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arxiv: 2606.31124 · v1 · pith:5M5ITOS3new · submitted 2026-06-30 · ✦ hep-ph

The effect of TMD evolution on the Sivers asymmetry in back-to-back J/psi+γ and J/psi+jet production at the Electron-Ion-Collider

Arghya Jana , Asmita Mukherjee , Sangem Rajesh This is my paper

Pith reviewed 2026-07-01 05:18 UTC · model grok-4.3

classification ✦ hep-ph
keywords Sivers asymmetryTMD evolutiongluon Sivers functionJ/ψ productionElectron-Ion ColliderNRQCDback-to-back production
0
0 comments X

The pith

Sivers asymmetry in back-to-back J/ψ + photon and J/ψ + jet production at the EIC remains sizable after TMD evolution and provides a robust probe of the gluon Sivers function.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper estimates the Sivers asymmetry for back-to-back J/ψ-photon and J/ψ-jet production in electron-proton collisions at the future Electron-Ion Collider using a transverse momentum dependent factorization approach that includes TMD evolution. The calculations rely on the non-relativistic QCD model for charmonium production, where the gluon-induced channel is dominant. The results show that the asymmetry stays sizable even after accounting for evolution effects in the Collins-Soper-Sterman framework. For the jet case the asymmetry is largely independent of the choice of long-distance matrix elements, and for the photon case it is independent at leading order. These features make the asymmetry a robust probe of the gluon Sivers function.

Core claim

The Sivers asymmetry in both J/ψ + γ and J/ψ + jet back-to-back production is a robust probe of the gluon Sivers function at the EIC. It remains sizable after TMD evolution, is largely unaffected by LDME choices in the jet channel, and is independent of LDME at leading order in the photon channel.

What carries the argument

TMD factorization in the Collins-Soper-Sterman evolution approach combined with NRQCD for J/ψ production.

If this is right

  • The asymmetry provides a way to access the gluon Sivers function at the EIC.
  • The cross section for J/ψ-jet depends on LDME but the asymmetry does not.
  • The asymmetry for J/ψ-photon is independent of LDME at LO.
  • Both processes can probe the gluon Sivers function reliably even with evolution included.

Where Pith is reading between the lines

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

  • If confirmed, this would allow clean extraction of gluon Sivers from EIC data without needing precise LDME knowledge.
  • Similar robustness might apply to other quarkonium production processes at hadron colliders.
  • Future measurements could test if evolution effects suppress the asymmetry more than predicted.

Load-bearing premise

The gluon-induced channel dominates the production and the NRQCD model accurately describes J/ψ production in the relevant EIC kinematics.

What would settle it

A measurement at the EIC showing the Sivers asymmetry much smaller than the predicted size after evolution, or strong dependence on LDME choices for the photon case, would falsify the claim.

Figures

Figures reproduced from arXiv: 2606.31124 by Arghya Jana, Asmita Mukherjee, Sangem Rajesh.

Figure 1
Figure 1. Figure 1: FIG. 1: Illustration of azimuthal angles in [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Unpolarized differential cross section in [PITH_FULL_IMAGE:figures/full_fig_p020_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Unpolarized differential cross section in [PITH_FULL_IMAGE:figures/full_fig_p021_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Sivers asymmetry in [PITH_FULL_IMAGE:figures/full_fig_p023_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Sivers asymmetry in [PITH_FULL_IMAGE:figures/full_fig_p024_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Sivers asymmetry in [PITH_FULL_IMAGE:figures/full_fig_p027_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Sivers asymmetry in [PITH_FULL_IMAGE:figures/full_fig_p027_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Sivers asymmetry in [PITH_FULL_IMAGE:figures/full_fig_p028_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Sivers asymmetry in [PITH_FULL_IMAGE:figures/full_fig_p029_9.png] view at source ↗
read the original abstract

We present an estimate of the Sivers asymmetry in back-to-back $J/\psi$-photon and $J/\psi$-jet production in electron-proton collisions in the kinematics of the upcoming Electron-Ion Collider (EIC) in a transverse momentum dependent (TMD) factorization framework, and also incorporating the TMD evolution. We use the non-relativistic Quantum Chromodynamics (NRQCD) model to study the production mechanism of $J/\psi$. The gluon induced channel dominates, and these are promising probes of the less known gluon Sivers function. We incorporate the TMD evolution in the cross section and Sivers asymmetry in the Collins-Soper-Sterman (CSS) approach and show that the asymmetry is sizable even after the evolution. Although the cross section for $J/\psi$-jet production depends on the long-distance matrix element (LDME) set chosen, the asymmetry remains largely unaffected. The asymmetry is independent of the LDME at leading order for $J/\psi$-photon production. Thus, the Sivers asymmetry in both processes is a robust probe of the gluon Sivers function.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper calculates the Sivers asymmetry for back-to-back J/ψ+γ and J/ψ+jet production in ep collisions at EIC kinematics using TMD factorization with CSS evolution and NRQCD for J/ψ production. It claims gluon-induced channels dominate, the asymmetry remains sizable after TMD evolution, is independent of LDME at leading order for the photon case, and largely unaffected by LDME choice for the jet case, making both processes robust probes of the gluon Sivers function.

Significance. If the results hold, this supplies concrete EIC predictions for accessing the poorly constrained gluon Sivers function via TMD observables that incorporate evolution. The explicit demonstration of LDME independence (at LO for γ and largely for jet) and the inclusion of evolution effects are strengths that enhance the utility of these channels as probes.

major comments (2)
  1. [§3] §3 (Production mechanism and NRQCD): The central claim that 'the gluon induced channel dominates' is load-bearing for the robustness interpretation, yet the manuscript provides no explicit channel decomposition (e.g., relative fractions of gluon- vs. quark-initiated subprocesses or color-singlet vs. octet contributions) as a function of kinematics or LDME set. Without such a breakdown or a scale-variation study, the 20-30% contamination threshold raised in the stress-test note cannot be bounded, undermining the assertion that the asymmetry is a clean gluon-Sivers probe.
  2. [§4] §4 (Numerical results and asymmetry plots): The statement that the asymmetry 'remains largely unaffected' by LDME choice for J/ψ+jet and is 'independent of the LDME at leading order' for J/ψ+γ is presented without showing the full variation across multiple LDME sets (including color-octet dominated ones) or higher-order relativistic corrections relevant at moderate p_T ~ few GeV. If non-gluon channels contribute appreciably, the reported LDME independence would not hold, directly affecting the probe interpretation.
minor comments (2)
  1. [§2] The CSS evolution implementation (kernel choice, b* prescription, and non-perturbative Sudakov parameters) should be stated explicitly in §2 to allow reproduction of the 'sizable even after evolution' result.
  2. Figure captions for the asymmetry plots should include the specific LDME sets and kinematic cuts used, as well as error bands from scale variation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and indicate the revisions we plan to make.

read point-by-point responses

  1. Referee: [§3] §3 (Production mechanism and NRQCD): The central claim that 'the gluon induced channel dominates' is load-bearing for the robustness interpretation, yet the manuscript provides no explicit channel decomposition (e.g., relative fractions of gluon- vs. quark-initiated subprocesses or color-singlet vs. octet contributions) as a function of kinematics or LDME set. Without such a breakdown or a scale-variation study, the 20-30% contamination threshold raised in the stress-test note cannot be bounded, undermining the assertion that the asymmetry is a clean gluon-Sivers probe.

    Authors: We agree that an explicit channel decomposition would strengthen the presentation of the gluon-dominance claim. The manuscript is based on the standard NRQCD expectation that gluon-fusion channels dominate J/ψ production in the EIC kinematics considered, but numerical fractions were not provided. In the revised version we will add a table (or supplementary figure) showing the relative contributions of gluon- versus quark-initiated subprocesses and color-singlet versus octet channels for the default LDME set across the relevant kinematic range. We will also perform a modest scale-variation exercise to bound the possible contamination level. revision: yes

  2. Referee: [§4] §4 (Numerical results and asymmetry plots): The statement that the asymmetry 'remains largely unaffected' by LDME choice for J/ψ+jet and is 'independent of the LDME at leading order' for J/ψ+γ is presented without showing the full variation across multiple LDME sets (including color-octet dominated ones) or higher-order relativistic corrections relevant at moderate p_T ~ few GeV. If non-gluon channels contribute appreciably, the reported LDME independence would not hold, directly affecting the probe interpretation.

    Authors: We partially agree. For the J/ψ+γ process the LDME independence at leading order follows directly from NRQCD factorization: the same LDME multiplies both the unpolarized and Sivers-modulated cross sections and therefore cancels in the asymmetry ratio. For J/ψ+jet the asymmetry remains largely insensitive because the dominant gluon channel’s LDME likewise factors out. To make this more explicit we will add results for two additional LDME sets (including one with larger color-octet weight) in the revised manuscript. Higher-order relativistic corrections lie outside the scope of the present leading-order TMD+NRQCD calculation; we will add a clarifying remark to this effect. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation uses external inputs and standard frameworks

full rationale

The paper applies TMD factorization in the CSS evolution framework to the Sivers asymmetry for the specified processes, taking the gluon Sivers function from prior parametrizations and using NRQCD with stated dominance of the gluon channel. No step reduces a claimed prediction or first-principles result to a fitted parameter or self-citation by construction; the LDME independence statements and post-evolution size claims follow from explicit cross-section formulas rather than redefinition of inputs. The derivation remains self-contained against external benchmarks and does not invoke uniqueness theorems or ansatze traceable only to the authors' own prior unverified work.

Axiom & Free-Parameter Ledger

2 free parameters · 3 axioms · 0 invented entities

Abstract-only review limits visibility into exact parameters; typical TMD+NRQCD calculations rely on fitted Sivers parametrizations and LDME values chosen from other processes.

free parameters (2)
  • gluon Sivers function parameters
    The less-known gluon Sivers function must be parametrized from existing data fits to compute the asymmetry.
  • LDME sets
    Long-distance matrix elements in NRQCD; abstract states cross section depends on choice but asymmetry does not for the jet case.
axioms (3)
  • domain assumption TMD factorization holds for back-to-back kinematics at EIC
    Framework used for the cross section and asymmetry calculation.
  • domain assumption NRQCD model describes J/ψ production mechanism
    Used to study the production and identify gluon dominance.
  • domain assumption CSS evolution correctly captures TMD scale dependence
    Incorporated to show evolution effect on asymmetry.

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discussion (0)

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