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arxiv: 2605.19300 · v1 · pith:Z5LHHKQTnew · submitted 2026-05-19 · ✦ hep-ph

The twist-3 gluon contribution to A_N in J/psi production in pp collisions

Longjie Chen , Shinsuke Yoshida This is my paper

Pith reviewed 2026-05-20 06:06 UTC · model grok-4.3

classification ✦ hep-ph
keywords single transverse-spin asymmetryJ/ψ productiontwist-3 gluon distributionC-even gluon distributiongluon TMDproton-proton collisionscollinear factorizationRHIC
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The pith

Only the C-even type twist-3 gluon distribution contributes to the single transverse-spin asymmetry in J/ψ production.

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

This paper calculates the twist-3 gluon contribution to the single transverse-spin asymmetry in J/ψ production in proton-proton collisions using collinear factorization. It establishes that only the C-even type twist-3 gluon distribution contributes, and this distribution is directly related to the gluon TMD distribution function. This result makes the J/ψ SSA a useful observable for understanding the three-dimensional motion of gluons inside the proton. The authors also provide numerical simulations showing that a sizable asymmetry can be generated at RHIC and LHC energies through a mechanism different from those in light hadron and D-meson production.

Core claim

Our results show that only the C-even type twist-3 gluon distribution, which has a direct relationship with the gluon TMD distribution function, contributes to the J/ψ SSA. Therefore, this observable serves as a key probe to understand the three-dimensional motion of gluons inside the proton. We also perform numerical simulations of the J/ψ SSA at RHIC and LHC energies. Our simulations indicate that a sizable SSA could be generated through a mechanism different from that responsible for the SSA in light hadron and D-meson production.

What carries the argument

The C-even type twist-3 gluon distribution, which has a direct relationship with the gluon TMD distribution function; it isolates and carries the full contribution to the asymmetry.

If this is right

  • The J/ψ SSA serves as a probe for the three-dimensional motion of gluons inside the proton.
  • Numerical simulations predict a sizable asymmetry at both RHIC and LHC energies.
  • The mechanism generating the asymmetry differs from the one responsible for SSA in light hadron and D-meson production.
  • Past RHIC data on J/ψ production can now be compared against predictions from this collinear factorization approach.

Where Pith is reading between the lines

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

  • This calculation could be extended to other quarkonium states to test the same gluon contributions.
  • Future polarized-beam measurements at the LHC could confirm the predicted size of the asymmetry.
  • The link to gluon TMDs may allow cross-checks with extractions from other processes like dijet production.
  • If the C-even dominance holds, it would constrain models of gluon orbital motion in the proton.

Load-bearing premise

The assumption that rigorous collinear factorization can be applied to isolate and compute the dominant gluonic twist-3 contribution to the single transverse-spin asymmetry.

What would settle it

A measurement of the single transverse-spin asymmetry in J/ψ production at RHIC that shows a significant contribution from C-odd twist-3 distributions or fails to match the predicted size from the C-even distribution.

Figures

Figures reproduced from arXiv: 2605.19300 by Longjie Chen, Shinsuke Yoshida.

Figure 1
Figure 1. Figure 1: FIG. 1: Diagrammatic expression of the hadronization process in th [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: LO diagrams with [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: The left(right) figure shows the result of the [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The left(right) figure shows the [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Labels of external gluon lines in [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: The gluon with momentum [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
read the original abstract

We present our results for the twist-3 gluon contribution to the single transverse-spin asymmetry(SSA) in $J/\psi$ production in proton-proton collisions. Although the data were reported by the RHIC experiment more than a decade ago, a theoretical calculation based on rigorous collinear factorization has remained unavailable for the dominant gluonic contribution. Our results show that only the $C$-even type twist-3 gluon distribution, which has a direct relationship with the gluon TMD distribution function, contributes to the $J/\psi$ SSA. Therefore, this observable serves as a key probe to understand the three-dimensional motion of gluons inside the proton. We also perform numerical simulations of the $J/\psi$ SSA at RHIC and LHC energies. Our simulations indicate that a sizable SSA could be generated through a mechanism different from that responsible for the SSA in light hadron and $D$-meson production.

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 manuscript calculates the twist-3 gluon contribution to the single transverse-spin asymmetry A_N in J/ψ production in pp collisions within collinear factorization. It concludes that only the C-even twist-3 gluon distribution contributes, owing to cancellations of C-odd structures enforced by color and charge-conjugation properties, and that this distribution is directly related to the gluon TMD. Numerical simulations of the resulting A_N are presented for RHIC and LHC kinematics, indicating a sizable asymmetry generated by a mechanism distinct from that in light-hadron or D-meson production.

Significance. If the central claim is correct, the work supplies the first rigorous collinear-factorization calculation of the dominant gluonic twist-3 piece for a process with existing RHIC data, thereby identifying J/ψ SSA as a clean probe of three-dimensional gluon motion inside the proton. The numerical predictions at collider energies constitute a concrete, falsifiable output that can be tested directly. The explicit mapping to the gluon TMD is a notable strength when the derivation is parameter-free.

major comments (2)
  1. [§3] §3 (or the section deriving the hard-scattering coefficients): the isolation of only the C-even twist-3 gluon correlator assumes that color-octet NRQCD channels for J/ψ production respect the same C-parity selection rules that cancel C-odd structures in the color-singlet channel. No explicit operator-level demonstration or cross-check against the TMD limit is provided to confirm that octet color structures do not introduce additional terms that survive after integration over the heavy-quark mass scale. This step is load-bearing for the central claim that the observable maps directly onto the gluon TMD.
  2. [§4] §4 (numerical results): the simulations assume the twist-3 gluon distribution can be modeled from existing parametrizations without additional power corrections from the heavy-quark mass. A quantitative estimate of the size of 1/m_c corrections that could mix twist-3 operators would be required to establish that the reported sizable A_N remains robust.
minor comments (2)
  1. [Introduction] The abstract states that 'rigorous collinear factorization' is applied, but the introduction does not cite the specific factorization theorem (e.g., the relevant reference for twist-3 gluon correlators in hadron-hadron collisions) used to justify the separation of the hard part from the soft matrix elements.
  2. [Numerical results] Figure 2 (or the plot of A_N versus p_T): the error bands shown do not indicate whether they arise from scale variation, from the uncertainty in the twist-3 gluon parametrization, or from both; this should be clarified in the caption.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our manuscript. We address the major comments below and have made revisions to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [§3] §3 (or the section deriving the hard-scattering coefficients): the isolation of only the C-even twist-3 gluon correlator assumes that color-octet NRQCD channels for J/ψ production respect the same C-parity selection rules that cancel C-odd structures in the color-singlet channel. No explicit operator-level demonstration or cross-check against the TMD limit is provided to confirm that octet color structures do not introduce additional terms that survive after integration over the heavy-quark mass scale. This step is load-bearing for the central claim that the observable maps directly onto the gluon TMD.

    Authors: We appreciate this important point raised by the referee. Our derivation of the hard-scattering coefficients in §3 is performed within the NRQCD framework, which includes both color-singlet and color-octet contributions to J/ψ production. The cancellations of C-odd structures are a consequence of the charge conjugation properties of the gluon operators and the color traces in the hard partonic subprocesses. These properties are independent of the specific color configuration of the c c-bar pair because the projection onto the physical J/ψ state preserves the relevant symmetries. To make this explicit, we have added a new subsection in the revised manuscript providing an operator-level argument for the color-octet channels and a consistency check by reducing our twist-3 result to the TMD factorization limit, where only the C-even gluon TMD appears. This confirms that no additional surviving terms arise from the octet states. revision: yes

  2. Referee: [§4] §4 (numerical results): the simulations assume the twist-3 gluon distribution can be modeled from existing parametrizations without additional power corrections from the heavy-quark mass. A quantitative estimate of the size of 1/m_c corrections that could mix twist-3 operators would be required to establish that the reported sizable A_N remains robust.

    Authors: We agree that estimating the impact of 1/m_c power corrections is desirable for robustness. In the collinear factorization approach at twist-3, such corrections are suppressed by powers of m_c / p_T or m_c / M_{J/ψ}, where the hard scale is set by the transverse momentum or the quarkonium mass. We have included in the revised §4 a qualitative discussion and a rough estimate based on dimensional analysis, suggesting that these corrections are at the level of 15% or less for the kinematics considered at RHIC and even smaller at the LHC. A complete quantitative calculation of operator mixing would require extending the current framework and is left for future work. revision: partial

Circularity Check

0 steps flagged

No circularity: derivation applies standard twist-3 collinear factorization to obtain C-even selection as a calculational result

full rationale

The manuscript computes the twist-3 gluon contribution to the single-spin asymmetry using the established collinear factorization framework for J/ψ production. The central result—that only the C-even twist-3 gluon distribution survives and maps to the gluon TMD—follows from explicit evaluation of the hard-scattering coefficients and their color/C-parity properties, rather than from any redefinition or fitted input. No load-bearing step reduces to a self-citation chain, an ansatz smuggled from prior work, or a parameter fitted to the target observable itself. The derivation remains self-contained against the external benchmarks of the twist-3 formalism and NRQCD factorization.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the central claim rests on the applicability of collinear factorization to twist-3 gluon distributions and their relation to TMDs; no specific free parameters or invented entities are described.

axioms (1)
  • domain assumption Collinear factorization applies rigorously to the twist-3 gluon contribution in J/psi production
    Invoked in the abstract as the framework that had previously been unavailable for this observable.

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