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REVIEW 3 major objections 3 minor 69 references

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

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

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Pith's one-line read Almost back-to-back $J/\psi$-jet photoproduction at the EIC is argued to give a gluon-dominated Sivers asymmetry of a few percent, making the channel a practical probe of the gluon Sivers function.

desk verdict A transparent, useful pheno estimate of a few-percent gluon Sivers asymmetry for J/psi+jet at the EIC, with a real caveat about the unspecified f/d mixture in color-octet channels. read the letter →

arxiv 1908.03698 v2 pith:RJBY3JSV submitted 2019-08-10 hep-ph

Raj Kishore , Asmita Mukherjee , Sangem Rajesh This is my paper · ORCID
classification hep-ph
keywords SiversasymmetrygluonfunctiontransversemomentumdependentdistributionsJ/psiphotoproductionelectron-ioncolliderNRQCDTMDevolutionback-to-backjets
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 argues that photoproduction of a nearly back-to-back $J/\psi$-jet pair at the future Electron-Ion Collider (EIC) provides a clean, gluon-dominated window into the gluon Sivers function, the transverse-momentum-dependent distribution describing how gluons are distributed asymmetrically inside a transversely polarized proton. The authors calculate the $\sin\phi_q$-weighted single-spin asymmetry $A_N^{\sin(\phi_q)}$ for $ep^\uparrow \to J/\psi+\mathrm{jet}+X$ using the generalized parton model (GPM), which keeps the initial parton's intrinsic transverse momentum in the hard scattering, together with NRQCD for the quarkonium production rate. They include both color-singlet and color-octet mechanisms and find a few-percent asymmetry: about 3%, 1%, and 6% at $\sqrt{s}=45$ GeV for three DGLAP-evolved gluon Sivers fits, and up to 8% in an exploratory TMD-evolved parametrization, while quark-initiated contributions are negligible. If this holds, the EIC could determine the gluon Sivers function in a kinematic region where the $J/\psi$ does not have to be forward, complementing existing probes.

What carries the argument

The central object is the weighted Sivers asymmetry $A_N^{\sin(\phi_q)}$, the ratio of the $\sin\phi_q$-modulated difference of cross sections for transversely polarized protons to the unpolarized cross section, where $\phi_q$ is the azimuthal angle of the total transverse momentum $q_\perp=P_{\Psi\perp}+P_{j\perp}$ of the $J/\psi$-jet pair. The argument is carried by the generalized parton model, which assumes TMD factorization and retains the initial parton transverse momentum in the hard-scattering amplitudes, applied to the subprocesses $\gamma g \to J/\psi g$ and $\gamma q \to J/\psi q$. Quarkonium production is treated with NRQCD, with color-singlet $^3S_1^{(1)}$ and color-octet $^3S_1^{(8)}$, $^1S_0^{(8)}$, $^3P_J^{(8)}$ channels; the gluon Sivers function enters through a Gaussian model whose $x$-dependent normalization is fixed by available fits (DGLAP) or by averaging the known quark Sivers normalizations (TMD-a/TMD-b). The TMD-evolution treatment adds standard $b_\perp$-space evolution with a $b_*$ prescription and nonperturbative Gaussian factors, and this difference in treatment is what produces the sign and size differences between the two schemes.

What would settle it

A measurement of the $\sin\phi_q$-weighted asymmetry in $e p^\uparrow \to J/\psi+\mathrm{jet}+X$ at the EIC at $\sqrt{s}=45$ GeV with $K_\perp=3$ GeV, $z=0.3$, and $0<q_\perp<1$ GeV would settle the claim: the prediction is a positive few-percent gluon-dominated asymmetry under DGLAP evolution and a negative few-percent asymmetry under the exploratory TMD evolution, with quark-initiated contributions suppressed. Observing a very different size, sign, or $q_\perp$ dependence, or a significant quark contribution, would falsify the proposed interpretation.

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Extended reading notes

Core claim

The central claim is that the back-to-back $J/\psi+\mathrm{jet}$ photoproduction channel at the EIC is a viable gluon Sivers probe because the asymmetry is both sizable and gluon-dominated. For $K_\perp=3$ GeV, $z=0.3$, and $0<q_\perp<1$ GeV, the weighted asymmetry reaches roughly 3%, 1%, and 6% at $\sqrt{s}=45$ GeV for the SIDIS1, SIDIS2, and SIDIS3 DGLAP-evolved gluon Sivers parametrizations, drops to about 2% at $\sqrt{s}=100$ GeV, and reaches up to 8% (4% at $\sqrt{s}=100$ GeV) in the TMD-evolved TMD-b scheme with a negative sign. The largest contributions come from the $^3S_1^{(1)}$ color-singlet and $^1S_0^{(8)}$ color-octet NRQCD states, and the result is insensitive to which published long-distance matrix-element set is used. The paper also reports that the sign of the asymmetry flips from positive to negative when TMD evolution is applied, a feature it attributes to the different gluon Sivers parametrizations used in the two schemes.

Load-bearing premise

The load-bearing premise is that a factorization scheme in which the initial parton's transverse momentum is kept in the hard scattering, called the generalized parton model here, is valid for heavy-quarkonium-plus-jet photoproduction; the paper states this assumption but does not prove it, and it does not specify which gluon Sivers component enters the color-octet diagrams.

Editorial extensions

If this is right

  • If the central claim is right, the EIC can measure the gluon Sivers function through $J/\psi+\mathrm{jet}$ photoproduction without requiring the $J/\psi$ to be produced in the forward region.
  • Quark- and antiquark-initiated subprocesses contribute negligibly in the considered kinematics, so the measured asymmetry can be interpreted as essentially a gluon Sivers signal.
  • Both $^3S_1^{(1)}$ and $^1S_0^{(8)}$ NRQCD channels must be kept; their combined contribution, and the insensitivity to the long-distance matrix-element set, make the prediction stable across model choices.
  • The sign of the asymmetry distinguishes the evolution treatments: positive and a few percent under DGLAP-evolved fits, negative and up to about 8% under the exploratory TMD-evolved parametrization.
  • Higher $K_\perp$ or larger $z$ suppresses the gluon channel because the parton momentum fraction grows quadratically with $K_\perp$, so the optimal measurement region is $K_\perp\sim M_{J/\psi}$ and $z\sim0.3$.

Reading between the lines

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

  • Because the sign flip between DGLAP and TMD-evolved treatments is driven by the unknown gluon Sivers parametrization rather than by the hard scattering itself, a precise measurement of both sign and $q_\perp$ shape could discriminate between evolution schemes and constrain nonperturbative TMD parameters.
  • A dedicated gluon Sivers fit using this channel, rather than rescaling quark Sivers parameters, could test the transverse-momentum sum rule with gluon data: the TMD-a proxy satisfies the sum rule to about 1%, while TMD-b violates it by about 19%.
  • The numerical estimates omit resolved-photon contributions, $\psi(2S)$ feed-down (about 15%), and $\chi_c$ decays (about 1%); a full experimental analysis would likely need these corrections to reach the few-percent precision claimed.
  • The paper leaves open which combination of f-type and d-type gluon Sivers functions enters the color-octet diagrams; disentangling these process-dependent components is a natural follow-up.
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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 / 3 minor

Summary. The manuscript calculates the transverse-spin (Sivers) asymmetry for the quasi-real photoproduction process e p^↑ → J/ψ + jet + X at the future Electron-Ion Collider, using the generalized parton model (GPM) together with NRQCD for the J/ψ production mechanism. Color-singlet and color-octet intermediate states (3S1^1, 3S1^8, 1S0^8, 3P_J^8) are included, with matrix elements taken from the authors' earlier gluon-channel paper and from new quark-channel expressions in Appendix B. The asymmetry is evaluated both with DGLAP-evolved Sivers parametrizations (SIDIS1, SIDIS2, SIDIS3) and with an exploratory TMD-evolution scheme in which the gluon Sivers function is built from u/d quark Sivers parameters. The authors find a gluon-dominated asymmetry of a few percent for DGLAP sets, up to about 6% at √s=45 GeV, and up to about 8% in the TMD-evolved TMD-b scheme. They conclude that almost back-to-back J/ψ+jet photoproduction is a promising probe of the gluon Sivers function.

Significance. The observable is well motivated and complementary to existing and proposed gluon-Sivers probes: the additional jet makes the kinematics more differential and avoids restricting J/ψ to the forward region. The manuscript provides explicit analytic matrix elements, a clear tabulation of input parameters, and a maximized-asymmetry study that isolates the role of each NRQCD channel. If the calculation were fully justified, the predicted asymmetry of several percent would be a useful benchmark for EIC planning. The main caveats are that the prediction rests on TMD factorization in the GPM for color-octet quarkonium production, which is not proven for this process, and that the color (f-type versus d-type) process dependence of the gluon Sivers function is not implemented for the color-octet channels that are shown to be numerically important.

major comments (3)
  1. [Section II, Eq. (9) and Fig. 2] The paper introduces in Section I the fact that the gluon Sivers function for any process is generally a combination of two independent color structures, conventionally called f-type and d-type, but the calculation in Eq. (9) inserts the same ΔN f_{g/p↑}(x_g,q⊥) for every partonic channel. This is not a harmless simplification for the NRQCD color-octet channels 3S1^8, 1S0^8, and 3P_J^8, whose amplitudes in Appendix B and Ref. [29] involve color-octet operators; the relevant gluon Sivers function for such channels is generally a process-dependent linear combination of f- and d-type functions, and that combination is never identified. Since Fig. 2 shows that the 1S0^8 channel is one of the two dominant contributions, the quoted few-percent asymmetries are not actually predictions for the f-type Sivers function unless the f/d combination is specified and modeled. The sign and magnitude of the color-octet contributions could shift, and this directly affects the central claim that the process is a clean probe of the gluon Sivers function.
  2. [Section III, Eqs. (28) and Fig. 4] The TMD-evolved results do not use a gluon Sivers function extracted from gluon-sensitive data. Instead, Eqs. (28) construct a gluon Sivers function from u/d quark parameters via Ng=(Nu+Nd)/2 (TMD-a) or Ng=Nd (TMD-b), and the text notes that the TMD-b choice violates the Burkardt sum rule by about 19%. The up-to-8% negative asymmetry in Fig. 4 and the statement in the Conclusion that the asymmetry becomes negative when TMD evolution is incorporated are therefore driven by an exploratory, quark-inspired model rather than by a quantitative gluon fit. This is an interesting illustration, but the manuscript should label the TMD-evolved numbers as model estimates in the abstract and conclusion, and should not present the sign flip as a robust prediction.
  3. [Section II, after Eq. (2) and Section IV] The calculation assumes TMD factorization in the GPM, as the authors state explicitly after Eq. (2), but no factorization proof is given for ep → J/ψ + jet + X with NRQCD color-octet contributions, and Ref. [39] is cited only for the status in pp collisions. Since the entire numerical estimate and the conclusion that the process can determine the gluon Sivers function rely on this assumption, the manuscript should include a critical discussion of its range of validity for the color-octet channels in the q⊥ ≪ K⊥ kinematics. If the GPM is intended as a phenomenological model rather than a proven factorization, this should be stated more prominently, and the consequences for the interpretation of the asymmetry should be assessed.
minor comments (3)
  1. [Throughout] There are several typographical errors that should be corrected, including 'inreaction' in Section II, 'avavilable' and 'wthin' in Section III, and the axis labels in Figs. 2–4 that are rendered as 'q¦ HGeVL' and 'AN sin IfqM'.
  2. [Section II] The sentence following Eq. (2) that introduces the Weizsäcker-Williams distribution states Qmax² = 1 GeV², but it is not explained how this choice interacts with the quasi-real photon condition Q² ≈ 0; a brief justification would improve clarity.
  3. [Section IV] The text says the range 0 ≤ q⊥ ≤ 1 GeV is considered to satisfy |q⊥| ≪ |K⊥| for K⊥ = 3 GeV; since the ratio reaches 1/3, the authors should either justify that this is sufficiently small for the back-to-back approximation or restrict the plotted range further.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the asymmetry is a model convolution of externally fitted Sivers functions with fixed NRQCD hard matrix elements.

full rationale

The derivation chain is self-contained as a phenomenological estimate. The Sivers asymmetry is built from Eqs. (2)-(10) and (12)-(17) as a convolution of independently fitted TMD inputs (gluon Sivers functions from Refs. [7,8] fitted to RHIC data, quark Sivers functions from Ref. [13] fitted to SIDIS data) with NRQCD hard-scattering amplitudes, evaluated at fixed EIC kinematics. Nothing in the calculation is fitted to the J/psi+jet asymmetry itself, and the numerator and denominator share the same parametrizations, so the reported few-percent asymmetries are not forced by construction. The only author-overlapping input is Ref. [29], cited for the gamma g -> J/psi g matrix elements; those are fixed perturbative NRQCD amplitudes, not outputs of the present paper, and the paper does not invoke any uniqueness theorem or fitted parameter to make its central prediction. The paper explicitly flags its limitations in Section II ('We have assumed TMD factorization in the GPM model') and Section III ('as so far a fit for the gluon Sivers function is not available in the TMD evolution approach... we use an exploratory approach'), but these are caveats about model validity rather than circular reductions. No quoted equation reduces to its own input by definition, so the appropriate finding is no significant circularity.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The prediction depends on a set of Sivers function parameters fitted to SIDIS/RHIC data (Table I), on the assumed validity of TMD factorization for this NRQCD process, and on nonperturbative evolution parameters taken from Ref. [13]. No new entities are invented, but the gluon Sivers function in the TMD-evolved case is constructed from quark Sivers functions, which is a working assumption, not a fit.

free parameters (6)
  • Na (gluon Sivers normalization) = 0.65 (SIDIS1), 0.05 (SIDIS2), 0.25 (SIDIS3)
    Normalization of the gluon Sivers function in Eq. (12), from DGLAP-evolution fits in Refs. [7,8].
  • Sivers x-shape parameters alpha, beta = alpha=2.8,0.8,0.6; beta=2.8,1.4,0.6
    Shape parameters in Eq. (13) from the same fits.
  • Sivers Gaussian width parameter rho = 0.687, 0.576, 0.1
    Parameter in Eq. (15) controlling the q_T dependence of the Sivers function.
  • Unpolarized TMD width <q_T^2> = 0.25 GeV^2 (SIDIS1/2), 1.0 GeV^2 (SIDIS3)
    Gaussian width in Eq. (17) used in the denominator of the DGLAP-evolved asymmetry.
  • TMD evolution nonperturbative parameters = g2=0.16 GeV^2, bmax=1.5 GeV^-1, Q0=sqrt(2.4) GeV, <p_s^2>=0.282 GeV^2
    Parameters of the RNP factor in Eq. (22), taken from Ref. [13].
  • TMD-a/TMD-b gluon Sivers construction = Nu=0.106, Nd=-0.163, alpha, beta, rho=0.38
    Exploratory GSF built from u/d quark Sivers fits via Eq. (28), used for the TMD-evolved asymmetry.
assumptions (5)
  • domain assumption TMD factorization (GPM) is valid for ep -> J/psi + jet photoproduction with NRQCD color octet contributions.
    Stated as an assumption in Sec. II after Eq. (2). TMD factorization has not been proved for heavy quarkonium production (see Ref. [39]).
  • domain assumption NRQCD factorization applies and the LDMEs of Ref. [64] are reliable.
    The hard scattering amplitudes are computed in NRQCD; LDMEs are taken from literature fits.
  • domain assumption The gluon Sivers function entering the asymmetry is the f-type distribution as parametrized in Refs. [7,8]; the d-type component is ignored.
    The introduction mentions f- and d-type gluon Sivers functions (Refs. [25,26]) but the calculation uses one parametrization without specifying the process-dependent combination.
  • domain assumption The Weizsacker-Williams equivalent photon approximation describes the quasi-real photon flux.
    The photon distribution of the electron, Eq. (3), is a standard QED approximation.
  • domain assumption Resolved photon, feed-down, and fragmentation contributions can be neglected in the chosen kinematics.
    Section IV states direct inelastic photoproduction region 0.3<z<0.9 and neglects resolved contributions and feed-down from psi(2S) and chi_c decays.

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Pith. "Pith review of Sivers Asymmetry in Photoproduction of $J/\psi$ and Jet at the EIC." pith.science (2026). https://pith.science/paper/RJBY3JSV

@misc{pith2026190803698,
  author       = {Pith},
  title        = {Pith review of: Sivers Asymmetry in Photoproduction of $J/\psi$ and Jet at the EIC},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RJBY3JSV}},
  note         = {Machine review of arXiv:1908.03698}
}
abstract

We calculate the Sivers asymmetry in the photoproduction of almost back-to-back $J/\psi$-jet pair in the process $ep^\uparrow \to J/\psi+\mathrm{jet}+X$, which will be possible at the future planned electron-ion collider (EIC). We use the framework of generalized parton model (GPM), and NRQCD for calculating the $J/\psi$ production rate. We include contributions from both color singlet and color octate states in the asymmetry. We obtain sizable Sivers asymmetry that can be promising to determine the gluon Sivers function. We also investigate the effect of TMD evolution on the asymmetry.

Figures

Figures reproduced from arXiv: 1908.03698 by the authors.

Figure 1
Figure 1. FIG. 1: Illustration of azimuthal angles in the [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: (color online) Maximized Sivers asymmetry in [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: (color online) The weighted Sivers asymmetry in [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4: (color online) The weighted Sivers asymmetry in [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

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Reviewed August 14, 2026 · model on record in the stance chip above.