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Azimuthal asymmetries in semi-inclusive $J/\psi\,+\,\mathrm{jet}$ production at an EIC

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Pith's one-line read Semi-inclusive J/psi plus jet production in electron-proton collisions at an EIC gives azimuthal asymmetries driven by gluon TMDs, with positivity-bound maxima up to roughly 60% in favorable kinematics.

desk verdict A transparent leading-order TMD phenomenology paper that derives new azimuthal moments for J/psi+jet at an EIC and uses positivity bounds correctly as ceilings; the main caveat, an unproven factorization assumption, is the authors' own. read the letter →

arxiv 1908.00446 v2 pith:6I777BCF submitted 2019-08-01 hep-ph

Umberto D'Alesio , Francesco Murgia , Cristian Pisano , Pieter Taels This is my paper · ORCID
classification hep-ph
keywords asymmetriesazimuthalgluonmathrmpolarizedunpolarizedaccessibleaddition
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

Inside every proton, quarks and gluons move sideways as well as along the beam. Transverse momentum dependent distributions (TMDs) describe that sideways motion. The gluon versions are almost unmeasured, especially the linearly polarized gluon distribution in an unpolarized proton and the gluon Sivers function in a transversely polarized proton. This paper works out a way to see them at a future Electron-Ion Collider: smash an electron into a proton, and look for an event with a J/psi meson and a jet flying out roughly back to back, with the pair carrying a small total transverse momentum.

The authors compute, at leading order in QCD and within NRQCD, the azimuthal modulations of the cross section: how the number of events depends on the angle between the pair's total momentum and the lepton plane. Quark-initiated contributions are shown to be small in the kinematic regions they choose, so the modulation is driven by gluon TMDs. They then apply two independent tools. First, positivity bounds put model-independent ceilings on how large each modulation can be, and several ceilings reach tens of percent, which is promising for a measurement. Second, in the small-x limit they use the McLerran-Venugopalan model to predict the actual qT dependence of the cos 2 phi asymmetries.

The calculation is explicitly a leading-order estimate. The paper does not include TMD evolution, Sudakov resummation, quarkonium TMD shape functions, or a proof of TMD factorization for this process. Those are named as future work. The value of the paper is that it identifies a concrete, measurable channel that could open a new window on gluon TMDs.

Extended reading notes

Core claim

The azimuthal modulations in ep -> e J/psi jet X are dominated by gluon TMDs and can reach tens of percent, up to about 60% within positivity bounds, making the process a viable probe of linearly polarized and transversely polarized gluon distributions at the EIC. This is supported by the moment formulas in Eqs. (32)-(37), the positivity-bound maxima in Eqs. (42), and the numerical estimates in Sec. V.

Load-bearing premise

TMD factorization for ep -> e J/psi jet X is assumed in Eq. (5) without a proof. The authors note in Sec. VI that it would be highly desirable to have a proof of TMD factorization for this process, but none is available. If factorization fails, the measured azimuthal moments cannot be unambiguously interpreted as gluon TMD ratios.

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Editorial analysis

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Referee Report

3 major / 4 minor

Summary. This paper studies the process e p -> e J/ψ (Υ) jet X in the TMD factorization framework combined with NRQCD at leading order. Assuming the soft scale q_T (the total transverse momentum of the J/ψ+jet pair) is much smaller than the hard scale K_⊥, the authors derive the azimuthal structure of the cross section in terms of gluon TMDs: the unpolarized f_1^g, the linearly polarized h_1^{⊥g}, and the transversely polarized TMDs f_{1T}^{⊥g}, h_{1T}^{⊥g}, h_{1T}^{g}. The unpolarized cross section is shown to be dominated by gluon-initiated subprocesses in the chosen kinematics by comparing collinear quark and gluon contributions. The authors define azimuthal moments that project onto ratios of gluon TMDs, compute model-independent upper bounds from positivity, and provide numerical estimates for J/ψ and Υ within the McLerran-Venugopalan model. The main results are the new analytic hard-scattering functions for the color-singlet channel, the reduction of the angular structure to a few TMD ratios, and the finding that the positivity-allowed asymmetries can reach tens of percent, up to about 60% in some kinematic corners.

Significance. The paper's analytic expressions are a useful addition to the TMD phenomenology toolbox; the color-singlet hard parts are given explicitly and the q_T-integrated limit reproduces the collinear result of Kniehl-Zwirner, which is a good check. The use of positivity bounds as model-independent ceilings is informative, and the MV-model estimates provide concrete predictions for the linearly-polarized-gluon asymmetries. The authors are also unusually transparent about the limitations: no factorization proof, leading order only, no Sudakov or TMD evolution, no shape functions, and large LDME dependence. If the factorization assumption is granted, the moment ratios in Eqs. (38)-(40) are particularly valuable because the dependence on LDMEs cancels. These features make the paper a worthwhile contribution to the planning of gluon TMD measurements at a future EIC, provided the central claims are appropriately conditioned.

major comments (3)
  1. [Sec. II, Eq. (5); Sec. VI] TMD factorization is assumed in Eq. (5) without proof, and Sec. VI explicitly concedes that no factorization theorem is available for this process. This assumption is load-bearing because the azimuthal moments in Sec. IV are interpreted as direct ratios of gluon TMDs. The paper should make the conditional nature of the proposal explicit in the abstract and introduction, and should expand the discussion of what is known about the soft factor for quarkonium+jet production (e.g., the analogy to pp→ηc X and the role of TMD jet functions). As written, the opening sentence of the abstract ('show how they can be probed') overstates the certainty given the admitted absence of a factorization proof.
  2. [Sec. IV A, Figs. 4-6; Sec. VI] The statement that positivity-bound maxima 'suggest the feasibility of their measurement' is not logically warranted: the bounds are ceilings that would be saturated only if the actual TMD ratios reach their maximal allowed values. The MV-model curves in Fig. 7 give real predictions for the cos2φ asymmetries, but no model estimate is presented for the Sivers-type asymmetry A^{sin(φS−φT)} or for the other transversely-polarized-proton asymmetries in Eqs. (35)-(37). The abstract and conclusions should be rephrased to say that the asymmetries are not kinematically suppressed and that dedicated model or data-driven estimates are needed to establish observability.
  3. [Sec. IV B, Sec. V, Fig. 7] The MV-model predictions are obtained by extrapolating a large-nucleus model to a proton and by fixing the saturation scale at x=10^-2 from a quark DIS fit, without modeling the x evolution of the saturation scale. The kinematics used in Fig. 7 (with √s of order 65-100 GeV, y=0.3-0.7 and K⊥=2-6 GeV) give x values of order 0.01-0.07 from Eq. (12), so the 'small-x' regime is only marginally satisfied. The paper should quote the x values for each panel and discuss the uncertainty from the nuclear-to-proton extrapolation and the absence of x dependence in Q_s. Without that, the quantitative curves in Fig. 7 are hard to interpret as small-x predictions.
minor comments (4)
  1. [Eq. (26)] The range 'for J = 1, 2, 3' should read 'for J = 0, 1, 2', since the 3P_J color-octet states in NRQCD have J = 0, 1, 2.
  2. [Fig. 7] Please add the corresponding x values (computed from Eq. (12)) and the value of √s used for each curve, so the reader can judge the validity of the small-x MV model at the chosen kinematics.
  3. [Sec. III, Eqs. (24)-(27)] The color-octet hard-scattering amplitudes are not shown, even though they drive the large upper bounds in Figs. 4-5; providing them as ancillary files (or as a Mathematica notebook) would allow independent verification of the central numerical results.
  4. [Abstract and Sec. I] The abstract refers to 'cos2φ' without definition; since the paper deals with cos2φ_T and cos2(φ_T−φ_⊥), these should be defined at first use in the introduction.
Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

No new particles, mediators, forces, or conserved quantities are introduced. The paper pulls in external fitted inputs (saturation scale, Lambda_QCD, LDME sets) and standard TMD/NRQCD assumptions; the new content is the process-level calculation and the numerical estimates built on those inputs.

free parameters (4)
  • Q_sq0^2 (quark saturation scale at x=1e-2) = 0.35 GeV^2
    Taken from the Golec-Biernat-Wusthoff fit (Ref. [46]); Q_sg0^2 = (N_c/C_F) Q_sq0^2 enters Eqs. (43)-(45) and sets the overall magnitude of the MV-model asymmetries in Fig. 7.
  • Lambda_IR (infrared cutoff) = 0.2 GeV
    Chosen by hand as Lambda_QCD in the MV integrals (Eqs. 43-45) to regulate the logarithmic divergence; it is an input to the model, not fitted to the studied process.
  • J/psi and Upsilon LDMEs from Sharma-Vitev (SV) = Table I/II values
    External NRQCD matrix elements fitted to quarkonium data; they normalize the CS and CO contributions in Eq. (24) and strongly affect the positivity-bound maxima (Fig. 4).
  • J/psi LDMEs from Chao et al. (CMSWZ) = Table I values
    Alternative external fit used to quantify the LDME dependence of the NRQCD results; the spread between SV and CMSWZ is a major uncertainty.
assumptions (5)
  • domain assumption TMD factorization holds for ep -> e J/psi jet X in the region qT << K_perp.
    The cross section is written in factorized form in Eq. (5); no factorization theorem is available, as acknowledged in Sec. VI.
  • domain assumption NRQCD factorization and v-power counting justify keeping the CS and CO channels with the LDMEs from external fits.
    Used in Eqs. (24)-(27) and Tables I/II; standard for quarkonium production but not proven for TMD observables at small qT.
  • domain assumption The positivity bounds for gluon TMDs from Refs. [1,2] are valid for the process-dependent TMDs probed here.
    Used to set the upper limits in Sec. IV A; the bounds are cited as model independent but their applicability to WW-type gauge links is assumed.
  • domain assumption The McLerran-Venugopalan model, originally for large nuclei at small x, applies to the proton at x ~ 1e-2.
    Adopted in Sec. IV B following Ref. [12]; an extrapolation used to generate the qT predictions in Fig. 7.
  • domain assumption Quark-induced subprocesses are negligible in the studied TMD region, as inferred from the collinear ratio sigma_q/sigma in Sec. V.
    The TMD cross section keeps only gluon-initiated terms; the quark contamination is checked only at collinear level.

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Pith. "Pith review of Azimuthal asymmetries in semi-inclusive $J/\psi\,+\,\mathrm{jet}$ production at an EIC." pith.science (2026). https://pith.science/paper/6I777BCF

@misc{pith2026190800446,
  author       = {Pith},
  title        = {Pith review of: Azimuthal asymmetries in semi-inclusive $J/\psi\,+\,\mathrmjet$ production at an EIC},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6I777BCF}},
  note         = {Machine review of arXiv:1908.00446}
}
abstract

We consider transverse momentum dependent gluon distributions inside both unpolarized and transversely polarized protons and show how they can be probed by looking at azimuthal modulations in $e \, p \to e \, J/\psi \, \mathrm{jet} \, X$. We find that the contribution due to quark induced subprocesses is always suppressed in the considered kinematic regions, accessible in principle at a future Electron-Ion Collider. Our model-independent estimates of the maximal values of these asymmetries allowed by positivity bounds suggest the feasibility of their measurement. In addition, by adopting the McLerran-Venugopalan model for the unpolarized and linearly polarized gluon densities, we study the behavior of the $\cos2\phi$ asymmetries in the small-$x$ limit.

Figures

Figures reproduced from arXiv: 1908.00446 by the authors.

Figure 1
Figure 1. FIG. 1: Schematic illustration of the reaction [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Azimuthal angles for the process [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Feynman diagrams representing the partonic subprocesses underlying the reaction [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Upper bounds for the absolute values of [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Upper bounds for the absolute values of [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Upper bounds for the absolute values of [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Absolute values of [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: Upper bound for the absolute values of [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]

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Forward citations

Cited by 2 Pith papers

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

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

    hep-ph 2025-09 conditional novelty 6.0 of 10

    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.

  2. Sivers Asymmetry in Photoproduction of $J/\psi$ and Jet at the EIC

    hep-ph 2019-08 conditional novelty 6.0 of 10

    Photoproduction of J/psi+jet at the EIC shows a gluon-dominated Sivers asymmetry of up to 6-8% in the models studied, making it a promising probe of the gluon Sivers function.

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