{"id":"d34b89c7-a1a7-42d7-97a5-ed731d9f4e92","arxiv_id":"2608.03374","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":9,"one_line_summary":"Nuclear photoproduction of X(6900) off carbon and tungsten is predicted to differ by 10-30% between compact-tetraquark, J/psi-psi(3770) molecular, and hybrid interpretations, potentially allowing future electron-ion colliders to identify its internal structure.","lead":"The paper predicts how often the X(6900), a four-quark particle candidate, would be produced when high-energy photons hit carbon and tungsten nuclei. The predictions differ measurably for compact-tetraquark, molecular, and mixed internal structures, so future electron-ion collider data could distinguish these pictures.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Scenario separation rests entirely on unvalidated absorption cross sections: sigma_psi(3770)N=17.7 mb follows from a 1977 SLAC value and a size-scaling factor, and a few mb shift erodes the quoted 20-30% discrimination.","rationale":"The paper is a transparent application of the author's spectral-function collision model, and the use of transparency ratios as normalization-robust observables is sensible. The event-rate estimates are a useful first guide for planning. The load-bearing weakness is not the nuclear-model machinery but the mapping from internal structure to absorption cross sections: every structure-sensitive observable is a functional of sigma_XN only, so the conclusions inherit the uncertainty in Eq. 12. The reader's weakest assumption identifies this same point; the additional observation that the adopted mass places the J/psi psi(3770) system above threshold reinforces the concern, because the molecular scenario is then not a bound state in the usual sense. This does not invalidate the paper, but it means the predictions should be presented with uncertainty bands and with an independent assessment of psi(3770)N before being used to plan experiments. The conditional verdict is therefore appropriate and no change is needed.","tokens_in":19394,"tokens_out":6502,"duration_ms":67204,"concrete_test":"Recompute Figs. 3-9 with sigma_mol_XN set to 12, 18, and 25 mb (e.g., psi(3770)N = 8.5, 14.5, and 21.5 mb for sigma_J/psiN=3.5 mb) and with hybrid weights of 30/70 and 70/30, then evaluate the smallest separation between molecular, hybrid, and compact predictions for the 184W excitation function and T_A at E_gamma=35 GeV. If any scenario pair overlaps within ~5% across this range, the quoted 20-30% discrimination is not robust and the paper should present sensitivity bands before claiming that EIC/EicC can determine the internal configuration.","verdict_should_be":"UNCHANGED","load_bearing_attack":"All claimed sensitivity to X(6900) structure enters through sigma_XN in the effective nucleon number I_V (Eq. 3). The three values in Eq. 12 are not measured: the compact value is a geometric estimate, the molecular value assumes sigma_J/psiN=3.5 mb from SLAC [100] and scales psi(3770)N by the squared size ratio (0.9/0.4)^2=5.06 to obtain 17.7 mb, and the hybrid value assumes exactly 50/50 incoherent mixing. The resulting sigma_mol_XN=21.2 mb is far above the only explicit microscopic estimate quoted for psi(3770)N, the quark-interchange value of 10^-2 mb [101], which the paper dismisses without a replacement calculation. Furthermore, for the adopted m_X=6.886 GeV the J/psi psi(3770) threshold is 6.8706 GeV, so the state sits about 15 MeV above threshold; it is not a bound molecule, which undermines the loose-binding picture used to justify additive constituent absorption in Eq. (9). Since the nuclear observables are monotonic functions of sigma_XN, a plausible psi(3770)N in the 3-10 mb range would bring the molecular and hybrid curves close to the compact curve, shrinking or removing the claimed separation. The paper provides no uncertainty bands around Eq. (12), so the central claim is conditional on these point values.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":19782,"tokens_out":5048,"duration_ms":45372,"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":[{"comment":"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).","section":"Section 2, Eq. (12)"},{"comment":"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.","section":"Section 2, Eq. (9) and footnote 10"},{"comment":"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.","section":"Section 2, Eq. (7)"},{"comment":"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).","section":"Section 3, Figs. 3-9"}],"minor_comments":[{"comment":"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.","section":"Figure 1"},{"comment":"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.","section":"Eq. (9)"},{"comment":"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.","section":"Section 2, footnote 10"},{"comment":"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.","section":"Section 3, event-rate estimates"},{"comment":"The introductory review is somewhat long relative to the new material; condensing the discussion of other fully-heavy tetraquark predictions would improve readability.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"This is a straightforward application of the author's previously published spectral-function formalism to X(6900). Its main value is the concrete set of predictions for EIC and EicC. The principal risk is that the scenario separation is driven entirely by the unvalidated absorption cross sections in Eq. (12). I would ask for a sensitivity analysis and a resolution of the bound/unbound-state inconsistency before considering the paper for publication. The self-citations to Refs. [96,108,114] are appropriate given that the framework is the author's own."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper does what it says: it takes the author's established spectral-function collision model and applies it to inclusive X(6900) photoproduction off 12C and 184W, with three structure scenarios encoded as different X(6900)-nucleon absorption cross sections. The new piece is the nuclear-target study itself, and the transparency ratios T_A and S_A are sensible observables because they partly cancel the dominant uncertainty, the unknown elementary gamma p -> X(6900) p cross section. The event-rate estimates for EIC and EicC are a practical plus. This is a genuine, if incremental, contribution. The soft spot, as the stress-test note says, is that all scenario separation flows through three point values in Eq. (12): sigma_XN = 10, 15.6, and 21.2 mb. The molecular value is built from a 1977 SLAC measurement of sigma_J/psi N and a size-squared scaling to psi(3770), giving 17.7 mb, and the paper dismisses the quark-interchange value of 10^-2 mb without a replacement calculation. Since the observables are monotonic in sigma_XN, a psi(3770) N cross section in the 3-10 mb range would bring the molecular and hybrid curves close to the compact one, and the claimed 20-30% discrimination on 184W would shrink to something hard to measure. The paper provides no uncertainty bands or sensitivity scan around Eq. (12). That is an addressable weakness, not a fatal flaw. One more tension worth flagging: the adopted mass 6.886 GeV sits about 15 MeV above the J/psi psi(3770) threshold, so this is not a bound molecule in the usual sense. The author acknowledges this in the footnote by using m_X = 6876 MeV and a negative binding energy, but still treats the constituents as individual on-shell mesons. That should be discussed more carefully. The citation pattern is fine. The self-citations are to the author's own prior formalism, which is legitimate when you are reusing a published method, and the elementary cross section is external. Who is this for? Hadron spectroscopists and EIC/EicC phenomenologists who want a concrete prediction to plan against. It deserves a serious referee, not a desk reject. The referee should ask for an uncertainty budget on the absorption cross sections and a scan over sigma_XN to show which regions preserve the claimed discrimination.","headline":"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.","tokens_in":766,"tokens_out":786,"would_cite":true,"duration_ms":29213,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["X(6900)","fully-charmed tetraquark","photoproduction off nuclei","nuclear spectral function","transparency ratio","hadronic molecule","compact tetraquark","electron-ion collider"],"falsifier":"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.","tokens_in":19141,"feed_emoji":"⚛️","tokens_out":10927,"duration_ms":82998,"temperature":0.7,"pith_summary":"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.","feed_headline":"Nuclear photoproduction can identify the true structure of X(6900)","feed_subtitle":"Predicted yields on tungsten and carbon differ by 20-30% and 10% between tetraquark, molecule, and hybrid scenarios.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Provides the nuclear spectral function model, the effective nucleon number $I_V[A,\\sigma]$, and the inclusive $\\gamma A$ production formalism that the paper adapts to $X(6900)$.","marker":"[96]"},{"why":"Supplies the $\\omega$-exchange $\\gamma p \\to X(6900)p$ total cross-section parametrization used as the elementary production input.","marker":"[80]"},{"why":"Reports the measured $X(6900)$ mass and width (6.886 and 6.905 GeV; 0.168 and 0.08 GeV) adopted in the kinematics and decay-rate estimates.","marker":"[19]"},{"why":"Provides the $J/\\psi$–nucleon absorption cross section of 3.5 mb that anchors the molecular absorption scenario.","marker":"[100]"},{"why":"Gives the diquark and inter-diquark radii used to estimate the compact-tetraquark radius and hence the 10 mb geometrical cross section.","marker":"[54]"},{"why":"Basis for the incoherent probability-weighted combination of compact and molecular absorption cross sections in the hybrid scenario.","marker":"[108]"},{"why":"Supplies the off-shell differential cross-section expressions that the paper reuses for the momentum-dependent photoproduction distributions.","marker":"[114]"},{"why":"Specifies the integrated luminosity and detector assumptions used to estimate yearly $X(6900)$ event numbers at one of the planned colliders.","marker":"[92]"}],"fun_headline_variants":["X(6900) photoproduction off nuclei reveals its structure","Nuclear targets expose X(6900) internal configuration","Tungsten and carbon yields distinguish X(6900) models","Photoproduction off nuclei: a sensitive X(6900) structure test","20-30% gap: X(6900) structure via nuclear photoproduction"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["X(6900) photoproduction off nuclei reveals its structure","Nuclear targets expose X(6900) internal configuration","Tungsten and carbon yields distinguish X(6900) models","Photoproduction off nuclei: a sensitive X(6900) structure test","20-30% gap: X(6900) structure via nuclear photoproduction"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000664,"raw_usage":{"total_tokens":3093,"prompt_tokens":1067,"completion_tokens":2026,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":683,"completion_tokens_details":{"reasoning_tokens":1932}},"tokens_in":683,"tokens_out":2026,"duration_ms":15487,"temperature":1.0,"reasoning_tokens":1932,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T14:50:29.207119+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[],"review_version":2}