{"id":"fc6e9dfb-3a75-4bec-9bd8-f13b5062c2f5","arxiv_id":"2504.19617","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"A process-dependent soft-gluon term in the J/psi TMD shape function is needed to keep the matched cross-section and cos(2phi) asymmetry predictions physical at the EIC, which supports the analytic result of Boer et al. and suggests a node-based test for the gluon TMD sign.","lead":"This paper computes predictions for the transverse-momentum spectrum of J/psi particles produced in electron-proton collisions at the future EIC, matching low-momentum TMD factorization to high-momentum collinear factorization. It finds that a process-dependent soft-gluon term keeps the predictions within physical bounds and proposes a way to determine the sign of the linearly polarized gluon distribution in the proton.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The O(qT^2/Mpsi^2) corrections to the z≈1 approximation are largest exactly where the BCO=1 pathologies appear, so the claim that physical constraints require Bep is not yet established.","rationale":"Agree with the reader: the weakest assumption is the z ≈ 1 dominance. Section III states the approximation is valid up to O(qT^2/Mpsi^2) corrections; footnote 7 explicitly ties the asymmetry overshoot to possible corrections to z ≈ 1. The stress-test adds that the discriminating region is precisely where this expansion parameter is large (qT^2/Mpsi^2 ~ 5-16 for the Q = 14 and 25 GeV cases), so the comparison is not in the regime where the approximation is controlled. The paper is honest about this, but honesty does not remove the gap; the numerical support for Ref. [1] is conditional on the uncalculated subleading terms. A dedicated model calculation of the z-dependent shape function would settle it. No ad hominem; the concern is technical. Verdict remains CONDITIONAL; if the test fails, the claim would be weakened to the point of being unsupported.","tokens_in":22104,"tokens_out":6560,"duration_ms":68334,"concrete_test":"Recompute the matched cross section and <cos(2phi_psi)> for the BCO = 1 and Bep != 0 cases with a minimal z-dependent TMD-ShF, e.g. Delta(z,k_T^2) = C delta(1-z) + lambda (1-z) D(k_T^2), with lambda and D(k_T^2) chosen to match the leading O(qT^2/Mpsi^2) corrections from Refs. [55,56]. Then test (i) whether the negative cross-section region for Lambda_QCD << qT <= mu/2 persists for BCO = 1 across a range of lambda and cutoff choices; and (ii) whether the matched asymmetry band stays within [-1,1]. If both pathologies persist only for Bep = 0 with all acceptable z-dependence, the claim is supported; if they are removed or appear for Bep != 0, the discrimination is an artifact of the z = 1 approximation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim (abstract; Sec. V) is that positivity of the matched cross section and |<cos(2phi_psi)>| <= 1 select Bep != 0 over BCO = 1. The comparison is made in the z-integrated cross section, Eq. (32), with z integrated over 0 < z < 1, but the TMD-ShF and the Sudakov coefficients are evaluated at z = 1 (Sec. III, paragraph after Eq. (32); footnote 7; Sec. V). The justification is that at low qT momentum conservation forces z -> 1; however, the unphysical features used to discriminate the two cases occur for Lambda_QCD << qT <= mu/2 (Sec. III and Fig. 5), where mu/2 ≈ 12.6 GeV for Q = 25 GeV and ≈ 7.2 GeV for Q = 14 GeV. There qT^2/Mpsi^2 is of order 5-16, so the neglected corrections are not small. The Bep term is a Q-dependent coefficient in the Sudakov exponent; if z < 1 contributions have different relative weight for the two BCO choices, the comparison is biased. The authors acknowledge this possibility in footnote 7 and Sec. V, stating that a definitive exclusion of BCO = 1 requires a study of the subleading z ≈ 1 terms. Since the paper's positive case (Bep required) rests on the absence of such a study, the conclusion is conditional.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper studies J/ψ production in semi-inclusive deep inelastic scattering at the EIC, matching TMD and collinear factorizations with the inverse-error weighting (InEW) method. The authors compute the qT-dependent cross section and the cos(2φ) asymmetry, comparing three choices of the color-octet coefficient in the TMD shape function: no TMD-ShF (BCO=0), the universal term only (BCO=1, Bep=0), and the process-dependent term of Ref. [1] (Bep≠0). They find that for high Q the BCO=1 case leads to a negative TMD cross section and to an asymmetry band overshooting unity, while the Bep≠0 case does not, and interpret this as numerical support for the process-dependent term. They also propose the presence or absence of a node in the cos(2φ) asymmetry as a way to determine the sign of the linearly polarized gluon TMD.","tokens_in":22604,"tokens_out":7135,"duration_ms":66744,"significance":"If the central comparison is robust, the paper would provide one of the first numerical indications for a process-dependent soft factor in quarkonium TMD factorization, and the node prediction offers a falsifiable experimental test for the sign of h⊥g1. The analysis is systematic: it uses two LDME sets, several Q values, and explicit positivity and bound checks, and it displays the unphysical outputs rather than hiding them. However, the central claim is conditional: the discriminating region in qT is exactly where the z≈1 approximation is expected to be poor, and the matching error was modified in a way inspired by the term under test. The significance therefore rests on a point that the authors themselves acknowledge needs further study.","major_comments":[{"comment":"The z≈1 approximation is used to evaluate the TMD-ShF and Sudakov coefficients at z=1 for all qT, with corrections of order qT^2/Mψ^2 neglected. The unphysical features used to discriminate BCO=1 from Bep≠0 — negative TMD cross section and asymmetry overshoot — occur for ΛQCD ≪ qT ≲ μ/2 (Sec. III and Fig. 5), where for Q=14 and 25 GeV the ratio qT^2/Mψ^2 ranges from roughly 5 to 16, so the neglected corrections are not small. The Bep term enters as a Q-dependent coefficient in the Sudakov exponent; if z<1 contributions carry different relative weight for the two BCO choices, the comparison is biased. The authors acknowledge in footnote 7 that a definitive exclusion of BCO=1 requires a study of subleading z≈1 terms, but the abstract and Sec. V state the conclusion without this qualification. The manuscript should either quantify the uncertainty from the z<1 contributions (for example, by using a model for the full z-dependence of the TMD-ShF or by limiting the claim to qT ≪ Mψ) or soften the central claim accordingly.","section":"Sec. III, paragraph after Eq. (32); footnote 7; Sec. V"},{"comment":"The modification of the InEW error term ΔFO is introduced as 'inspired by the divergent behavior found in Ref. [1]' — that is, by the very Bep term whose inclusion the paper aims to support. Since the InEW weights in Eq. (29) are constructed from these errors evaluated with the BCO-dependent cross sections, the numerical support for Bep is in part a self-consistency check. The comparison with BCO=0 and BCO=1 provides some independent grounding, but the robustness of the conclusion should be tested with an alternative matching prescription (e.g., the conventional W+Y formalism) or by a sensitivity scan over the functional form of ΔFO, including the original squared-log version of Ref. [36].","section":"Sec. II, Eq. (30)"}],"minor_comments":[{"comment":"In the caption of Fig. 4, the sentence 'Figs. 3a and 3b: Q = 3 GeV...' should refer to panels (a) and (b) of Fig. 4, not Fig. 3.","section":"Fig. 4 caption"},{"comment":"In Eq. (15), the expansion of Cnn′ is written with C(k) aa′(z) in the second line; the subscript should be nn′.","section":"Eq. (15)"},{"comment":"In the caption of Fig. 6, 'SV12 is used for the lower ones' should read 'SV13'.","section":"Fig. 6 caption"},{"comment":"The last paragraph of Sec. V states that the presence (absence) of a node is related to the positive (negative) sign of h⊥g1; this is the reverse of what is shown in Figs. 6 and 7 and stated in Sec. IV.","section":"Sec. V, last paragraph"},{"comment":"The sentence in Sec. III about negative cross sections 'also observed for other sets, e.g., those reported in [61]' is vague; please specify which sets or remove the clause.","section":"Sec. III"}],"recommendation":"major_revision","confidential_remarks":"The authors' own caveats (footnote 7, Sec. V) essentially concede the main limitation: a definitive exclusion of BCO=1 requires the subleading z≈1 study that the paper does not perform. The abstract and conclusions should be moderated to match the conditional nature of the finding. The comparison with BCO=0 and BCO=1 does provide some independent grounding, and the node prediction is a worthwhile contribution. I see no ethical concerns; the self-citation pattern is natural given the subject."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Maxia, Boer, and Bor match TMD and collinear descriptions of J/psi SIDIS at the EIC with inverse-error weighting and ask whether the color-octet shape function needs the process-dependent Bep term from their earlier analytic work. Two things to know. First, the new results—matched qT spectra and cos(2phi) asymmetries including the TMD shape function, plus a node-based test for the sign of the linearly polarized gluon TMD—are worth a look. Second, the headline claim that physical constraints require Bep is conditional; the authors themselves say a definitive exclusion of BCO=1 needs a study of subleading z≈1 corrections, which are not small in the very region where the two cases differ.\n\nWhat the paper does well: it is clearly laid out, shows results for two LDME sets and several Q values, and shows explicitly that setting Bep=0 produces negative TMD cross sections in Lambda_QCD << qT <= mu/2 and asymmetry bands exceeding unity. Including Bep removes those pathologies in the central choices. The authors flag their own limitations in footnotes 3 and 7 and in Sec. V, which is honest. The node test is a genuinely new suggestion and could be useful even if the Bep conclusion changes.\n\nThe main soft spot is the one they admit: z is integrated from 0 to 1, but the TMD shape function and Sudakov are evaluated at z=1, with corrections of order qT^2/Mpsi^2 neglected. The unphysical features used to discriminate BCO=1 from Bep appear for qT such that this ratio is of order 5-16, so the approximation is not under control there. The comparison with BCO=0 and BCO=1 does provide some independent grounding, but the numerical support for Bep is partly a self-consistency check, since Bep and the matching-error modification trace back to the same group's earlier result. No code or data are included, and several nonperturbative parameters are free; the reported sensitivity to gpsi is small, but a reader cannot easily test the intermediate-qT behavior.\n\nThis paper is for people working on gluon TMDs, quarkonium production, and TMD-factorization phenomenology. It deserves a serious referee. My recommendation: send it to peer review, with a request that the authors either give a proper estimate of the z≈1 corrections or mark the Bep conclusion as provisional.","headline":"Plausible but provisional: the z≈1 approximation is weakest exactly where the Bep term matters, so the headline claim needs a subleading-correction study or a provisional label.","tokens_in":23039,"tokens_out":4154,"would_cite":true,"duration_ms":40750,"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":"Including the process-dependent Bep term in the J/ψ TMD shape function preserves positivity and boundedness of matched predictions at the EIC.","keywords":["TMD factorization","J/psi production","semi-inclusive deep inelastic scattering","TMD shape function","Sudakov resummation","inverse-error weighting","gluon TMD distributions","Electron-Ion Collider"],"falsifier":"Measure the J/ψ qT spectrum and cos(2φψ) asymmetry at the EIC at Q ≈ 14–25 GeV and compare with the two prescriptions: if the data follow the BCO = 1 (Bep = 0) band with a positive cross section and |⟨cos(2φψ)⟩| ≤ 1 everywhere, the claim that Bep is required is refuted. A second decisive test is to compute the order-qT²/Mψ² corrections to the z-integrated cross section and show whether they alter the sign of the difference between the two prescriptions in the region ΛQCD ≪ qT ≲ μ/2.","tokens_in":21898,"feed_emoji":"⚛️","tokens_out":6686,"duration_ms":60118,"temperature":0.7,"pith_summary":"The paper asks whether the transverse-momentum-dependent (TMD) shape function that describes J/ψ hadronization needs a process-dependent term in its perturbative Sudakov coefficient. Using the inverse-error weighting method to join the TMD description at low transverse momentum qT with the collinear description at high qT, the authors produce matched predictions for the J/ψ cross section and its cos(2φψ) asymmetry in electron–proton collisions at the future Electron-Ion Collider. They find that when the color-octet term Bψ is included alone (BCO = 1, Bep = 0), the matched cross section becomes negative in the region ΛQCD ≪ qT ≲ μ/2 and the asymmetry band can exceed unity. Adding the process-dependent term Bep from Ref. [1] removes both violations. If right, this means future EIC data can distinguish between competing definitions of the TMD shape function and thereby test TMD factorization in quarkonium production, which matters for extracting gluon TMD distributions.","feed_headline":"Process-dependent TMD term keeps J/psi spectra physical at EIC","feed_subtitle":"Without it, the matched cross section goes negative and the cos(2φ) asymmetry can exceed one.","key_machinery":"The load-bearing object is the TMD shape function Δ(z, kT²), which incorporates TMD effects in the quarkonium formation mechanism; its perturbative matching to NRQCD long-distance matrix elements feeds the Sudakov exponent through the coefficient BCO = Bψ + Bep in the W-term of the differential cross section. The matching of the low-qT TMD expression to the high-qT fixed-order result is performed with the inverse-error weighting (InEW) method [36], which averages the two descriptions with weights built from their estimated errors; this is what allows the cross section and asymmetry to be evaluated over the full qT range. For the cos(2φψ) asymmetry, the numerator involves the linearly polarized gluon TMD distribution $h_1^{{⊥g}}$, whose perturbative expansion is taken from Ref. [20]. The choice of BCO changes the shape and height of the matched curves and is what drives the positivity and boundedness violations that the paper reports.","core_discovery":"The central claim is that the physical constraints of positivity of the matched cross section and |⟨cos(2φψ)⟩| ≤ 1 act as a diagnostic for the correct perturbative tail of the TMD shape function in J/ψ production. In the TMD region the color-octet contribution to the Sudakov exponent is BCO = Bψ + Bep, where Bψ = -CA/2 is the universal term and Bep = (CA/2) log((Mψ²+Q²)/Mψ²) is the process-dependent term derived in Ref. [1]. Evaluating the InEW-matched cross section at √s = 140 GeV with Q = 14 and 25 GeV, the authors find that the choice BCO = 1 (i.e. Bep = 0, as in Ref. [29]) produces negative cross sections for ΛQCD ≪ qT ≲ μ/2 and matched asymmetry bands that overshoot unity, whereas the choice with Bep ≠ 0 satisfies both constraints. The paper therefore concludes that the numerical results support the analytic derivation of Bep, and that the presence or absence of this term is testable by EIC data.","pith_inferences":["If the z ≈ 1 dominance assumption fails at intermediate qT, the size of Bep's effect could be different, but the qualitative mechanism — a process-dependent single logarithm in the Sudakov factor — would likely survive in a full z-dependent treatment.","The same positivity-and-boundedness diagnostic could be applied to other quarkonium states such as Υ or ψ′ in SIDIS and photoproduction, where the analogue of Bep depends on the mass ratio and could be predicted before data arrive.","The double-peak structure seen in the matched cross section at high Q is a matching artifact candidate; it may serve as a sensitive probe of the TMD-to-collinear transition and could be used to tune the InEW weights once data exist.","The paper's method suggests that checking whether the TMD W-term turns negative in the intermediate-qT region is a cheap, model-independent test that any future TMD-ShF parametrization should pass."],"forward_implications":["At Q ≈ 14–25 GeV the matched cross section differs substantially between the Bep = 0 and Bep ≠ 0 prescriptions, so high-Q EIC data can discriminate between them even with current LDME uncertainties.","The cos(2φψ) asymmetry develops a node at intermediate qT for a negative sign of the linearly polarized gluon TMD, while no node appears for a positive sign; measuring the node would settle the sign.","The BCO = 1 (Bep = 0) prediction fails basic physical constraints in the intermediate-qT region, so fits to future data should not use that prescription for the TMD shape function's perturbative tail.","If Bep is confirmed, TMD factorization for J/ψ production must include process-dependent soft-gluon effects, extending the usual universal-TMD picture.","The matching method itself, with its error-based weights, provides a practical route to predict full-qT spectra for quarkonia without relying on the full z-dependence of the TMD shape function."],"supporting_citations":[{"why":"Supplies the analytic derivation of the process-dependent term Bep that the paper's numerics support.","marker":"[1]"},{"why":"Gives the alternative BCO = 1 prescription (Bep = 0) that produces the unphysical negative cross section and asymmetry overshoot.","marker":"[29]"},{"why":"Introduces the inverse-error weighting method used to match TMD and collinear results.","marker":"[36]"},{"why":"Introduced the TMD shape function for color-singlet quarkonium production in pp collisions.","marker":"[24]"},{"why":"Extended the TMD shape function formalism to the color-octet channel in quarkonium decay.","marker":"[25]"},{"why":"Provides the NRQCD factorization framework that relates the TMD shape function to long-distance matrix elements.","marker":"[26]"},{"why":"Supplies the perturbative expansion of the linearly polarized gluon TMD used for the cos(2φψ) numerator.","marker":"[20]"},{"why":"Provides the CM12 long-distance matrix element set used for the numerical predictions.","marker":"[58]"},{"why":"Provides the SV13 long-distance matrix element set used for the numerical predictions.","marker":"[59]"}],"fun_headline_variants":["TMD shape function term keeps J/psi cross section positive","Process-dependent term essential for physical J/psi spectra","EIC J/psi production: missing term breaks positivity","New term in Sudakov exponent fixes J/psi TMD matching","Including Bep term preserves J/psi cross section constraints"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire comparison relies on the cross section being dominated by z close to 1 over the whole qT range, so the TMD shape function can be evaluated at z = 1 and corrections of order qT²/Mψ² can be dropped; if those corrections matter in the intermediate-qT region, the relative behavior of the BCO = 1 and Bep ≠ 0 predictions could change.","fun_headline_variants_meta":{"raw":{"variants":["TMD shape function term keeps J/psi cross section positive","Process-dependent term essential for physical J/psi spectra","EIC J/psi production: missing term breaks positivity","New term in Sudakov exponent fixes J/psi TMD matching","Including Bep term preserves J/psi cross section constraints"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000228,"raw_usage":{"total_tokens":1514,"prompt_tokens":1022,"completion_tokens":492,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":638,"completion_tokens_details":{"reasoning_tokens":422}},"tokens_in":638,"tokens_out":492,"duration_ms":4366,"temperature":1.0,"reasoning_tokens":422,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T05:48:21.388037+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the J/ψ qT spectrum and cos(2φψ) asymmetry at the EIC at Q ≈ 14–25 GeV and compare with the two prescriptions: if the data follow the BCO = 1 (Bep = 0) band with a positive cross section and |⟨cos(2φψ)⟩| ≤ 1 everywhere, the claim that Bep is required is refuted. A second decisive test is to compute the order-qT²/Mψ² corrections to the z-integrated cross section and show whether they alter the sign of the difference between the two prescriptions in the region ΛQCD ≪ qT ≲ μ/2.","supporting_citations":[{"cited_title":"However, the evolution of the LDMEs is off diagonal [29, 44]","cited_arxiv_id":null,"evidence_quote":"Supplies the analytic derivation of the process-dependent term Bep that the paper's numerics support."},{"cited_title":"Spectator-model studies for spin-dependent gluon TMD PDFs at the LHC and EIC","cited_arxiv_id":"2310.19916","evidence_quote":"Gives the alternative BCO = 1 prescription (Bep = 0) that produces the unphysical negative cross section and asymmetry overshoot."},{"cited_title":"$J/\\psi$ polarization in large-$P_T$ semi-inclusive deep-inelastic scattering at the EIC","cited_arxiv_id":"2301.11987","evidence_quote":"Introduces the inverse-error weighting method used to match TMD and collinear results."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the CM12 long-distance matrix element set used for the numerical predictions."},{"cited_title":"PrecisOnium","cited_arxiv_id":null,"evidence_quote":"Provides the SV13 long-distance matrix element set used for the numerical predictions."}],"review_version":1}