phys. Rev. D 105, 054018 (2022)

    work page 2022

  53. [53]

    G.-J. Wang, L. Meng, L.-Y . Xiao, M. Oka, and S.-L. Zhu, Eur. Phys. J. C 81, 188 (2021) , arXiv:2010.09395 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  54. [54]

    Liu, J.-J

    M.-Z. Liu, J.-J. Xie, and L.-S. Geng, Phys. Rev. D 102, 091502(R) (2020)

    work page 2020

  55. [55]

    Kong, J.-T

    S.-Y . Kong, J.-T. Zhu, D. Song, and J. He, Phys. Rev. D 104, 094012 (2021)

    work page 2021

  56. [56]

    How to understand the $X(2900)$?

    B. Wang and S.-L. Zhu, Eur. Phys. J. C 82, 419 (2022) , arXiv:2107.09275 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  57. [57]

    String breaking by light and strange quarks in QCD

    J. Bulava, B. H¨ orz, F. Knechtli, V . Koch, G. Moir, C. Mor n- ingstar, and M. Peardon, Phys. Lett. B 793, 493 (2019) , arXiv:1902.04006 [hep-lat]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  58. [58]

    G. S. Bali, H. Ne ff, T. Duessel, T. Lippert, and K. Schilling (SESAM), Phys. Rev. D 71, 114513 (2005) , arXiv:hep-lat/0505012

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  59. [59]

    Locating Quark-Antiquark String Breaking in QCD through Chiral Symmetry Restoration and Hawking-Unruh Effect

    W. Kou and X. Chen, Phys. Lett. B 856, 138942 (2024) , arXiv:2405.18697 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  60. [60]

    Fully strange tetraquark resonant states as the cousins of $X(6900)$

    Y . Ma, W.-L. Wu, L. Meng, Y .-K. Chen, and S.-L. Zhu, Phys. Rev. D 110, 074026 (2024) , arXiv:2408.00503 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  61. [61]

    W.-L. Wu, Y . Ma, Y .-K. Chen, L. Meng, and S.-L. Zhu, Phys. Rev. D 110, 094041 (2024) , arXiv:2409.03373 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  62. [62]

    H.-M. Yang, Y . Ma, W.-L. Wu, and S.-L. Zhu, Phys. Rev. D 111, 074040 (2025) , arXiv:2502.10798 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  63. [63]

    Zheng, Y

    X.-H. Zheng, Y . Ma, and S.-L. Zhu, Phys. Rev. D 113, 054027 (2026) , arXiv:2510.01505 [hep-ph]

    work page arXiv 2026

  64. [64]

    Wu, Y .-K

    W.-L. Wu, Y .-K. Chen, Y . Ma, L. Meng, and S.- L. Zhu, J. Subatomic Part. Cosmol. 4, 100184 (2025), arXiv:2508.11161 [hep-ph]

    work page arXiv 2025

  65. [65]

    Zhang, W.-N

    W.-X. Zhang, W.-N. Liu, and D. Jia, Phys. Rev. D 112, 114039 (2025) , arXiv:2510.04103 [hep-ph]

    work page arXiv 2025

  66. [66]

    Searching for compact pentaquark state within the bag model framework

    W.-N. Liu, W.-X. Zhang, and F.-Q. Dou, Phys. Rev. D 111, 114031 (2025) , arXiv:2501.12727 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  67. [67]

    Barnes, F

    T. Barnes, F. E. Close, and F. de Viron, Nucl. Phys. B 224, 241 (1983)

    work page 1983

  68. [68]

    M. S. Chanowitz and S. R. Sharpe, Nucl. Phys. B 222, 211 (1983) , [Erratum: Nucl.Phys.B 228, 588–588 (1983)]

    work page 1983

  69. [69]

    R. L. Ja ffe, Phys. Rev. D 15, 267 (1977)

    work page 1977

  70. [70]

    R. L. Ja ffe, Phys. Rev. D 15, 281 (1977)

    work page 1977

  71. [71]

    T. A. DeGrand, R. L. Ja ffe, K. Johnson, and J. E. Kiskis, Phys. Rev. D 12, 2060 (1975)

    work page 2060

  72. [72]

    Masses and magnetic moments of hadrons with one and two open heavy quarks: heavy baryons and tetraquarks

    W.-X. Zhang, H. Xu, and D. Jia, Phys. Rev. D 104, 114011 (2021) , arXiv:2109.07040 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  73. [73]

    Mass spectra of hidden heavy-flavor tetraquarks with two and four heavy quarks

    T.-Q. Yan, W.-X. Zhang, and D. Jia, Eur. Phys. J. C 83, 810 (2023) , arXiv:2304.01684 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  74. [74]

    Liu, W.-X

    W.-N. Liu, W.-X. Zhang, and F.-Q. Dou, Phys. Rev. D 111, 114031 (2025)

    work page 2025

  75. [75]

    H.-T. An, K. Chen, Z.-W. Liu, and X. Liu, Phys. Rev. D 103, 074006 (2021)

    work page 2021

  76. [76]

    Triply heavy tetraquark states: masses and other properties

    Z.-H. Zhu, W.-X. Zhang, and D. Jia, Eur. Phys. J. C 84, 344 (2024) , arXiv:2312.01908 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  77. [77]

    Baryons with two heavy quarks: Masses, production, decays, and detection

    M. Karliner and J. L. Rosner, Phys. Rev. D 90, 094007 (2014) , arXiv:1408.5877 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  78. [78]

    Quark-level analogue of nuclear fusion with doubly-heavy baryons

    M. Karliner and J. L. Rosner, Nature 551, 89 (2017) , arXiv:1708.02547 [hep-ph] . 20

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  79. [79]

    Discovery of doubly-charmed Xi_{cc} baryon implies a stable (b b ubar dbar) tetraquark

    M. Karliner and J. L. Rosner, Phys. Rev. Lett. 119, 202001 (2017) , arXiv:1707.07666 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  80. [80]

    First exotic hadron with open heavy flavor: $cs\bar u\bar d$ tetraquark

    M. Karliner and J. L. Rosner, Phys. Rev. D 102, 094016 (2020) , arXiv:2008.05993 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2020

Showing first 80 references.