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REVIEW 4 major objections 5 minor 117 references

On the nature of fully-charmed four-quark exotic state $X(6900)$ from its photoproduction off nuclei

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Photoproduction off nuclei can reveal whether X(6900) is a compact tetraquark, a charmonium molecule, or a 50/50 mixture, because predicted yields differ by 20–30% on tungsten and 10% on carbon.

desk verdict A straightforward extension of the author's spectral-function model to X(6900) photoproduction; the claimed structure discrimination is conditional on three unvalidated absorption cross sections. read the letter →

arxiv 2608.03374 v1 pith:NUBI3LCQ submitted 2026-08-04 hep-ph hep-exnucl-exnucl-th

E. Ya. Paryev This is my paper · ORCID
classification hep-phhep-exnucl-exnucl-th
keywords X(6900)fully-charmedtetraquarkphotoproductionoffnucleinuclearspectralfunctiontransparencyratiohadronicmoleculecompactelectron-ioncollider
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper aims to establish that near-threshold photoproduction of the fully-charmed exotic state $X(6900)$ off nuclear targets can serve as a probe of the state's internal structure. Using a collision model based on the nuclear spectral function, it computes excitation functions, momentum distributions, and transparency ratios for three scenarios: a compact four-quark state, a $J/\psi$–$\psi(3770)$ molecule, and an equal mixture of the two. The calculated observables differ by about 20–30% for a heavy nucleus ($^{184}$W) and about 10% for a light one ($^{12}$C), which the paper argues is experimentally accessible at the planned electron-ion colliders. If the predictions hold, comparing these observables with future data would discriminate which internal configuration nature realizes.

What carries the argument

The key object is the in-medium absorption cross section $\sigma_{X(6900)N}$, which parameterizes how strongly the produced $X(6900)$ is attenuated inside the nucleus through inelastic collisions with nucleons. The model folds this cross section into the effective nucleon number $I_V[A,\sigma]$ of the nuclear spectral function formalism, together with the elementary $\gamma p \to X(6900)p$ cross section, scaled from a $0^{++}$ calculation by a 5/1 spin-counting factor for the $2^{++}$ state. Three scenarios are encoded purely in $\sigma$: 10 mb for the compact tetraquark, 21.2 mb for the molecule, and 15.6 mb for the hybrid. The transparency ratios $S_A$ and $T_A$ are the designed probes: being cross-section ratios, they suppress theoretical uncertainties in the elementary production cross section and isolate the absorption term.

What would settle it

Measure the inclusive photoproduction yield and forward momentum distribution of $X(6900)$ on $^{12}$C and $^{184}$W at photon energy near 35 GeV, and extract the $^{184}$W/$^{12}$C transparency ratio as a function of momentum with enough statistics to resolve 5% differences. If the compact-tetraquark scenario is right, the heavy-nucleus yield should sit near the top of the predicted 20–30% spread and follow the 10 mb absorption curve; if the molecular scenario is right, it should sit near the bottom and follow the 21.2 mb curve. A direct measurement of the $X(6900)$–nucleon absorption cross section from the $A$-dependence of nuclear yields would settle it without relying on the elementary cross-section parametrization.

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Extended reading notes

Core claim

The central claim is that the $X(6900)$–nucleon absorption cross section $\sigma_{X(6900)N}$ encodes the internal structure of the state, and that this cross section controls inclusive photoproduction observables on nuclear targets in a measurable way. For a compact tetraquark the paper takes $\sigma_{X(6900)N} = 10$ mb; for a $J/\psi\psi(3770)$ molecule it derives 21.2 mb by adding a $J/\psi$–nucleon cross section of 3.5 mb to a $\psi(3770)$–nucleon cross section scaled by the square of the charmonium size ratio; for a 50/50 hybrid it takes 15.6 mb as an incoherent probability-weighted sum. These values translate into differences of 20–30% in the $X(6900)$ yield from $^{184}$W and about 10% from $^{12}$C, as well as distinguishable $A$-dependences of the transparency ratios $S_A$ and $T_A$. The paper concludes that absolute and relative photoproduction observables off nuclei are useful for determining which internal configuration is realized.

Load-bearing premise

The load-bearing premise is that the three absorption cross sections—10, 15.6, and 21.2 mb—correctly represent the three internal-structure scenarios, especially the molecular value built from a 1977 $J/\psi$–nucleon measurement of 3.5 mb and a size-squared scaling to $\psi(3770)$, and the hybrid value's exactly 50/50 mixing, so that if these estimates are off by more than a few mb the predicted 10–30% differences could shrink or disappear.

Editorial extensions

If this is right

  • At photon energies 33–40 GeV, the predicted total cross sections are 10–40 nb on $^{12}$C and 100–400 nb on $^{184}$W, large enough for the planned electron-ion collider program to collect thousands to hundreds of thousands of $X(6900)$ events in a one-year run.
  • The $^{184}$W/$^{12}$C transparency ratio $T_A$ is nearly flat in photon energy and in $X(6900)$ momentum except at low energies and high momenta, so deviations from this flat behavior would carry structure information.
  • The transparency ratio $S_A$ falls with nuclear mass number in all scenarios and reaches values around 0.2 for Pb and U in the molecular case, a large deviation from unity that should be easy to observe.
  • The momentum distributions at 35 GeV in the forward 0–5° cone differ sizeably between the molecular and compact-tetraquark treatments, with measurable strengths of 10–200 nb/(GeV/c) in the central momentum region near 33–33.5 GeV/c.

Reading between the lines

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

  • A direct measurement of $\sigma_{X(6900)N}$ from the nuclear attenuation pattern—comparing yields on light and heavy targets—could settle the interpretation even before the elementary $\gamma p$ cross section is precisely known, because the transparency ratios are designed to cancel that uncertainty.
  • The same absorption logic should apply to the neighboring fully-charmed states $X(6600)$ and $X(7100)$: once their elementary photoproduction cross sections are known, the formalism could be used to test whether all three states share the same internal configuration.
  • The high-momentum tail of the $X(6900)$ momentum distribution may offer a sharper molecular-versus-compact discriminator than the total yield, since a loosely bound molecule is more likely to be stripped in the nucleus; this specific prediction is not made in the paper but follows from its absorption mechanism.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper studies inclusive photoproduction of the fully-charmed tetraquark candidate X(6900) off 12C and 184W nuclei near threshold, using a nuclear spectral-function model previously developed by the author. Three internal-structure scenarios are considered: a compact diquark-antidiquark tetraquark, a J/psi psi(3770) hadronic molecule, and a 50/50 hybrid of the two. The scenarios enter the model through the X(6900)-nucleon absorption cross section sigma_XN, set to 10.0, 21.2, and 15.6 mb in Eq. (12). The paper computes excitation functions, momentum distributions, and transparency ratios S_A and T_A, and claims differences of about 20-30% for 184W and about 10% for 12C, which it argues are measurable at the future EIC and EicC colliders.

Significance. If the predicted scenario separation is robust, the paper would provide a new, experimentally accessible way to determine the internal structure of X(6900), complementing LHCb, ATLAS, and CMS data. The transparency ratios T_A and S_A are well-chosen observables because they partly cancel the uncertainty in the elementary cross section, and the event-rate estimates for EIC and EicC make the proposal concrete. The predictions are explicit and falsifiable, and the paper is transparent about the sources of its inputs. However, the central claim depends heavily on the three point values of sigma_XN in Eq. (12), which are not measured and are not accompanied by uncertainty estimates; this makes the significance of the discrimination claim conditional.

major comments (4)
  1. [Section 2, Eq. (12)] The molecular absorption cross section sigma_XN^mol = 21.2 mb is the load-bearing input for the claimed scenario separation. It is derived from sigma_J/psiN = 3.5 mb from the 1977 SLAC experiment [100], together with a size-squared scaling factor (0.9/0.4)^2 = 5.06 to obtain sigma_psi(3770)N = 17.7 mb. All nuclear observables depend on sigma_XN only through the effective nucleon number I_V in Eq. (3), and the curves in Figs. 3-9 are monotonic in sigma_XN. The quark-interchange estimate of about 10^-2 mb [101] is dismissed as unrealistic without a replacement calculation, and no plausible range for sigma_psi(3770)N is given. Since a value in the 3-10 mb range would bring the molecular and hybrid curves close to the compact curve, the paper should provide a sensitivity scan or explicit uncertainty bands around Eq. (12).
  2. [Section 2, Eq. (9) and footnote 10] The manuscript adopts m_X(6900) = 6.886 GeV in Eq. (8), which is about 15 MeV above the J/psi psi(3770) threshold of 6870.6 MeV. In the main calculation, therefore, the 'molecule' is not a bound state. Footnote 10 switches to m_X = 6876 MeV and obtains delta = -5.4 MeV, which is a negative binding energy, while still referring to the system as loosely bound. This undermines the on-shell two-constituent picture used to justify the additive absorption formula in Eq. (9). The authors should either use a mass consistent with a bound-state interpretation or provide a physical justification for applying Eq. (9) to a state above threshold.
  3. [Section 2, Eq. (7)] The elementary cross section in Eq. (7) is the 0++ result from the omega-exchange model of Ref. [80], assuming Br[X(6900)->J/psi omega] = 1%, and it is converted to the 2++ cross section by a 5/1 spin-counting rule with no further derivation. The absolute nuclear cross sections and the S_A transparency ratios inherit this normalization uncertainty, even though T_A partly cancels it. The authors should quantify how the spin-factor assumption and the branching-fraction assumption affect the absolute predictions, and compare their 2++ cross section with any other available estimates.
  4. [Section 3, Figs. 3-9] No uncertainty bands are shown on any of the predictions. Because the central claim is that the observables separate the three scenarios by 20-30% on heavy nuclei, the paper should propagate at least the uncertainties in sigma_XN, the elementary cross section, and the assumed branching fraction Br[X->J/psi J/psi] = 50%. Without this, the reader cannot judge whether the quoted scenario separation is statistically meaningful or an artifact of the point values chosen in Eq. (12).
minor comments (5)
  1. [Figure 1] The axis labels in Figure 1 appear garbled in the manuscript version (e.g., '23 43 63 84' and '840p'); the final typeset figure should be checked carefully.
  2. [Eq. (9)] The approximate equality in Eq. (9) should specify whether sigma_J/psiN and sigma_psi(3770)N are total inelastic cross sections or include elastic scattering, since the additive formula is used as an absorption cross section.
  3. [Section 2, footnote 10] The sign convention for the binding energy delta is confusing: delta = m_J/psi + m_psi(3770) - m_X is negative above threshold, yet the text calls the state loosely bound. Please state explicitly that delta < 0 corresponds to an unbound system.
  4. [Section 3, event-rate estimates] The value Br[X(6900)->J/psi J/psi] = 50% is described as conservative, but the cited Refs. [77,115] suggest a range of 30-45%; quoting the full range would make the event-rate estimates more transparent.
  5. [General] The introductory review is somewhat long relative to the new material; condensing the discussion of other fully-heavy tetraquark predictions would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the nuclear observables are forward-model outputs from external elementary cross sections and assumed absorption scenarios; the claimed structure sensitivity is a derived consequence, not a fitted input.

full rationale

The derivation chain is forward-modeling, not circular. The nuclear observables (Eqs. 3 and 15) are functions of the elementary gamma-p cross section (Eq. 7, taken from Ref. [80] and rescaled by spin counting) and of the effective nucleon number I_V[A, sigma_XN]. The three structure scenarios enter only through the absorption cross sections in Eq. (12): sigma_4c = 10 mb from geometric radii, sigma_mol = 21.2 mb from sigma_J/psi N = 3.5 mb (SLAC [100]) plus a size-squared scaling to sigma_psi(3770)N ~ 17.7 mb, and sigma_hyb = 15.6 mb from the incoherent 50/50 sum (Eq. 11). None of these parameters is fitted to the excitation functions, momentum distributions, or transparency ratios calculated in Section 3; those are outputs. The claimed ~20-30% (184W) and ~10% (12C) separations are a direct consequence of I_V being a monotonic function of sigma_XN: different inputs produce different outputs. That is a derivation, not a reduction of the prediction to its input. The self-citations [96,108,114] provide the general spectral-function collision model and the incoherent weighting formula, previously applied to X(3872) and Upsilon(1S); they do not presuppose the X(6900) outcome, and no fitted parameter or uniqueness theorem is imported from them. Concerns that sigma_psi(3770)N is poorly known, that the J/psi psi(3770) system is unbound at the adopted m_X = 6.886 GeV (footnote 10 gives delta = -5.4 MeV), and that no uncertainty bands are given are correctness and robustness objections, not circularity.

Assumptions & free parameters 9 free parameters · 7 assumptions · 0 invented entities

The calculation imports most of its physics from prior literature: the elementary cross section from [80], densities and I_V formalism from [96], angular distribution machinery from [114], and charmonium-nucleon cross sections from [100, 105-107]. The paper's own contribution is the choice of three structure scenarios and the numerical application to X(6900). No new particles or forces are introduced. The main free inputs are the absorption cross sections, the spin-counting factor, the hybrid mixing weight, the branching fraction, and the t-slope.

free parameters (9)
  • sigma_{4c}^{X(6900)N} = 10 mb
    Geometric area estimated from r_4c about 0.575 fm using interquark distances from Ref. [54]; average of 10.4 and 9.7 mb.
  • sigma_{J/psi N} = 3.5 mb
    Adopted from the 1977 SLAC J/psi photoproduction analysis [100].
  • sigma_{psi(3770)N} = 17.7 mb
    Obtained by scaling sigma_{J/psi N}=3.5 mb by (0.9/0.4)^2 = 5.06, assuming charmonium-nucleon cross section scales with spatial size squared.
  • sigma_{mol}^{X(6900)N} = 21.2 mb
    Sum sigma_{J/psi N} + sigma_{psi(3770)N} in Eq. (9) for the molecular scenario.
  • alpha^2, beta^2 hybrid weights = 0.5, 0.5
    Assumed equal weights in Eq. (10) for the hybrid scenario; no derivation is provided.
  • Elementary cross section normalization and exponent = 2.253 nb and 0.576
    Eq. (7) is a fit to the omega-exchange model results of Ref. [80] for 0++ production, with a nominal Br[X->J/psi omega]=1%.
  • Spin-counting factor 2++/0++ = 5
    Applied to Eq. (7) to convert the 0++ gamma p cross section to the 2++ X(6900) cross section, from simple spin-state counting.
  • Br[X(6900)->J/psi J/psi] = 50%
    Adopted as a conservative central value from QCD sum rule and width estimates, as stated in footnote 12.
  • t-slope b_{X(6900)} = 3.0 GeV^{-2}
    Taken equal to the J/psi slope in gamma p -> J/psi p at 35 GeV, used for the c.m. angular distribution.
assumptions (7)
  • domain assumption The gamma A cross section factorizes as I_V[A, sigma_XN] times the Fermi-averaged gamma N cross section (Eq. 3 following Ref. [96]).
    Standard nuclear spectral function and transport approximation; equations for I_V and averaging are cited from Ref. [96] rather than rederived.
  • domain assumption The in-medium gamma N cross section equals the vacuum cross section evaluated at shifted s* (Eqs. 4-6).
    Impulse approximation: binding and Fermi motion enter through s*, with no in-medium modification of the production vertex.
  • domain assumption The incident photon is not distorted and X(6900) decay inside the nucleus is neglected.
    Justified by the small photon interaction strength and by lambda_X of about 5-11 fm versus nuclear radii; stated in Sec. 2 and footnote 7.
  • ad hoc to paper The 2++ gamma p cross section is 5 times the 0++ cross section from the omega-exchange model, by spin-state counting.
    No direct calculation of 2++ photoproduction exists; the 5/1 ratio is a counting rule adopted from Refs. [81-83, 97, 98] in Sec. 2 after Eq. (7).
  • domain assumption Molecular absorption proceeds via single constituent scattering while the other charmonium is a spectator, with charmonium-nucleon cross sections scaling with size squared.
    Used to derive sigma_mol = 21.2 mb in Eq. (9) and footnote 10; the scaling factor 5.06 comes from Refs. [105-107].
  • ad hoc to paper The hybrid X(6900) wave function is 50% compact and 50% molecular (Eq. 10).
    The 50/50 weight is chosen to extend the model, not derived from QCD or data.
  • domain assumption Nuclear density distributions, including a neutron skin for heavy nuclei, are taken from Ref. [96].
    Input for I_V; the densities are not reproduced in the paper.

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Cite this review

Pith. "Pith review of On the nature of fully-charmed four-quark exotic state $X(6900)$ from its photoproduction off nuclei." pith.science (2026). https://pith.science/paper/NUBI3LCQ

@misc{pith2026260803374,
  author       = {Pith},
  title        = {Pith review of: On the nature of fully-charmed four-quark exotic state $X(6900)$ from its photoproduction off nuclei},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NUBI3LCQ}},
  note         = {Machine review of arXiv:2608.03374}
}
abstract

The possibility to study the nature of fully-charmed tetraquark state $X(6900)$ from its inclusive photoproduction off nuclei near the kinematic threshold is investigated within the collision model based on the nuclear spectral function. The model accounts for $X(6900)$ production in direct photon--nucleon interactions as well as three different scenarios for its internal structure: compact tetraquark, molecule of the two hidden-charm $J/\psi$ and $\psi(3770)$ mesons and the mixture of both of them. We calculate within these scenarios the absolute and relative excitation functions on $^{12}$C and $^{184}$W nuclei at near-threshold photon energies of 30--40 GeV, the absolute momentum differential cross sections and ratios of them for the $X(6900)$ meson production off these target nuclei at laboratory polar angles of 0$^{\circ}$--5$^{\circ}$ and for photon energy of 35 GeV as well as the A-dependences of its transparency ratios at photon energy of 35 GeV. We show that these observables reveal a definite sensitivity to the $X(6900)$ intrinsic structure. Therefore, they might be useful for the determination of this structure from the comparison of them with the experimental data from the future experiments at the upcoming experimental facilities, such as the planned electron-ion colliders in the United States and China.

Figures

Figures reproduced from arXiv: 2608.03374 by the authors.

Figure 1
Figure 1. (Color online.) The kinematically allowed [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. (Color online.) The decay mean free path of the [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. (Color online.) Excitation function for production of [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: (Color online.) The same as in Fig. 3, but for the [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: (Color online.) Momentum differential cross sections for the production of [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: (Color online.) Transparency ratio TA for the X(6900) mesons from the direct processes (1), (2) proceeding on an off-shell target nucleons as a function of the incident photon energy for combination 184W/12C in the considered theoretical pictures describing their inter…
Figure 7
Figure 7. Figure 7: (Color online.) Transparency ratio TA for the X(6900) mesons from the direct processes (1), (2) proceeding on an off-shell target nucleons as a function of the X(6900) laboratory momentum for incident photon energy of 35 GeV for combination 184W/12C, calculated in the …
Figure 8
Figure 8. Figure 8: (Color online.) Transparency ratio SA for the X(6900) mesons from the direct processes (1), (2) proceeding on an off-shell target nucleons at incident photon energy of 35 GeV in the laboratory system as a function of the nuclear mass number A, in the considered theoret…
Figure 9
Figure 9. Figure 9: (Color online.) The same as in Fig. 8, but for the transparency ratio [PITH_FULL_IMAGE:figures/full_fig_p016_9.png]

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