Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

$J/\psi$ Polarization and $p_T$ distribution in $c\ \!\bar{c}$ associated hadroproduction at $\mathcal{O}(\alpha_s^5)$

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The first complete NLO QCD calculation of gluon fusion to J/psi plus a charm pair shows the NLO corrections multiply the color-singlet yield severalfold and make the polarization nearly unpolarized, matching LHC data.

desk verdict A technically substantial NLO calculation that likely fills a real gap in quarkonium hadroproduction, but the numerical results are not yet secured without cutoff-independence checks and a clearer novelty statement. read the letter →

arxiv 2507.20654 v1 pith:MRNU2UGA submitted 2025-07-28 hep-ph

Qi-Ming Feng , Cong-Feng Qiao This is my paper · ORCID
classification hep-ph PACS 12.38.Bx13.85.Ni14.40.Pq
keywords J/psiproductionNRQCDfactorizationnext-to-leading-orderQCDcolor-singletchannelquarkoniumpolarizationassociatedheavy-quarkpairhadroproductioncorrections
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper addresses a standing puzzle in charmonium production: the color-singlet mechanism alone seemed unable to reproduce measured J/psi yields and polarization. It presents the first complete next-to-leading-order QCD calculation of the gluon-fusion process $gg\to J/\psi+c\bar{c}$ within NRQCD factorization, at $\mathcal{O}(\alpha_s^5)$. The result is that the NLO corrections are large, enhancing the leading-order color-singlet yield by several times, so that this associated-production channel dominates over $J/\psi+g$ among color-singlet mechanisms. The predicted $p_T$ spectrum matches the shape of direct-J/psi data and the polarization stays nearly unpolarized over a wide $p_T$ range, consistent with CMS measurements, while a normalization gap of roughly an order of magnitude remains. If the calculation is right, global fits of color-octet matrix elements need to include this channel, and the J/psi-plus-open-charm signature becomes a clean way to probe the production mechanism.

What carries the argument

The load-bearing object is the short-distance coefficient for the $2\to4$ partonic process $gg\to c\bar{c}[{}^3S_1]+c\bar{c}$, evaluated in NRQCD factorization with the color-singlet matrix element $\langle \mathcal{O}^{J/\psi}({}^3S_1)\rangle$. The calculation combines helicity amplitudes for the finite parts with a projection tensor that isolates the longitudinal polarization, and the finiteness of the result rests on an infrared-cancellation identity: the virtual and real divergences are matched through color-decomposed Born amplitudes and a $3\times3$ kernel $\Delta$, which lets the two-cutoff phase-space slicing of the real corrections cancel the one-loop poles. This matching turns a formally divergent expression into a finite cross section and a finite polarization parameter.

What would settle it

Recompute the NLO cross section and $\lambda_\theta$ with substantially different phase-space-slicing cutoffs, or with an independent subtraction scheme; if the results move beyond integration uncertainties, the reported enhancement and near-unpolarized polarization are artifacts of the slicing prescription.

Watch

Extended reading notes

Core claim

The central discovery is that the $\mathcal{O}(\alpha_s^5)$ corrections to $gg\to J/\psi+c\bar{c}$ are not a small refinement. In the color-singlet NRQCD channel they enhance the leading-order cross section by several times and flatten the $p_T$ distribution. The polarization parameter $\lambda_\theta$ comes out close to zero from low to high transverse momentum in the helicity frame, matching the mildly varying values observed by CMS, whereas the $J/\psi+g$ channel predicts strong longitudinal polarization. The paper concludes that associated $J/\psi+c\bar{c}$ production is a dominant color-singlet source of prompt $J/\psi$ and should be included when extracting color-octet long-distance matrix elements from global fits, even though a residual gap of about one order of magnitude between theory and data remains.

Load-bearing premise

The final cross sections are reliable only if the artificial cutoffs used to separate soft and collinear real emissions leave the result unchanged; the paper states the infrared cancellation analytically but does not demonstrate numerical cutoff independence.

Editorial extensions

If this is right

  • The color-singlet contribution to inclusive $J/\psi$ production is no longer negligible: at NLO, the $J/\psi+c\bar{c}$ process dominates over $J/\psi+g$ in the color-singlet channel and falls off more slowly with $p_T$.
  • Global fits of color-octet long-distance matrix elements should include this process; without it, octet matrix elements will absorb yield that is actually color-singlet.
  • The near-unpolarized prediction for this channel brings color-singlet calculations into closer agreement with the CMS polarization measurements across the measured $p_T$ range.
  • At high $p_T$, charm-quark fragmentation eventually overtakes the associated-production process but with a different shape and normalization, so the two mechanisms can be distinguished experimentally.
  • A residual gap of roughly one order of magnitude remains after including this channel, so additional prompt-$J/\psi$ production mechanisms are still required.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the NLO enhancement is as large as reported, the same calculation should be repeated for $\psi(2S)+c\bar{c}$ and for bottomonium counterparts; those channels would receive comparable corrections and could be tested with existing data.
  • The near-zero polarization implies that a global fit that includes this process will shift the fitted color-octet matrix elements downward, which would alter predictions for other observables such as $J/\psi$ production in photoproduction or in proton-nucleus collisions.
  • A direct experimental test would be to reconstruct $J/\psi$ mesons accompanied by open-charm hadrons ($D$ or $\bar{D}$ mesons) at the LHC; the predicted $p_T$ shape, normalization, and polarization of that subsample separate the associated-production mechanism from fragmentation.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This Letter reports what it claims to be the first complete next-to-leading-order QCD calculation, at O(α_s^5), of the hadroproduction process gg → J/ψ + c cbar in the NRQCD color-singlet framework. The authors compute the J/ψ transverse-momentum distribution and the polarization parameter λθ at LO and NLO, compare their results with ATLAS data at 13 TeV and CMS data at 7 TeV, include ψ(2S) and χcJ feeddown estimates, and compare the associated-production channel with charm-quark fragmentation. The main findings are that the NLO corrections enhance the color-singlet yield substantially, that the J/ψ + c cbar channel is nearly unpolarized over a wide pT range, and that including this process improves agreement with data while a gap of about one order of magnitude remains.

Significance. If the numerical results are correct, this is a significant step forward for NRQCD phenomenology: it extends the NLO program for inclusive quarkonium hadroproduction to a 2→4 partonic final state, and it shows that this channel can alter the predicted polarization pattern, which is directly testable with existing LHC data. The paper has notable strengths: the analytic IR-cancellation check in Eq. (7), the use of modern amplitude techniques such as integrand reduction and NeatIBP, the use of external inputs for PDFs, fragmentation functions, and the CS LDME, and the explicit caveat that a residual factor-of-ten gap with data remains. However, the absence of any numerical validation of the two-cutoff phase-space slicing, the lack of numerical tables, and the vague treatment of the ψ(2S) feeddown fit mean that the quantitative claims are not yet fully secured. The central prediction is not tuned to the data it is compared with, and the polarization prediction is falsifiable, which is to the paper's credit.

major comments (3)
  1. [§II, Eqs. (6)–(7)] The central numerical results in §III rest on the two-cutoff phase-space slicing separation in Eq. (6), but the manuscript gives no evidence that the finite remainders are independent of the slicing parameters. The analytic check in Eq. (7) verifies cancellation of the 1/ε IR poles between virtual and real corrections; it does not test for cutoff leakage or errors in the numerical 2→4 body phase-space integration, which affect exactly the finite parts that produce the reported K-factors and λθ values. Please report the values of δ_s and δ_c used, and show that σ, dσ/dpT, and λθ are stable over a range of cutoffs, or provide an independent subtraction or Monte Carlo validation. Without this, the claimed "several times" enhancement and the nearly unpolarized polarization could be numerical artifacts.
  2. [§I and §IV] The paper states in §I that the full NLO QCD corrections to gg→J/ψ+c cbar "have never been computed" and in §IV that it presents "the first calculation," yet §I cites Refs. [8] and [23] as earlier NLO studies of J/ψ+c cbar associated production. This apparent conflict must be resolved: please specify precisely what those earlier calculations did and did not include, and compare at least one common observable, such as the total NLO cross section or pT distribution, to demonstrate that the present calculation is new and consistent with the earlier results. Without this, the novelty claim and the assessment of the size of the NLO corrections cannot be evaluated.
  3. [§III, Fig. III.1 and feeddown procedure] The ψ(2S) feeddown is said to be "fitted up to 120 GeV using ATLAS data [35]," but the fit function, the fitted parameters, and the propagation of the associated uncertainties into the "direct J/ψ" data are not described. Because the same ATLAS sample is then used to compare both direct J/ψ and prompt ψ(2S) in Fig. III.1, the comparison is partly circular for the feeddown component. Please specify the fitting procedure and its uncertainty, and ideally show that the main NLO conclusions are insensitive to reasonable variations of this feeddown subtraction.
minor comments (5)
  1. [§III, Eq. (5) and Fig. III.2] The polarization parameter is quoted in the HX frame in Fig. III.2, but Eq. (5) defines the longitudinal axis from the partonic momentum k1; the transformation to the experimental HX frame should be stated explicitly so that the comparison with CMS data is unambiguous.
  2. [Throughout] Several typographical errors should be corrected: "was found plays" in the abstract, "caculable" in §I, "extracted form" in §III, "evquation" in §III, and "convolution production" in the description of Eq. (11).
  3. [§III, Figs. III.1–III.3] No numerical values are given for the K-factor, for the integration errors on the plotted cross sections, or for the phase-space slicing cutoffs; since the figures are log-scale, the reader cannot verify the claimed "several times" enhancement or the size of the residual gap.
  4. [§III, Eq. (11)] The charm-quark fragmentation estimate mixes an NLO cross section with a LO fragmentation function plus an LO cross section with a NLO fragmentation function; a sentence explaining why this combination, rather than a fully NLO convolution, is appropriate and does not introduce double counting would be helpful.
  5. [References] Reference [40] is cited only as an arXiv preprint; please update it to the published version, if one exists, and check that all cited branching ratios and feeddown fractions are the most recent values.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the central NLO calculation is independent of the data it is compared with, and the only fit is a feeddown subtraction that does not enter the J/psi + c-cbar parameters.

full rationale

The paper's derivation chain is self-contained with respect to the central claims. The J/psi + c-cbar cross sections and polarization are computed from the NRQCD factorization formula (Eq. 1) with external inputs: the color-singlet LDME is fixed by the measured leptonic width, the PDFs and alpha_s are standard external sets, and the charm mass is set to half the J/psi mass. No parameter of the J/psi + c-cbar calculation is adjusted to the ATLAS or CMS data shown in Figs. III.1-III.3. The only fitted quantity is the psi(2S) feeddown, which the text explicitly states is fitted to ATLAS data and used to subtract feeddown from the prompt data; this subtraction is a data-processing step and does not enter the J/psi + c-cbar matrix elements, the pT shapes, or the lambda_theta values. The residual order-of-magnitude gap in Fig. III.1(c) confirms that the comparison is not statistically forced. The analytic IR-cancellation check in Eq. (7) checks the pole structure; the absence of a numerical cutoff-independence study is a validation gap, not a circularity. The self-citation to Ref. [25] is methodological (the amplitude-computation strategy), not a load-bearing result or a uniqueness claim. No step in the paper reduces by construction to its own input.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central calculation rests on standard NRQCD factorization and external inputs. The main unstated assumptions are the numerical stability of the phase-space slicing and the leading-order velocity expansion for J/psi. No new particles or entities are introduced.

free parameters (3)
  • Charm quark mass mc = 1.5 GeV (default), 1.4 GeV (uncertainty)
    Set to half the J/psi mass following NRQCD convention; varied in Fig III.3 to estimate uncertainty. The result is moderately sensitive (cross section increases by about a factor of two).
  • Renormalization/factorization scale mu = mu = mT (default), mu = mT/2 (uncertainty)
    Central scale choice; the paper shows that varying to mT/2 changes the cross section by roughly a factor of two. No scale variation bands are shown in the main figures.
  • Phase-space slicing cutoffs
    The two-cutoff method (Ref [31]) requires soft and collinear cutoff parameters; the paper does not state their values or demonstrate cutoff independence. This is an unstated numerical input.
assumptions (4)
  • domain assumption NRQCD factorization at leading order in v: the J/psi is produced as a c cbar pair in the 3S1[1] color-singlet state, with the cross section given by Eq (1).
    Used throughout Section II; color-octet contributions are omitted by design, limiting the comparison to direct-J/psi data.
  • domain assumption The CS LDME satisfies <O(3S1)> = 9/(2 pi)|R(0)|^2, with |R(0)|^2 fixed by Gamma(J/psi -> e+e-) = 5.55 keV.
    Used to normalize the pT distributions; the leptonic width is an external input.
  • domain assumption The two-cutoff phase-space slicing method yields results independent of the slicing cutoffs, and the IR cancellation in Eq (7) is complete.
    The paper states the analytic cancellation but does not show numeric cutoff stability for the final curves.
  • standard math CTEQ6L1/CTEQ6M PDFs and the two-loop running of alpha_s are appropriate for these LHC predictions.
    Standard inputs used in the numerical section.

how reviews work

0 comments
Cite this review

Pith. "Pith review of $J/\psi$ Polarization and $p_T$ distribution in $c\ \!\bar{c}$ associated hadroproduction at $\mathcal{O}(\alpha_s^5)$." pith.science (2026). https://pith.science/paper/MRNU2UGA

@misc{pith2026250720654,
  author       = {Pith},
  title        = {Pith review of: $J/\psi$ Polarization and $p_T$ distribution in $c\ \!\barc$ associated hadroproduction at $\mathcalO(\alpha_s^5)$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MRNU2UGA}},
  note         = {Machine review of arXiv:2507.20654}
}
abstract

The quarkonium production in association with a heavy-quark pair of the same flavor was found plays an important role in various production schemes, let alone it provides a distinctive signature that could be studied in experiment. Within the NRQCD framework, we perform the first complete calculation of the hadroproduction process $gg\to J/\psi+c\bar{c}$ at the next-to-leading order (NLO) in the expansion of strong coupling constant $\alpha_s$. The result tells that the NLO corrections substantially enhance the color-singlet yield and alter the predicted polarization patterns, and hence lead to a better agreement with experimental data across the $p_T$ spectrum. In contrast to charm-quark fragmentation, the $J/\psi$ and $c\bar{c}$ associated production channel displays a markedly different kinematic behavior, underscoring its distinct role in the production mechanism. While the inclusion of this process greatly reduces the discrepancy between color-singlet theoretical prediction and experimental measurement, a residual gap of approximately one order of magnitude still remains.

Review history (2 revisions) →

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Impact of relativistic corrections to high-pT prompt-psi(2S) production at hadron colliders

    hep-ph 2025-10 conditional novelty 6.0 of 10

    Relativistic O(v^2) corrections to color-singlet fragmentation functions, especially for gluons, bring leading-power NRQCD predictions for prompt psi(2S) at high pT into agreement with LHC data without color-octet mat...

Reference graph

Works this paper leans on

40 extracted references · 9 canonical work pages · cited by 1 Pith paper

  1. [8]

    Gong and J

    B. Gong and J. X. Wang, Phys. Rev. Lett. 100, 232001 (2008) [arXiv:0802.3727 [hep-ph]]

    arXiv 2008

  2. [23]

    Y. J. Zhang and K. T. Chao, Phys. Rev. Lett. 98, 092003 (2007) [arXiv:hep-ph/0611086 [hep-ph]]. 11

    arXiv 2007

  3. [35]

    Aad et al

    G. Aad et al. [ATLAS], Eur. Phys. J. C 84, no.2, 169 (2024) [arXiv:2309.17177 [hep-ex]]

    arXiv 2024

  4. [1]

    G. T. Bodwin, E. Braaten and G. P. Lepage, Phys. Rev. D 51 (1995), 1125-1171 [erratum: Phys. Rev. D 55 (1997), 5853] [arXiv:hep-ph/9407339 [hep-ph]]

    arXiv 1995

  5. [2]

    G. T. Bodwin, [arXiv:1208.5506 [hep-ph]]

    arXiv

  6. [3]

    C. H. Chang, R. Li and J. X. Wang, Phys. Rev. D 80, 034020 (2009) [arXiv:0901.4749 [hep-ph]]

    arXiv 2009

  7. [4]

    Artoisenet, J

    P. Artoisenet, J. M. Campbell, F. Maltoni and F. Tramontano, Phys. Rev. Lett. 102, 142001 (2009) [arXiv:0901.4352 [hep-ph]]

    arXiv 2009

  8. [5]

    J. M. Campbell, F. Maltoni and F. Tramontano, Phys. Rev. Lett. 98, 252002 (2007) [arXiv:hep-ph/0703113 [hep-ph]]

    arXiv 2007

Show all 40 references
  1. [6]

    J. P. Lansberg, Phys. Lett. B 695, 149-156 (2011) [arXiv:1003.4319 [hep-ph]]. 10

    2011 arXiv

  2. [7]

    Artoisenet, J

    P. Artoisenet, J. P. Lansberg and F. Maltoni, Phys. Lett. B 653, 60-66 (2007) [arXiv:hep- ph/0703129 [hep-ph]]

    2007

  3. [9]

    Kramer, J

    M. Kramer, J. Zunft, J. Steegborn and P. M. Zerwas, Phys. Lett. B 348, 657-664 (1995) [arXiv:hep-ph/9411372 [hep-ph]]

    1995 arXiv

  4. [10]

    Kr¨ amer, Nucl

    M. Kr¨ amer, Nucl. Phys. B459, 3-50 (1996) [arXiv:hep-ph/9508409 [hep-ph]]

    1996 arXiv

  5. [11]

    Butenschoen and B

    M. Butenschoen and B. A. Kniehl, Phys. Rev. Lett. 104, 072001 (2010) [arXiv:0909.2798 [hep-ph]]

    2010 arXiv

  6. [12]

    Butenschoen and B

    M. Butenschoen and B. A. Kniehl, Phys. Rev. Lett. 108, 172002 (2012) [arXiv:1201.1872 [hep-ph]]

    2012 arXiv

  7. [13]

    Butenschoen and B

    M. Butenschoen and B. A. Kniehl, Phys. Rev. Lett. 107, 232001 (2011) [arXiv:1109.1476 [hep-ph]]

    2011 arXiv

  8. [14]

    K. T. Chao, Y. Q. Ma, H. S. Shao, K. Wang and Y. J. Zhang, Phys. Rev. Lett. 108, 242004 (2012) [arXiv:1201.2675 [hep-ph]]

    2012 arXiv

  9. [15]

    Y. Q. Ma, K. Wang and K. T. Chao, Phys. Rev. D 84, 114001 (2011) [arXiv:1012.1030 [hep-ph]]

    2011 arXiv

  10. [16]

    Y. Q. Ma, K. Wang and K. T. Chao, Phys. Rev. Lett. 106, 042002 (2011) [arXiv:1009.3655 [hep-ph]]

    2011 arXiv

  11. [17]

    Y. J. Zhang, Y. Q. Ma, K. Wang and K. T. Chao, Phys. Rev. D 81, 034015 (2010) [arXiv:0911.2166 [hep-ph]]

    2010 arXiv

  12. [18]

    B. Gong, L. P. Wan, J. X. Wang and H. F. Zhang, Phys. Rev. Lett. 110, no.4, 042002 (2013) [arXiv:1205.6682 [hep-ph]]

    2013 arXiv

  13. [19]

    Brambilla, M

    N. Brambilla, M. Butenschoen and X. P. Wang, [arXiv:2411.16384 [hep-ph]]

    arXiv

  14. [20]

    Chatrchyan et al

    S. Chatrchyan et al. [CMS], Phys. Lett. B 727, 381-402 (2013) [arXiv:1307.6070 [hep-ex]]

    2013 arXiv

  15. [21]

    Hayrapetyan et al

    A. Hayrapetyan et al. [CMS], Phys. Lett. B 858, 139044 (2024) [arXiv:2406.14409 [hep-ex]]

    2024 arXiv

  16. [22]

    C. F. Qiao and J. X. Wang, Phys. Rev. D 69, 014015 (2004) [arXiv:hep-ph/0308244 [hep- ph]]

    2004 arXiv

  17. [24]

    Z. Q. Chen, L. B. Chen and C. F. Qiao, Phys. Rev. D 95, no.3, 036001 (2017) [arXiv:1608.06231 [hep-ph]]

    2017 arXiv

  18. [25]

    Q. M. Feng and C. F. Qiao, Phys. Rev. D 110, no.9, 094047 (2024) [arXiv:2405.05683 [hep-ph]]

    2024 arXiv

  19. [26]

    Braaten and J

    E. Braaten and J. Russ, Ann. Rev. Nucl. Part. Sci. 64, 221-246 (2014) [arXiv:1401.7352 [hep-ex]]

    2014 arXiv

  20. [27]

    Faccioli, C

    P. Faccioli, C. Lourenco, J. Seixas and H. K. Wohri, Eur. Phys. J. C 69, 657-673 (2010) [arXiv:1006.2738 [hep-ph]]

    2010 arXiv

  21. [28]

    Mastrolia, E

    P. Mastrolia, E. Mirabella and T. Peraro, JHEP 06, 095 (2012) [erratum: JHEP 11, 128 (2012)] [arXiv:1203.0291 [hep-ph]]

    2012 arXiv

  22. [29]

    Peraro, Comput

    T. Peraro, Comput. Phys. Commun. 185, 2771-2797 (2014) [arXiv:1403.1229 [hep-ph]]

    2014 arXiv

  23. [30]

    Z. Wu, J. Boehm, R. Ma, H. Xu and Y. Zhang, Comput. Phys. Commun. 295, 108999 (2024) [arXiv:2305.08783 [hep-ph]]

    2024 arXiv

  24. [31]

    B. W. Harris and J. F. Owens, Phys. Rev. D 65, 094032 (2002) [arXiv:hep-ph/0102128 [hep-ph]]

    2002 arXiv

  25. [32]

    Dittmaier, Nucl

    S. Dittmaier, Nucl. Phys. B 675, 447-466 (2003) [arXiv:hep-ph/0308246 [hep-ph]]

    2003 arXiv

  26. [33]

    Pumplin, D

    J. Pumplin, D. R. Stump, J. Huston, H. L. Lai, P. M. Nadolsky and W. K. Tung, JHEP 07, 012 (2002) [arXiv:hep-ph/0201195 [hep-ph]]

    2002 arXiv

  27. [34]

    P. A. Zyla et al. [Particle Data Group], PTEP 2020, no.8, 083C01 (2020)

    2020

  28. [36]

    Aad et al

    G. Aad et al. [ATLAS], JHEP 07, 154 (2014) [arXiv:1404.7035 [hep-ex]]

    2014 arXiv

  29. [37]

    Y. J. Zhang, Y. Q. Ma and K. T. Chao, Phys. Rev. D 78, 054006 (2008) [arXiv:0802.3655 [hep-ph]]

    2008 arXiv

  30. [38]

    Braaten, K

    E. Braaten, K. m. Cheung and T. C. Yuan, Phys. Rev. D 48, 4230-4235 (1993) [arXiv:hep- ph/9302307 [hep-ph]]

    1993

  31. [39]

    X. C. Zheng, C. H. Chang and X. G. Wu, Phys. Rev. D 100, no.1, 014005 (2019) [arXiv:1905.09171 [hep-ph]]

    2019 arXiv

  32. [40]

    B. Gong, R. Li and J. X. Wang, [arXiv:1102.0118 [hep-ph]]. 12

    arXiv

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.