{"id":"2e36eb10-98bc-451d-89c9-a29309982c2c","arxiv_id":"2505.04357","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Color-singlet NRQCD at next-to-leading order reproduces most LHCb double-J/psi data but undershoots CMS and ATLAS by factors of 10 to 29.","lead":"Physicists calculated the next-to-leading-order strong-force corrections to producing pairs of J/psi particles at the LHC, using the color-singlet mechanism. The result explains most LHCb data but falls far short of CMS and ATLAS measurements, pointing to additional production mechanisms.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The NLO result hinges on an unspecified gq/qg hard-collinear subtraction, validated only by private communication; if that subtraction is wrong, the LHCb/CMS/ATLAS comparisons shift.","rationale":"The reader's CONDITIONAL verdict is appropriate, and the load-bearing concern is exactly the reader's weakest assumption: the gq/qg hard-collinear subtraction is not specified, is validated only through private communication with an author of Ref. [25], and is not covered by the visible δs-stability check. The paper does present real supporting evidence: IR pole cancellation, the δs-independence of the total cross section in Fig. 1, use of standard reduction/integration packages, and a documented comparison with Ref. [25]. Those checks are not sufficient, however, to pin down the finite hard-collinear terms, and a 15% difference in the NLO correction (K=1.04 vs. 1.19) is not negligible. The CMS/ATLAS qualitative conclusion (CS contribution far below the data, by factors of 10–30) is robust to this uncertainty, so the concern does not warrant rejection; it warrants keeping the conditional status until the hard-collinear formulas are made explicit or an independent third-party reproduction is available.","tokens_in":13932,"tokens_out":7526,"duration_ms":77164,"concrete_test":"Obtain or independently re-derive the explicit gq/qg hard-collinear subtraction terms (the integrated Altarelli-Parisi collinear counterterms and the finite δc-dependent pieces) used in this two-cutoff implementation, and replace them in the calculation by the exact collinear-limit expansion of the gq→ccbar+ccbar+q matrix element. Recompute the 7 TeV LHCb total NLO cross section and the 13 TeV LHCb dσ/dpT^J/ψ in the first and last bins. If the result deviates from the published values (4.57 nb; Fig. 3(e)) by more than the claimed ±2% slicing uncertainty, the hard-collinear correction is the load-bearing failure mode; if it agrees, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central quantitative claim—that the CS contribution at NLO describes the LHCb data and undershoots CMS/ATLAS with K factors of 2–3—rests on the correctness of the NLO calculation. The weakest point is the treatment of the hard-collinear region in the gq and qg channels. In Sec. III the authors state that the residual NLO difference with Ref. [25] (their K=1.04 vs. Ref. [25]'s 1.19 at 7 TeV LHCb) is traced to 'a slightly incorrect implementation of the hard-collinear corrections' in Ref. [25], and that this was confirmed only through private communication [47]. The corrected hard-collinear terms are not written down, no code is released, and the derivation is not independently checkable from the paper. The δs-stability check in Fig. 1 is necessary but not sufficient: it validates cancellation between the two- and three-body contributions for the total cross section, but it does not validate the finite hard-collinear terms themselves, and it is not shown for the differential pT bins where the NLO corrections are largest. Furthermore, the comparison with Ref. [25] is made only at the level of the 7 TeV total cross section, not the differential distributions that are central to the LHCb pT-shape discussion. If the gq/qg hard-collinear subtraction is wrong, the NLO cross sections—and hence the LHCb agreement in the pT^J/ψ and pT^ψψ distributions and the quoted K factors—shift by an amount not bounded by the ±2% slicing band.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper presents an independent next-to-leading-order (NLO) QCD calculation of the color-singlet (CS) contribution to prompt double J/ψ hadroproduction in the NRQCD factorization framework. The two-cutoff phase-space slicing method is used, with analytical treatment of soft and hard-collinear divergences and numerical evaluation of the hard-non-collinear contribution. The authors compare their LO and NLO predictions with LHCb 7 and 13 TeV, CMS 7 TeV, and ATLAS 8 TeV data. They find that the CS contribution describes most LHCb differential distributions, with caveats near threshold and in phase-space regions where soft/hard-collinear radiation spoils fixed-order perturbation theory, while it undershoots CMS and ATLAS cross sections by about one order of magnitude despite K factors of 2–3. They also compare with the earlier NLO calculation of Ref. [25] and report agreement after adjusting inputs and correcting a 'slightly incorrect implementation' of the hard-collinear corrections in the gq/qg channels, identified via private communication.","tokens_in":14307,"tokens_out":5649,"duration_ms":52560,"significance":"If the calculation is correct, this is a valuable independent cross-check of the only existing full NLO treatment of CS double J/ψ hadroproduction, and it provides a transparent, up-to-date phenomenological benchmark. The paper is careful in several respects: it documents slicing-parameter stability (Fig. 1), uses established tools for diagram generation and integral reduction (QGRAF, FORM, Reduze 2, FIRE6, Package-X, QCDloop, Cuba), and does not fit any parameter to the double-J/ψ data: the CS LDME comes from a potential model, PDFs from CTEQ, and mc = 1.5 GeV. The main limitation is that the crucial correction to the hard-collinear terms in the gq/qg channels is not presented in the paper, so the independent verification is incomplete as written.","major_comments":[{"comment":"The paper's claim of an independent NLO verification is not fully checkable because the corrected hard-collinear treatment in the gq/qg channels is not specified. The authors state that the difference between their K = 1.04 and the K = 1.19 of Ref. [25] is traced to 'a slightly incorrect implementation of the hard-collinear corrections' and that this was confirmed by private communication [47]. Since this adjustment is the only substantive difference between the two NLO computations, the manuscript should present the explicit hard-collinear subtraction terms, or the precise correction applied to the gq/qg channels, so that the reader can verify the calculation. As it stands, the agreement with Ref. [25] is asserted on the basis of an unpublished comparison, and the central claim that the CS NLO prediction describes the LHCb data is not independently auditable.","section":"Section III, comparison with Ref. [25]; Section II, Eq. (4)"},{"comment":"The slicing-stability check is performed only for the total cross section at 13 TeV LHCb. The most dramatic NLO effects appear in the differential distributions, for example the 61-fold enhancement in the last bin of dσ/dpT^{J/ψ} and the sign-changing first bins of dσ/dpT^{ψψ}, dσ/dA^{ψψ}_{pT}, and dσ/d|ΔΦ^{ψψ}|. The ±2% flatness of the total cross section does not bound the slicing error in these bins, where the soft and hard-collinear subtractions are largest. The authors should show δs-dependence curves for representative pT bins, or at least for the first bin of dσ/dpT^{ψψ}, to support the shape and normalization claims.","section":"Section III, Fig. 1"},{"comment":"The comparison with Ref. [25] is made only at the level of the 7 TeV LHCb total cross section. Since the alleged hard-collinear inconsistency affects the gq/qg channels, which contribute differently to the pT and rapidity distributions, a total-rate check cannot validate the differential shapes used in the LHCb/CMS/ATLAS comparisons. I ask the authors to provide a differential-level comparison with Ref. [25] under identical inputs and cuts, for at least one distribution such as dσ/dm_{ψψ} or dσ/dpT^{J/ψ}, once the corrected hard-collinear terms are specified.","section":"Section III, Eqs. (6)–(13)"}],"minor_comments":[{"comment":"The notation 'HC' is used for both 'hard collinear' and 'hard non-collinear', which is confusing; please rename the latter, for instance σ_HNC.","section":"Section II, around Eq. (4)"},{"comment":"The text says 'This is illustrated in Fig. [12]' but the figure referred to is Fig. 1; the cross-reference appears broken.","section":"Section III, first paragraph after Eq. (4)"},{"comment":"The exponents are rendered as '2 − 14' and '2 − 10', which look like subtraction; please use superscripts, e.g., 2^{-14} and 2^{-10}.","section":"Figure 1 caption"},{"comment":"The phrase 'emission of soft or hard-collinear gluons' is slightly misleading because the gq/qg channels also involve hard-collinear quarks; consider writing 'soft or hard-collinear partons'.","section":"Abstract and conclusions"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the journal's scope and addresses a genuine gap (independent verification of the only prior full NLO calculation for this process). My main concern is that the central computational cross-check relies on a private communication with an author of Ref. [25]; this weakens the independence claim and should be addressed by making the relevant technical detail public in the revision. The additional request for differential slicing checks is intended to support the shape claims that are central to the phenomenological conclusions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The useful kernel here is narrow but real: an independent NLO color-singlet calculation of double prompt J/psi hadroproduction that reproduces the existing 2016 Sun-Han-Chao result once their input choices are copied, and can only do so by identifying a specific error in their hard-collinear treatment for the gq/qg channels. That is worth having on record, because nobody else had checked it. The paper also gives a clean, up-to-date comparison with all three LHC experiments, and the conclusion—CS undershoots CMS/ATLAS by an order of magnitude despite K factors of 2–3, while describing much of the LHCb data—is consistent with the prior literature and with the general NRQCD picture. The slicing stability plot is a legitimate internal check, and the IR cancellation statement is standard but welcome.\n\nThe soft spots are real but not fatal. The exact hard-collinear correction to Ref. [25] is never written down; the validation rests on reproducing their result after deliberately implementing their inconsistency, plus a private communication. That leaves the central new quantitative claim—their K factor of 1.04 versus 1.19—not independently checkable from the paper. No code is released, and the differential comparison with Ref. [25] is not given, only the total at 7 TeV LHCb. The delta_s scan covers only the total cross section, not the pT bins where the NLO corrections are largest, so it does not certify the hard-collinear subtraction in the region that matters most. None of this makes me think the calculation is wrong, but it does mean the one genuinely new result rests on the reader's trust that the private communication was correct.\n\nI would also note the framing is a bit odd: the paper says the CS mechanism can describe LHCb, but the agreement is mostly at low pT and the failures at small pT_psi-psi are attributed to fixed-order breakdown. That is consistent and not misleading, but it would be easy to overread the abstract.\n\nWho is this for? Practitioners working on quarkonium pair production, NRQCD global fits, and DPS studies. A serious referee should be appointed: the calculation is demanding, the independent check has value even if incomplete, and the phenomenological comparison is useful. My own verdict would be conditional on the authors either releasing the code, writing down the corrected hard-collinear terms, or at least comparing differential distributions with Ref. [25]. Without one of those, the 1.04-versus-1.19 K-factor claim stays a claim verified only by assertion.","headline":"Independent NLO CS double-J/psi calculation that mostly confirms the known mechanism failure, but the paper's one new quantitative claim rests on an unpublished gq/qg subtraction.","tokens_in":14839,"tokens_out":682,"would_cite":false,"duration_ms":9001,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"An independent NLO QCD calculation of color-singlet double $J/\\psi$ hadroproduction shows that this single channel describes the LHCb data in most bins, while CMS and ATLAS require additional mechanisms.","keywords":["double J/psi hadroproduction","NRQCD factorization","color-singlet contribution","next-to-leading order QCD","LHC phenomenology","phase-space slicing","heavy quarkonium","prompt J/psi pair production"],"falsifier":"Recompute the NLO cross sections for the LHCb, CMS, and ATLAS setups with a different fully differential infrared-subtraction scheme and the same inputs; if the total cross sections move beyond the quoted $\\pm2\\%$ slicing uncertainty, the numerical control claimed here fails. A sharper target is the $gq\\to 2J/\\psi+q$ hard-collinear remainder: an independent derivation of that piece that disagrees with the paper's implementation would shift the agreement with LHCb and the gap with CMS/ATLAS.","tokens_in":13757,"feed_emoji":"⚛️","tokens_out":11425,"duration_ms":98249,"temperature":0.7,"pith_summary":"The paper aims to settle how much of the LHC's double-$J/\\psi$ cross section is carried by the color-singlet (CS) channel of nonrelativistic QCD, by presenting a new, independent next-to-leading-order (NLO) calculation. It establishes that the CS contribution alone describes the LHCb measurements at 7 and 13 TeV in most kinematic bins, with NLO corrections close to unity for the total cross section. The exceptions are the threshold region, where relativistic corrections are known to be important, and the small-$p_T^{\\psi\\psi}$ region, where fixed-order perturbation theory is spoiled by soft and hard-collinear gluon emission. For CMS and ATLAS, the same CS prediction undershoots the measured cross sections by roughly an order of magnitude even though the NLO $K$ factors reach 2--3. This matters because it isolates where color-octet, double-parton-scattering, or resummation effects are required and where the simpler CS picture may be trusted.","feed_headline":"Color-singlet QCD explains LHCb J/psi pairs but not CMS or ATLAS","feed_subtitle":"An independent NLO QCD calculation confirms the LHCb fit and quantifies the CMS/ATLAS gap.","key_machinery":"The load-bearing device is the NRQCD factorization formula for double heavy-quarkonium hadroproduction, applied to the color-singlet Fock state $^3S_1^{[1]}$. At NLO the real-emission phase space is split into soft, hard-collinear, and hard-non-collinear regions using the two-cutoff phase-space slicing method; the analytic poles from the soft and hard-collinear pieces cancel against the virtual corrections and against the redefinition of the parton distribution functions, while the hard-non-collinear piece is integrated numerically in four dimensions. The central identity at work is this cancellation, checked by the numerical flatness of the total cross section as the slicing parameters vary.","core_discovery":"Working in NRQCD factorization, the paper computes the complete $\\alpha_s$ corrections to the color-singlet $^3S_1^{[1]}$ contribution to prompt $J/\\psi$ pair production, including the $gg\\to 2c\\bar c$ virtual and real-emission processes and the $gq(\\bar q)\\to 2c\\bar c+q(\\bar q)$ real processes. Infrared divergences are separated with the two-cutoff phase-space slicing method, and the residual dependence on the slicing parameters is shown to stay within roughly $\\pm2\\%$ for the total cross section. The central quantitative claims are that the NLO CS prediction agrees with LHCb in most bins -- total cross sections of $6.46^{+3.99}_{-2.01}$ nb at 7 TeV and $11.4^{+5.8}_{-3.2}$ nb at 13 TeV against measured values of $5.1\\pm1.0\\pm1.1$ nb and $7.9\\pm1.2\\pm1.1$ nb -- whereas it undershoots CMS by about a factor of 10 and ATLAS by factors of 10--12. The paper also reports that its independent calculation reproduces the earlier NLO result once the inputs are matched and an inconsistency in the hard-collinear corrections of the $gq$ and $qg$ channels in that earlier work is corrected.","pith_inferences":["If the hard-collinear $gq$/$qg$ correction in the earlier calculation is indeed incorrect, previous phenomenological conclusions drawn from that code for quark-initiated channels may shift, especially in kinematic regions where quark PDFs are not negligible.","The discrepancies in the extracted effective double-parton-scattering cross section $\\sigma_{\\rm eff}$ between LHCb, ATLAS, and D0 could partly reflect that the SPS templates used in the experimental separation are not yet NLO-CS-based; re-extracting $\\sigma_{\\rm eff}$ with an NLO CS plus color-octet SPS template would be a direct test.","A natural extension would be to repeat the calculation with a fully differential infrared-subtraction scheme, which would turn the private-communication validation of the $gq$/$qg$ hard-collinear terms into a publicly checkable statement.","The paper's breakdown at small $p_T^{\\psi\\psi}$ suggests that resumming the soft and collinear gluon emission in that region would make the CS contribution testable in the very bins where the fixed-order prediction is currently negative."],"forward_implications":["If the CS channel alone fits LHCb in most bins, then global NRQCD fits should not infer a large color-octet component from forward LHCb double-$J/\\psi$ data; the octet and other mechanisms are instead required mainly at large $m_{\\psi\\psi}$, large $|\\Delta y_{\\psi\\psi}|$, and in the CMS and ATLAS acceptances.","The NLO $K$ factors of 2--3 for the CMS and ATLAS total cross sections are far too small to close the gap, so those measurements cannot be explained by fixed-order CS QCD corrections alone.","Fixed-order NLO predictions for the $p_T^{\\psi\\psi}$, $A_{pT}^{\\psi\\psi}$, and $|\\Delta\\Phi^{\\psi\\psi}|$ distributions are unreliable in the endpoint bins, meaning those bins should be compared with resummed or matched calculations rather than with the present fixed-order curves.","The independent verification of the earlier NLO code, up to the identified hard-collinear inconsistency, provides a stable benchmark for future beyond-fixed-order or color-octet-improved calculations of double $J/\\psi$ hadroproduction."],"supporting_citations":[{"why":"Supplies the earlier NLO color-singlet calculation that this paper verifies and corrects for a hard-collinear inconsistency; the central benchmark of the independent check.","marker":"[25]"},{"why":"LHCb 13 TeV measurement with SPS/DPS separation; constitutes the main data set the CS prediction is claimed to describe.","marker":"[12]"},{"why":"CMS 7 TeV prompt J/psi pair measurement used to establish the order-of-magnitude undershoot of the CS prediction.","marker":"[13]"},{"why":"ATLAS 8 TeV measurement in central and forward rapidity regions; second data set where the CS prediction fails.","marker":"[14]"},{"why":"Two-cutoff phase-space slicing method that provides the soft, hard-collinear, and hard-non-collinear separation used in the NLO calculation.","marker":"[42]"},{"why":"Nonrelativistic QCD factorization, which defines the CS long-distance matrix element and the Fock-state expansion used in the cross section.","marker":"[17]"},{"why":"Relativistic corrections near threshold that the paper uses to explain the residual overshoot in the low-$m_{\\psi\\psi}$ bins.","marker":"[22]"},{"why":"Complete NRQCD prediction showing the color-octet contributions dominate at large $m_{\\psi\\psi}$ and large $|\\Delta y_{\\psi\\psi}|$, filling gaps left by CS.","marker":"[19]"},{"why":"Parton Reggeization approach with high-energy resummation used to assess where soft-gluon and octet effects improve the description.","marker":"[29]"}],"fun_headline_variants":["NLO QCD color-singlet fits LHCb but misses CMS/ATLAS by 10x","Color-singlet NLO calculation: LHCb ok, CMS/ATLAS off by an order","J/psi pairs: NLO QCD color-singlet explains LHCb, fails CMS/ATLAS","New NLO QCD result: J/psi pairs match LHCb, not CMS/ATLAS","CS NLO QCD: LHCb data explained, CMS/ATLAS gap remains"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation's conclusions rest on how the nearly-collinear and soft-gluon parts of the real-emission corrections are split off, a step checked for stability within about $\\pm2\\%$ but whose quark-gluon subtraction is validated only through private communication with an author of the earlier calculation.","fun_headline_variants_meta":{"raw":{"variants":["NLO QCD color-singlet fits LHCb but misses CMS/ATLAS by 10x","Color-singlet NLO calculation: LHCb ok, CMS/ATLAS off by an order","J/psi pairs: NLO QCD color-singlet explains LHCb, fails CMS/ATLAS","New NLO QCD result: J/psi pairs match LHCb, not CMS/ATLAS","CS NLO QCD: LHCb data explained, CMS/ATLAS gap remains"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000889,"raw_usage":{"total_tokens":3862,"prompt_tokens":998,"completion_tokens":2864,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":614,"completion_tokens_details":{"reasoning_tokens":2733}},"tokens_in":614,"tokens_out":2864,"duration_ms":18380,"temperature":1.0,"reasoning_tokens":2733,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T23:31:39.105517+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the NLO cross sections for the LHCb, CMS, and ATLAS setups with a different fully differential infrared-subtraction scheme and the same inputs; if the total cross sections move beyond the quoted $\\pm2\\%$ slicing uncertainty, the numerical control claimed here fails. A sharper target is the $gq\\to 2J/\\psi+q$ hard-collinear remainder: an independent derivation of that piece that disagrees with the paper's implementation would shift the agreement with LHCb and the gap with CMS/ATLAS.","supporting_citations":[{"cited_title":"Next-to-lead ing-order relativistic and QCD corrections to prompt J/ψ pair photoproduction at future e+e− colliders,","cited_arxiv_id":null,"evidence_quote":"Supplies the earlier NLO color-singlet calculation that this paper verifies and corrects for a hard-collinear inconsistency; the central benchmark of the independent check."},{"cited_title":"Complete NRQCD prediction fo r prompt double J/ψ production at Hadron Collider,","cited_arxiv_id":null,"evidence_quote":"Relativistic corrections near threshold that the paper uses to explain the residual overshoot in the low-$m_{\\psi\\psi}$ bins."},{"cited_title":"J/ψ pair hadroproduction at next-to-leading order in nonrelat ivistic-QCD at ATLAS,","cited_arxiv_id":null,"evidence_quote":"Parton Reggeization approach with high-energy resummation used to assess where soft-gluon and octet effects improve the description."}],"review_version":1}