{"id":"64c60d55-43b7-424b-a7c1-a5f1d5cb547d","arxiv_id":"2507.19022","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Updated NRQCD plus fragmenting jet function calculations, including threshold resummation, show that LHCb psi(2S) in-jet momentum distributions can distinguish between competing quarkonium production mechanisms, though no single model set fully fits the data.","lead":"This physics paper compares new LHCb measurements of J/psi and psi(2S) particles inside jets with quantum chromodynamics calculations based on NRQCD and fragmenting jet functions. It finds that the psi(2S) data, binned by both jet and particle momentum, separates competing production models better than older J/psi data.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Omitted perturbative scale uncertainties and the absence of a statistical comparison leave the claimed LDME discrimination undemonstrated.","rationale":"The paper's central claim is that the binned psi(2S) z_H distributions can discriminate between NRQCD LDME sets. For that claim to hold, the predicted curves from different LDME sets must be separated by more than the combined theoretical and experimental uncertainty, and the comparison must be quantitative. The paper itself states that perturbative scale uncertainties are intentionally excluded, and it offers no statistical comparison such as chi-square or likelihood. This is a self-identified missing support, and it directly affects the central claim: the B&K set has very small LDME uncertainties, so its apparently distinctive prediction could be an artifact of choosing one scale. A scale-variation test would settle whether the three sets remain distinguishable. I do not elevate the reader's unpolarized-decay concern to the primary one: in the mid-z_H region used for the discrimination, the muon pT cuts are largely saturated for the high-pT bins considered (e.g., z_H = 0.5 in the 30-40 GeV psi(2S) bin gives muon pT well above the 6 GeV threshold), so the z-dependent acceptance is less sensitive to the assumed angular distribution. The polarization assumption is a legitimate secondary systematic, but the missing scale uncertainty and statistical test are more load-bearing. Since the paper's conclusions are plausible but not fully supported by the presented evidence, the existing CONDITIONAL verdict remains appropriate; no change is required.","tokens_in":9680,"tokens_out":10108,"duration_ms":110295,"concrete_test":"Recompute the three z_H predictions in Fig. 1 (40-60 GeV jet-pT and 30-40 GeV psi(2S)-pT bins) with independent variations of the renormalization, factorization, and resummation scales by factors 1/2 and 2 around the default, including the same mid-z normalization. Then compute a profile chi-square against the LHCb psi(2S) data with the normalization as a nuisance parameter. If the three LDME scale bands overlap in 0.5 < z_H < 0.8, or if the minimum chi-square values for the three sets differ by less than about 4, the central discrimination claim is not supported and the conclusions should be weakened.","verdict_should_be":"UNCHANGED","load_bearing_attack":"To support the central claim that the psi(2S) z_H data can discriminate between LDME sets, the predicted z_H distributions must be distinguishable after all relevant uncertainties are included. The letter states: 'For clarity in comparing LDME effects, we intentionally exclude perturbative uncertainties from scale variations' (Numerical calculation), and conclusions are drawn from visual comparison in Fig. 1. Because the B&K set has very small LDME uncertainties in Table I, its apparent separation from the Brambilla and Bodwin curves could be inflated; an omitted scale band can easily cover the differences among the three central predictions, especially since the comparison is normalized to the area in 0.5 < z_H < 0.8 and no chi-square or likelihood is reported. The Bodwin set is explicitly called difficult to assess because of its large uncertainties; without scale bands the same ambiguity applies to the other sets. Thus the load-bearing condition, that the predicted shapes are meaningfully different at the accuracy of the calculation, is not currently demonstrated by the paper's own evidence.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This letter compares LHCb measurements of J/psi and psi(2S) transverse-momentum-fraction (z_H) distributions within jets with NRQCD predictions based on the semi-inclusive fragmenting jet function (FJF) formalism. The calculation uses NLO partonic cross sections, DGLAP evolution of fragmentation functions, threshold resummation in the z_H -> 1 limit, and a model of the LHCb muon acceptance. Three representative color-octet LDME sets are taken from the literature and compared visually with the data. The paper claims that the psi(2S) data, binned in both jet pT and quarkonium pT, have the potential to discriminate between NRQCD production mechanisms.","tokens_in":9882,"tokens_out":5226,"duration_ms":53420,"significance":"If the discrimination claim is quantitatively established, this would be a valuable step: it would show that quarkonium-in-jet distributions provide sharper constraints on NRQCD production mechanisms than inclusive cross sections, and it would validate the threshold-resummed, semi-inclusive FJF framework against new LHCb data. The technical advance over Ref. [10] is real, including the use of semi-inclusive FJFs matched to LHCb kinematics, threshold resummation that cures the earlier z_H -> 1 divergence, and the first comparison to the binned psi(2S) data. The paper also avoids circularity by using independent LDME sets rather than fitting new ones. However, the central claim is not yet demonstrated because perturbative scale uncertainties are omitted, the comparisons are normalized to the data in a mid-z_H window and judged visually, and no goodness-of-fit statistic is reported. These are fixable within a revision, so I do not regard the current form as ready for publication.","major_comments":[{"comment":"The statement that \"we intentionally exclude perturbative uncertainties from scale variations\" directly undermines the discrimination claim. Because the B&K LDME uncertainties in Table I are very small, the apparent separation between the B&K band and the Brambilla/Bodwin bands in Fig. 1 could be inflated by the missing scale uncertainty. The authors should estimate scale uncertainties, for example by varying the fragmentation scale, the FJF scale, and the renormalization scale in the NLO cross section and in the resummation, and show that the three LDME sets remain visually and statistically separated after adding the scale uncertainty in quadrature.","section":"Numerical calculation"},{"comment":"The claim that \"the Brambilla set provides a better description at low zH and the B&K set performs better at high zH\" is based only on visual inspection after normalizing the theory to the data area in 0.5 < zH < 0.8, and no chi-square, likelihood, or other goodness-of-fit statistic is reported. The choice of normalization window can itself trade against shape differences, so the current evidence does not quantitatively support the abstract's conclusion that the psi(2S) data can discriminate between production mechanisms. The authors should provide a quantitative comparison, ideally a chi-square or likelihood per LDME set using the experimental covariance matrix, or explicitly weaken the conclusion to an illustrative comparison.","section":"Prompt-psi(2S) results"},{"comment":"The acceptance model assumes \"unpolarized quarkonium decays with isotropic mu+mu- angular distributions in the quarkonium rest frame.\" Since NRQCD allows significant quarkonium polarization and the z_H-dependent acceptance of the LHCb muon cuts is polarization-dependent, this assumption could change the predicted shapes and hence the discrimination conclusions. The authors should quantify the sensitivity by repeating the acceptance computation with maximally longitudinal and maximally transverse polarization scenarios, or by using measured polarizations where available, and state whether the discrimination conclusions survive.","section":"Numerical calculation (acceptance model)"}],"minor_comments":[{"comment":"The caption refers to \"the factor sigma\" but does not define it; please define it explicitly or point to the corresponding equation in the text.","section":"Fig. 1 caption"},{"comment":"Figs. 3 and 4 are not referenced in the main text; add explicit references when describing the lower-pT bins in the supplementary material.","section":"Supplementary material"},{"comment":"In the sentence \"This complimentary dual binning\", \"complimentary\" should be \"complementary\".","section":"Prompt-psi(2S) results"},{"comment":"In the psi(2S) row for Bodwin et al., the color-singlet LDME is listed as 0.76[16] with no uncertainty; please state whether this value is held fixed when propagating LDME uncertainties.","section":"Table I"},{"comment":"The abstract's phrase \"has the potential to discriminate\" is weaker than the conclusions' phrasing that the data \"enable discrimination\"; please harmonize these statements with the level of quantitative support provided in the paper.","section":"Abstract"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is clearly written and the technical calculation appears to follow established formalisms, but the letter format forces the central claim to rest on visual comparisons without scale-uncertainty bands or a statistical test. These concerns are load-bearing for the stated conclusion, yet they are addressable within the scope of a revision: adding scale-variation bands, a chi-square comparison, and a polarization-sensitivity check would make the discrimination claim testable. I would not recommend reject, because the underlying framework and the comparison to the new LHCb psi(2S) data are of genuine interest."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a solid, incremental paper that makes a real technical step—first threshold resummation inside the semi-inclusive FJF framework—and puts it immediately to work on LHCb's new psi(2S) z_H data. The threshold resummation cures the z_H → 1 divergence that plagued the earlier J/psi-only analysis, and the dual pT binning of psi(2S) is genuinely more informative than the integrated J/psi distribution. Those are the new pieces, and they are worth having.\n\nThe paper also does a good job of situating the three LDME sets in the literature's three categories, and it is honest that no set reproduces the data everywhere. The low-z_H deviations and the z_H ≈ 1 peaks are discussed as mass corrections and possible double-parton contributions, not swept under the rug.\n\nNow the soft spots, in proportion. The largest is the central claim of LDME discrimination. The authors intentionally omit perturbative scale uncertainties “for clarity,” and then compare narrow LDME bands. The B&K band is tiny because that set's LDME errors are tiny, but the scale variation at LL could easily be as large as the spread between the Brambilla and B&K central curves. Without a scale band, or at least a one-line estimate of the scale uncertainty, the statement that the data \"enable discrimination\" is stronger than what the figure demonstrates. The abstract wisely says \"potential\"—the conclusion overreaches. There is also no goodness-of-fit statistic; the theory is area-normalized in 0.5 < z_H < 0.8, which can mask shape differences. The acceptance model assumes unpolarized decays; if polarization is large, the z_H-dependent acceptance shifts. These are addressable in a revision.\n\nOne oddity: the Bodwin set goes negative over significant z_H ranges, yet is still used as a representative set. The authors note it, but it undermines using that set for a clean discrimination test.\n\nIs the central idea sound? Yes. The comparison is a natural next step, the formalism is established, and the qualitative conclusion—psi(2S) z_H with dual pT binning is more discriminating than J/psi—survives the caveats. The paper deserves a serious referee. I would send it to peer review and ask for scale bands, a chi-square or likelihood, and a polarization sensitivity check; then the discrimination claim can be stated at the level the data actually support.","headline":"Solid incremental step—threshold resummation in semi-inclusive FJFs applied to LHCb psi(2S) data—but the LDME-discrimination claim outruns the omitted scale uncertainties.","tokens_in":10449,"tokens_out":3442,"would_cite":true,"duration_ms":35272,"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":"The paper shows that LHCb's psi(2S) momentum-fraction distributions inside jets, binned in both jet and quarkonium transverse momentum, can discriminate between NRQCD production mechanisms, and that threshold-resummed fragmenting jet…","keywords":["quarkonium production","NRQCD factorization","long-distance matrix elements","fragmenting jet function","threshold resummation","psi(2S)","J/psi","jet fragmentation"],"falsifier":"Measure the polarization of prompt psi(2S) inside jets from the angular distribution of the two muons in the quarkonium rest frame and recompute the acceptance-corrected z_H predictions with that polarization; if the three LDME sets no longer separate in the binned distributions, or if the shape agreement changes materially, the discrimination claim fails. Alternatively, add the double-parton fragmentation contribution and test whether the z_H = 1 peaks in the LHCb data are reproduced; if they persist unexplained, the framework is missing another ingredient.","tokens_in":9454,"feed_emoji":"🎯","tokens_out":10261,"duration_ms":93343,"temperature":0.7,"pith_summary":"The paper argues that the momentum fraction a psi(2S) carries inside a jet, measured by LHCb in bins of both the jet's transverse momentum and the meson's transverse momentum, can tell apart competing sets of NRQCD long-distance matrix elements, something inclusive cross sections have not been able to do. Using the semi-inclusive fragmenting jet function formalism with DGLAP evolution and, for the first time in this framework, threshold resummation, the authors compute z_H distributions for J/psi and psi(2S) at LL+NLO accuracy. They compare three representative LDME sets and find that the psi(2S) data discriminate between them, even though no single set reproduces every bin. The comparison also reveals where the leading-power calculation fails: a low-z_H region that needs mass corrections and sharp peaks at z_H=1 that point to a double-parton production process. If correct, quarkonium-in-jet distributions become a decisive probe of how quarkonia form, and the psi(2S) measurement is a stronger version of that probe than the existing J/psi data.","feed_headline":"psi(2S) jet data can pick out the quarkonium production mechanism","feed_subtitle":"Binned momentum-fraction data separate competing NRQCD fits and expose missing double-parton production.","key_machinery":"The carrying object is the semi-inclusive fragmenting jet function (FJF), which factorizes the cross section into a convolution $G_i^H(z,z_H,p_TR,\\mu)=\\sum_j J_{ij}(z,z_H,\\mu)\\otimes D_j^H(z_H,\\mu)$, where $J_{ij}$ describes a mother parton splitting into a daughter parton inside the jet and $D_j^H$ is the quarkonium fragmentation function. The hierarchy $m_H \\ll p_TR \\ll p_T$ produces large logarithms $\\ln(p_TR/m_H)$ and $\\ln R$; the paper resums them by DGLAP evolution of the fragmentation function from $2m_c$ to the jet scale $p_TR$, then FJF evolution from $p_TR$ to the hard scale $p_T$, all at LL, reaching LLR + LL_threshold + NLO. Threshold resummation of the double logarithms $\\log(1-z_H)/(1-z_H)$ is what makes the $z_H \\to 1$ predictions finite and positive-definite. The experimental acceptance is implemented by modeling quarkonium decays as unpolarized and isotropic in the rest frame, boosting the muons to the lab frame, and applying the LHCb muon cuts, which produces the $z_H$-dependent acceptance that shapes the predictions.","core_discovery":"The central claim is that the LHCb psi(2S) z_H distribution, measured separately in bins of jet pT and of psi(2S) pT, has enough discriminating power to tell apart competing sets of NRQCD long-distance matrix elements, something inclusive quarkonium pT spectra have failed to do. The paper reaches this by computing the distribution with semi-inclusive fragmenting jet functions at LL+NLO accuracy, including DGLAP evolution and, for the first time in this framework, threshold resummation of the double logarithms log(1-z_H)/(1-z_H). The threshold resummation cures the divergent growth toward z_H = 1 that plagued earlier FJF predictions. Comparing three representative LDME sets, the paper finds that none reproduces the full LHCb psi(2S) spectrum: one set does better at low z_H, a second at high z_H, and the third is less constraining because of its large uncertainties and negative direct-production predictions. The peaks the data show at z_H = 1, which the leading-power calculation cannot produce, are attributed to power-suppressed double-parton fragmentation, while low-z_H deviations in fixed jet-pT bins signal kinematical mass corrections of order (m_H/p_H^T)^2. The conclusion is that quarkonium production within jets is a critical probe of the NRQCD production mechanism, and that the psi(2S) dual-binning measurement is a sharper version of that probe than the pT-integrated J/psi measurement.","pith_inferences":["A natural next step, not performed here, is a global fit that treats NRQCD LDMEs and the double-parton fragmentation strength as free parameters against the binned psi(2S) data; the current paper stops at comparing three fixed LDME sets.","The same dual-binning logic could be applied to other identified hadrons inside jets, such as B mesons or charmed baryons, to test whether their fragmentation functions also separate competing nonperturbative matrix elements.","The unpolarized-decay acceptance model could be checked by computing polarization-dependent dimuon distributions from the same NRQCD channels; if the z-dependent acceptance is sensitive, the discrimination statement would need to be made polarization-dependent.","Because the paper normalizes predictions to the mid-z_H region, a next test is to insist on absolute normalization, which would turn the overall yield into an additional constraint on the LDME sets rather than just the shape."],"forward_implications":["The psi(2S) dual-binning strategy can separate LDME sets that inclusive pT spectra cannot, making it a practical discriminator for the quarkonium production mechanism.","Threshold resummation turns the previously divergent z_H -> 1 predictions into finite, positive-definite distributions, so high-z_H bins become usable for comparisons.","The z_H = 1 excess seen in the LHCb psi(2S) data, which grows at lower pT, indicates that power-suppressed double-parton fragmentation must be included for a complete description.","For J/psi, the current pT-integrated data are less discriminating; analogous J/psi measurements binned in both pT variables would be needed to resolve LDME tensions in that channel.","The calculation validates the semi-inclusive FJF framework against high-pT bins where mass corrections are small, supporting the use of this formalism for future quarkonium-in-jet analyses."],"supporting_citations":[{"why":"Supplies the semi-inclusive fragmenting jet function coefficients J_ij used to match the LHCb jet kinematics.","marker":"[11]"},{"why":"Provides the threshold resummation formula that removes the divergent z_H -> 1 behavior of the fragmentation functions.","marker":"[12]"},{"why":"The LHCb psi(2S) data binned in jet and quarkonium pT, which the paper's discrimination claim rests on.","marker":"[9]"},{"why":"The earlier LHCb J/psi data used for the pT-integrated comparison.","marker":"[6]"},{"why":"One of the three representative NRQCD LDME sets (Category 1) compared in the analysis.","marker":"[13]"},{"why":"A second representative LDME set (Category 2), which predicts negative direct contributions that feeddown must compensate.","marker":"[14]"},{"why":"The B&K J/psi LDME set (Category 3) used for the J/psi comparison.","marker":"[15]"},{"why":"The B&K psi(2S) LDME set used for the psi(2S) comparison.","marker":"[17]"},{"why":"The earlier FJF comparison with LHCb J/psi data that this paper updates and improves.","marker":"[10]"},{"why":"Cited as the double-parton fragmentation process that could explain the z_H = 1 peaks.","marker":"[41]"}],"fun_headline_variants":["Threshold resummation sharpens psi(2S) jet probe of quarkonium","psi(2S) jet data: NRQCD sets fall short, exposing double-parton","No single NRQCD fit matches LHCb psi(2S) jet spectrum","psi(2S) jet data yields sharper NRQCD mechanism test than J/psi"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation assumes the quarkonia decay unpolarized and isotropically in their rest frame when modeling the LHCb muon acceptance; if prompt J/psi or psi(2S) are strongly polarized, the z-dependent acceptance corrections change and the comparison between LDME sets could shift.","fun_headline_variants_meta":{"raw":{"variants":["Threshold resummation sharpens psi(2S) jet probe of quarkonium","psi(2S) jet data: NRQCD sets fall short, exposing double-parton","No single NRQCD fit matches LHCb psi(2S) jet spectrum","psi(2S) jet data yields sharper NRQCD mechanism test than J/psi"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001121,"raw_usage":{"total_tokens":4673,"prompt_tokens":960,"completion_tokens":3713,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":576,"completion_tokens_details":{"reasoning_tokens":3620}},"tokens_in":576,"tokens_out":3713,"duration_ms":27735,"temperature":1.0,"reasoning_tokens":3620,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T18:02:27.775968+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the polarization of prompt psi(2S) inside jets from the angular distribution of the two muons in the quarkonium rest frame and recompute the acceptance-corrected z_H predictions with that polarization; if the three LDME sets no longer separate in the binned distributions, or if the shape agreement changes materially, the discrimination claim fails. Alternatively, add the double-parton fragmentation contribution and test whether the z_H = 1 peaks in the LHCb data are reproduced; if they persist unexplained, the framework is missing another ingredient.","supporting_citations":[],"review_version":2}