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arxiv: 2606.06979 · v1 · pith:BXQJ3VIMnew · submitted 2026-06-05 · ✦ hep-ph

Investigation of fully heavy tetraquark within chiral quark model

Yuheng Wu , Xuejie Liu , Ye Yan , Yue Tan , Qi Huang , Hongxia Huang , Jialun Ping This is my paper

Pith reviewed 2026-06-27 22:06 UTC · model grok-4.3

classification ✦ hep-ph
keywords fully heavy tetraquarkschiral quark modelresonance statesX(6900)X(7200)real-scaling methodcc bar c bar cbb bar b bar b
0
0 comments X

The pith

The chiral quark model finds two resonance states in the fully charmed tetraquark system matching the X(6900) and X(7200).

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

The paper applies the chiral quark model to fully heavy tetraquarks with quantum numbers J^{PC}=2^{++}, considering both meson-meson and diquark-antidiquark structures. No bound states appear in either the ccar{c}ar{c} or bbar{b}ar{b} systems. Resonance states are extracted via the real-scaling method. For the charmed system restricted to three S-wave channels, two resonances appear near 7002 MeV (width 54 MeV) and 7227 MeV (width 66 MeV); these survive when additional channels involving excited charmonia are added. For the bottomed system a single resonance appears near 19743 MeV (width 67 MeV) independent of channel content. The work proposes experimental searches in the ar{ u}ar{ u} and ar{ u}ar{ u}(2S) invariant-mass spectra.

Core claim

Within the chiral quark model, the ccar{c}ar{c} system yields two resonant states at masses around 7002 MeV (decay width ~54 MeV) and 7227 MeV (~66 MeV) when only three S-wave channels are coupled; these states remain after inclusion of ar{ u}_{c0}ar{ u}_{c2}, ar{ u}_{c1}ar{ u}_{c1}, ar{ u}_{c1}ar{ u}_{c2} and ar{ u}_{c2}ar{ u}_{c2} channels and are offered as candidates for X(6900) and X(7200). The bbar{b}ar{b} system produces one resonance at ~19743 MeV with width ~67 MeV whether or not the four excited-meson channels are included.

What carries the argument

The real-scaling method applied inside the chiral quark model to separate physical resonances from continuum states.

If this is right

  • The observed X(6900) can be assigned as a ccar{c}ar{c} resonance with J^{PC}=2^{++}.
  • A second resonance near 7227 MeV is predicted to appear in the same mass spectrum.
  • A single resonance near 19743 MeV should appear in the ar{ u}ar{ u} or ar{ u}ar{ u}(2S) invariant-mass spectrum.
  • Inclusion of additional two-meson channels built from excited charmonia or bottomonia leaves the reported resonances intact.

Where Pith is reading between the lines

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

  • Confirmation of the bottomed resonance would indicate that the same model framework applies uniformly across charm and bottom sectors.
  • The lack of bound states implies fully heavy tetraquarks exist only as resonances rather than stable particles.
  • The method could be applied to other J^{PC} assignments to predict additional states in the same systems.
  • Experimental non-observation of the predicted bottom resonance in the suggested channels would require revision of the channel-coupling assumptions.

Load-bearing premise

The real-scaling procedure inside the chiral quark model correctly isolates physical resonances without introducing artifacts that depend on the specific model parameters or cutoff choices.

What would settle it

Absence of a resonance peak near 7002 MeV in the J/ar{ u} J/ar{ u} invariant-mass distribution would remove the candidate assignment for the lower state.

Figures

Figures reproduced from arXiv: 2606.06979 by Hongxia Huang, Jialun Ping, Qi Huang, Xuejie Liu, Ye Yan, Yue Tan, Yuheng Wu.

Figure 1
Figure 1. Figure 1: FIG. 1: The schematic energy spectrum in the real-scaling [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The stabilization plots of the energies including th [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The stabilization plots of the energies including se [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The stabilization plots of the energies including th [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: The stabilization plots of the energies including se [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
read the original abstract

In the framework of the Chiral quark model (ChQM), we investigate the fully charmed and fully bottomed tetraquark with $J^{PC}=2^{++}$ including two structures: $Q\bar{Q}-Q\bar{Q}$ and $QQ-\bar{Q}\bar{Q}$. The bound-state calculation shows that there is no bound state in either $cc\bar{c}\bar{c}$ or $bb\bar{b}\bar{b}$ systems. However, by using the real-scaling method, some resonance states are obtained. For the $cc\bar{c}\bar{c}$ system, when the channel-coupling includes only three $S$-wave channels, two resonant states are obtained: one with a mass around $7002$ MeV and decay width near $54$ MeV, and another with a mass around $7227$ MeV and a decay width near $66$ MeV. The former can be regarded as a candidate for the $X(6900)$, and the latter can be considered as a candidate for the $X(7200)$. Upon adding the $\chi_{c0}\chi_{c2}$, $\chi_{c1}\chi_{c1}$, $\chi_{c1}\chi_{c2}$, $\chi_{c2}\chi_{c2}$ channels, both resonant states still remain. For the $bb\bar{b}\bar{b}$ system, only one resonant state is obtained, regardless of whether the four channels composition of the excited mesons are included or excluded. The mass and width of this resonant state are around $19743$ MeV and $67$ MeV, respectively. We suggest that future experiments search for the possible resonance state in the invariant mass spectrum of $\Upsilon \Upsilon$ or $\Upsilon \Upsilon(2S)$.

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

3 major / 0 minor

Summary. The manuscript applies the chiral quark model to fully heavy tetraquarks with J^{PC}=2^{++} in the ccar{c}ar{c} and bbar{b}ar{b} systems, considering Qar{Q}-Qar{Q} and QQ-ar{Q}ar{Q} structures. It finds no bound states but reports resonances extracted via the real-scaling method: two states in the charm sector (masses ~7002 MeV width 54 MeV and ~7227 MeV width 66 MeV, proposed as X(6900) and X(7200) candidates) that persist with additional excited-meson channels, and one bottom-sector resonance (~19743 MeV, width 67 MeV).

Significance. If the resonance positions and widths are shown to be stable under parameter variation and method validation, the work would add to the theoretical catalog of fully heavy tetraquark candidates and could guide experimental searches in ar{\Upsilon}ar{\Upsilon} spectra. The explicit demonstration that certain resonances survive channel enlargement is a positive feature of the calculation.

major comments (3)
  1. [Abstract] Abstract: The resonance masses and widths (7002 MeV/54 MeV, 7227 MeV/66 MeV, 19743 MeV/67 MeV) are stated without any tabulation or citation of the numerical values adopted for the ChQM parameters (constituent quark masses, g_{ch}, cutoffs Λ, confinement strength, etc.). Because the chiral-exchange terms become irrelevant for fully heavy systems, the predictions reduce to the OGE plus confinement sector; without a consistency check against heavy-quarkonium spectra or a sensitivity study, shifts of tens to hundreds of MeV cannot be excluded and directly affect the candidate assignments.
  2. [Abstract] Abstract: The real-scaling method is used to distinguish resonances from continuum states and to extract widths, yet no information is supplied on the range of the scaling parameter, the criterion for identifying avoided crossings, the basis size, or any benchmark test on a known narrow resonance. This information is load-bearing for the central claim that the reported states are physical resonances rather than artifacts.
  3. [Abstract] Abstract: The statement that the two ccar{c}ar{c} resonances "still remain" after inclusion of the χ_{c0}χ_{c2}, χ_{c1}χ_{c1}, χ_{c1}χ_{c2}, χ_{c2}χ_{c2} channels is given without quantitative shifts in mass or width, without the number of channels or the radial basis functions employed, and without a comparison to the three-channel results. The stability claim therefore cannot be assessed from the supplied information.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address each major comment below and will revise the manuscript to improve transparency on parameters, method details, and quantitative results.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The resonance masses and widths (7002 MeV/54 MeV, 7227 MeV/66 MeV, 19743 MeV/67 MeV) are stated without any tabulation or citation of the numerical values adopted for the ChQM parameters (constituent quark masses, g_{ch}, cutoffs Λ, confinement strength, etc.). Because the chiral-exchange terms become irrelevant for fully heavy systems, the predictions reduce to the OGE plus confinement sector; without a consistency check against heavy-quarkonium spectra or a sensitivity study, shifts of tens to hundreds of MeV cannot be excluded and directly affect the candidate assignments.

    Authors: The parameters are the standard set from our prior ChQM studies on heavy systems (cited in the model section), where the OGE+confinement sector was fitted to charmonium and bottomonium spectra. We will add an explicit table of all numerical values in the revised manuscript and include a short consistency check plus sensitivity test to variations in confinement strength and cutoff, showing resonance positions stable within ~25 MeV. revision: yes

  2. Referee: [Abstract] Abstract: The real-scaling method is used to distinguish resonances from continuum states and to extract widths, yet no information is supplied on the range of the scaling parameter, the criterion for identifying avoided crossings, the basis size, or any benchmark test on a known narrow resonance. This information is load-bearing for the central claim that the reported states are physical resonances rather than artifacts.

    Authors: Section III describes the real-scaling procedure, but we agree more technical specifics are needed. In the revision we will expand the section to state the scaling-parameter range, avoided-crossing identification criterion, basis size, and add a benchmark test on a known narrow state to validate width extraction. revision: yes

  3. Referee: [Abstract] Abstract: The statement that the two ccar{c}ar{c} resonances "still remain" after inclusion of the χ_{c0}χ_{c2}, χ_{c1}χ_{c1}, χ_{c1}χ_{c2}, χ_{c2}χ_{c2} channels is given without quantitative shifts in mass or width, without the number of channels or the radial basis functions employed, and without a comparison to the three-channel results. The stability claim therefore cannot be assessed from the supplied information.

    Authors: We agree that quantitative information is required. The revised manuscript will include a table comparing masses and widths between the three-channel and seven-channel calculations, together with the total channel count and basis details, demonstrating that the resonances persist with only modest shifts. revision: yes

Circularity Check

0 steps flagged

No significant circularity; standard model application to new systems

full rationale

The paper applies the established Chiral Quark Model (with parameters from prior literature) plus the real-scaling method to compute bound states and resonances for cc cbar cbar and bb bbar bbar tetraquarks. The reported masses and widths (e.g., 7002 MeV, 7227 MeV) are outputs of solving the model's Hamiltonian for the four-body system with channel coupling; they are not equivalent to the inputs by construction, nor do any quoted steps reduce fitted parameters directly to the target resonances. No self-definitional, fitted-input-called-prediction, or load-bearing self-citation patterns are exhibited in the provided text. This is a normal phenomenological calculation whose validity is a separate correctness question.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the applicability of the chiral quark model to fully heavy systems and the validity of the real-scaling method for resonance identification; both are domain assumptions without independent verification supplied in the abstract. No new entities are postulated.

free parameters (1)
  • Chiral quark model parameters (quark masses, couplings)
    Standard ChQM parameters are typically fitted to meson spectra or other data and are required for the bound-state and resonance calculations.
axioms (2)
  • domain assumption The chiral quark model provides an accurate description of interactions in fully heavy tetraquark systems.
    Invoked to perform the bound-state and channel-coupling calculations.
  • domain assumption The real-scaling method correctly identifies physical resonances in the coupled-channel tetraquark wave functions.
    Used to extract the reported resonance states and widths.

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discussion (0)

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Reference graph

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