{"id":"9f31b756-cbcd-479a-839f-ac25bb85a80c","arxiv_id":"2506.09484","paper_version":2,"verdict":"REJECT","confidence":"HIGH","novelty_score":3.0,"correctness_risk":"high","formal_verification":"none","parameter_count":6,"one_line_summary":"Predicted rapidity cross sections for J/ψ, ψ(2S), Υ(1S), Υ(2S), Υ(3S) in p-p and O-O at 5.44 TeV, with ψ(2S) and Υ(3S) treated as mixed hybrids enhanced by π²/4.","lead":"The paper predicts production rates for heavy quark-antiquark particles (quarkonia) in proton-proton and oxygen-oxygen collisions at the LHC. It claims two of these states contain an extra gluon and should be produced more often, a claim future oxygen-collision data could test.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The measurability claim for the hybrid Υ(3S) in O-O collisions rests on hand-assigned absolute normalization factors (R_E_pp=0.005, R_E_OO=0.25) and an unspecified N_bin; the paper itself disclaims absolute magnitudes, so the central conclusion is unsupported.","rationale":"The reader's weakest-assumption analysis identifies the hand-assigned absolute normalization factors R_E_pp=0.005 and R_E_OO=0.25 as the load-bearing premise. I agree, and I sharpen the point: the paper's headline experimental claim ('could be measured') is precisely an absolute-rate claim, yet Sec. 2.1 disclaims the reliability of absolute magnitudes. The O-O rates also depend on N_bin, which is never stated, so the figures cannot be checked or reproduced. This is not a mere stylistic caveat; it is an internal tension between the stated uncertainty and the conclusion. Independently, the relative hybrid enhancement is an input from previous work, so the only genuinely new quantitative content is the absolute scale, and that scale is exactly what remains unjustified. A sensitivity scan over R_E_OO and N_bin would settle whether the measurability conclusion survives. Given this, the reader's REJECT verdict remains appropriate; no adjustment is needed.","tokens_in":5158,"tokens_out":11225,"duration_ms":121816,"concrete_test":"Recompute the O-O Υ(3S)(hybrid) dσ/dy from Eqs. (9)–(12) for R_E_OO ∈ {0.05, 0.25, 0.5} and N_bin ∈ {50, 100, 200} (Glauber estimates for O-O), and compare the integrated yield over |y|<1 with the expected Υ(3S) reconstruction capability at LHC O-O luminosities. If the yield spans values both above and below the detection threshold across this plausible parameter range, the measurability claim is not supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that the hybrid Υ(3S) differential rapidity cross section in O-O 'could be measured in future CERN LHC experiments' (Sec. 2.2) is a statement about absolute rates. Those rates are fixed by R_E_pp=0.005 and R_E_OO=0.25, introduced without derivation (Secs. 2.1–2.2; R_E_OO is merely 'R_E_XeXe/2'), and by N_bin, which appears in Eq. (9) but is never specified for O-O. The plotted O-O cross sections are therefore not reproducible from the text. Moreover, Sec. 2.1 explicitly says 'The absolute magnitudes are uncertain, and the shapes and relative magnitudes are our main predictions,' which directly contradicts the later measurability claim. If R_E_OO or N_bin differ by even a factor of a few, the predicted Υ(3S)(hybrid) yield can move across any plausible LHC detection threshold, so the conclusion is not robust. The relative enhancement (hybrid > standard) is itself an input (π²/4 from Ref. [16]), leaving the fragile absolute scale as the only new quantitative content.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper computes differential rapidity cross sections dσ/dy for J/Ψ, Ψ(2S), Υ(1S), Υ(2S), and Υ(3S) production in p-p and O-O collisions at √s_pp = 5.44 TeV, under the assumption that Ψ(2S) and Υ(3S) are mixed hybrid mesons with roughly a 50% valence-gluon component. The calculation uses the color-octet model formula in Eq. (11), nuclear modification factors R_E_pp = 0.005 and R_E_OO = 0.25, and a π²/4 enhancement for hybrid states taken from Ref. [16]. The paper's highlighted conclusion is that the hybrid Υ(3S) differential rapidity cross section in O-O collisions is larger than the standard Υ(3S) cross section and 'could be measured in future CERN LHC experiments.'","tokens_in":5507,"tokens_out":6458,"duration_ms":66892,"significance":"If the calculation were reliable, the paper would offer a concrete small-system prediction for O-O collisions and a possible experimental test of mixed-hybrid charmonium/bottomonium states. The paper is also transparent about the physical picture it assumes and states its main predictions in a falsifiable form. However, the quantitative output relies on unstated inputs and hand-assigned normalization factors, and the central 'hybrid > standard' ordering is imported as an input rather than derived. The paper provides no experimental comparison, no error bars, and no sensitivity analysis, and it explicitly disclaims the absolute magnitudes that the measurability claim depends on. The significance is therefore currently limited to a restatement of prior assumptions in a new collision system.","major_comments":[{"comment":"The constants A_Φ are given only for J/Ψ and Υ(1S); no values are supplied for Ψ(2S), Υ(2S), or Υ(3S), which are precisely the states emphasized in the paper. In addition, the gluon distribution f_g(x̄(y), 2m) is not identified with a specific PDF set, Q² scheme, or numerical implementation. Without these inputs, the curves in Figs. 2, 4, 6, and 8 cannot be reproduced or checked, so the quantitative content of the central plots is missing from the manuscript.","section":"Section 2.1, Eq. (11)"},{"comment":"The O-O cross sections depend on N_bin, the number of binary nucleon-nucleon collisions, which is never defined or specified for O-O. The factor R_E_OO = 0.25 is introduced as 'R_E_XeXe/2' with no derivation, reference, or physical justification. Since these quantities set the absolute scale of every O-O curve, a factor of a few in either one changes the predicted Υ(3S)(hybrid) yield across any plausible LHC detection threshold. The measurability claim in Sec. 2.2 is therefore not robust to the unspecified inputs.","section":"Sections 2.1-2.2, Eq. (9)"},{"comment":"The statement that the hybrid Υ(3S) cross section is larger than the standard Υ(3S) cross section is an input, not an output: the text says 'With Ψ(2S), Υ(3S) enhanced by π²/4 [16]' before plotting the curves. Because Ref. [16] is by the same first author, the claimed 'test of the validity of the mixed hybrid theory' reduces to re-inserting that enhancement factor. For the prediction to be a genuine test, the π²/4 factor would need to follow from the formalism developed in this paper or be independently justified here, rather than being adopted from prior work.","section":"Section 2.1 and Section 2.2"},{"comment":"The paper explicitly disclaims absolute magnitudes in Sec. 2.1, stating that 'the absolute magnitudes are uncertain, and the shapes and relative magnitudes are our main predictions.' Yet the highlighted conclusion in Sec. 2.2 ('could be measured in future CERN LHC experiments') is an absolute-rate statement. The manuscript needs a concrete LHC luminosity and acceptance estimate, together with a sensitivity study of the yield to R_E_OO, N_bin, and the PDF choice, or it should abandon the measurability claim and restrict itself to shape/relative predictions.","section":"Section 2.1 vs. Section 2.2"}],"minor_comments":[{"comment":"The coefficients in Eq. (3), -√2 and +√2, are not normalized, and they are inconsistent with Eq. (2), where f ≃ √2 would imply coefficients √2 and 1, and with the normalized form in Eqs. (7)-(8).","section":"Eqs. (2)-(3)"},{"comment":"Equation (9) is introduced as the Xe-Xe expression but is then used for p-p and O-O; the role of N_bin for p-p should be stated explicitly (presumably 1), and N_bin for O-O must be defined.","section":"Eq. (9)"},{"comment":"The nuclear shadowing parameter ξ_g² is introduced but its value is never specified; because it enters the effective parton momentum fraction, it affects the rapidity dependence of the predictions.","section":"Eq. (12)"},{"comment":"Figure 4 appears within Section 2.2, which is about O-O collisions, but its caption says 'via p-p collisions'; the placement and caption should be reconciled.","section":"Figures, Section 2.2"},{"comment":"There are numerous typographical errors, including 'Collaboratin', 'In stitute', 'P ACS', and 'Pittsburgh PA 1 5213 USA', and the PACS entry '14.40Nd' is malformed.","section":"References and text"},{"comment":"The uncertainty α = 0.7 ± 0.1 is given but never propagated into the figures or conclusions; the paper should state that the shown curves correspond to the central value and discuss the sensitivity to α.","section":"Section 2, Eqs. (7)-(8)"},{"comment":"The paper states that the ratios Ψ(2S)/J/Ψ and Υ(3S)/Υ(1S) 'agreed with experimental results', but no comparison with data is shown; a table or plot with the experimental values would make this claim verifiable.","section":"Section 2, Results"}],"recommendation":"reject","confidential_remarks":"The manuscript is very short and overlaps substantially with the authors' prior publications, Refs. [3,4,5,6,11,16], from which the mixed-hybrid states and the π²/4 enhancement are drawn. The principal new element, the application to O-O collisions, rests on an unexplained division of the Xe-Xe nuclear modification factor by two and on an unspecified N_bin. The journal may wish to consider whether the incremental content meets its novelty and completeness bar; the missing technical details (PDF specification, A_Φ values for the hybrid states, N_bin, and sensitivity analysis) are substantial enough that even a major revision would require a largely new calculation and comparison with data."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nQuick take: the paper is an application note that transplants Kisslinger's mixed-hybrid formalism from earlier papers to O-O collisions at 5.44 TeV. The new content is a set of differential rapidity curves. The central claim—that the hybrid Υ(3S) cross section exceeds the standard one and could be measured at the LHC—is not an outcome of the calculation; it is an input (the π²/4 enhancement from Ref [16]) and the absolute scale comes from hand-assigned factors R_E_pp=0.005 and R_E_OO=0.25. I agree with the reader's rejection.\n\nWhat the paper does well: it is clearly organized, states its hybrid assignments, and flags that absolute magnitudes are uncertain. That last caveat is the right instinct, but the paper then undermines it by asserting the O-O Υ(3S) hybrid signal could be measured. If the absolute scale is uncertain by a factor of a few, as the text admits, that measurability claim has no basis.\n\nThe soft spots are exactly where the reader put them. R_E_OO is set to half the Xe-Xe value with no derivation. N_bin appears in Eq. (9) and is never specified for O-O, so the plotted absolute rates cannot be reproduced. The enhancement factor and the mixing parameter come from the authors' earlier work; self-citation is fine, but here the conclusion is logically downstream of those inputs. There are no data comparisons or error bars, and the 'shapes and relative magnitudes' are not enough to test the model because the hybrid-vs-standard relative size is fixed by assumption.\n\nOne thing I'd push back on: the stress-test note is correct on the normalization problem, but it slightly overstates the circularity. There is an actual prediction here about the rapidity dependence of dσ/dy, which is not just a restatement of the enhancement. If the normalization could be fixed by data, the shape comparison would have some value. But that value is not realized in this manuscript.\n\nBottom line: the paper is a plausible exercise but not a credible prediction. I would not cite it. I would let a referee look at it if the journal wants a record of the O-O proposal, but the likely and appropriate outcome is rejection unless the authors justify the nuclear factors and N_bin, and remove or soften the measurability claim.\n\nBest,\n[you]","headline":"A short phenomenology note whose only new numbers are not reproducible from the text; the main 'prediction' is an input assumption, so rejection is warranted.","tokens_in":6062,"tokens_out":2798,"would_cite":false,"duration_ms":30519,"reading_group":"no","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["12.38.Aw","13.60.Le","14.40.Lb","14.40.Nd"],"model":"deepseek-v4-flash","headline":"A gluon-rich Υ(3S) hybrid should outproduce the ordinary Υ(3S) in O-O collisions, new rapidity cross sections predict.","keywords":["heavy quark state production","relativistic heavy ion collisions","heavy quark state suppression","small systems","mixed hybrid mesons","differential rapidity cross section","color octet model","bottomonium"],"falsifier":"At the LHC, measure $d\\sigma/dy$ for $\\Upsilon(3S)$ in O-O collisions at $\\sqrt{s_{NN}}=5.44$ TeV and in p-p collisions, and compare it with the pure $b\\bar{b}$ prediction. The paper's central prediction is that the hybrid-enhanced $\\Upsilon(3S)$ curve lies above the standard $\\Upsilon(3S)$ curve, with the same ordering for $\\Psi(2S)$ against $J/\\Psi$; a measured $\\Upsilon(3S)$ rate at or below the standard-model curve, or a $\\Psi(2S)/J/\\Psi$ ratio matching the naive color-octet value, would rule out the $\\pi^2/4$ hybrid enhancement.","tokens_in":4902,"feed_emoji":"⚛️","tokens_out":17983,"duration_ms":141844,"temperature":0.7,"pith_summary":"The paper predicts the differential rapidity cross sections $d\\sigma/dy$ for five heavy quark states — $J/\\Psi$, $\\Psi(2S)$, $\\Upsilon(1S)$, $\\Upsilon(2S)$, and $\\Upsilon(3S)$ — produced in proton-proton and oxygen-oxygen collisions at $\\sqrt{s_{pp}}=5.44$ TeV, the energy planned for O-O runs at the LHC. Its central move is to treat $\\Psi(2S)$ and $\\Upsilon(3S)$ not as ordinary quark-antiquark mesons but as mixed hybrids, roughly half standard meson and half quark-antiquark-gluon state, with a mixing parameter $\\alpha = 0.7 \\pm 0.1$ fixed by earlier QCD sum-rule work. Because hybrid production is enhanced by a factor $\\pi^2/4$, the predicted rate for the hybrid $\\Upsilon(3S)$ exceeds that of the standard $\\Upsilon(3S)$, and the authors argue this excess could be measured in future LHC experiments. The paper itself notes that the absolute magnitudes are uncertain and that the shapes and relative magnitudes of the distributions are its main predictions.","feed_headline":"New rates put hybrid Υ(3S) above its ordinary twin in O-O collisions","feed_subtitle":"Predictions for five heavy quark states at √s_pp = 5.44 TeV give LHC oxygen runs a concrete signal to hunt for.","key_machinery":"The load-bearing objects are the mixed hybrid wavefunctions for $\\Psi(2S)$ and $\\Upsilon(3S)$, $|\\Psi(2S)\\rangle = \\alpha|c\\bar{c}(2S)\\rangle + \\sqrt{1-\\alpha^2}|c\\bar{c}g(2S)\\rangle$ and $|\\Upsilon(3S)\\rangle = \\alpha|b\\bar{b}(3S)\\rangle + \\sqrt{1-\\alpha^2}|b\\bar{b}g(3S)\\rangle$ with $\\alpha = 0.7 \\pm 0.1$, so that each state is about half ordinary quark-antiquark meson and half quark-antiquark-gluon hybrid. These feed the color octet model formula $d\\sigma_{pp\\to\\Phi}/dy = A_\\Phi\\, x^{-1} f_g(\\bar{x},2m)\\, f_g(a/\\bar{x},2m)\\, dx/dy$, with the $\\Psi(2S)$ and $\\Upsilon(3S)$ hybrid amplitudes multiplied by the enhancement factor $\\pi^2/4$, and the whole result scaled by the nuclear factors $R^E_{pp}=0.005$ and $R^E_{OO}=0.25$ for proton-proton and oxygen-oxygen collisions respectively.","core_discovery":"The paper claims that $\\Psi(2S)$ and $\\Upsilon(3S)$ are mixed hybrid states, $|\\Psi(2S)\\rangle = \\alpha|c\\bar{c}(2S)\\rangle + \\sqrt{1-\\alpha^2}|c\\bar{c}g(2S)\\rangle$ and $|\\Upsilon(3S)\\rangle = \\alpha|b\\bar{b}(3S)\\rangle + \\sqrt{1-\\alpha^2}|b\\bar{b}g(3S)\\rangle$ with $\\alpha = 0.7 \\pm 0.1$, so each has roughly a 50% probability of being a standard quark-antiquark meson and a 50% probability of being a color-octet quark-antiquark pair with an active gluon. Using the color octet model formula for the differential rapidity cross section, with the hybrid amplitudes multiplied by $\\pi^2/4$, it computes $d\\sigma/dy$ for $J/\\Psi$, $\\Psi(2S)$, $\\Upsilon(1S)$, $\\Upsilon(2S)$, and $\\Upsilon(3S)$ in p-p and O-O collisions at $\\sqrt{s_{pp}}=5.44$ TeV. The central quantitative prediction is that the hybrid $\\Upsilon(3S)$ rate lies above the standard pure-$b\\bar{b}$ $\\Upsilon(3S)$ rate in both collision systems, and in O-O it sits in a range the authors say could be measured in future LHC experiments, making the measurement both a test of the mixed hybrid theory and a guide for small-system runs.","pith_inferences":["The ratio of O-O to p-p rates for a given state cancels the uncertain absolute normalization, so the most robust test of the $\\pi^2/4$ enhancement is the ratio of measured yields, not the absolute cross section.","If O-O data come in, the same framework should be extended to Pb-Pb, where the larger $R^E_{AA}$ values would make the hybrid excess larger in absolute terms; a failure of that scaling would point to the hand-set normalization factors rather than the hybrid wavefunctions.","A natural next step the paper does not take is to compute $R^E_{OO}$ from first principles using the dissociation cross sections of the hybrid states, which would turn the assumed factor 0.25 into a derived quantity and sharpen the measurability claim.","Because hybrid states carry a valence gluon, the same $\\pi^2/4$ mechanism predicts enhanced production in gluon-rich environments, suggesting the O-O signal could be cross-checked against high-multiplicity p-p events at the same energy."],"forward_implications":["In O-O collisions at $\\sqrt{s_{pp}}=5.44$ TeV, the measured $\\Upsilon(3S)$ rate should lie above the standard bottomonium-only curve, providing a direct test of the mixed hybrid theory.","The $\\Psi(2S)$ charmonium state should show a similar hybrid-enhanced $d\\sigma/dy$ in both p-p and O-O, visible as an excess over the standard $c\\bar{c}$ curve.","The predicted shapes and relative magnitudes of the five rapidity distributions, not just their absolute sizes, are the paper's stated main predictions, so shape comparisons against data at the same energy would be decisive.","A confirmed excess would validate the $\\alpha = 0.7 \\pm 0.1$ hybrid admixture extracted from earlier QCD sum rules and extend it to bottomonium as well as charmonium."],"supporting_citations":[{"why":"establishes the mixed hybrid wavefunctions and the QCD sum-rule value $f \\simeq \\sqrt{2}$ for $\\Psi(2S)$ and $\\Upsilon(3S)$ that define the hybrid admixtures.","marker":"[4]"},{"why":"supplies the color octet model formula for $d\\sigma/dy$, the constants $A_\\Phi$, and the $\\pi^2/4$ hybrid enhancement factor used in the rate predictions.","marker":"[16]"},{"why":"provides the nuclear-modified formula $d\\sigma_{AA\\to\\Phi}/dy = R^E_{AA} N_{bin}\\langle d\\sigma_{pp\\to\\Phi}/dy\\rangle$ that scales the p-p rates to O-O.","marker":"[6]"},{"why":"documents the earlier application of the mixed hybrid theory whose predicted $\\Psi(2S)/J/\\Psi$ and $\\Upsilon(3S)/\\Upsilon(1S)$ ratios matched experiment, validating the admixtures used here.","marker":"[11]"},{"why":"gives the proton-proton production formalism on which the p-p differential cross sections are built.","marker":"[3]"},{"why":"derives the helicity decomposition for $J/\\Psi$ and the hybrid $\\Psi(2S)$ used in the color octet treatment.","marker":"[8]"},{"why":"documents the proposed LHC O-O collision opportunities that set the $\\sqrt{s_{pp}}=5.44$ TeV scenario.","marker":"[21]"}],"fun_headline_variants":["Hybrid Υ(3S) tops ordinary state in O-O collisions","Mixed hybrid Υ(3S) outpaces ordinary twin in p-p and O-O","Hybrid Υ(3S) enhancement predicted for LHC oxygen collisions","Mixed hybrid Υ(3S) cross section exceeds ordinary in both systems","Hybrid Υ(3S) signal could test quark-gluon mix in O-O"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the hand-assigned normalization factors $R^E_{pp}=0.005$ and $R^E_{OO}=0.25$ — the oxygen value taken as half the Xe-Xe value without derivation — set the true absolute scale of every predicted cross section, so that a wrong factor of even a few would shift the claimed measurability of the $\\Upsilon(3S)$ hybrid signal and all plotted rates.","fun_headline_variants_meta":{"raw":{"variants":["Hybrid Υ(3S) tops ordinary state in O-O collisions","Mixed hybrid Υ(3S) outpaces ordinary twin in p-p and O-O","Hybrid Υ(3S) enhancement predicted for LHC oxygen collisions","Mixed hybrid Υ(3S) cross section exceeds ordinary in both systems","Hybrid Υ(3S) signal could test quark-gluon mix in O-O"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000743,"raw_usage":{"total_tokens":3351,"prompt_tokens":1021,"completion_tokens":2330,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":637,"completion_tokens_details":{"reasoning_tokens":2227}},"tokens_in":637,"tokens_out":2330,"duration_ms":18609,"temperature":1.0,"reasoning_tokens":2227,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T04:47:28.727104+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"At the LHC, measure $d\\sigma/dy$ for $\\Upsilon(3S)$ in O-O collisions at $\\sqrt{s_{NN}}=5.44$ TeV and in p-p collisions, and compare it with the pure $b\\bar{b}$ prediction. The paper's central prediction is that the hybrid-enhanced $\\Upsilon(3S)$ curve lies above the standard $\\Upsilon(3S)$ curve, with the same ordering for $\\Psi(2S)$ against $J/\\Psi$; a measured $\\Upsilon(3S)$ rate at or below the standard-model curve, or a $\\Psi(2S)/J/\\Psi$ ratio matching the naive color-octet value, would rule out the $\\pi^2/4$ hybrid enhancement.","supporting_citations":[{"cited_title":"Kisslinger, Phys","cited_arxiv_id":null,"evidence_quote":"establishes the mixed hybrid wavefunctions and the QCD sum-rule value $f \\simeq \\sqrt{2}$ for $\\Psi(2S)$ and $\\Upsilon(3S)$ that define the hybrid admixtures."},{"cited_title":"Kisslinger, M.X","cited_arxiv_id":null,"evidence_quote":"supplies the color octet model formula for $d\\sigma/dy$, the constants $A_\\Phi$, and the $\\pi^2/4$ hybrid enhancement factor used in the rate predictions."},{"cited_title":"Kisslinger, M.X","cited_arxiv_id":null,"evidence_quote":"provides the nuclear-modified formula $d\\sigma_{AA\\to\\Phi}/dy = R^E_{AA} N_{bin}\\langle d\\sigma_{pp\\to\\Phi}/dy\\rangle$ that scales the p-p rates to O-O."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"documents the earlier application of the mixed hybrid theory whose predicted $\\Psi(2S)/J/\\Psi$ and $\\Upsilon(3S)/\\Upsilon(1S)$ ratios matched experiment, validating the admixtures used here."},{"cited_title":"Heavy quark state production in Pb-Pb collisions at $\\sqrt{s_{NN}}$=5.02 TeV","cited_arxiv_id":"1612.02269","evidence_quote":"gives the proton-proton production formalism on which the p-p differential cross sections are built."},{"cited_title":"Braaten and Y-Q Chen, Phys","cited_arxiv_id":null,"evidence_quote":"derives the helicity decomposition for $J/\\Psi$ and the hybrid $\\Psi(2S)$ used in the color octet treatment."}],"review_version":1}