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REVIEW 4 major objections 6 minor 78 references

Probing Heavy-Quark Spin Symmetry in Double $J/\psi$ Hadroproduction

T0 review · 4 major / 6 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read This paper claims that LHC data on pairs of J/psi mesons provide the first experimental verification of heavy-quark spin symmetry in quarkonium, without putting that symmetry into the fit.

desk verdict First complete O(alpha_s^5) NRQCD calculation for double J/psi hadroproduction, with a clever LDME-combination argument and a novel HQSS test; the central result is solid but the unpropagated spread in the ratio r0 is a real weakness. read the letter →

arxiv 2608.03510 v1 pith:5DUEZV5M submitted 2026-08-04 hep-ph hep-ex

Zhi-Guo He , Xiao-Bo Jin , Bernd A. Kniehl This is my paper
classification hep-phhep-ex
keywords heavyquarkoniumproductionNRQCDfactorizationcolor-octetmatrixelementsJ/psipairhadroproductionheavy-quarkspinsymmetryeta_cLHCphenomenologylong-distance
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

This paper attempts to establish that double J/psi hadroproduction at the LHC can resolve a long-standing ambiguity in how quark-antiquark pairs become J/psi mesons, and can test a symmetry that theorists have often assumed. It reports the first complete calculation of prompt J/psi pair production at order alpha_s^5 in nonrelativistic QCD, including all 28 pairings of quark-antiquark Fock states. The key finding is that high-transverse-momentum CMS and ATLAS data do not fix the two dominant color-octet matrix elements separately, but only their linear combination M_{0,1.8}; combining this with two combinations already fixed by single-J/psi production yields a new set of matrix elements. That set agrees with world data on J/psi yield and polarization and, when spin symmetry is applied, with LHCb data on eta_c production. The paper reads this agreement as evidence that heavy-quark spin symmetry is real rather than an input.

What carries the argument

The load-bearing object is the linear combination M_{0,1.8}^{J/psi} = <O^{J/psi}(1S_0^[8])> + (1.8/m_c^2)<O^{J/psi}(3P_0^[8])>, defined in Eq. (3). It exists because the short-distance coefficient ratio R_{3S1[1],3PJ[8]}/R_{3S1[1],1S0[8]} stays close to 1.80 (observed range 1.77-1.86) over the 14 CMS/ATLAS bins at large pair pT. This lets two nonperturbative parameters collapse into the single combination the data can actually constrain; the companion combinations M_{0,3.9} and M_{1,-0.56} from single-J/psi production then break the remaining degeneracy. The full O(alpha_s^5) calculation of all 28 Fock-state pairings is the computational carrier that makes the comparison quantitative.

What would settle it

A reanalysis that lets <O(1S0^[8])> and <O(3P0^[8])> float separately in the CMS/ATLAS bins, or a measurement of d sigma/d pT^{psi psi} at lower pair pT where the 2->2 and 2->3 contributions differ, would show whether the 1.80 collapse is legitimate; if the extracted combination changes bin-by-bin or substantially improves the fit when split into two free parameters, the constancy assumption fails.

Watch

Extended reading notes

Core claim

The paper performs the first complete O(alpha_s^5) NRQCD computation of prompt J/psi pair hadroproduction, keeping every Fock-state combination of the two charm-anticharm pairs. Comparing with CMS and ATLAS data at large pair transverse momentum, it finds that the short-distance coefficients for the 3P_0^[8] and 1S_0^[8] color-octet channels have an almost constant ratio of about 1.80 across the 14 fitted bins. As a result, the data constrain only the combination <O^{J/psi}(1S_0^[8])> + (1.8/m_c^2)<O^{J/psi}(3P_0^[8])>, which the fit fixes at (3.49 +/- 0.59) x 10^-2 GeV^3. Combined with two LDME combinations from single-J/psi hadroproduction, this pins down the three color-octet matrix eleme

Load-bearing premise

The extraction treats the short-distance coefficient ratio of the 3P0^[8] to 1S0^[8] channels as fixed at 1.80 across all 14 fitted bins; if that ratio actually shifts with kinematics, scale choice, or higher orders, the merged matrix element and the spin-symmetry test would be biased.

Editorial extensions

If this is right

  • Large-pT double-J/psi production at the LHC is now described at order alpha_s^5 with all Fock states, closing the order-of-magnitude deficit of earlier color-singlet-only predictions through the color-octet mechanism.
  • The CMS and ATLAS data can be fitted with the color-singlet channel plus the 3S1^[8], 1S0^[8], and 3P0^[8] channels; adding all 21 retained channels changes the fit score by only about 5%.
  • The extracted LDME set reproduces the world prompt J/psi yield and polarization data and, under heavy-quark spin symmetry, the LHCb prompt eta_c data within uncertainties.
  • The lowest invariant-mass bins, which lie beyond leading-order kinematics, are also described, showing that the O(alpha_s^5) calculation covers real-radiation phase space.
  • Alternative LDME sets from the literature produce worse agreement on the same fit range, indicating that the pair-production data discriminate among existing extractions.

Reading between the lines

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

  • If the constancy of the 1.80 ratio survives scale and kinematic variations, the same collapse of 1S0^[8] and 3P0^[8] matrix elements could be applied to other charmonium pair observables, such as J/psi + psi' or J/psi + chi_c, to sharpen LDME determinations.
  • A dedicated measurement at lower pT^{psi psi}, or with finer bins, could test the constancy assumption directly and might separate <O(1S0^[8])> from <O(3P0^[8])>, giving a more stringent check of the spin-symmetry relation than the current comparison.
  • Because the fit fixes only the linear combination, the agreement with eta_c data depends on applying HQSS; a future precise eta_c measurement that disagrees could force a reanalysis even if the pair-production fit remains good.
  • With the single-parton-scattering contribution computed at this order, the same framework could provide an independent extraction of the double-parton-scattering effective cross section after subtracting the SPS background.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The paper presents the first complete O(α_s^5) NRQCD analysis of prompt J/ψ pair hadroproduction at large p_T^{ψψ}, including all allowed Fock-state pairings of the two c-cbar pairs. The authors compute the relevant short-distance coefficients with QGRAF/FORM/Cuba, classify the channels by power counting, and observe that CMS and ATLAS data constrain the linear combination M_{0,1.8}^{J/ψ}=<O^{J/ψ}(^1S_0^{[8]})> + (1.8/m_c^2)<O^{J/ψ}(^3P_0^{[8]})>. Combining this with two combinations extracted from single-J/ψ hadroproduction, they obtain a new CO LDME set. They then compare NLO NRQCD predictions for prompt η_c production with LHCb data, using HQSS to relate J/ψ and η_c LDMEs, and report good agreement (χ²/11 = 1.52 or 1.38 depending on the set). They also note that their O(α_s^5) predictions reproduce the lowest m^{ψψ} bins in CMS and ATLAS data, which are kinematically inaccessible at O(α_s^4). The central claim is that this constitutes the first genuine, data-driven verification of HQSS in heavy quarkonium production, because the J/ψ-pair fit itself does not assume HQSS.

Significance. If the extraction is robust, this is a valuable step. The computation covers a much larger set of Fock-state channels than previous double-J/ψ studies, and the observation that high-p_T^{ψψ} data pin down only a specific LDME combination is a useful and nontrivial finding. The paper also makes genuine predictions, particularly in the low-m^{ψψ} bins, and it provides an independent route to HQSS testing that does not build HQSS into the J/ψ fit. The agreement with the world J/ψ data and with LHCb η_c data is encouraging. However, the strength of the HQSS claim is currently limited by an unpropagated systematic uncertainty in the coefficient r0=1.8 and by a post-hoc choice of fit range. These issues are local and fixable, but they are load-bearing for the advertised conclusion.

major comments (4)
  1. [Section 'quantitative verification', Eq. (3)] The extraction of M_{0,1.8}^{J/ψ} rests on the near-constancy of the ratio R_{3S1[1],3PJ[8]}/R_{3S1[1],1S0[8]}, quoted as 1.77–1.86 with average 1.80 across the 14 fit bins. The spread is not propagated into the fit. This matters because the subsequent separation of <O(^1S0[8])> and <O(^3P0[8])> is a subtraction of two nearly equal combinations: with the central values, <O(^1S0[8])> = (3.9 M_{0,1.8} - 1.8 M_{0,3.9})/(3.9-1.8) ≈ 0.14×10^{-2} GeV^3. A change of r0 by ±0.06 shifts <O(^1S0[8])> by about ∓0.11×10^{-2} GeV^3, which is comparable to the difference between this fit and Ref. [24] that the paper itself identifies as responsible for the η_c χ² difference (1.52 vs 1.38). Please propagate the observed 1.77–1.86 range as a systematic uncertainty and show that the HQSS conclusion is stable under this variation.
  2. [Section 'quantitative verification', fit-range choice] The two ATLAS-I bins with p_T^{ψψ}>40 GeV are excluded because 'the data systematically undershoot the theoretical evaluations,' and the fit is then quoted with χ²/dof = 0.38. Later, including all bins gives χ²/dof = 0.40, and the excluded points are said to be 'very well described' except for two bins with small gaps. This is a post-hoc selection of the fit range based on the same data that are being fit. A principled criterion is needed, for example an a priori upper p_T^{ψψ} cutoff motivated by the validity of the power-counting or NRQCD factorization, or a systematic error obtained by repeating the fit with several cut choices (e.g., p_T>18, >20, >25, >30 GeV). Without this, the central value and uncertainty of M_{0,1.8}, and hence of the extracted LDME set, are not fully justified.
  3. [Section 'quantitative verification', η_c comparison] The claim of a 'first genuine verification of HQSS' is based on χ²/11 = 1.52 and 1.38 for the two LDME sets. These two values are very close, and the paper states that the small difference is due to <O(^1S0[8])>. This is not presented as a statistical test of HQSS, but as an affirmation of agreement. Please quantify the significance of the test: e.g., give the χ² for a hypothetical fit without HQSS, or the χ² obtained when the alternative LDME sets discussed in the paper are used for the η_c comparison. As written, the evidence for 'verification' is suggestive but not quantitatively calibrated.
  4. [Eq. (2) and Fig. 2] The paper's central quantitative results—the scaling ratios R_{m,n}, the ratio 1.77–1.86, and the fitted M_{0,1.8}—all rely on the multi-gigabyte numerical computation performed with QGRAF/FORM/Cuba, but no numerical tables or public code are provided. Since the SDC calculation is not independently checkable from the manuscript, the authors should provide at least the values of R_{m,n} for the 14 fit bins (and ideally a benchmark table for the CMS, ATLAS-I, ATLAS-II setups) in an appendix or supplementary material. This would also allow readers to reproduce the constancy of the crucial ratio.
minor comments (6)
  1. [Eq. (2)] The notation 'mdm+dn−6c' is unclear; it presumably means m_c^{d_m+d_n-6}. Please clarify.
  2. [Author affiliations] Typo: 'Mathemati cs' in the Beijing University affiliation.
  3. [References] Reference [26] appears twice in the bibliography list, with the second entry being a duplicate of the LHCb η_c paper.
  4. [Figure 3] The caption says 'dσ/p_T^{ψψ}' but the plots likely show dσ/dp_T^{ψψ}; please make the derivative explicit and specify the bin widths and units consistently.
  5. [Text near Eq. (3)] The combinations M_{0,3.9}^{J/ψ} and M_{1,-0.56}^{J/ψ} are taken from Refs. [11,17], but the definitions of r0=3.9 and r1=-0.56 are not restated. Please define them or refer explicitly to the equations in the original papers.
  6. [Fit statistics] The χ²/dof values are quoted as 0.38, 0.40, 1.31. Please give the number of data points, the number of fitted parameters, and the absolute χ² values so the reader can judge the goodness of fit.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the double-J/psi fit, the single-J/psi constraints, and the eta_c comparison are independent inputs used in a genuine prediction chain.

full rationale

The paper's derivation chain is self-contained and does not reduce to its inputs by construction. The double-J/psi SDCs are computed in this paper (with the CS channel taken from the authors' previous parameter-free calculation, Ref. [56]), and the near-constancy of the ratio R_{3S1[1],3P0[8]}/R_{3S1[1],1S0[8]} is a numerical observation from these SDCs, not an assumed output. The fitted quantity M_{0,1.8} is defined using this observed ratio and then constrained by CMS and ATLAS data; the individual LDMEs are obtained by combining this with two independent single-J/psi constraints from Refs. [11,17], which are external to the present paper. The eta_c comparison is a genuine prediction: LHCb eta_c data are not used in any step of the fit, and the HQSS test therefore has independent empirical content. The authors' reliance on their own earlier SDC calculations (Refs. [42,43,56]) is normal building-block citation of parameter-free, externally falsifiable results, not circular. The reader's concern about the unpropagated spread of the ratio r0 = 1.77–1.86 is a robustness/correctness issue, not a circularity, because the ratio is an input derived from the calculation and its uncertainty does not make the fitted combination logically equivalent to the data. No equation is defined in terms of the result it purports to derive, and no fitted parameter is relabeled as a prediction.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central claim rests on standard NRQCD factorization, external LDME constraints from single-J/psi fits, and a few modeling choices (fixed r=1.80, psi(2S) feed-down factor, DPS handling, and the post-hoc exclusion of two ATLAS-I bins). No new beyond-SM entities are introduced.

free parameters (6)
  • M_{0,1.8}^{J/psi} = <O(^1S_0^{[8]})> + 1.8/m_c^2 <O(^3P_0^{[8]})> = (3.49 +/- 0.59) x 10^-2 GeV^3
    Fitted to 14 CMS and ATLAS bins with p_T^psi psi > 18/20 GeV; the only quantity directly constrained by the double-J/psi data.
  • M_{0,3.9}^{J/psi} = (7.4 +/- 1.9) x 10^-2 GeV^3
    External constraint from single prompt J/psi hadroproduction fits [11,17]; used as input to separate the LDMEs.
  • M_{1,-0.56}^{J/psi} = (0.05 +/- 0.02) x 10^-2 GeV^3
    External constraint from single prompt J/psi hadroproduction fits [11,17]; used as input.
  • r = coefficient in M_{0,1.8} = 1.80 (average of computed 1.77-1.86)
    Derived from the computed SDC ratios; fixed without propagating its spread, a possible source of bias.
  • Charm quark mass m_c = 1.5 GeV
    Standard input; enters kinematics and the LDME combinations; not varied.
  • psi(2S) feed-down factor = 7/6 per J/psi
    Approximation from known branching fractions, applied to each J/psi to account for psi(2S) feed-down.
assumptions (6)
  • domain assumption NRQCD factorization applies to double J/psi hadroproduction with universal LDMEs (Eq. (1)).
    The calculation and fit are entirely within NRQCD factorization; known factorization-breaking for double P-wave pairings [61] is mentioned but not resolved for the included channels.
  • domain assumption Heavy-quark spin symmetry (HQSS) relations connect J/psi and eta_c LDMEs.
    Used to convert the fitted J/psi LDME set into prompt eta_c yield predictions for comparison with LHCb data; the agreement is presented as a test of this symmetry.
  • domain assumption CTEQ6L1 LO PDFs and alpha_s with n_f=4, Lambda_QCD^(4)=215 MeV.
    Standard fixed inputs; only the scale xi is varied for uncertainty.
  • domain assumption DPS contamination is negligible (CMS) or already subtracted (ATLAS) in the selected large-p_T^psi psi bins.
    Relies on Ref [51] for CMS and on the ATLAS DPS extraction; if wrong, the fitted LDMEs are biased.
  • ad hoc to paper The two ATLAS-I bins with p_T^psi psi > 40 GeV are excluded from the fit because data undershoot theory.
    Post-hoc selection; changes chi^2/dof from 1.31 to 0.38 and affects M_{0,1.8}; no a priori physical reason for exclusion.
  • domain assumption Higher-order v^2 and alpha_s corrections beyond those included do not alter the fitted combination.
    The fit uses LO-in-v SDCs for the CO channels and NLO for the CS channel; missing v^2 corrections could shift the ratio r and the combination.

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Cite this review

Pith. "Pith review of Probing Heavy-Quark Spin Symmetry in Double $J/\psi$ Hadroproduction." pith.science (2026). https://pith.science/paper/5DUEZV5M

@misc{pith2026260803510,
  author       = {Pith},
  title        = {Pith review of: Probing Heavy-Quark Spin Symmetry in Double $J/\psi$ Hadroproduction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5DUEZV5M}},
  note         = {Machine review of arXiv:2608.03510}
}
abstract

We perform the first complete $\mathcal{O}(\alpha_s^5)$ analysis of the prompt hadroproduction of $J/\psi$ pairs with large transverse momenta $p_T^{\psi\psi}$ in the nonrelativistic-QCD factorization framework, including all possible Fock state combinations $c\bar{c}(m)+c\bar{c}(n)$, with $m,n={}^3S_1^{[1,8]},{}^1S_0^{[8]},{}^3P_J^{[1,8]}$. We observe that CMS and ATLAS data constrain a specific linear combination of the long-distance matrix elements (LDMEs) $\langle\mathcal{O}^{J/\psi}({}^1S_0^{[8]})\rangle$ and $\langle\mathcal{O}^{J/\psi}({}^3P_0^{[8]})\rangle$. In conjunction with two other combinations fixed by single prompt $J/\psi$ hadroproduction, we gain a new LDME set, which turns out to be largely compatible with the world data of prompt $J/\psi$ yield and polarization and to probe heavy-quark spin symmetry, by which agreement is established with LHCb data of prompt $\eta_c$ yield. Our $\mathcal{O}(\alpha_s^5)$ predictions also nicely agree with CMS and ATLAS data in the lowest bins of $J/\psi$ pair invariant mass $m^{\psi\psi}$, beyond leading-order kinematics.

Figures

Figures reproduced from arXiv: 2608.03510 by the authors.

Figure 1
Figure 1. FIG. 1: Typical Feynman diagrams for [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Ratios [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: CMS [39] (left), ATLAS-I (center), and ATLAS-II [40] [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

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