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REVIEW 3 major objections 5 minor 75 references

Statistical analysis of the azimuthal asymmetry in the $J/\psi$ leptoproduction in unpolarized $ep$ collisions

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Two azimuthal modulations in J/ψ leptoproduction can separate the three leading production models at 1000 pb⁻¹.

desk verdict The paper's new observable is real and the LO NRQCD calculation is coherent, but the direct-vs-prompt/feed-down mismatch makes its central discrimination claim conditional rather than demonstrated. read the letter →

arxiv 1908.02521 v1 pith:UQ7HYYHJ submitted 2019-08-07 hep-ph hep-ex

Hong-Fei Zhang , Wen-Long Sang , Yu-Peng Yan This is my paper · ORCID
classification hep-phhep-ex
keywords azimuthalasymmetryJ/psiproductionleptoproductioncolor-singletmodelnonrelativisticQCDcolor-octetlong-distancematrixelements1S0[8]dominanceElectron-IonCollider
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 aims to show that the azimuthal asymmetry of $J/\psi$ production in unpolarized electron-proton collisions can serve as a discriminating test of competing quarkonium production mechanisms. It computes the two independent modulations, $\cos(\psi)$ and $\cos(2\psi)$, where $\psi$ is the azimuthal angle of the lepton scattering plane relative to the hadron-production plane, over the full kinematic range. In the chosen region $D$ ($x>0.001$, $0.751$ GeV), the color-singlet model predicts $A_{\cos\psi}=0.561$, the equal-color-octet NRQCD fit predicts $-0.246$, and the $^1S_0^{[8]}$-dominance picture gives $A_{\cos2\psi}=-0.203$ against $-0.0155$ for the other set. A 12-bin fit to the $\psi$ distribution at integrated luminosity $1000\ \mathrm{pb}^{-1}$ yields statistical uncertainties of $0.013$ on $A_{\cos\psi}$ and $0.004$ on $A_{\cos2\psi}$, small enough to tell the three models apart. If the prediction holds, a measurement at a future $ep$ collider would settle which production mechanism dominates.

What carries the argument

The machinery is the decomposition of the leptonic tensor into four azimuthally dependent structures, $l^{\mu\nu} = A_g(-g^{\mu\nu} - q^{\mu}q^{\nu}/Q^2) + A_L \epsilon_L^{\mu}\epsilon_L^{\nu} + A_{LT}(\epsilon_L^{\mu}\epsilon_T^{\nu} + \epsilon_T^{\mu}\epsilon_L^{\nu}) + A_T \epsilon_T^{\mu}\epsilon_T^{\nu}$, with the coefficients $A_g$, $A_L$, $A_{LT}$, and $A_T$ carrying the $\cos(2\psi)$, $\cos(\psi)$, and $\cos(2\psi)$ terms. Since the hadronic tensor for each intermediate $c\bar c$ state is independent of $\psi$, all azimuthal dependence enters through these coefficients, yielding the compact form $d\sigma = \sigma_0[1 + A_{\cos\psi}\cos\psi + A_{\cos2\psi}\cos2\psi]$ after the Fourier projections in Eq. (2.27). The paper computes the parton-level amplitudes for the four intermediate states ($^3S_1^{[1]}$, $^1S_0^{[8]}$, $^3S_1^{[8]}$, $^3P_J^{[8]}$), convolutes them with parton distribution functions, and then performs a 12-bin linear regression over $\psi$ to estimate the statistical uncertainty of the modulation coefficients. The crucial numerical fact is that $A_{\cos\psi}$ cleanly separates the color-singlet channel from the color-octet channels while $A_{\cos2\psi}$ isolates the $^1S_0^{[8]}$ channel, so the two modulations carry orthogonal discriminative information.

What would settle it

At an $ep$ collider with $\mathcal{L}=1000\ \mathrm{pb}^{-1}$, bin the $J/\psi$ yield in $\psi$ within region $D$ and fit $N_i = A v_1^{(i)} + B v_{\cos\psi}^{(i)} + C v_{\cos2\psi}^{(i)}$; if the best-fit $A_{\cos\psi}$ lies between $0.561$ and $-0.246$ with uncertainty comparable to the interval, or if $A_{\cos2\psi}$ comes out near $-0.016$ rather than $-0.203$ when the $^1S_0^{[8]}$-dominant set is assumed, the claimed discrimination is contradicted. A $\psi(2S)$-vetoed subsample would directly test the feed-down dilution.

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Extended reading notes

Core claim

The central claim is that the azimuthal modulations in $J/\psi$ leptoproduction are strongly channel-dependent and survive integration over a practical kinematic region. Because the cross section can be written as $d\sigma = \sigma_0[1 + A_{\cos\psi}\cos\psi + A_{\cos2\psi}\cos2\psi]\,d\psi$, the two modulation coefficients can be extracted by a linear regression on the $\psi$ distribution. In region $D$ the paper finds $A_{\cos\psi}^{CS} = 0.561$ for the color-singlet channel, and $-0.225$, $0.531$, and $-0.346$ for the $^1S_0^{[8]}$, $^3S_1^{[8]}$, and $^3P_J^{[8]}$ channels, respectively, while $A_{\cos2\psi}$ is $-0.281$ for $^1S_0^{[8]}$ and near zero or small for the others. Weighting these channels with three published long-distance matrix-element sets gives the model-level predictions $A_{\cos\psi}=0.561$ (color-singlet), $-0.246$ (equal-color-octet NRQCD), and $A_{\cos2\psi}=-0.203$ ($^1S_0^{[8]}$-dominant set) versus $-0.0155$ (equal-color-octet). The statistical analysis at $1000\ \mathrm{pb}^{-1}$ then shows the model predictions are separated by many times the expected uncertainty.

Load-bearing premise

The predicted cross section describes direct $J/\psi$ production, but the experimental event sample will contain feed-down from $\psi(2S)$, $\chi_{cJ}$, and $b$-hadron decays, which the paper does not model; if those sources have different azimuthal modulations, the measured asymmetries in region $D$ would be diluted relative to the model predictions.

Editorial extensions

If this is right

  • If the color-singlet model is correct, region $D$ at $\mathcal{L}=1000\ \mathrm{pb}^{-1}$ will show $A_{\cos\psi}=0.561\pm0.013$; if the equal-color-octet NRQCD fit is correct, the same measurement gives $-0.246$, so a single run separates the two.
  • If the $^1S_0^{[8]}$-dominance picture is correct, $A_{\cos2\psi}=-0.203\pm0.004$, versus $-0.0155$ for the equal-octet set, giving an independent test of the dominance hypothesis.
  • Because the modulations are ratios of integrated cross sections, most systematic uncertainties cancel, so the discrimination is statistics-limited and improves roughly as $\sqrt{\mathcal{L}}$.
  • The measurement is proposed for future $ep$ colliders, where the kinematics of region $D$ are experimentally accessible.

Reading between the lines

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

  • Extension: feed-down from $\psi(2S)$, $\chi_{cJ}$, and $b$-hadrons is not modeled; computing the azimuthal modulations of those sources and subtracting them would show whether the discrimination survives in an inclusive $J/\psi$ sample.
  • Extension: the same Fourier-projection test could be applied to $\Upsilon$ leptoproduction, where the long-distance matrix-element hierarchy differs, to see whether the $\cos(2\psi)$ separation between $^1S_0^{[8]}$ dominance and equal-octet NRQCD is a general feature.
  • Extension: the calculation is done at leading order; repeating the region-$D$ analysis at next-to-leading order would show whether the $0.013$ and $0.004$ margins persist after radiative corrections.
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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

3 major / 5 minor

Summary. The paper calculates the cos(ψ) and cos(2ψ) azimuthal asymmetries in J/ψ leptoproduction in unpolarized ep collisions, using a decomposition of the leptonic tensor and NRQCD factorization for the hadronic side. It presents the asymmetries as functions of x, y, z, and ξ for the four leading c-cbar intermediate states, then restricts the study to a kinematic region D (x>0.001, 0.75<z<0.9, 0.04<y<0.6, pt>1 GeV) where the cross sections are sizeable. Combining the per-channel asymmetries with three sets of NRQCD LDMEs (color-singlet, an NRQCD global fit, and a 1S0[8]-dominant set), the paper predicts that at an integrated luminosity of 1000 pb^-1 the two asymmetry modulations separate the three models: Acosψ≈0.561 (CS) versus −0.246 (NRQCD fit), and Acos2ψ≈−0.203 (Chao set) versus −0.0155 (NRQCD fit). A 12-bin statistical analysis yields uncertainties of order 0.01 and 0.004, leading the authors to conclude that a future ep collider such as the EIC could discriminate the production mechanisms.

Significance. If the predictions hold, the paper offers a new, falsifiable observable for discriminating charmonium production mechanisms in ep collisions; the explicit leptonic-tensor decomposition and the careful treatment of the bin-by-bin statistical analysis are strengths. The separation between models is large compared with the estimated statistical errors, making the proposed measurement potentially decisive. However, the paper does not address feed-down contributions, which are known to be important in J/ψ samples, and it does not display the hard-scattering amplitudes underlying the numerical predictions. The quantitative reach of the proposal therefore depends on additional modeling and on the theoretical stability of the LO asymmetries.

major comments (3)
  1. [Section 3, Eqs. (3.2)-(3.6)] The central predictions are computed from Eq. (2.22), which describes direct J/ψ production via NRQCD factorization over c-cbar(n) states with LDMEs. However, an experimental J/ψ sample in ep collisions will contain feed-down from ψ(2S) and χ_cJ decays and from b-hadron decays. The paper never mentions or models these sources, so the predicted Acosψ and Acos2ψ in region D cannot be compared with an event sample unless a direct-J/ψ selection is imposed, which is nontrivial at a collider. Moreover, the LDME sets in Eqs. (3.11) and (3.13) are taken from global fits to prompt/inclusive hadroproduction data; if feed-down was already absorbed in those fits, using them for the direct-production cross section in Eq. (2.22) is not automatically consistent. The authors should either quantify the feed-down contribution in region D and its azimuthal modulations or explicitly restrict the prediction to a direct-J/ψ sample.
  2. [Section 2.1, Eqs. (2.22)-(2.25)] The numerical results in Section 3 depend on the hadronic tensors W_i+γ*→c cbar(n)+i, but these amplitudes are not shown. After Eq. (2.25), the paper states that they 'can be easily evaluated via Feynman diagrams,' which is not sufficient for the reader to reproduce the central predictions, e.g., the values in Eqs. (3.3)-(3.4). The authors should provide the explicit expressions (or a supplement/code) and benchmark the implementation against known cross sections from Ref. [73].
  3. [Section 3, Eq. (3.10)] The statistical analysis estimates only statistical uncertainties. The cross sections are computed at LO QCD with a fixed scale choice μf = μr = sqrt(S(xy+ξ)), and no estimate of scale variation or NLO corrections is given. The claim that the three models can be told apart relies on differences in Acosψ of about 0.8 and in Acos2ψ of about 0.2, which are much larger than the quoted statistical errors (0.013 and 0.004), but a sizable NLO correction to the CS or CO channels could still shift the predicted asymmetries by more than the statistical precision. A theoretical uncertainty band should accompany the predictions.
minor comments (5)
  1. [Eqs. (3.11) and (3.13)] The color-octet LDMEs are written with a [1] superscript (e.g., ⟨O(1S[1]0)⟩, ⟨O(3P[1]J)⟩) instead of [8]; the same typo appears in Eq. (3.3) for the 1S0[8] channel. This is misleading and should be corrected.
  2. [Text after Eq. (3.7)] 'L = 103pb−1' should read 'L = 10^3 pb^{-1} = 1000 pb^{-1}', in agreement with the abstract and Section 4.
  3. [Section 3, Eqs. (3.10)-(3.15)] The statistical uncertainty is quoted for the CS prediction of Acosψ and for the Chao prediction of Acos2ψ, but not for the other model scenarios; please provide the full set of uncertainties for all three models so that the separation claim is quantified uniformly.
  4. [Figure captions (Figs. 2-7)] The captions list kinematics but never define the azimuthal angle ψ; adding a definition in Fig. 1 or in the text would improve readability.
  5. [Section 3, PDF choice] The analysis uses the GRV 1995 PDFs; since the publication date is 2019, a modern PDF set or a short statement on the PDF dependence of the asymmetries would be preferable.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the azimuthal asymmetry predictions derive from independent NRQCD hard-scattering coefficients and externally fitted LDMEs.

full rationale

The paper's azimuthal asymmetry predictions are not circular: the asymmetries are computed from the cross section in Eq. (2.22)/(2.25), where the ψ dependence enters through the leptonic-tensor coefficients Ci and the kinematic dependence through the hadronic-tensor contractions Wi[n]. The modulations A_cosψ and A_cos2ψ are defined as ratio observables in Eqs. (2.27) and (2.30), and their numerical values in the kinematic region D are obtained by integrating these ratios, not by fitting them to data. The LDMEs used for the NRQCD predictions (Eqs. (3.11) and (3.13)) are taken from global fits to hadroproduction yields and polarization data in Refs. [55,60,47]; the azimuthal asymmetries predicted here are not among the fitted observables. The paper also cites the authors' own prior work for the leptonic-tensor decomposition ([72]) and the hadronic-tensor simplification ([73]), but it re-derives these formulae in Section 2 and the numerical predictions require the new short-distance coefficients Wi[n] evaluated from Feynman diagrams. The self-citations are therefore background formalism, not load-bearing reductions of the predicted asymmetries to their own inputs. The unmodeled feed-down contribution from ψ(2S), χ_cJ, and B decays is a potential physics limitation of the comparison to an unfiltered J/ψ sample, but it is a correctness/validity concern, not a circularity. No equation in the paper is identical by construction to an input, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The paper introduces no new free parameters or invented entities. Its conclusions rest on external inputs (LDMEs fitted to other data), standard factorization assumptions, and the unshown hard-scattering calculation, plus the implicit assumption that the measured J/psi sample is direct.

free parameters (3)
  • NRQCD LDME sets (CS and CO) = Set A [75]: <O(3S1[1])>=1.16 GeV^3; Set B [55,60]: 0.645, 0.00785, 0.010, 0.038 (GeV^3 or GeV^5); Set C [47]: 1.16…
    The predicted cross sections in Eq. (3.3) and the resulting asymmetries are linearly proportional to these LDMEs, which are fitted to other production data and are not derived in this paper. The claimed model discrimination depends on these values being representative of the model classes.
  • Scale choice mu_f = mu_r = sqrt(S(xy+xi)) = Single scale, no variation
    The short-distance coefficients and PDFs depend on this scale; the paper does not estimate the resulting theoretical uncertainty on the asymmetries, despite claiming statistical errors as small as 0.004.
  • Charm quark mass mc = M/2 = 1.5 GeV = 1.5 GeV
    Fixed by hand with M=3.0 GeV; affects the hard-scattering coefficients and phase-space. No variation or relativistic corrections are considered.
assumptions (6)
  • domain assumption NRQCD factorization of quarkonium production into short-distance coefficients and process-independent LDMEs
    The paper assumes that J/psi production factorizes with contributions from the four intermediate c-cbar states (3S1[1], 1S0[8], 3S1[8], 3PJ[8]) as in Bodwin et al. [16], with no discussion of factorization-breaking corrections.
  • domain assumption Leptonic tensor decomposition and coefficients in Eq. (2.10)
    The decomposition of the normalized leptonic tensor into four tensors with the given coefficients is taken from Ref [72] without derivation. This decomposition generates the cos(psi) and cos(2psi) angular dependences that are central to the paper.
  • domain assumption Partonic hard-scattering amplitudes are known from Feynman diagram evaluation
    The amplitudes Wi+gamma*->c-cbar(n)+i in Eq. (2.24) are asserted to be easily evaluated but are not shown. All numerical results in Section 3 depend on their correctness.
  • domain assumption Collinear factorization with on-shell partons described by GRV PDFs
    The proton is described by collinear PDFs with no intrinsic transverse momentum, and the hadronic tensor is convoluted with PDFs as in Eq. (2.19). This is standard but an approximation that could affect the predictions.
  • domain assumption The observed J/psi sample is direct production with no feed-down
    The cross-section calculation models direct J/psi production. Feed-down from psi(2S), chi_cJ, and b-hadron decays is not included or discussed, despite contributing to experimental J/psi samples.
  • domain assumption Proton mass is neglected in the definition of rho
    In Eq. (2.11) the proton mass is set to zero to express rho in terms of x, y, z, and xi. This is a standard approximation but is not quantified.

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Pith. "Pith review of Statistical analysis of the azimuthal asymmetry in the $J/\psi$ leptoproduction in unpolarized $ep$ collisions." pith.science (2026). https://pith.science/paper/UQ7HYYHJ

@misc{pith2026190802521,
  author       = {Pith},
  title        = {Pith review of: Statistical analysis of the azimuthal asymmetry in the $J/\psi$ leptoproduction in unpolarized $ep$ collisions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UQ7HYYHJ}},
  note         = {Machine review of arXiv:1908.02521}
}
abstract

In this paper, we study the azimuthal asymmetry in the $J/\psi$ leptoproduction in unpolarized $ep$ collisions. There are two independent azimuthal asymmetry modulations, namely $\mathrm{cos}(\psi)$ and $\mathrm{cos}(2\psi)$, where $\psi$ is the azimuthal angle of the lepton scattering plane with respect to the hadron-interacting plane. We calculate the two modulations as functions of four kinematic variables, and find that they provide a very good laboratory to distinguish several models describing the heavy quarkonium production, including the color-singlet (CS) model, the nonrelativistic QCD (NRQCD) associated with the $^1S_0^{[8]}$ dominance picture, and the NRQCD in which the values of all the three color-octet (CO) long-distance matrix elements are of the same order. In order to make definite conclusions, we restrict our calculation in a specific kinematic region, where the CS and CO mechanisms can be distinguished by scrutinizing the values of the $\mathrm{cos}(\psi)$ modulation, while the $^1S_0^{[8]}$ dominance picture can be tested by measuring the values of the $\mathrm{cos}(2\psi)$ modulation. Calculating their values and carrying out a meticulous statistical analysis, we find that at an integrated luminosity $\mathcal{L}=1000\mathrm{pb}^{-1}$, the statistical uncertainties of the two quantities are small enough to tell the three models apart. When this experiment is implemented at the future $ep$ colliders such as the EIC, crucial information for the $J/\psi$ production mechanism might be discovered.

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Works this paper leans on

75 extracted references · 29 canonical work pages

  1. [8]

    J. C. Collins, S. F. Heppelmann, and G. A. Ladinsky, Measuring transversity densities in singly polarized hadron hadron and lepton - hadron collision s, Nucl. Phys. B420 (1994) 565–582, [ hep-ph/9305309]

    arXiv 1994

  2. [73]

    Sun and H.-F

    Z. Sun and H.-F. Zhang, QCD leading order study of the J/ψ leptoproduction at HERA within the nonrelativistic QCD framework , Eur. Phys. J. C77 (2017), no. 11 744, [arXiv:1702.02097]

    arXiv 2017

  3. [1]

    Dick et al., Spin Effects in the Inclusive Reactions pi+- Polarized p –> pi+- Anything at 8-GeV/c, Phys

    L. Dick et al., Spin Effects in the Inclusive Reactions pi+- Polarized p –> pi+- Anything at 8-GeV/c, Phys. Lett. 57B (1975) 93–96

    work page 1975

  4. [2]

    R. D. Klem, J. E. Bowers, H. W. Courant, H. Kagan, M. L. Mars hak, E. A. Peterson, K. Ruddick, W. H. Dragoset, and J. B. Roberts, Measurement of Asymmetries of Inclusive Pion Production in Proton Proton Interactions at 6-GeV/c and 11.8-GeV/c, Phys. Rev. Lett. 36 (1976) 929–931

    work page 1976

  5. [3]

    W. H. Dragoset, J. B. Roberts, J. E. Bowers, H. W. Courant, H. Kagan, M. L. Marshak, E. A. Peterson, K. Ruddick, and R. D. Klem, Asymmetries in Inclusive Proton-Nucleon Scattering at 11.75-GeV/c , Phys. Rev. D18 (1978) 3939–3954

    work page 1978

  6. [4]

    Bunce et al., Lambda0 Hyperon Polarization in Inclusive Production by 300- GeV Protons on Beryllium

    G. Bunce et al., Lambda0 Hyperon Polarization in Inclusive Production by 300- GeV Protons on Beryllium. , Phys. Rev. Lett. 36 (1976) 1113–1116

    work page 1976

  7. [5]

    D. W. Sivers, Single Spin Production Asymmetries from the Hard Scattering o f Point-Like Constituents, Phys. Rev. D41 (1990) 83

    work page 1990

  8. [6]

    D. W. Sivers, Hard scattering scaling laws for single spin production asym metries, Phys. Rev. D43 (1991) 261–263

    work page 1991

Show all 75 references
  1. [7]

    J. C. Collins, Fragmentation of transversely polarized quarks probed in tran sverse momentum distributions, Nucl. Phys. B396 (1993) 161–182, [ hep-ph/9208213]

    1993 arXiv

  2. [9]

    Airapetian et al., Single-spin asymmetries in semi-inclusive deep-inelastic scattering on a transversely polarized hydrog en target , Phys

    HERMES Collaboration, A. Airapetian et al., Single-spin asymmetries in semi-inclusive deep-inelastic scattering on a transversely polarized hydrog en target , Phys. Rev. Lett. 94 (2005) 012002, [ hep-ex/0408013]

    2005 arXiv

  3. [10]

    COMP ASSCollaboration, V. Yu. Alexakhin et al., First measurement of the transverse spin asymmetries of the deuteron in semi-inclusive deep inel astic scattering , Phys. Rev. Lett. 94 (2005) 202002, [ hep-ex/0503002]

    2005 arXiv

  4. [11]

    COMP ASSCollaboration, E. S. Ageev et al., A New measurement of the Collins and Sivers asymmetries on a transversely polarised deuteron target , Nucl. Phys. B765 (2007) 31–70, [hep-ex/0610068]. – 15 –

    2007 arXiv

  5. [12]

    Airapetian et al., Azimuthal distributions of charged hadrons, pions, and kaons produced in deep-inelastic scattering off un polarized protons and deuterons , Phys

    HERMES Collaboration, A. Airapetian et al., Azimuthal distributions of charged hadrons, pions, and kaons produced in deep-inelastic scattering off un polarized protons and deuterons , Phys. Rev. D87 (2013), no. 1 012010, [ arXiv:1204.4161]

    2013 arXiv

  6. [13]

    Adolph et al., Measurement of azimuthal hadron asymmetries in semi-inclusive deep inelastic scattering off unpolarised n ucleons, Nucl

    COMP ASSCollaboration, C. Adolph et al., Measurement of azimuthal hadron asymmetries in semi-inclusive deep inelastic scattering off unpolarised n ucleons, Nucl. Phys. B886 (2014) 1046–1077, [ arXiv:1401.6284]

    2014 arXiv

  7. [14]

    R. N. Cahn, Azimuthal Dependence in Leptoproduction: A Simple Parton Mo del Calculation , Phys. Lett. 78B (1978) 269–273

    1978

  8. [15]

    R. N. Cahn, Critique of Parton Model Calculations of Azimuthal Dependenc e in Leptoproduction, Phys. Rev. D40 (1989) 3107–3110

    1989

  9. [16]

    G. T. Bodwin, E. Braaten, and G. P. Lepage, Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium , Phys. Rev. D51 (1995) 1125–1171, [hep-ph/9407339]. [Erratum: Phys. Rev.D55,5853(1997)]

    1995 arXiv

  10. [17]

    Zhang, Y.-j

    Y.-J. Zhang, Y.-j. Gao, and K.-T. Chao, Next-to-leading order QCD correction to e+e− →J/ ψ +ηc at √s = 10.6GeV, Phys. Rev. Lett. 96 (2006) 092001, [ hep-ph/0506076]

    2006 arXiv

  11. [18]

    Zhang and K.-T

    Y.-J. Zhang and K.-T. Chao, Double charm production e+e− →J/ψ +c¯c at B factories with next-to-leading order QCD correction , Phys. Rev. Lett. 98 (2007) 092003, [ hep-ph/0611086]

    2007 arXiv

  12. [19]

    Gong and J.-X

    B. Gong and J.-X. Wang, QCD corrections to J/ψ plus ηc production in e+e− annihilation at √s=10.6GeV, Phys. Rev. D77 (2008) 054028, [ arXiv:0712.4220]

    2008 arXiv

  13. [20]

    Gong and J.-X

    B. Gong and J.-X. Wang, QCD corrections to double J/ψ production in e+e− annihilation at√s=10.6GeV, Phys. Rev. Lett. 100 (2008) 181803, [ arXiv:0801.0648]

    2008 arXiv

  14. [21]

    Ma, Y.-J

    Y.-Q. Ma, Y.-J. Zhang, and K.-T. Chao, QCD correction to e+e− →J/ψgg at B Factories , Phys. Rev. Lett. 102 (2009) 162002, [ arXiv:0812.5106]

    2009 arXiv

  15. [22]

    Gong and J.-X

    B. Gong and J.-X. Wang, Next-to-Leading-Order QCD Corrections to e+e− → J/ψgg at the B Factories, Phys. Rev. Lett. 102 (2009) 162003, [ arXiv:0901.0117]

    2009 arXiv

  16. [23]

    Gong and J.-X

    B. Gong and J.-X. Wang, Next-to-leading-order QCD corrections to e+e− → J/ψ(cc) at the B factories , Phys. Rev. D80 (2009) 054015, [ arXiv:0904.1103]

    2009 arXiv

  17. [24]

    Zhang, Y.-Q

    Y.-J. Zhang, Y.-Q. Ma, K. Wang, and K.-T. Chao, QCD radiative correction to color-octet J/ψ inclusive production at B Factories , Phys. Rev. D81 (2010) 034015, [ arXiv:0911.2166]

    2010 arXiv

  18. [25]

    Wang, Y.-Q

    K. Wang, Y.-Q. Ma, and K.-T. Chao, QCD corrections to e+e− →J/ψ(ψ(2S)) +χcJ (J=0,1,2) at B Factories , Phys. Rev. D84 (2011) 034022, [ arXiv:1107.2646]

    2011 arXiv

  19. [26]

    Y. Feng, Z. Sun, and H.-F. Zhang, Is the color-octet mechanism consistent with the double J/ψ production measurement at B-factories? , Eur. Phys. J. C77 (2017), no. 4 221, [arXiv:1701.00969]

    2017 arXiv

  20. [27]

    Jiang and Z

    Y. Jiang and Z. Sun, Further studies on the exclusive productions of J/ψ +χcJ ( J = 0, 1, 2 ) via e+e− annihilation at the B factories, Eur. Phys. J. C78 (2018), no. 11 892, [arXiv:1809.09071]

    2018 arXiv

  21. [28]

    Q.-R. Gong, Z. Sun, H.-F. Zhang, and X.-M. Mo, ηc production associated with light hadrons at the B-factories and the future Super B-factories , Eur. Phys. J. C76 (2016), no. 9 518, [arXiv:1606.08317]

    2016 arXiv

  22. [29]

    Klasen, B

    M. Klasen, B. A. Kniehl, L. N. Mihaila, and M. Steinhause r, J/ψ plus jet associated – 16 – production in two-photon collisions at next-to-leading or der, Nucl. Phys. B713 (2005) 487–521, [ hep-ph/0407014]

    2005 arXiv

  23. [30]

    Kramer, QCD corrections to inelastic J/ψ photoproduction, Nucl

    M. Kramer, QCD corrections to inelastic J/ψ photoproduction, Nucl. Phys. B459 (1996) 3–50, [ hep-ph/9508409]

    1996 arXiv

  24. [31]

    Maltoni, M

    F. Maltoni, M. L. Mangano, and A. Petrelli, Quarkonium photoproduction at next-to-leading order, Nucl. Phys. B519 (1998) 361–393, [ hep-ph/9708349]

    1998 arXiv

  25. [32]

    Artoisenet, J

    P. Artoisenet, J. M. Campbell, F. Maltoni, and F. Tramon tano,J/ψ production at HERA , Phys. Rev. Lett. 102 (2009) 142001, [ arXiv:0901.4352]

    2009 arXiv

  26. [33]

    Chang, R

    C.-H. Chang, R. Li, and J.-X. Wang, Jpsi polarization in photo-production up-to the next-to-leading order of QCD , Phys. Rev. D80 (2009) 034020, [ arXiv:0901.4749]

    2009 arXiv

  27. [34]

    Li and K.-T

    R. Li and K.-T. Chao, Photoproduction of J/ψ in association with a c anti-c pair , Phys. Rev. D79 (2009) 114020, [ arXiv:0904.1643]

    2009 arXiv

  28. [35]

    Butenschoen and B

    M. Butenschoen and B. A. Kniehl, Complete next-to-leading-order corrections to J/ψ photoproduction in nonrelativistic quantum chromodynami cs, Phys. Rev. Lett. 104 (2010) 072001, [ arXiv:0909.2798]

    2010 arXiv

  29. [36]

    Butenschoen and B

    M. Butenschoen and B. A. Kniehl, Probing nonrelativistic QCD factorization in polarized J/ψ photoproduction at next-to-leading order , Phys. Rev. Lett. 107 (2011) 232001, [arXiv:1109.1476]

    2011 arXiv

  30. [37]

    G. T. Bodwin, H. S. Chung, U.-R. Kim, and J. Lee, Fragmentation contributions to J/ÏĹ photoproduction at HERA , Phys. Rev. D92 (2015), no. 7 074042, [ arXiv:1504.06019]

    2015 arXiv

  31. [38]

    J. M. Campbell, F. Maltoni, and F. Tramontano, QCD corrections to J/psi and Upsilon production at hadron colliders , Phys. Rev. Lett. 98 (2007) 252002, [ hep-ph/0703113]

    2007 arXiv

  32. [39]

    Gong and J.-X

    B. Gong and J.-X. Wang, Next-to-leading-order QCD corrections to J/ψ polarization at Tevatron and Large-Hadron-Collider energies , Phys. Rev. Lett. 100 (2008) 232001, [arXiv:0802.3727]

    2008 arXiv

  33. [40]

    Gong and J.-X

    B. Gong and J.-X. Wang, QCD corrections to polarization of J/ψ and Υ at Tevatron and LHC, Phys. Rev. D78 (2008) 074011, [ arXiv:0805.2469]

    2008 arXiv

  34. [41]

    B. Gong, X. Q. Li, and J.-X. Wang, QCD corrections to J/ψ production via color octet states at Tevatron and LHC , Phys. Lett. B673 (2009) 197–200, [ arXiv:0805.4751]. [Erratum: Phys. Lett.B693,612(2010)]

    2009 arXiv

  35. [42]

    Y.-Q. Ma, K. Wang, and K.-T. Chao, J/ψ(ψ′) production at the Tevatron and LHC at O(α4 sv4) in nonrelativistic QCD , Phys. Rev. Lett. 106 (2011) 042002, [ arXiv:1009.3655]

    2011 arXiv

  36. [43]

    Butenschoen and B

    M. Butenschoen and B. A. Kniehl, ReconcilingJ/ψ production at HERA, RHIC, Tevatron, and LHC with NRQCD factorization at next-to-leading order , Phys. Rev. Lett. 106 (2011) 022003, [ arXiv:1009.5662]

    2011 arXiv

  37. [44]

    Y.-Q. Ma, K. Wang, and K.-T. Chao, A complete NLO calculation of the J/ψ and ψ′ production at hadron colliders , Phys. Rev. D84 (2011) 114001, [ arXiv:1012.1030]

    2011 arXiv

  38. [45]

    Butenschoen and B

    M. Butenschoen and B. A. Kniehl, World data of J/ψ production consolidate NRQCD factorization at NLO , Phys. Rev. D84 (2011) 051501, [ arXiv:1105.0820]

    2011 arXiv

  39. [46]

    Butenschoen and B

    M. Butenschoen and B. A. Kniehl, J/ψ polarization at Tevatron and LHC: Nonrelativistic-QCD factorization at the crossroads , Phys. Rev. Lett. 108 (2012) 172002, [arXiv:1201.1872]. – 17 –

    2012 arXiv

  40. [47]

    Chao, Y.-Q

    K.-T. Chao, Y.-Q. Ma, H.-S. Shao, K. Wang, and Y.-J. Zhan g, J/ψ Polarization at Hadron Colliders in Nonrelativistic QCD , Phys. Rev. Lett. 108 (2012) 242004, [ arXiv:1201.2675]

    2012 arXiv

  41. [48]

    Gong, L.-P

    B. Gong, L.-P. Wan, J.-X. Wang, and H.-F. Zhang, Polarization for Prompt J/ψ and ψ(2s) Production at the Tevatron and LHC , Phys. Rev. Lett. 110 (2013), no. 4 042002, [arXiv:1205.6682]

    2013 arXiv

  42. [49]

    Gong, J.-P

    B. Gong, J.-P. Lansberg, C. Lorce, and J. Wang, Next-to-leading-order QCD corrections to the yields and polarisations of J/ψ and Upsilon directly produced in association with a Z boson at the LHC , JHEP 03 (2013) 115, [ arXiv:1210.2430]

    2013 arXiv

  43. [50]

    Lansberg and H.-S

    J.-P. Lansberg and H.-S. Shao, Production of J/ψ +ηc versus J/ψ +J/ψ at the LHC: Importance of Real α5 s Corrections, Phys. Rev. Lett. 111 (2013) 122001, [ arXiv:1308.0474]

    2013 arXiv

  44. [51]

    Li and J.-X

    R. Li and J.-X. Wang, Next-to-leading-order study of the associated production of J/ψ +γ at the LHC , Phys. Rev. D89 (2014), no. 11 114018, [ arXiv:1401.6918]

    2014 arXiv

  45. [52]

    G. T. Bodwin, H. S. Chung, U.-R. Kim, and J. Lee, Fragmentation contributions to J/ψ production at the Tevatron and the LHC , Phys. Rev. Lett. 113 (2014), no. 2 022001, [arXiv:1403.3612]

    2014 arXiv

  46. [53]

    Lansberg and H.-S

    J.-P. Lansberg and H.-S. Shao, J/ÏĹ -pair production at large momenta: Indications for double parton scatterings and large Îś 5 s contributions, Phys. Lett. B751 (2015) 479–486, [ arXiv:1410.8822]

    2015 arXiv

  47. [54]

    H.-S. Shao, H. Han, Y.-Q. Ma, C. Meng, Y.-J. Zhang, and K. -T. Chao, Yields and polarizations of prompt J/ψ and ψ(2S) production in hadronic collisions , JHEP 05 (2015) 103, [ arXiv:1411.3300]

    2015 arXiv

  48. [55]

    Sun and H.-F

    Z. Sun and H.-F. Zhang, Reconciling charmonium production and polarization data in t he midrapidity region at hadron colliders within the nonrelati vistic QCD framework , Chin. Phys. C42 (2018), no. 4 043104, [ arXiv:1505.02675]

    2018 arXiv

  49. [56]

    G. T. Bodwin, K.-T. Chao, H. S. Chung, U.-R. Kim, J. Lee, a nd Y.-Q. Ma, Fragmentation contributions to hadroproduction of prompt J/ÏĹ , ÏĞ cJ , and ÏĹ(2S) states , Phys. Rev. D93 (2016), no. 3 034041, [ arXiv:1509.07904]

    2016 arXiv

  50. [57]

    Feng and H.-F

    Y. Feng and H.-F. Zhang, Double longitudinal-spin asymmetries in J/ψ production at RHIC , JHEP 11 (2018) 136, [ arXiv:1809.04894]

    2018 arXiv

  51. [58]

    Butenschoen, Z.-G

    M. Butenschoen, Z.-G. He, and B. A. Kniehl, ηc production at the LHC challenges nonrelativistic-QCD factorization, Phys. Rev. Lett. 114 (2015), no. 9 092004, [arXiv:1411.5287]

    2015 arXiv

  52. [59]

    Han, Y.-Q

    H. Han, Y.-Q. Ma, C. Meng, H.-S. Shao, and K.-T. Chao, ηc production at LHC and indications on the understanding of J/ψ production, Phys. Rev. Lett. 114 (2015), no. 9 092005, [ arXiv:1411.7350]

    2015 arXiv

  53. [60]

    Zhang, Z

    H.-F. Zhang, Z. Sun, W.-L. Sang, and R. Li, Impact of ηc hadroproduction data on charmonium production and polarization within NRQCD framewo rk, Phys. Rev. Lett. 114 (2015), no. 9 092006, [ arXiv:1412.0508]

    2015 arXiv

  54. [61]

    Lansberg, H.-S

    J.-P. Lansberg, H.-S. Shao, and H.-F. Zhang, η′ c Hadroproduction at Next-to-Leading Order and its Relevance to ψ′ Production, Phys. Lett. B786 (2018) 342–346, [ arXiv:1711.00265]

    2018 arXiv

  55. [62]

    Y. Feng, J. He, J.-P. Lansberg, H.-S. Shao, A. Usachov, a nd H.-F. Zhang, Phenomenological NLO analysis of ηc production at the LHC in the collider and fixed-target modes , Nucl. Phys. B945 (2019) 114662, [ arXiv:1901.09766]. – 18 –

    2019 arXiv

  56. [63]

    Y.-Q. Ma, K. Wang, and K.-T. Chao, QCD radiative corrections to χcJ production at hadron colliders, Phys. Rev. D83 (2011) 111503, [ arXiv:1002.3987]

    2011 arXiv

  57. [64]

    Li, Y.-Q

    D. Li, Y.-Q. Ma, and K.-T. Chao, χcJ production associated with a c¯c pair at hadron colliders, Phys. Rev. D83 (2011) 114037, [ arXiv:1106.4262]

    2011 arXiv

  58. [65]

    Shao and K.-T

    H.-S. Shao and K.-T. Chao, Spin correlations in polarizations of P-wave charmonia χcJ and impact on J/ψ polarization, Phys. Rev. D90 (2014), no. 1 014002, [ arXiv:1209.4610]

    2014 arXiv

  59. [66]

    Shao, Y.-Q

    H.-S. Shao, Y.-Q. Ma, K. Wang, and K.-T. Chao, Polarizations of χc1 and χc2 in prompt production at the LHC , Phys. Rev. Lett. 112 (2014), no. 18 182003, [ arXiv:1402.2913]

    2014 arXiv

  60. [67]

    Zhang, L

    H.-F. Zhang, L. Yu, S.-X. Zhang, and L. Jia, Global analysis of the experimental data on χc meson hadroproduction, Phys. Rev. D93 (2016), no. 5 054033, [ arXiv:1410.4032]. [Addendum: Phys. Rev.D93,no.7,079901(2016)]

    2016 arXiv

  61. [68]

    Sun and H.-F

    Z. Sun and H.-F. Zhang, QCD corrections to the color-singlet J/ψ production in deeply inelastic scattering at HERA , Phys. Rev. D96 (2017), no. 9 091502, [ arXiv:1705.05337]

    2017 arXiv

  62. [69]

    Barsuk, J

    S. Barsuk, J. He, E. Kou, and B. Viaud, Investigating charmonium production at LHC with the p pbar final state , Phys.Rev. D86 (2012) 034011, [ arXiv:1202.2273]

    2012 arXiv

  63. [70]

    Aaij et al., Measurement of the ηc(1S) production cross-section in proton-proton collisions via the decay ηc(1S) →p¯p, Eur

    LHCb Collaboration, R. Aaij et al., Measurement of the ηc(1S) production cross-section in proton-proton collisions via the decay ηc(1S) →p¯p, Eur. Phys. J. C75 (2015), no. 7 311, [arXiv:1409.3612]

    2015 arXiv

  64. [71]

    Zhang, Y

    H.-F. Zhang, Y. Feng, W.-L. Sang, and Y.-P. Yan, Kinematic distributions of the ηc photoproduction in ep collisions within the nonrelativistic QCD framework , Phys. Rev. D99 (2019), no. 11 114018, [ arXiv:1902.09056]

    2019 arXiv

  65. [72]

    Zhang and Z

    H.-F. Zhang and Z. Sun, Leptonic current structure and azimuthal asymmetry in deeply inelastic scattering, Phys. Rev. D96 (2017), no. 3 034002, [ arXiv:1701.08728]

    2017 arXiv

  66. [74]

    Gluck, E

    M. Gluck, E. Reya, and A. Vogt, Dynamical parton distributions of the proton and small x physics, Z. Phys. C67 (1995) 433–448

    1995

  67. [75]

    E. J. Eichten and C. Quigg, Quarkonium wave functions at the origin , Phys.Rev. D52 (1995) 1726–1728, [ hep-ph/9503356]. – 19 –

    1995 arXiv

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