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The paper claims that a new TMD soft transition function, equal in the perturbative limit to 2 α_s/(27 M^2 π b_T^2) ⟨O(3S1[1])⟩, controls J/ψ production at small transverse momentum and is 1/v enhanced over color-octet TMD shape functions.

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The paper derives new TMD soft transition functions and shows they dominate J/psi production at small transverse momentum by a factor of 1/v over previously used shape functions.

T0 review reviewed 2026-08-05 challenge →

load-bearing objection Solid vNRQCD extension with a genuinely new TMD soft transition function; the 1/bT^2 result is real but conditional on treating the soft scale as perturbative, which is numerically marginal for charmonium. the 4 major comments →

arxiv 2509.02977 v1 pith:BUNWZG2H submitted 2025-09-03 hep-ph hep-thnucl-th

The role of the soft scale for $J/\psi$ production in the transverse momentum dependent framework

Marston Copeland , Sean Fleming , Reed Hodges This is my paper
classification hep-ph hep-thnucl-th
keywords J/psi productiontransverse momentum dependent factorizationvNRQCDsoft gluon radiationTMD soft transition functioncolor-octet to color-singlet transitionsemi-inclusive deep inelastic scatteringNRQCD factorization
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

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 tries to establish that soft gluon radiation—not just the ultrasoft gluons encoded in the usual long-distance matrix elements—sets the transverse-momentum dependence of J/ψ production at small q_T. Working in vNRQCD, the authors classify the subleading-in-v operators that turn a color-octet c-cbar pair into a 3S1[1] state by emitting soft gluons, and they derive a transverse-momentum-dependent (TMD) factorization theorem for semi-inclusive deep inelastic scattering. The new ingredient, a TMD soft transition function (TMDSTF), appears in the hadronic tensor convoluted with the gluon TMDPDF; in the perturbative soft-scale limit it reduces to a single color-singlet long-distance matrix element divided by b_T^2. If this is right, previous analyses that kept only color-octet TMD shape functions missed the leading v-power contribution, and the low-q_T J/ψ spectrum becomes a cleaner probe of gluon TMDs.

Core claim

The central claim is Eq. (5.21): the factorized hadronic tensor for J/ψ production in SIDIS at small transverse momentum is W^{μν} = H ∫ d²b_T/(2π)² e^{-i q_T·b_T} G_{g/N}(ξ,b_T) T_{1S0[8]→3S1[1]}(b_T) δ(1-z), where T is the new TMD soft transition function. At leading order in the perturbative soft-scale limit, the TMDSTF is T = 2 α_s(μ_s)/(27 M^2 π) (1/b_T²) ⟨O^{J/ψ}(3S1[1])⟩ (Eq. 5.32). This object is enhanced by 1/v relative to the color-octet TMD shape functions used in previous studies, because those functions require extra suppressed vNRQCD Lagrangian insertions to reach the 3S1[1] state, whereas the TMDSTF already sits in that state after soft emission. The paper also notes that the

What carries the argument

The central object is the TMD soft transition function (TMDSTF), defined in Eq. (5.22) as a vacuum matrix element of heavy-quark fields, a soft chromomagnetic field, and soft Wilson lines that converts a 1S0[8] color-octet c-cbar pair into a 3S1[1] state. It carries the argument because it is the piece of the factorized tensor encoding soft-gluon hadronization dynamics, and it is built from the subleading vNRQCD operators derived in Section 3, specifically the single chromomagnetic and double chromoelectric transition operators. Its momentum-space version is matched onto the color-singlet LDME using spin and rotational symmetry, producing the 1/b_T² form.

Load-bearing premise

The derivation assumes the soft scale m v is perturbative, i.e. (m v)² is much larger than Λ²_QCD, so the TMDSTF can be matched onto the color-singlet LDME; the paper itself states it is not clear whether the soft scale is perturbative for charmonium.

What would settle it

Compute the chromomagnetic correlator ⟨0|(g B/(v·P))²|0⟩ on the lattice with charm quarks: if it is not consistent with the perturbative α_s result at the soft scale, Eq. (5.32) is falsified. Alternatively, measure the J/ψ q_T spectrum at small transverse momentum in e⁺e⁻ → J/ψ + gluon or in SIDIS kinematics at an electron-ion collider and check whether the spectrum contains the 1/k_T² tail implied by the 1/b_T² TMDSTF with the predicted normalization.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Low-q_T J/ψ production in SIDIS factorizes into the gluon TMDPDF times the TMDSTF, so if the soft scale is perturbative, gluon-TMD extraction can proceed with only one well-constrained free parameter, the color-singlet LDME.
  • The TMDSTF is enhanced by 1/v over the color-octet TMD shape functions, so at moderate b_T ≲ 0.5 GeV⁻¹ it is at least as large as the 3P0[8] shape function and often larger than the 1S0[8] one.
  • Because the TMDSTF scales as 1/b_T² while the leading-order TMD shape functions are b_T-independent, there is a crossover: the TMDSTF dominates at small b_T and the shape functions dominate at large b_T.
  • In the collinear (transverse-momentum-integrated) limit, the soft-transition operator gives a scaleless integral that vanishes in dimensional regularization, so this contribution is purely a TMD effect rather than a modification of collinear NRQCD factorization.
  • The matching reproduces the pNRQCD expression for ⟨O(1S0[8])⟩ in terms of a chromomagnetic correlator times the singlet LDME, serving as a check on the operator construction.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the soft scale is genuinely non-perturbative for charmonium (mv ≈ 750 MeV ≈ Λ_QCD), the 1/b_T² perturbative prediction fails; the TMDSTF then becomes a process-dependent non-perturbative function to be extracted, although the v-enhancement relative to the shape functions may persist in the power counting.
  • The same operator technology should generate TMDSTFs for other color-octet channels, including 3S1[8]→3S1[1]; the 3S1[8] current has a vanishing leading-order matching coefficient but could contribute at higher orders in α_s, so the complete small-q_T picture may need several such functions.
  • Because bottomonium has a larger soft scale (m_b v ≈ 1.5 GeV), the perturbative matching is more likely to hold there; a testable extension is predicting low-q_T Υ production with the same formula scaled by the Υ color-singlet LDME.
  • A direct experimental discriminator would be J/ψ production in e⁺e⁻ annihilation at small transverse momentum, where only hadronization dynamics enter: the TMDSTF predicts a 1/k_T² tail coming from the Fourier transform of 1/b_T², while a flat TMD shape function would give a softer spectrum.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper develops a vNRQCD/SCET treatment of soft-gluon radiation in J/psi production at small transverse momentum. It categorizes subleading-v production operators that convert color-octet cbar-c pairs to the color-singlet 3S1[1] configuration, defines new "TMD soft transition functions" (TMDSTFs), and derives a factorization formula for SIDIS J/psi production, Eq. (5.21), in terms of the gluon TMDPDF and a TMDSTF. In the perturbative-soft-scale limit the TMDSTF is matched onto the color-singlet LDME, giving Eq. (5.32), which scales as ~1/bT^2 and is claimed to be enhanced by 1/v relative to the color-octet TMD shape functions. The paper includes checks against explicit one- and two-gluon emission amplitudes and a comparison with pNRQCD matching of the 1S0[8] LDME. It also contains several explicit caveats, including the statement that it is unclear whether the soft scale is perturbative and that the perturbative matching onto the LDME is not a true factorization theorem.

Significance. If the central claims hold, the paper introduces a genuinely new ingredient for quarkonium TMD phenomenology: a soft transition function that is leading in v power counting relative to the previously used color-octet TMD shape functions. The explicit checks in Appendix A and the reproduction of the pNRQCD matching coefficient are strengths, and the operator classification is a useful contribution. However, the quantitative predictive content of the paper rests on the perturbative treatment of the soft scale, which the authors themselves flag as uncertain. The value of the paper is therefore more in the EFT construction and the identification of the TMDSTF than in the specific numerical prediction of Eq. (5.32).

major comments (4)
  1. [Sec. 5.1, Eq. (5.32)] The central quantitative result assumes (mv)^2 >> Lambda_QCD^2. For charmonium, mv ~ 750 MeV and alpha_s(mv) ~ 0.8, so the expansion parameter alpha_s/pi ~ 0.25 and the truncation of the J/psi Fock state to the |cbar-c(3S1[1]) g> component brings O(v) ~ 50% corrections. The paper itself states, in the closing paragraph of Sec. 5.1, that 'It is not clear whether the soft scale is perturbative or not.' If the soft scale is non-perturbative, Eq. (5.32) loses both its 1/bT^2 shape and its one-parameter predictive content, and the advertised gluon-TMDPDF extraction from Eq. (5.21) no longer follows. The authors should quantify the perturbative error or explicitly frame Eq. (5.32) as a scenario rather than the main result.
  2. [Sec. 5.1, Eqs. (5.24)-(5.32) and (5.38)] The matching of the TMDSTF onto <O(3S1[1])> is performed with a one-gluon intermediate state and the replacement |J/psi> ~ |cbar-c>. The authors later state that Eq. (5.36) is 'purely a leading order perturbative statement and not a true factorization theorem' and that <O(3S1[1])> contains soft states, Eq. (5.38). The same caveat applies to Eq. (5.32): it is not shown that the coefficient obtained is the first term of a legitimate operator product expansion rather than an artifact of the leading-order Fock-state truncation. This distinction is load-bearing for the claim that Eq. (5.32) is a parameter-free prediction.
  3. [Sec. 4, after Eq. (3.45)] The statement that the Gamma_a and Gamma_d contributions in O3 and O4 cancel when Gamma is proportional to gamma^mu is asserted without derivation ('It is straightforward to show...'). The effective current in Eq. (5.10) and the factorization theorem in Eq. (5.21) keep only the Gamma_b term; if the cancellation is not exact, additional equal-power structures contribute and the TMDSTF definition in Eq. (5.22) is incomplete. A derivation or a reference is needed.
  4. [Sec. 5.1, Eqs. (5.30)-(5.32)] The treatment of the UV pole is incomplete. Eq. (5.31) is presented as canceling the 1/epsilon_UV pole, but it is a bare phase-space operator with a theta-function cutoff, not a renormalized counterterm; no renormalization condition is specified and the dependence on the cutoff P_T is not tracked. In addition, the Fourier transform from Eq. (5.30) to Eq. (5.32) is not shown. Since the coefficient of 1/bT^2 is central to the claimed 1/v enhancement, the normalization should be verified explicitly, including the known constant in the two-dimensional Fourier transform of log(k_T^2).
minor comments (4)
  1. [Eq. (5.4)] The leptonic tensor L^mu nu = e^{-4} <l'| J^mu(0) |l> <l| J^nu dagger(0) |l'> is written without spin sums or lepton momenta in the states; this should be clarified or a reference provided.
  2. [Fig. 7] The figure compares TMDSTF and TMDShFs for several LDME extractions, but the text does not specify the line colors in the caption, and no uncertainty from alpha_s(mu_s) or from the choice mu_s = 750 MeV is shown. A brief statement that the plot is an illustrative fixed-order comparison would help.
  3. [Eqs. (5.32) and (5.33)] The statement that the TMDSTF is 'subleading in the TMD power-counting' because it goes as 1/bT^2 while TMDShFs are constant is bT-dependent; a sentence clarifying that this comparison is made at a fixed bT and that the hierarchy changes with bT would prevent misreading.
  4. [General] There are several typos and notation inconsistencies, e.g., the mixed use of pQ and p_Q in Sec. 3, and the unusual placement of the 1/2 factor in Eq. (5.30). A careful proofreading pass is recommended.

Circularity Check

0 steps flagged

No significant circularity: the TMDSTF is independently defined and computed via a standard OPE; the 1/b_T^2 result and 1/v enhancement are derived, not fitted.

full rationale

The central object, the TMDSTF, is introduced in eq. (5.22) as a vacuum matrix element of vNRQCD/SCET fields, independent of the color-singlet LDME. The claimed result eq. (5.32) is obtained by a leading-order operator product expansion (sec. 5.1): one-gluon intermediate states are inserted (eq. 5.24), the phase-space integral is evaluated (eqs. 5.28-5.30), and only the spin trace is identified with ⟨O(J/ψ, 3S1[1])⟩ via spin/rotational symmetry (eq. 5.26). The 1/b_T^2 shape comes from the Fourier transform of the k_T-space integral; the α_s/M^2 coefficient comes from the chromomagnetic vertex. No term in the derivation is defined to equal eq. (5.32); the input is an external LDME and the output has additional b_T dependence. The v-counting claim (v^6 vs v^7) likewise follows from these definitions plus standard NRQCD scalings, not from an ansatz that encodes the conclusion. Self-citations (notably ref. [48], with coauthor Fleming) supply the 'magic formula' and the leading-order vNRQCD operator basis, but the formula is explicitly proved in the paper ('no actual magic involved in eq. (B.8) as it can be proved to be true') and the new subleading operators are derived from tree-level QCD amplitudes in section 3, with independent checks in appendix A and against pNRQCD refs. [46,47]. The paper's own caveats—'If it is indeed valid to treat the soft scale in quarkonium production as perturbative', 'It is not clear whether the soft scale is perturbative or not', 'our analysis of eq. (5.36) is purely a leading order perturbative statement and not a true factorization theorem', and the soft-state overlap noted after eq. (5.38)—limit the regime of validity and undermine the numerical reliability of eq. (5.32) for charmonium, but they are correctness risks, not circular reductions. The plotted 'predicted' curves in figure 7 use external fitted LDMEs from table 1 to fix normalization; the shapes and relative v-enhancement are not fit to the plotted observables. No prediction reduces by construction to its input.

Axiom & Free-Parameter Ledger

3 free parameters · 6 axioms · 2 invented entities

The central derivation rests on standard vNRQCD/SCET power counting plus two regime assumptions: lambda ~ v and a perturbative soft scale. The free parameters are the color-singlet LDME used as an input, an arbitrary plot scale, and an underspecified UV subtraction scale. No new physical particles or forces are introduced; the new objects are EFT operators and a non-perturbative function.

free parameters (3)
  • Soft scale mu_s = 750 MeV (arbitrary choice in Fig. 7)
    Chosen by hand for all curves in figure 7; affects the numerical comparison but not the formal power-counting claim.
  • UV subtraction scale P_T in eq. (5.31) = unspecified
    Introduced via the theta-function counterterm to cancel the 1/epsilon_UV pole in eq. (5.30); its precise definition is not given.
  • Color-singlet LDME <O(3S1[1])> = 1.16 to 1.32 GeV^3 from Table 1 fits
    Input number taken from prior global fits; the TMDSTF prediction in eq. (5.32) is proportional to this fitted parameter.
axioms (6)
  • domain assumption NRQCD v-scaling of LDMEs: singlet scales as v^3, octet states as v^7
    Invoked in Section 5.1 to claim the TMDSTF is enhanced by 1/v over TMDShFs. This scaling is contested by some extractions, and the paper itself documents that fits disagree by orders of magnitude.
  • domain assumption Overlap of SCET and vNRQCD power countings, lambda ~ v
    Stated in Section 5: 'We work in a regime where the SCET power-counting parameter is of the same order as the vNRQCD power-counting parameter, i.e., lambda ~ v.' Required for the combined SCET+vNRQCD factorization.
  • standard math vNRQCD field content and momentum scaling (soft q ~ mv, ultrasoft k ~ mv^2)
    Defines the EFT framework used throughout; standard for vNRQCD, Section 2.2.
  • standard math Magic formula identities in eq. (3.13) and eq. (B.8)
    Used to resum soft Wilson lines; the paper states one version is provable but does not give a full proof for both cases.
  • domain assumption Spin-symmetry matching in eq. (5.26): M^2 xi^dagger sigma^k eta eta^dagger sigma^n xi = (1/3) delta^{kn} <O(3S1[1])>
    Standard leading-order NRQCD spin symmetry used to map the spinor structure onto the LDME.
  • domain assumption Perturbative soft scale: (mv)^2 >> Lambda_QCD^2
    Needed for the operator product expansion leading to eq. (5.32); the paper itself questions whether this holds for charmonium.
invented entities (2)
  • TMD soft transition function (TMDSTF) independent evidence
    purpose: Non-perturbative function describing the transition of a 1S0[8] ccbar pair to a 3S1[1] state via soft gluon emission; enters the factorization theorem eq. (5.21).
    At leading order in the perturbative soft-scale regime it predicts a 1/bT^2 shape (eq. 5.32), a falsifiable handle in SIDIS or e+e- measurements.
  • Subleading vNRQCD production operators O3 and O4 independent evidence
    purpose: Mediate color-octet to color-singlet transitions via soft gluons at next-to-leading power in v.
    They reproduce the tree-level single and double gluon emission amplitudes in appendix A and yield the pNRQCD matching coefficient checked in Section 5.1.

reviewed 2026-08-05 · how reviews work

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Pith. "Pith review of The role of the soft scale for $J/\psi$ production in the transverse momentum dependent framework." pith.science (2026). https://pith.science/paper/BUNWZG2H

@misc{pith2026250902977,
  author       = {Pith},
  title        = {Pith review of: The role of the soft scale for $J/\psi$ production in the transverse momentum dependent framework},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BUNWZG2H}},
  note         = {Machine review of arXiv:2509.02977}
}
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abstract

We use vNRQCD to study power corrections in the ${\rm v}$ expansion due to soft gluon radiation during $J/\psi$ production at small transverse momentum. We categorize four new $J/\psi$ production operators that mediate the transition of perturbatively produced color-octet charm quark/anti-quark pairs to charm quarks in a $^3S_1^{[1]}$ state via soft gluon emission. We then use Soft Collinear Effective Theory and vNRQCD to derive a factorization theorem for $J/\psi$ production in SIDIS in terms of the gluon transverse momentum dependent (TMD) PDFs in the proton and new objects which we call TMD soft transition functions. We show that the TMD soft transition function leads in the ${\rm v}$ power-counting with respect to the color-octet TMD shape functions that have been used in previous studies of $J/\psi$ production at small transverse momentum.

discussion (0)

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Forward citations

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Reference graph

Works this paper leans on

94 extracted references · 11 canonical work pages · cited by 4 Pith papers · 11 internal anchors

  1. [1]

    of Energy and N.S

    U.D. of Energy and N.S. Foundation, A new era of discovery: The 2023 long range plan for nuclear science, October, 2023

    2023

  2. [2]

    Butterworth, S

    J. Butterworth, S. Carrazza, A. De Roeck et al., Pdf4lhc recommendations for lhc run ii , J. Phys. G 43 (2016) 023001 [ 1510.03865]

    Pith/arXiv arXiv 2016

  3. [3]

    Boussarie et al., TMD Handbook, 2304.03302

    R. Boussarie et al., TMD Handbook, 2304.03302

    Pith/arXiv arXiv

  4. [4]

    Bodwin, E

    G.T. Bodwin, E. Braaten and G.P. Lepage, Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium , Phys. Rev. D 51 (1995) 1125 [ hep-ph/9407339]

    Pith/arXiv arXiv 1995

  5. [5]

    Fleming and T

    S. Fleming and T. Mehen, Leptoproduction of J / psi , Phys. Rev. D 57 (1998) 1846 [hep-ph/9707365]

    Pith/arXiv arXiv 1998

  6. [6]

    Yuan and K.-T

    F. Yuan and K.-T. Chao, Polarized J/ψ production in deep inelastic scattering at HERA , Phys. Rev. D 63 (2001) 034017 [ hep-ph/0008301]

    Pith/arXiv arXiv 2001

  7. [7]

    Beneke, M

    M. Beneke, M. Kramer and M. Vanttinen, Inelastic photoproduction of polarized J / psi , Phys. Rev. D 57 (1998) 4258 [ hep-ph/9709376]

    Pith/arXiv arXiv 1998

  8. [8]

    Z. Chu, J. Chen, X.-P. Wang and H. Xing, On the role of J/ψ production in electron-ion collisions, 2406.01406

    Pith/arXiv arXiv

  9. [9]

    Maxia and F

    L. Maxia and F. Yuan, Azimuthal Angular Correlation of J/ψ Plus Jet Production at the EIC, 2403.02097

    Pith/arXiv arXiv

  10. [10]

    Bodwin, X

    G.T. Bodwin, X. Garcia i Tormo and J. Lee, Factorization in exclusive quarkonium production, Phys. Rev. D 81 (2010) 114014 [ 1003.0061]

    Pith/arXiv arXiv 2010

  11. [11]

    Braaten and J

    E. Braaten and J. Lee, Exclusive Double Charmonium Production from e+e− Annihilation into a Virtual Photon , Phys. Rev. D 67 (2003) 054007 [ hep-ph/0211085]

    Pith/arXiv arXiv 2003

  12. [12]

    Hagiwara, E

    K. Hagiwara, E. Kou and C.-F. Qiao, Exclusive J/ψ productions at e+e− colliders, Phys. Lett. B 570 (2003) 39 [ hep-ph/0305102]

    Pith/arXiv arXiv 2003

  13. [13]

    Bodwin, X

    G.T. Bodwin, X. Garcia i Tormo and J. Lee, Factorization theorems for exclusive heavy-quarkonium production, Phys. Rev. Lett. 101 (2008) 102002 [ 0805.3876]

    Pith/arXiv arXiv 2008

  14. [14]

    Braaten, M.A

    E. Braaten, M.A. Doncheski, S. Fleming and M.L. Mangano, Fragmentation production of J/ψ and ψ′ at the Tevatron, Phys. Lett. B 333 (1994) 548 [ hep-ph/9405407]

    Pith/arXiv arXiv 1994

  15. [15]

    Braaten and S

    E. Braaten and S. Fleming, Color octet fragmentation and the psi-prime surplus at the Tevatron, Phys. Rev. Lett. 74 (1995) 3327 [ hep-ph/9411365]

    Pith/arXiv arXiv 1995

  16. [16]

    Baumgart, A.K

    M. Baumgart, A.K. Leibovich, T. Mehen and I.Z. Rothstein, Probing Quarkonium Production Mechanisms with Jet Substructure , JHEP 11 (2014) 003 [ 1406.2295]

    Pith/arXiv arXiv 2014

  17. [17]

    R. Bain, L. Dai, A. Hornig, A.K. Leibovich, Y. Makris and T. Mehen, Analytic and Monte Carlo Studies of Jets with Heavy Mesons and Quarkonia , JHEP 06 (2016) 121 [1603.06981]

    Pith/arXiv arXiv 2016

  18. [18]

    R. Bain, L. Dai, A. Leibovich, Y. Makris and T. Mehen, NRQCD Confronts LHCb Data on Quarkonium Production within Jets , Phys. Rev. Lett. 119 (2017) 032002 [ 1702.05525]

    Pith/arXiv arXiv 2017

  19. [19]

    Kang, J.-W

    Z.-B. Kang, J.-W. Qiu, F. Ringer, H. Xing and H. Zhang, J/ψ production and polarization within a jet , Phys. Rev. Lett. 119 (2017) 032001 [ 1702.03287]

    Pith/arXiv arXiv 2017

  20. [20]

    Dai and P

    L. Dai and P. Shrivastava, Quarkonium Polarization and the Long Distance Matrix Elements Hierarchies using Jet Substructure , Phys. Rev. D 96 (2017) 036020 [ 1707.08629]. – 35 –

    Pith/arXiv arXiv 2017

  21. [21]

    Y. Wang, D. Kang and H.S. Chung, NRQCD Re-Confronts LHCb Data on Quarkonium Production within Jets , 2507.19022

    Pith/arXiv arXiv

  22. [22]

    Copeland, L

    M. Copeland, L. Dai, Y. Fu and J. Roy, ψ(2S) production in jets using NRQCD , 2508.00814

    Pith/arXiv arXiv

  23. [23]

    Flett, J.P

    C.A. Flett, J.P. Lansberg, S. Nabeebaccus, M. Nefedov, P. Sznajder and J. Wagner, Exclusive vector-quarkonium photoproduction at NLO in αs in collinear factorisation with evolution of the generalised parton distributions and high-energy resummation , Phys. Lett. B 859 (2024) 139117 [ 2409.05738]

    Pith/arXiv arXiv 2024

  24. [24]

    Ivanov, A

    D.Y. Ivanov, A. Schafer, L. Szymanowski and G. Krasnikov, Exclusive photoproduction of a heavy vector meson in QCD , Eur. Phys. J. C 34 (2004) 297 [ hep-ph/0401131]

    Pith/arXiv arXiv 2004

  25. [25]

    Chen and C.-F

    Z.-Q. Chen and C.-F. Qiao, NLO QCD corrections to exclusive electroproduction of quarkonium, Phys. Lett. B 797 (2019) 134816 [ 1903.00171]

    Pith/arXiv arXiv 2019

  26. [26]

    Blask, S

    S.K. Blask, S. Fleming, T. Mehen, J. Roy, I.W. Stewart and F. Zhao, Relativistic corrections to exclusive photoproduction of Quarkonia near-threshold , 2506.18905

    Pith/arXiv arXiv

  27. [27]

    Sharma and I

    R. Sharma and I. Vitev, High transverse momentum quarkonium production and dissociation in heavy ion collisions , Phys. Rev. C 87 (2013) 044905 [ 1203.0329]

    Pith/arXiv arXiv 2013

  28. [28]

    Yao and T

    X. Yao and T. Mehen, Quarkonium in-medium transport equation derived from first principles, Phys. Rev. D 99 (2019) 096028 [ 1811.07027]

    Pith/arXiv arXiv 2019

  29. [29]

    X. Yao, W. Ke, Y. Xu, S.A. Bass, T. Mehen and B. M¨ uller, Quarkonium Production in Heavy Ion Collisions: From Open Quantum System to Transport Equation , Nucl. Phys. A 1005 (2021) 121854 [ 2002.04079]

    Pith/arXiv arXiv 2021

  30. [30]

    Yang and X

    D.-L. Yang and X. Yao, Quarkonium Polarization in Medium from Open Quantum Systems and Chromomagnetic Correlators , 2405.20280

    Pith/arXiv arXiv

  31. [31]

    Hoang, Heavy quarkonium dynamics , hep-ph/0204299

    A.H. Hoang, Heavy quarkonium dynamics , hep-ph/0204299

    Pith/arXiv arXiv

  32. [32]

    Brambilla et al., Heavy Quarkonium: Progress, Puzzles, and Opportunities , Eur

    N. Brambilla et al., Heavy Quarkonium: Progress, Puzzles, and Opportunities , Eur. Phys. J. C 71 (2011) 1534 [ 1010.5827]

    Pith/arXiv arXiv 2011

  33. [33]

    Nayak, J.-W

    G.C. Nayak, J.-W. Qiu and G.F. Sterman, Fragmentation, factorization and infrared poles in heavy quarkonium production, Phys. Lett. B 613 (2005) 45 [ hep-ph/0501235]

    Pith/arXiv arXiv 2005

  34. [34]

    Nayak, J.-W

    G.C. Nayak, J.-W. Qiu and G.F. Sterman, Fragmentation, NRQCD and NNLO factorization analysis in heavy quarkonium production , Phys. Rev. D 72 (2005) 114012 [ hep-ph/0509021]

    Pith/arXiv arXiv 2005

  35. [35]

    NRQCD Factorization and Velocity-dependence of NNLO Poles in Heavy Quarkonium Production

    G.C. Nayak, J.-W. Qiu and G.F. Sterman, NRQCD Factorization and Velocity-dependence of NNLO Poles in Heavy Quarkonium Production , Phys. Rev. D 74 (2006) 074007 [hep-ph/0608066]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  36. [36]

    Butenschoen and B.A

    M. Butenschoen and B.A. Kniehl, World data of J/psi production consolidate NRQCD factorization at NLO , Phys. Rev. D 84 (2011) 051501 [ 1105.0820]

    Pith/arXiv arXiv 2011

  37. [37]

    Butenschoen and B.A

    M. Butenschoen and B.A. Kniehl, Next-to-leading-order tests of NRQCD factorization with J/ψ yield and polarization , Mod. Phys. Lett. A 28 (2013) 1350027 [ 1212.2037]

    Pith/arXiv arXiv 2013

  38. [38]

    Chao, Y.-Q

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

    Pith/arXiv arXiv 2012

  39. [39]

    Bodwin, H.S

    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) 022001 [ 1403.3612]. – 36 –

    Pith/arXiv arXiv 2014

  40. [40]

    Brambilla, M

    N. Brambilla, M. Butenschoen and X.-P. Wang, How well does nonrelativistic QCD factorization work at next-to-leading order? , Phys. Rev. D 112 (2025) L011902 [2411.16384]

    Pith/arXiv arXiv 2025

  41. [41]

    LHCb collaboration, Measurement of J/ψ polarization in pp collisions at √s = 7 TeV, Eur. Phys. J. C 73 (2013) 2631 [ 1307.6379]

    Pith/arXiv arXiv 2013

  42. [42]

    Brambilla, A

    N. Brambilla, A. Pineda, J. Soto and A. Vairo, Potential NRQCD: An Effective theory for heavy quarkonium, Nucl. Phys. B 566 (2000) 275 [ hep-ph/9907240]

    Pith/arXiv arXiv 2000

  43. [43]

    Brambilla, A

    N. Brambilla, A. Pineda, J. Soto and A. Vairo, Effective Field Theories for Heavy Quarkonium, Rev. Mod. Phys. 77 (2005) 1423 [ hep-ph/0410047]

    Pith/arXiv arXiv 2005

  44. [44]

    Luke, A.V

    M.E. Luke, A.V. Manohar and I.Z. Rothstein, Renormalization group scaling in nonrelativistic QCD, Phys. Rev. D 61 (2000) 074025 [ hep-ph/9910209]

    Pith/arXiv arXiv 2000

  45. [45]

    Rothstein, P

    I.Z. Rothstein, P. Shrivastava and I.W. Stewart, Manifestly Soft Gauge Invariant Formulation of vNRQCD , Nucl. Phys. B 939 (2019) 405 [ 1806.07398]

    Pith/arXiv arXiv 2019

  46. [46]

    Brambilla, H.S

    N. Brambilla, H.S. Chung, A. Vairo and X.-P. Wang, Production and polarization of S-wave quarkonia in potential nonrelativistic QCD , Phys. Rev. D 105 (2022) L111503 [ 2203.07778]

    Pith/arXiv arXiv 2022

  47. [47]

    Brambilla, H.S

    N. Brambilla, H.S. Chung, A. Vairo and X.-P. Wang, Inclusive production of J/ ψ, ψ(2S), and Υ states in pNRQCD , JHEP 03 (2023) 242 [ 2210.17345]

    Pith/arXiv arXiv 2023

  48. [48]

    Fleming, Y

    S. Fleming, Y. Makris and T. Mehen, An effective field theory approach to quarkonium at small transverse momentum , JHEP 04 (2020) 122 [ 1910.03586]

    Pith/arXiv arXiv 2020

  49. [49]

    Echevarria, A

    M.G. Echevarria, A. Idilbi and I. Scimemi, Factorization Theorem For Drell-Yan At Low qT And Transverse Momentum Distributions On-The-Light-Cone , JHEP 07 (2012) 002 [1111.4996]

    Pith/arXiv arXiv 2012

  50. [50]

    Echevarr ´ ıa, A

    M.G. Echevarr ´ ıa, A. Idilbi and I. Scimemi,Soft and Collinear Factorization and Transverse Momentum Dependent Parton Distribution Functions , Phys. Lett. B 726 (2013) 795 [1211.1947]

    Pith/arXiv arXiv 2013

  51. [51]

    von Kuk, J.K.L

    R. von Kuk, J.K.L. Michel and Z. Sun, Transverse momentum distributions of heavy hadrons and polarized heavy quarks , JHEP 09 (2023) 205 [ 2305.15461]

    Pith/arXiv arXiv 2023

  52. [52]

    von Kuk, J.K.L

    R. von Kuk, J.K.L. Michel and Z. Sun, Transverse momentum-dependent heavy-quark fragmentation at next-to-leading order , JHEP 07 (2024) 129 [ 2404.08622]

    Pith/arXiv arXiv 2024

  53. [53]

    von Kuk, Heavy-quark Effects in Factorization and Resummation , Ph.D

    R.O. von Kuk, Heavy-quark Effects in Factorization and Resummation , Ph.D. thesis, U. Hamburg (main), 2025

    2025

  54. [54]

    L. Dai, C. Kim and A.K. Leibovich, Heavy quark transverse momentum dependent fragmentation, 2310.19207

    work page internal anchor Pith review Pith/arXiv arXiv

  55. [55]

    Transverse Momentum Dependent PDFs in Chiral Effective Theory

    M. Copeland and T. Mehen, Transverse momentum dependent PDFs in chiral effective theory, Phys. Rev. D 110 (2024) 114026 [ 2405.14965]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  56. [56]

    Probing nonperturbative transverse momentum dependent PDFs with chiral perturbation theory: the $\bar{d}-\bar{u}$ asymmetry

    M. Copeland and T. Mehen, Probing nonperturbative transverse momentum dependent PDFs with chiral perturbation theory: the ¯d − ¯u asymmetry, 2412.07717

    work page internal anchor Pith review Pith/arXiv arXiv

  57. [57]

    W. Ke, J. Terry and I. Vitev, Toward a first-principles description of transverse momentum dependent Drell-Yan production in proton-nucleus collisions , JHEP 02 (2025) 102 [2408.10310]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  58. [58]

    Catani, M

    S. Catani, M. Grazzini and A. Torre, Transverse-momentum resummation for heavy-quark hadroproduction, Nucl. Phys. B 890 (2014) 518 [ 1408.4564]. – 37 –

    Pith/arXiv arXiv 2014

  59. [59]

    Kang, Y.-Q

    Z.-B. Kang, Y.-Q. Ma, J.-W. Qiu and G. Sterman, Heavy Quarkonium Production at Collider Energies: Factorization and Evolution , Phys. Rev. D 90 (2014) 034006 [ 1401.0923]

    Pith/arXiv arXiv 2014

  60. [60]

    Sun, C.P

    P. Sun, C.P. Yuan and F. Yuan, Heavy Quarkonium Production at Low Pt in NRQCD with Soft Gluon Resummation , Phys. Rev. D 88 (2013) 054008 [ 1210.3432]

    Pith/arXiv arXiv 2013

  61. [61]

    Catani and M

    S. Catani and M. Grazzini, QCD transverse-momentum resummation in gluon fusion processes, Nucl. Phys. B 845 (2011) 297 [ 1011.3918]

    Pith/arXiv arXiv 2011

  62. [62]

    Mukherjee and S

    A. Mukherjee and S. Rajesh, Linearly polarized gluons in charmonium and bottomonium production in color octet model , Phys. Rev. D 95 (2017) 034039 [ 1611.05974]

    Pith/arXiv arXiv 2017

  63. [63]

    Probing Transverse Momentum Dependent Parton Distributions in Charmonium and Bottomonium Production

    A. Mukherjee and S. Rajesh, Probing Transverse Momentum Dependent Parton Distributions in Charmonium and Bottomonium Production , Phys. Rev. D 93 (2016) 054018 [1511.04319]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  64. [64]

    Boer and C

    D. Boer and C. Pisano, Polarized gluon studies with charmonium and bottomonium at LHCb and AFTER , Phys. Rev. D 86 (2012) 094007 [ 1208.3642]

    Pith/arXiv arXiv 2012

  65. [65]

    Echevarria, Proper TMD factorization for quarkonia production: pp → ηc,b as a study case, JHEP 10 (2019) 144 [ 1907.06494]

    M.G. Echevarria, Proper TMD factorization for quarkonia production: pp → ηc,b as a study case, JHEP 10 (2019) 144 [ 1907.06494]

    Pith/arXiv arXiv 2019

  66. [66]

    $J/\psi$ polarization in semi-inclusive DIS at low and high transverse momentum

    U. D’Alesio, L. Maxia, F. Murgia, C. Pisano and S. Rajesh, J/ψ polarization in semi-inclusive DIS at low and high transverse momentum , JHEP 03 (2022) 037 [2110.07529]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  67. [67]

    D. Boer, U. D’Alesio, F. Murgia, C. Pisano and P. Taels, J/ψ meson production in SIDIS: matching high and low transverse momentum , JHEP 09 (2020) 040 [ 2004.06740]

    Pith/arXiv arXiv 2020

  68. [68]

    Bor and D

    J. Bor and D. Boer, TMD evolution study of the cos2 ϕ azimuthal asymmetry in unpolarized J/ψ production at EIC , Phys. Rev. D 106 (2022) 014030 [ 2204.01527]

    Pith/arXiv arXiv 2022

  69. [69]

    $Cos(2\phi_h)$ asymmetry in $J/\psi$ production in unpolarized $ep$ collision

    R. Kishore, A. Mukherjee and M. Siddiqah, Cos(2ϕh) asymmetry in J/ ψ production in unpolarized ep collision, Phys. Rev. D 104 (2021) 094015 [ 2103.09070]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  70. [70]

    Scarpa, D

    F. Scarpa, D. Boer, M.G. Echevarria, J.-P. Lansberg, C. Pisano and M. Schlegel, Studies of gluon TMDs and their evolution using quarkonium-pair production at the LHC , Eur. Phys. J. C 80 (2020) 87 [ 1909.05769]

    Pith/arXiv arXiv 2020

  71. [71]

    D’Alesio, F

    U. D’Alesio, F. Murgia, C. Pisano and P. Taels, Azimuthal asymmetries in semi-inclusive J/ψ + jet production at an EIC , Phys. Rev. D 100 (2019) 094016 [ 1908.00446]

    Pith/arXiv arXiv 2019

  72. [72]

    Bacchetta, D

    A. Bacchetta, D. Boer, C. Pisano and P. Taels, Gluon TMDs and NRQCD matrix elements in J/ψ production at an EIC , Eur. Phys. J. C 80 (2020) 72 [ 1809.02056]

    Pith/arXiv arXiv 2020

  73. [73]

    Mukherjee and S

    A. Mukherjee and S. Rajesh, J/ψ production in polarized and unpolarized ep collision and Sivers and cos 2ϕ asymmetries, Eur. Phys. J. C 77 (2017) 854 [ 1609.05596]

    Pith/arXiv arXiv 2017

  74. [74]

    Rajesh, R

    S. Rajesh, R. Kishore and A. Mukherjee, Sivers effect in Inelastic J/ψ Photoproduction in ep↑ Collision in Color Octet Model , Phys. Rev. D 98 (2018) 014007 [ 1802.10359]

    Pith/arXiv arXiv 2018

  75. [75]

    Godbole, A

    R.M. Godbole, A. Misra, A. Mukherjee and V.S. Rawoot, Transverse Single Spin Asymmetry in e + p↑ → e + J/ψ + X and Transverse Momentum Dependent Evolution of the Sivers Function, Phys. Rev. D 88 (2013) 014029 [ 1304.2584]

    Pith/arXiv arXiv 2013

  76. [76]

    Godbole, A

    R.M. Godbole, A. Misra, A. Mukherjee and V.S. Rawoot, Sivers Effect and Transverse Single Spin Asymmetry in e + p↑ → e + J/ψ + X, Phys. Rev. D 85 (2012) 094013 [ 1201.1066]

    Pith/arXiv arXiv 2012

  77. [77]

    den Dunnen, J.P

    W.J. den Dunnen, J.P. Lansberg, C. Pisano and M. Schlegel, Accessing the Transverse Dynamics and Polarization of Gluons inside the Proton at the LHC , Phys. Rev. Lett. 112 (2014) 212001 [ 1401.7611]. – 38 –

    Pith/arXiv arXiv 2014

  78. [78]

    Heavy Quarkonium Production at Collider Energies: Partonic Cross Section and Polarization

    Z.-B. Kang, Y.-Q. Ma, J.-W. Qiu and G. Sterman, Heavy Quarkonium Production at Collider Energies: Partonic Cross Section and Polarization , Phys. Rev. D 91 (2015) 014030 [1411.2456]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  79. [79]

    R. Zhu, P. Sun and F. Yuan, Low Transverse Momentum Heavy Quark Pair Production to Probe Gluon Tomography, Phys. Lett. B 727 (2013) 474 [ 1309.0780]

    Pith/arXiv arXiv 2013

  80. [80]

    Copeland, S

    M. Copeland, S. Fleming, R. Gupta, R. Hodges and T. Mehen, Polarized J/ψ production in semi-inclusive DIS at large Q2: Comparing quark fragmentation and photon-gluon fusion , 2310.13737

    Pith/arXiv arXiv

Showing first 80 references.

This paper was first reviewed by deepseek-v4-flash on August 5, 2026.