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High Energy Physics - Phenomenology · arXiv:2610.29297 v1 · submitted 21 Oct 2026 · 67 references

Prompt charmonia hadroproduction in High Energy Factorization with tree-level NLO corrections

A.A. Prokhorov, S.P. Baranov, A.V. Lipatov, M.A. Malyshev

PDF · arXiv · The abstract, sentence by sentence · Cite

The paper says

“We consider prompt J/ψ, χcJ and ηc production in high energy pp collisions in the framework of non-relativistic QCD. We apply high-energy factorization with taking into account tree-level next-to-leading order corrections to the production amplitudes.”

more of the abstract

Using several CCFM-evolved gluon densities in the proton and a previously proposed matching scheme to merge the leading and higher-order contributions, we extract the long-distance matrix elements for the entire charmonium family from a simultaneous fit to available LHC data. We provide predictions for the transverse momentum spectra and relative production rates σ(ψ′)/σ(J/ψ) and σ(χcJ)/σ(J/ψ) and find them to be in good agreement with the LHC data within the theoretical and experimental uncertainties across a wide kinematic region. We demonstrate that taking into account the tree-level NLO corrections improves the global description of the data.

from the abstract

Pith says

Machine review · deepseek-v4-flash · 22 Oct 2026 · what was read was not recorded · not checked by a person

It can be wrong. Challenge this review or reply to it.

Holds up, with conditions. An honest, useful extension of the NLO† program, but the 'simultaneous description' headline is conditional on how chi_c2/chi_c1 is treated and on HQSS assumptions the paper itself shows to be shaky. This line is wrong

4 major objections · 4 minor

How often objections from reviews like this one are right: not yet measured

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Not checked: figures, code, what the 67 references say.

The paper says, at §3, Table 3 and footnote 6

The review did not quote this passage.

Pith says: Objection 1 of 4 · major

The headline conclusion (sentence b160) is stronger than the fit conditions reported in Table 3. In the default HQSS-constrained scenario, all R_χ_c2/χ_c1 datasets are excluded from the fit 'to maintain a physically consistent result' (footnote 6 after b133), and Table 3 reports χ² values for this observable only in the 'neq. |R|²' columns.

more of objection 1

In that alternative scenario the data are described only after |R'_χ_c1(0)|² and |R'_χ_c2(0)|² deviate by roughly 50% in opposite directions, which b122 itself describes as 'well beyond the expected scales of NRQCD relativistic effects'. The simultaneous-description claim should therefore be stated with the explicit caveat that it holds either without the χ_c2/χ_c1 ratio or with HQSS-breaking wave-function parameters.

The paper says, at §3, Table 4 and Fig. 1

The review did not quote this passage.

Pith says: Objection 2 of 4 · major

The claim that both CCFM gluon densities give a good description is conditional on a p_T>6 GeV cut for the JH'2013 set 2 density. Table 4 gives χ²/n.d.f.=15.1 for the full JH'2013 sample versus 3.27 after the cutoff, while the A0 density does not require that restriction.

more of objection 2

Since the abstract and b160 refer to 'all available data', the central claim should carry the qualifier that one of the two gluon densities fails in the low-p_T forward region; sentence b151 already contains this qualifier, but the abstract and conclusion do not.

The paper says, at §2.3–2.4, Eqs. (5)–(9), (13)–(14)

The review did not quote this passage.

Pith says: Objection 3 of 4 · major

The 'parameter-free' η_c predictions are not independent of the HQSS assumption whose validity the fit itself questions. Eqs. (7)–(9) fix the η_c color-octet LDMEs from the J/ψ ones, and the two-parameter fit uses the regressions (13)–(14) obtained under the same spin-symmetry framework.

more of objection 3

The alternative scenario in Table 2 requires |R'_χ_c1(0)|² and |R'_χ_c2(0)|² to differ by about 50% in opposite directions, which is outside the expected size of NRQCD relativistic corrections. The paper acknowledges this, but it does not quantify how such HQSS breaking would change the η_c cross sections or the extracted J/ψ LDMEs; without that sensitivity study, the parameter-free characterization in Sec. 2.4 remains fragile.

The paper says, at §3, Figs. 5–11 and Tables 3–4

The review did not quote this passage.

Pith says: Objection 4 of 4 · major

Most of the 'agreement' displayed in the paper is agreement with data that entered the fitting procedure: the J/ψ p_T spectra are the first-step fit dataset (Table 4), and the χ_cJ spectra and ratios are the second-step fit dataset (Table 3).

more of objection 4

These figures substantiate fit quality, not predictive power. The genuinely predictive comparisons are σ(ψ′)/σ(J/ψ) in Fig. 12 and the η_c spectra in Fig. 13, and the η_c comparison is not successful. The conclusion and abstract should therefore distinguish a 'simultaneous fit of the available data' from 'predictions in agreement with data'.

4 minor objections

The paper says, at §2.3

Pith says: minor objection 1 of 4

The notation for the J/ψ color-octet S-wave LDME is inconsistent: Eq. (10) and the text mix ⟨O^{J/ψ}[3S_1^8]⟩ with the form ⟨O^{J/ψ}[3S_1^8]) in the paragraph below Eq. (12); one notation should be used throughout.

The paper says, at Fig. 13

Pith says: minor objection 2 of 4

There are two 13 TeV panels with identical captions, although the text says the two LHCb analyses differ by the rapidity interval (2<y<4.5 vs 2<y<4); the caption should identify which panel corresponds to which dataset.

show 2 more

The paper says, at Table 2

Pith says: minor objection 3 of 4

The caption says 'LDMEs for J/ψ meson' but the table also reports |R'_χ_c1(0)|², |R'_χ_c2(0)|² and ⟨O^{χ_c0}[3S_1^8]⟩; the caption should state that it collects the fitted parameters for the whole charmonium family.

The paper says, at Table 4

Pith says: minor objection 4 of 4

The n.d.f. values in parentheses, which correspond to the p_T>6 GeV cutoff, are not explained in the table caption; a short sentence noting this convention would help the reader compare the two JH'2013 columns.

What would settle it

Re-run the second-step fit of Sec. 2.3 in the identical-HQSS scenario including the ATLAS, CMS and LHCb σ(χ_c2)/σ(χ_c1) datasets, using the same covariance treatment as the other χ_cJ observables, and report the change in χ² per degree of freedom relative to the 'neq.|R|²' fit. If including them costs no more than roughly one unit of χ² per point, the exclusion was harmless and the simultaneous-description claim survives. If the cost is large, the central claim is conditional on exactly the observable that the default parameter set cannot describe.

from the skeptic's reading

How the review went

4 readings by deepseek-v4-flash · 22 Oct 2026

  1. Reader holds up, with conditions confidence moderate
  2. Skeptic partly agrees 1 min 5 s · 22,521 tokens read, 9,044 written
  3. Editor wrote the verdict above 26 s · 23,640 tokens read, 3,503 written
  4. Referee major revision: 4 major objections, 4 minor 1 min 7 s · 22,996 tokens read, 10,926 written

Not run on this paper: the simulated authors' defence.

Pith did not check this review's objections against the paper.

The review in full

The review in brief, machine-written

The genuinely new content here is the extension of the group's NLO† scheme to J/psi and eta_c, with a two-step fit that pulls sigma(chi_cJ)/sigma(J/psi) into the LDME extraction. That is a real step. The eta_c predictions are derived from J/psi CO LDMEs through HQSS relations, within the allowed ranges forced by the linear combination, and the psi'/J/psi comparison is not fitted. The paper is also unusually candid: it states the eta_c overshoot, the LHCb energy-scaling drift, the need for a pT>6 GeV cutoff for JH'2013 set 2, and the HQSS tension explicitly.

What it does well: the pT spectra cover a large body of ATLAS/CMS/LHCb data with two CCFM gluon densities; tree-level NLO corrections improve over LO; the psi'/J/psi ratio is reproduced; and the known eta_c problem is confirmed rather than papered over. The central derivation is inherited from [26,27], so this paper is not the place to revalidate the DCE cut, and I would not press it.

Now the soft spots, in proportion. The stress-test concern basically lands. The headline conclusion at b160 is stronger than the fit supports. Under the default HQSS-constrained fit, the sigma(chi_c2)/sigma(chi_c1) data are excluded from the fit, as footnote 6 states, to keep a physically consistent result. The alternative that describes that ratio requires |R'_chi_c1|^2 and |R'_chi_c2|^2 to deviate by about 50% in opposite directions, which the authors themselves call beyond expected NRQCD relativistic effects. Since HQSS is also what reduces the parameter count and generates the eta_c relations, it is simultaneously load-bearing and contradicted when the most discriminating chi_cJ ratio is included. The abstract's 'good agreement' should carry a caveat: global chi2/n.d.f. of 3.8 for A0 and 3.27 for JH'2013 set 2 with the cutoff, with LHCb 5 TeV at 13-18, sits uneasily with that phrase. Much of the validation uses fitted data, and the chi_cJ/J/psi ratios are now inside the fit rather than independent checks. No code or parameter files are shipped, which limits independent re-fitting. None of these are hidden; they are in the text.

Who gets value: quarkonium phenomenologists and people working in small-x/kT-factorization. The eta_c section is a useful negative result. I would send this to a serious referee rather than desk reject; the main requested changes would be a caveated abstract and conclusion, and release of the fit inputs.

The strongest objection

The central claim (b160) is that the NLO† scheme simultaneously describes all unpolarized prompt ψ′, χ_cJ and J/ψ data, including relative production rates. That claim rests on how σ(χ_c2)/σ(χ_c1) is handled. Under the default HQSS-constrained fit, these data are not described and are excluded from the fit (footnote 6 after b133) 'to maintain a physically consistent result'. The alternative 'neq.|R|²' scenario describes them only by letting |R′_χ_c1(0)|² and |R′_χ_c2(0)|² float independently; Table 2 and b122 report approximately 50% deviations in opposite directions, which the authors themselves call 'well beyond the expected scales of NRQCD relativistic effects'. Since HQSS is the basis of the reduced parameter set in Sec. 2.2 and of the parameter-free η_c predictions via relations (7)–(9), the same symmetry is simultaneously load-bearing and contradicted at the 50% level when the most discriminating χ_cJ observable is included. This tension is partly acknowledged, but what remains unresolved is that the headline conclusion is stated without the caveat that it depends either on excluding the χ_c2/χ_c1 datasets or on promoting two wave-function parameters to values incompatible with NRQCD power counting. I would not press the DCE cut: it is inherited from the published [26,27] scheme, and the paper states that it strictly follows that approach.

The reader's conditional verdict is appropriate, and the most load-bearing weakness is the HQSS/χ_c2-to-χ_c1 tension. I agree with that part of the reader's weakest_assumption, but I do not share the second part: the DCE cut is defined and validated in the published [26,27] papers, and this manuscript explicitly adopts that scheme, so by itself the inheritance is not a correctness risk. The HQSS issue is more serious because the conclusion b160 claims a simultaneous description 'including their different relative production rates', while the default scenario removes exactly the χ_c2/χ_c1 ratio from the fit. The neq.|R|² scenario restores agreement only by introducing 50% HQSS breaking in opposite directions, a size the paper itself calls beyond NRQCD expectations. The 'parameter-free' η_c prediction inherits the same relations (7)–(9), so it cannot serve as a clean independent check while this tension is unresolved. I would not upgrade to REJECT: the σ(ψ′)/σ(J/ψ) ratio is a genuine non-fitted observable and is reproduced, and the paper is unusually explicit about its limitations. The proposed check would decide whether the exclusion of χ_c2/χ_c1 is harmless or is the pivot on which the central claim depends.

The referee's report

If the claim were established, the paper would be a useful step: a single set of LDMEs combined with CCFM-evolved gluon densities would connect J/ψ, ψ′, χ_cJ and η_c production over a wide p_T and rapidity range, and it would provide quantitative evidence that the NLO† merging scheme works beyond the species studied in the authors' earlier papers. The paper's strengths are its comprehensive data compilation, explicit χ²/n.d.f. tables for every dataset, a clearly described two-step fitting procedure, and the transparency of reporting the alternative 'neq. |R|²' scenario with its large HQSS violations. The η_c comparison is a genuinely falsifiable prediction and is reported as such. However, the headline claim is currently stated more broadly than the fit conditions allow, and the predictive reach of the 'parameter-free' η_c test is weakened by its dependence on the same HQSS relations whose violation is required in the alternative scenario.

Pith's reading of the paper (a machine's summary, not the authors')

The paper presents a NLO† scheme that merges leading-order and tree-level next-to-leading-order off-shell amplitudes with a double-counting-exclusion cut to describe prompt J/ψ, χ_cJ, and η_c production in pp collisions. By fitting long-distance matrix elements (LDMEs) to LHC data using CCFM-evolved gluon densities, the authors achieve a consistent simultaneous description of unpolarized transverse momentum distributions for the entire charmonium family. Including tree-level NLO corrections improves the global description compared to LO. The study also tests heavy quark spin symmetry (HQSS) relations and finds significant violations in χ_cJ wave functions, but NLO† reduces these violations.

What carries the argument. The NLO† matching scheme, which combines leading and tree-level next-to-leading-order off-shell amplitudes with a double-counting-exclusion (DCE) cut to avoid double counting between the 2→1 and 2→2 subprocesses, along with the use of CCFM-evolved TMD gluon densities and the chromo-electric dipole model for bound state formation, carries the argument.

Core claim. The central claim is that the NLO† scheme, which merges LO and NLO off-shell amplitudes with a double-counting-exclusion cut, provides a consistent and simultaneous description of all available data for transverse momentum distributions of unpolarized prompt ψ', χ_cJ, and J/ψ production in pp collisions at high energies (conclusion, sentence b160). Including tree-level NLO corrections improves the global description versus LO (abstract, sentence b6). One set of fitted LDMEs plus CCFM-evolved gluon densities describes the full unpolarized charmonium dataset at the LHC.

The premise it rests on. The heavy quark spin symmetry (HQSS) relations (5)-(9) are assumed to reduce the number of independent LDMEs, but the fit reveals violations in χ_cJ wave functions that are well beyond the expected NRQCD relativistic corrections, and the NLO† double-counting-exclusion cut is inherited from previous work without independent validation.

If the paper is right (Pith's inferences, not the authors')

The NLO† scheme can be extended to charmonium polarization observables, which were left for future study.

The fitted LDMEs can serve as input for predictions at future colliders or in nuclear collisions.

The approach validates the kT-factorization framework for heavy quarkonium production beyond leading order.

The simultaneous fit reduces parameter degeneracies and leads to more reliable LDME values for J/ψ and χ_cJ.

The observed HQSS violations in χ_cJ wave functions motivate further theoretical work on spin-dependent NRQCD corrections.

The significant violation of HQSS for χ_cJ (50% deviations in wave function derivatives) suggests that spin-dependent corrections in NRQCD may be larger than the expected O(v²) scale, possibly requiring resummation or reanalysis of NRQCD factorization.

The failure of parameter-free η_c predictions indicates that the HQSS relations linking η_c LDMEs to J/ψ LDMEs are not reliable at the current level of precision; a separate fit for η_c data may be needed.

The energy scaling discrepancy in forward-rapidity LHCb data (overestimation at 5 TeV to underestimation at 13 TeV) points to possible limitations in the CCFM-evolved gluon densities at low x, which could be tested by incorporating additional forward data from Runs 3 and 4.

The double-counting-exclusion cut inherited from [26,27] has not been independently validated; a dedicated study of its effect on the fit stability would strengthen the NLO† claim.

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The paper

Abstract

We consider prompt J/ψ, χcJ and ηc production in high energy pp collisions in the framework of non-relativistic QCD. We apply high-energy factorization with taking into account tree-level next-to-leading order corrections to the production amplitudes. Using several CCFM-evolved gluon densities in the proton and a previously proposed matching scheme to merge the leading and higher-order contributions, we extract the long-distance matrix elements for the entire charmonium family from a simultaneous fit to available LHC data. We provide predictions for the transverse momentum spectra and relative production rates σ(ψ′)/σ(J/ψ) and σ(χcJ)/σ(J/ψ) and find them to be in good agreement with the LHC data within the theoretical and experimental uncertainties across a wide kinematic region. We demonstrate that taking into account the tree-level NLO corrections improves the global description of the data.

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. No sentence in this record was written by a model.

abstract compiled · 2026-10-22

The authors' main claim, as the classifier picked it out 0.59

“We demonstrate that taking into account the tree-level NLO corrections improves the global description of the data.”

How the main claim is stated: asserted 1.00

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.17 · human participants 0.01 · controlled comparison 0.18 · randomized assignment 0.01 · states quantitative result 0.14 · compares with prior results 0.53 · mentions code or data availability 0.02

The abstract, sentence by sentence

This table labels the abstract only (arXiv listing abstract v1). The number is the probability the classifier gave the label.

SentenceRoleThe authors' own workStates the main conclusionStrength
We consider prompt $J/\psi$, $\chi_{cJ}$ and $\eta_c$ production in high energy $pp$ collisions in the framework of non-relativistic QCD. contribution 0.62 0.73 0.02 asserted 0.74
We apply high-energy factorization with taking into account tree-level next-to-leading order corrections to the production amplitudes. method 0.96 0.92 0.04 asserted 0.95
Using several CCFM-evolved gluon densities in the proton and a previously proposed matching scheme to merge the leading and higher-order contributions, we extract the long-distance matrix elements for the entire charmonium family from a simultaneous fit to available LHC data. method 0.89 0.95 0.10 asserted 1.00
We provide predictions for the transverse momentum spectra and relative production rates $\sigma(\psi^\prime)/\sigma(J/\psi)$ and $\sigma(\chi_{cJ})/\sigma(J/\psi)$ and find them to be in good agreement with the LHC data within the theoretical and experimental uncertainties across a wide kinematic region. result 1.00 0.97 0.60 asserted 1.00
We demonstrate that taking into account the tree-level NLO corrections improves the global description of the data. result 0.75 0.96 0.51 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.62 · evidence from analysis of existing data 0.81

What was examined, and what was not

Sources read

  • arXiv listing abstract v1

Not examined

  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers

Levels run

  • P abstract

Not run

  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

How the labels were made

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-10-22: 1 request, 4,421 input tokens.

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. This record as JSON

Figures (13)
Figure 1 of the paper
Figure 1. Lowest values of χ 2/n.d.f. as function of minimal J/ψ transverse momenta. 3 Numerical results In this section, we present the results of our global two-step fitting. In
Figure 2 of the paper
Figure 2. The differential cross sections for inclusive
Figure 3 of the paper
Figure 3. Ratios of differential cross sections σ(χc1+χc2)/σ(J/ψ) in pp collisions at √ s = 7 TeV as functions of the J/ψ transverse momentum at the central (left plot) and forward (right plot) rapidity regions. The ATLAS data are taken from [45] and LHCb [51]. also remains between the results from the ATLAS and CMS Collaborations taken at √ s = 13 TeV. The results of our calculations for J/ψ transverse momentum spectra are presented in
Figure 4 of the paper
Figure 4. Ratios of differential cross sections σ(χc2)/σ(χc1) in pp collisions at √ s = 7 TeV as functions of the J/ψ transverse momentum at the central (upper plots) and forward (lower plot) rapidity regions. The ATLAS data are taken from [45], CMS [52] and LHCb [53]. 12
Figure 5 of the paper
Figure 5. Ratios of differential cross sections for inclusive
Figure 6 of the paper
Figure 6. Ratios of differential cross sections for inclusive
Figure 7 of the paper
Figure 7. Ratios of differential cross sections for inclusive
Figure 8 of the paper
Figure 8. Ratios of differential cross sections for inclusive
Figure 9 of the paper
Figure 9. Ratios of differential cross sections for inclusive
Figure 10 of the paper
Figure 10. Ratios of differential cross sections for inclusive
Figure 11 of the paper
Figure 11. Ratios of differential cross sections for inclusive
Figure 12 of the paper
Figure 12. Ratios of differential cross sections σ(ψ ′ )/σ(J/ψ) in pp collisions at √ s = 13 TeV as functions of the ψ transverse momentum at the central (left plot) and forward (right plot) rapidity regions. The ATLAS data are taken from [56] and LHCb [64]. wanger, P. Faccioli, A. Gabareen Mokhtar, X. Garcia i Tormo, C. Hanhart, F.A. Har￾ris, D.M. Kaplan, S.R. Klein, H. Kowalski, J.-P. Lansberg, E. Levichev, V. Lombardo, C. Lourenco, F. Maltoni, A. Mocsy, R. Mussa, F.S. Navarra, M. Negrini, M. Nielsen, S.L. Olsen, P. Pakhlov, G. Pakhlova, K. Peters, A.D. Polosa, W. Qian, J.-W. Qiu, G. Rong, M
Figure 13 of the paper
Figure 13. The differential cross sections for inclusive

Figures are the authors', reproduced from the paper.

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