{"id":"595d6242-077e-4763-9476-0a1686baa208","arxiv_id":"2504.14850","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"NLO NRQCD predictions for exclusive J/psi pair and eta_c pair production in ultraperipheral Pb-Pb and p-p collisions at HL-LHC and FCC energies, plus Low-formula estimates for the X(6900) state.","lead":"This paper computes how often two charmonium mesons are produced when heavy ions or protons pass each other closely without colliding, using next-to-leading-order QCD. It predicts cross sections and distributions for the HL-LHC and FCC and argues the clean event signature makes the process measurable.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central NLO predictions are scale-unstable and yield negative differential cross sections at large |Δy|, so the quoted 28.0 nb is not a robust result.","rationale":"The reader's weakest assumption identifies the same issue: the truncated NLO series may not be physically meaningful at the chosen scale. Our stress-test agrees. The strongest evidence is internal: Table I shows a factor-7.6 scale dependence, Table III shows negative differential cross sections, and the K-factor for J/ψ is 0.25. The X(6900) discussion is also self-admittedly abnormal, but it is secondary to the main claim. Since the paper acknowledges these issues only as a caveat and does not provide a cured prediction, the central numbers are conditional. The proposed check would determine whether the scale choice is the only source of the instability; if the spread is as large as indicated, the paper should be revised to present the scale uncertainty as the dominant uncertainty or to adopt a more appropriate scale-setting procedure. Verdict remains CONDITIONAL (unchanged from the reader).","tokens_in":12745,"tokens_out":7945,"duration_ms":71632,"concrete_test":"Recompute the J/ψ-pair NLO total cross section at μ = 2m_c and at μ = sqrt(s_γγ), and use the resulting spread to assign a scale uncertainty. If the scale band spans more than a factor of three (roughly 11–84 nb), the central value 28.0 nb and its quoted mass uncertainty are not representative, and the measurability conclusion must be reassessed.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim is the NLO total cross section of 28.0 nb for J/ψ-pair production at μ = sqrt(4m_c^2 + p_T^2). This number is not stable: Table I shows the NLO total varies from 11.0 nb at μ = 2m_c to 83.8 nb at μ = sqrt(s_γγ), a factor of 7.6. At the chosen scale, Table III gives negative NLO differential cross sections for |Δy| > 2 (e.g., -0.47 nb in the bin 2.5–3), which is unphysical for a differential cross section. The authors acknowledge this and suggest scale resetting or resummation, but the quoted central value is still at the scale where negativity occurs. The NLO correction is about −75% of the LO (K ≈ 0.25), so the fixed-order expansion is not a small correction. The paper itself flags this limitation in the text around Table III. Consequently, the headline NLO predictions and the derived event yields are not reliable as absolute numbers; the central result depends strongly on an arbitrary scale choice.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper computes next-to-leading-order (NLO) QCD corrections, in the NRQCD color-singlet framework, to exclusive γγ→J/ψJ/ψ and γγ→ηcηc production in ultraperipheral collisions, using the equivalent-photon approximation. It reports total cross sections of 28.0 nb for J/ψ-pair and 65.1 nb for ηc-pair production in Pb-Pb UPC at √sNN=5.52 TeV, along with differential distributions in transverse momentum, diphoton invariant mass, and rapidity difference, and estimates of event rates at the HL-LHC and FCC. The paper also estimates two-photon production of the fully charmed tetraquark X(6900) using the Low formula with several model assumptions for its diphoton width.","tokens_in":13031,"tokens_out":11579,"duration_ms":116147,"significance":"If the central NLO predictions were robust, this study would offer a clean test of NRQCD factorization in an exclusive two-photon process, with color-octet contributions strongly suppressed and UPC event topologies providing large rapidity gaps. The paper usefully extends the authors' earlier NLO calculation to heavy-ion UPCs, provides explicit flux-convolution formulas, and tabulates cross sections for many collision systems. The X(6900) discussion, though speculative, points to a possible two-photon production window for fully charmed tetraquarks. However, as detailed in the major comments, the scale dependence of the NLO series and the occurrence of negative differential cross sections at the chosen central scale mean that the headline numbers are not yet reliable as quantitative predictions.","major_comments":[{"comment":"The central NLO predictions are not robust because the central scale choice is both ambiguous for integrated observables and strongly scale-dependent. For the J/ψ pair, the NLO total cross section varies from 11.0 nb at μ=2mc to 83.8 nb at μ=√ŝγγ (Table I), a factor of about 7.6, while the quoted charm-mass uncertainty on the central value is only +18.4/−11.1 nb. At the central scale μ=√(4mc^2+p_T^2), the NLO correction is approximately −75% of the LO result (28.0 nb versus 111 nb), and Table III shows that the NLO differential cross section dσ/d|Δy| becomes negative for |Δy|>2, e.g., −0.47 nb in the 2.5–3 bin. The text acknowledges this and defers to scale resetting or resummation, but no such improved calculation is provided. The paper also never defines which p_T value is used when this scale is applied to the total cross section, since p_T is integrated over. These issues directly affect the abstract's headline value of 28.0 nb, so they are load-bearing rather than cosmetic.","section":"§III, Table I and Table III"},{"comment":"The qualitative claim that NLO corrections are large and negative for J/ψ pairs and positive for ηc pairs is not scale-invariant. Table I shows that for J/ψ pairs the NLO correction is negative at μ=2mc (11.0 nb versus 120 nb LO) but positive at μ=√ŝγγ (83.8 nb versus 62.6 nb LO). The K-factors are approximately 0.25 for J/ψ and 2.35 for ηc, both far from unity, indicating that the fixed-order expansion is not a small perturbation. Therefore, the sign and magnitude of the NLO corrections, and hence the claimed qualitative NRQCD test, depend strongly on an arbitrary renormalization-scale choice. The abstract and conclusions should be revised to present these results as scale-sensitive fixed-order estimates rather than definitive predictions.","section":"§III, Table I and Abstract"},{"comment":"The quoted theoretical uncertainties are incomplete: Table I gives only the variation with mc at fixed renormalization scale, while the scale dependence itself is an order of magnitude larger than the mass uncertainty. For a phenomenological claim based on total cross sections, the scale variation should be included as an uncertainty band, and the negative bins in Table III should be addressed by a concrete prescription rather than a statement that the problem 'could be cured' by resetting the scale. Without such a treatment, the event-rate projections derived from the central values (e.g., 140–194 J/ψ-pair events in heavy-ion UPCs) inherit an uncontrolled systematic uncertainty.","section":"§III, Table I and text after Table III"}],"minor_comments":[{"comment":"Please clarify how the NLO-extracted radial wave function |R_NLO_J/ψ(0)|^2=0.907 GeV^3 is obtained from Eq. (8) with the two-loop running coupling, and state explicitly which value of μ0 is used in the numerical extraction beyond the statement μ0=2mc.","section":"§III, Eq. (7) and Eq. (8)"},{"comment":"In the submitted version many axis labels and panel annotations in Figures 2–4 are unreadable. Please ensure the final figures have clearly legible labels, legends, and units.","section":"§III, Fig. 2, Fig. 3, Fig. 4"},{"comment":"Table III is titled as the rapidity-difference distribution of the J/ψ pair, but the text and Figure 4 suggest the same distribution is shown for ηc pairs as well. Please clarify whether Table III applies to both channels or only to J/ψ pairs.","section":"§III, Table III"},{"comment":"The X(6900) cross-section estimates in Table IV are orders of magnitude larger than the direct double-charmonium yields, and the text itself states this may reflect overestimated diphoton and di-charmonium decay fractions. Please label these values as model-dependent upper-bound-like estimates or remove the quantitative comparison, since the current presentation invites an unjustified quantitative interpretation.","section":"§III, Table IV"},{"comment":"The feasibility conclusion is based on reconstructed event counts of 2–12 per year after branching ratios, but no background estimate or detection-efficiency assumption is given. A quantitative background assessment, even a rough one, is needed to support the claim that these channels are experimentally accessible.","section":"§III, feasibility discussion"}],"recommendation":"major_revision","confidential_remarks":"The scale-instability problem identified in the stress-test note is confirmed by the manuscript's own Table I and Table III, so the central predictions are not robust as they stand. The underlying NLO calculation appears to be a legitimate extension of the authors' previous work, and the topic is suitable for the journal, but the authors need to provide a principled scale-setting prescription, include scale-variation uncertainties, and address or remove the negative differential cross sections before the headline numerical claims can be accepted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper does exactly what it says: it takes the NLO gamma-gamma -> charmonium-pair amplitudes from the authors' previous work, convolutes them with equivalent-photon fluxes for a range of ion species at the HL-LHC and FCC, and produces total and differential cross sections. That is a real extension and the numerical results are new. The treatment of the EPA is standard, the input parameters are documented, and the authors are transparent about the large scale dependence and even flag the negative differential bins. I appreciate that honesty.\n\nThe problem is not the calculation, which looks sound in structure; it is the interpretation of the central numbers. The J/psi-pair NLO total cross section changes from 11.0 nb to 83.8 nb when the scale goes from 2m_c to sqrt(s_γγ), and the chosen \"central\" scale sqrt(4m_c^2+p_T^2) gives a K-factor around 0.25 and negative dsigma/d|Δy| for |Δy| > 2. The paper acknowledges this and suggests scale resetting or resummation, but then still quotes 28.0 nb as the headline result. That is not a reliable absolute prediction. If the expansion breaks down at the central scale, the number should carry a strong caveat or a different scale should be used. The eta_c channel is less dramatic, but the same issue of a large positive NLO correction and scale sensitivity applies.\n\nThe X(6900) section is the weakest part. The estimated cross sections range from 6e3 to 2e5 nb, which the authors themselves call abnormal and attribute to overestimated branching fractions. That is a self-admitted unphysical result, and it does not strengthen the paper. I would remove it or reframe it as a rough upper-limit illustration with the caveat front and center.\n\nThe citation pattern is fine; the relevant NRQCD and UPC literature is covered. No code or data is shipped, so the reproducibility rests on the formulas in the paper, which are sufficiently detailed for a specialist to reproduce.\n\nBottom line: this is a useful phenomenological paper for people working on UPC and double-charmonium searches, but the headline cross sections should not be used as solid numbers until the scale issue is dealt with. The flaws are fixable with a careful revision, so I would send it to peer review rather than reject it outright. A serious referee should push the authors to either choose a scale where the NLO expansion is well-behaved or present the scale sensitivity as the main uncertainty, and to remove or heavily qualify the X(6900) estimates.","headline":"A legitimate but modest extension of an existing NLO NRQCD calculation to UPC; the central cross sections are not robust because the NLO expansion itself signals a breakdown at the chosen scale.","tokens_in":13558,"tokens_out":1935,"would_cite":false,"duration_ms":20971,"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":"This paper predicts that exclusive J/ψ-pair and ηc-pair production in ultraperipheral Pb-Pb collisions has measurable rates at NLO in NRQCD, with opposite-sign NLO corrections for the two channels.","keywords":["charmonium pair production","ultraperipheral collision","NRQCD","NLO QCD corrections","photon-photon fusion","J/ψ pair","ηc pair","X(6900)"],"falsifier":"Measure the rapidity-difference distribution of exclusive J/ψ-pair production in Pb-Pb UPC at the HL-LHC; if the bins with |Δy|>2 show positive rates near the leading-order size, or if the total rate differs from 28 nb by more than the quoted uncertainties, the NLO NRQCD prediction is falsified. The ηc-pair rate of 65.1 nb offers an independent check.","tokens_in":12527,"feed_emoji":"⚛️","tokens_out":14813,"duration_ms":113661,"temperature":0.7,"pith_summary":"This paper aims to establish that exclusive double charmonium production via photon-photon fusion in ultraperipheral heavy-ion collisions at the HL-LHC and FCC can serve as a clean test of NRQCD factorization. Using next-to-leading-order QCD corrections in the color-singlet sector, it predicts total cross sections of 28.0 nb for J/ψ pairs and 65.1 nb for ηc pairs in Pb-Pb collisions at 5.52 TeV, with large negative corrections for J/ψ and positive for ηc. The resulting event rates are small but topologically clean because UPC events lack pileup and have large rapidity gaps, so backgrounds from QCD interactions are suppressed. The paper also estimates X(6900) production through two-photon fusion using the two-photon-width formula for resonance production.","feed_headline":"Photon fusion of lead ions gives 28 nb of J/psi pairs","feed_subtitle":"NLO QCD puts ηc pairs at 65 nb with opposite-sign corrections, a sharp NRQCD test at LHC and FCC.","key_machinery":"The central machinery is NRQCD (non-relativistic QCD) factorization at next-to-leading order in QCD, applied to the color-singlet γγ→H+H amplitudes using covariant spin and color projectors, combined with the equivalent-photon approximation for ultraperipheral collisions. The NLO amplitudes are regularized dimensionally, with on-shell renormalization for the heavy quark field and mass and MS renormalization for the strong coupling. The observable UPC cross section is obtained by convolving the NLO parton-level cross section with the ion photon spectral function for heavy ions, and this factorization is what carries the argument from a QCD calculation to measurable rates.","core_discovery":"The paper's central claim is that at next-to-leading order in QCD, the photon-photon fusion cross sections for exclusive J/ψ-J/ψ and ηc-ηc production in ultraperipheral Pb-Pb collisions are 28.0 nb and 65.1 nb respectively, and that the NLO corrections have opposite signs: large negative for J/ψ pairs and positive for ηc pairs. These predictions follow from NRQCD factorization with color-singlet matrix elements, and the paper argues that UPC event topologies suppress QCD backgrounds enough that the rates are measurable at the HL-LHC and FCC. The J/ψ-pair K-factor is about 0.25 and the ηc-pair about 2.35, and differential distributions in pT, mγγ, and |Δy| are provided. At the default scale, the J/ψ-pair differential cross section becomes negative for |Δy|>2, which the authors attribute to large negative loop corrections and suggest may be cured by scale resetting or resummation.","pith_inferences":["Not stated in the paper: if the negative NLO differential cross section at |Δy|>2 reflects a genuine breakdown of fixed-order perturbation theory rather than a scale artifact, the 28.0 nb total may be unreliable; a resummed or next-to-next-to-leading-order calculation would settle this.","A test that follows from the sign asymmetry but is not proposed by the authors: measuring the ratio σ(ηc-ηc)/σ(J/ψ-J/ψ) as a function of pT would isolate the spin dependence of the NLO corrections and could expose missing relativistic or color-octet effects.","The X(6900) estimates span two orders of magnitude across the three two-photon-width models; a UPC measurement of the di-J/ψ invariant mass near 6.9 GeV would effectively measure Γ(X→γγ) and discriminate among those models, going beyond the paper's tabulated estimates.","The same NLO machinery could be applied to other exclusive channels, such as J/ψ plus ψ(2S), to test whether the opposite-sign correction pattern is specific to the spin-triplet versus spin-singlet ground states."],"forward_implications":["At the HL-LHC, the predicted yields are 140-194 J/ψ-pair events and 325-456 ηc-pair events per run from heavy-ion UPCs, with 835 and 1980 from p-p UPCs, before decay branching ratios.","Using the branching fractions quoted in the paper, J/ψ→l+l− at 12% and ηc→K\\bar Kπ at 7.3%, reconstructed candidates would be 2-12 per year for J/ψ pairs and 1-10 for ηc pairs at the HL-LHC; at the FCC the J/ψ-pair yield grows to 180-200.","The opposite signs of the NLO K-factors, about 0.25 for J/ψ pairs and 2.35 for ηc pairs, mean the two channels respond very differently to higher-order QCD, so a simultaneous measurement would be a sensitive NRQCD test.","The differential cross sections in pT, mγγ, and |Δy| are given without cuts, providing specific shapes that UPC experiments can compare directly with data.","The X(6900) production cross section via two-photon fusion is estimated at 6×10^3 to 2×10^5 nb depending on the two-photon width model, implying a potentially large di-charmonium signal if the state decays predominantly into charmonium pairs."],"supporting_citations":[{"why":"supplies the NRQCD factorization formalism and velocity-scaling power counting that organizes the calculation.","marker":"[1]"},{"why":"is the authors' earlier NLO QCD calculation of γγ→J/ψ+J/ψ that this paper extends to ultraperipheral collisions.","marker":"[11]"},{"why":"provides the equivalent-photon approximation that turns photon fluxes into the UPC cross section.","marker":"[12, 13]"},{"why":"gives the ion photon spectral function used to compute the two-photon luminosity.","marker":"[14]"},{"why":"supplies the input values for the charmonium leptonic width, masses, and decay branching ratios.","marker":"[17]"},{"why":"is the prior work showing the opposite-sign NLO corrections for J/ψ and ηc pairs that the present results confirm.","marker":"[23]"},{"why":"provides the effective charge radii of the ions, which set the impact-parameter cutoff and hence the photon fluxes and total cross sections.","marker":"[32]"}],"fun_headline_variants":["Photon fusion yields 28 nb J/psi pairs, 65 nb eta_c pairs at NLO","NLO QCD flips charmonium pair rates: J/psi down, eta_c up","UPC photon-photon gives 28 nb charmonium pairs, 65 nb for eta_c","NRQCD predicts opposite-sign NLO corrections for charmonium pairs in UPC","28 nb J/psi pairs and 65 nb eta_c pairs from photon fusion in UPC at NLO"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The central numbers depend on the assumption that the next-to-leading-order QCD correction is a small, trustworthy correction; the paper's own J/ψ-pair distribution turning negative at large rapidity differences is a warning that this may not hold.","fun_headline_variants_meta":{"raw":{"variants":["Photon fusion yields 28 nb J/psi pairs, 65 nb eta_c pairs at NLO","NLO QCD flips charmonium pair rates: J/psi down, eta_c up","UPC photon-photon gives 28 nb charmonium pairs, 65 nb for eta_c","NRQCD predicts opposite-sign NLO corrections for charmonium pairs in UPC","28 nb J/psi pairs and 65 nb eta_c pairs from photon fusion in UPC at NLO"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000666,"raw_usage":{"total_tokens":3069,"prompt_tokens":1001,"completion_tokens":2068,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":617,"completion_tokens_details":{"reasoning_tokens":1944}},"tokens_in":617,"tokens_out":2068,"duration_ms":14573,"temperature":1.0,"reasoning_tokens":1944,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T11:40:07.813968+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the rapidity-difference distribution of exclusive J/ψ-pair production in Pb-Pb UPC at the HL-LHC; if the bins with |Δy|>2 show positive rates near the leading-order size, or if the total rate differs from 28 nb by more than the quoted uncertainties, the NLO NRQCD prediction is falsified. The ηc-pair rate of 65.1 nb offers an independent check.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"is the authors' earlier NLO QCD calculation of γγ→J/ψ+J/ψ that this paper extends to ultraperipheral collisions."},{"cited_title":"Next-to-leading-order relativistic and QCD corrections to prompt $\\boldsymbol{J/\\psi}$ pair photoproduction at future $\\boldsymbol{e^+e^-}$ colliders","cited_arxiv_id":"2404.08945","evidence_quote":"is the prior work showing the opposite-sign NLO corrections for J/ψ and ηc pairs that the present results confirm."}],"review_version":1}