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Double quarkonium production mirrors Drell-Yan azimuthal structure

2026-07-09 14:26 UTC pith:ME7O7QZK

load-bearing objection Clean analytical result on double-quarkonium TMD structure; phenomenological claims need more support at LHC energies the 2 major comments →

arxiv 2607.07312 v1 pith:ME7O7QZK submitted 2026-07-08 hep-ph hep-exnucl-th

Double quarkonium production in hadronic collisions at fixed-target experiments

Carlo Flore , Cristian Pisano This is my paper
classification hep-ph hep-exnucl-th PACS 12.38.Bx13.85.Ni13.88.+e
keywords experimentsfixed-targetcollisionscrossdoublehadronicproductionquarkonium
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 paper establishes that the quark-antiquark annihilation channel for double quarkonium production—producing pairs of heavy quark-antiquark bound states like J/ψ pairs—shares the same azimuthal modulations and TMD convolution structure as the Drell-Yan process. This structural equivalence arises because when both quarkonium pairs are produced in a color-singlet state, only initial-state interactions occur, giving the process a color-flow identical to Drell-Yan. The authors derive the full angular structure of the cross section analytically, showing that only two hard factors govern all structure functions, and that the azimuthal modulations match those of Drell-Yan exactly. They then provide concrete phenomenological predictions: at COMPASS energies (√s ≈ 19 GeV), a sizable Sivers asymmetry of 10–15% is expected, driven by the valence region of the pion-proton system, while at LHC fixed-target energies (√s ≈ 70–115 GeV), the asymmetry becomes small and negative (1–2%) due to competing flavor contributions, making the process a sensitive probe of the gluon Sivers function.

Core claim

The central result is the exact correspondence between the q̄q-induced double quarkonium channel and Drell-Yan: both processes factorize into the same set of TMD convolutions and exhibit identical azimuthal modulations. This means double quarkonium production at fixed-target energies can serve as a direct probe of quark TMDs—particularly the Sivers function—in a kinematic regime complementary to semi-inclusive deep inelastic scattering and Drell-Yan. The paper predicts a 10–15% Sivers asymmetry at COMPASS and 1–2% at LHC fixed-target energies, with the sign flip between the two regimes tracing back to the different flavor compositions of pion versus proton beams.

What carries the argument

The argument rests on three components: (1) the Color-Singlet Model, in which both quark-antiquark pairs are produced directly in a colorless state, suppressing color-octet contributions by O(v³) and ensuring only initial-state interactions; (2) TMD factorization, which separates the cross section into hard perturbative parts and soft TMD correlators encoding the three-dimensional momentum structure of partons inside hadrons; and (3) the analytical proof that only two independent hard factors appear and that all azimuthal modulations and TMD convolutions are identical to those of the Drell-Yan process at leading order.

Load-bearing premise

The analysis assumes that single-parton scattering dominates and that color-octet contributions are suppressed as predicted by NRQCD velocity scaling, with the authors checking that the color-singlet to color-octet background ratio is at most about 10%. If double-parton scattering or color-octet mechanisms are larger than estimated—particularly at LHC energies—the predicted asymmetries would be diluted or altered.

What would settle it

Measurement of a Sivers asymmetry at COMPASS that is either vanishingly small or opposite in sign to the predicted 10–15% would challenge either the Color-Singlet Model description, the assumed Sivers sign change, or the TMD parametrizations used. At LHC energies, an asymmetry significantly exceeding 2% in magnitude would indicate that gluon Sivers contributions or color-octet mechanisms are larger than assumed.

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

If this is right

  • If the predicted 10–15% Sivers asymmetry at COMPASS is confirmed by data, it would validate both the Color-Singlet Model description of double quarkonium production and the assumed sign change of the Sivers function between SIDIS and Drell-Yan-like processes.
  • A measured asymmetry at LHC fixed-target energies significantly larger than the predicted 1–2% would indicate a nonzero gluon Sivers function, constraining a quantity that is currently poorly determined.
  • The structural equivalence to Drell-Yan means double quarkonium production can serve as an independent cross-check on TMD extractions, with different flavor sensitivities due to the quark-antiquark initial state.
  • The di-Υ channel at LHC fixed-target energies could constrain unpolarized TMDs in the large-x region of the proton, where current data is sparse.

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

2 major / 6 minor

Summary. This proceedings contribution summarizes the authors' study (Ref. [11]) of double quarkonium production in the quark-antiquark annihilation channel at fixed-target energies, within TMD factorization and the Color-Singlet Model. The paper presents analytical expressions for the azimuthal structure of the cross section, finding that the modulations and TMD convolutions match those of the Drell-Yan process. Phenomenological predictions are given for the unpolarized cross section and Sivers asymmetries at COMPASS/AMBER and LHC fixed-target experiments (SMOG2, LHCspin). At COMPASS energies, a sizable Sivers asymmetry of 10–15% is predicted, while at LHC fixed-target energies small negative asymmetries (1–2%) are expected. The comparison with the ~25-event COMPASS data is described as 'fairly good.'

Significance. The correspondence between the q-qbar-induced double quarkonium channel and Drell-Yan modulations is a non-trivial and useful analytical result, providing a new complementary probe of quark TMDs. The Sivers sign-change test (assuming the DY sign relative to SIDIS) is a falsifiable prediction. The predictions for multiple fixed-target programs (COMPASS, AMBER, SMOG2, LHCspin) across three quarkonium species are timely. The analytical derivation is verified against the independent result of Kartvelishvili and Esakiya (Ref. [15]), which is a valuable consistency check. As a proceedings contribution, the level of detail is appropriate for summarizing Ref. [11].

major comments (2)
  1. §3, paragraph on HELAC-Onia check: The statement that 'the CS-CO background is at most ~10% of the CS-CS channel' is a load-bearing assumption for the applicability of TMD factorization and the DY-like color-flow argument, but it is presented without specifying the energy, kinematic configuration, or systematic uncertainty of the check. This matters most at LHC fixed-target energies (sqrt(s) ~ 115 GeV), where the gg channel is stated to be 'about a factor of two larger' than the q-qbar channel. If the HELAC-Onia check was performed primarily at COMPASS energies or for the q-qbar channel, its relevance to the gg-dominated regime is unclear. Furthermore, if CO contributions involve non-trivial color flow with final-state interactions, the correspondence with Drell-Yan encoded in Eq. (4) and Eq. (6) could weaken. The authors should clarify the scope of this check and note whether the bound,
  2. §3, Fig. 2 (top): At sqrt(s) ~ 115 GeV, the gluon fusion channel is 'about a factor of two larger' than the q-qbar channel, yet the predictions shown are labeled 'q-qbar -> J/psi J/psi X' and the Sivers asymmetries in Fig. 2 (bottom) are computed for the q-qbar channel only. The text states that 'a larger measured asymmetry would therefore signal a nonzero gluon Sivers function,' but it is not quantified how the gg channel dilutes the predicted q-qbar asymmetries (1–2%) when both are measured together. Since the gg channel dominates at the highest energies, the observable asymmetry could be significantly smaller than the 1–2% quoted. A brief statement on the expected dilution factor, or at minimum an explicit caveat that the plotted asymmetries are channel-specific and the observable asymmetry requires weighting by the relative cross sections, would strengthen the phenomenological claims
minor comments (6)
  1. §2, Eq. (4): The prefactor 131072/243 appears without derivation or reference to where it comes from. A pointer to the corresponding expression in Ref. [11] would help the reader.
  2. §3, Fig. 1 caption: The figure label uses '□' (a box character) where a multiplication sign or arrow is intended (e.g., 'π□p' and 'φT □φS'). This appears to be a rendering issue but should be corrected for clarity.
  3. §3, Fig. 2: The same box-character rendering issue appears in the axis labels and titles ('q ¯q → J/ψ J/ψ X', 'Asin(φT □φS)').
  4. §3: The choice |R_Q(0)|^2 = 1.0 GeV^3 is stated to come from 'a power-law potential' but no reference is given. A citation would be appropriate.
  5. §3: The MAPTMDPion22 set is cited as 'private communication' (Ref. [20], L. Rossi, 2025). For reproducibility, it would be helpful to note whether this set is publicly available or forthcoming.
  6. §3: The hard scale is taken as Q = M_QQ. A brief comment on the expected size of NLL vs. NLO corrections at this scale would provide context for the 'fairly good' agreement with COMPASS data.

Circularity Check

0 steps flagged

No significant circularity; central analytical result independently verified against external Ref. [15], predictions use external TMD parametrizations

full rationale

The paper's central analytical claim—that the azimuthal modulations and TMD convolutions for the qq̄→QQ̄ channel match those of the Drell-Yan process (Eq. 4, Eq. 6)—is verified against the independent external result of Kartvelishvili and Esakiya (Ref. [15], 1983) for the unpolarized cross section: 'The corresponding unpolarized cross section, integrated over the azimuthal angles, agrees with the one obtained in Ref. [15].' The scattering amplitude is computed in Ref. [11] (same authors), but this is a proceedings contribution summarizing that work, and the amplitude calculation is a standard perturbative QCD computation, not a result defined in terms of its own outputs. The phenomenological predictions (Sivers asymmetries of 10-15% at COMPASS, 1-2% at LHC) use externally fitted TMD parametrizations (MAP22, PV17, PV20) from independent groups, and the Sivers sign change is assumed from a well-established QCD prediction, not from the authors' own prior work. The CS-CO suppression check via HELAC-Onia is an independent numerical verification using an external tool. No step in the derivation chain reduces to its own inputs by construction. The self-citation to Ref. [11] is for the detailed amplitude computation and full derivation, which is standard practice for a proceedings summary; it is not load-bearing in a circular sense because the key result is independently checked against Ref. [15].

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 0 invented entities

The paper introduces no new particles, forces, or entities. The free parameters are standard quarkonium radial wave functions taken from potential models. The axioms are standard domain assumptions in TMD physics: TMD factorization, CSM adequacy, Sivers sign change, and SPS dominance. No ad-hoc parameters are introduced to make the derivation work.

free parameters (3)
  • |R_Q(0)|^2 for J/psi = 1.0 GeV^3
    Radial wave function at the origin, taken from a power-law potential model. Used to normalize the cross section.
  • |R_psi(2S)(0)|^2 = 0.56 GeV^3
    Radial wave function for psi(2S), used in predictions for di-psi(2S) production.
  • |R_Upsilon(0)|^2 = 4.59 GeV^3
    Radial wave function for Upsilon, used in predictions for di-Upsilon production.
axioms (4)
  • domain assumption TMD factorization holds for double quarkonium production in the kinematic regime considered.
    Invoked in Eq. (2) to factorize the cross section into hard parts and TMD convolutions. Justified by the color-singlet nature of the final state and the analogy to Drell-Yan, but not proven.
  • domain assumption Color-Singlet Model is adequate, with color-octet contributions suppressed by O(v^3).
    Stated in the Introduction and used throughout. The authors check that CS-CO background is at most ~10% using HELAC-Onia, but this is an approximation.
  • domain assumption Sivers sign change w.r.t. SIDIS holds for this process.
    Stated in Section 2: 'as in the DY case, we assume the Sivers sign change w.r.t. SIDIS.' This is a well-known QCD prediction but is assumed, not derived here.
  • domain assumption Single-parton scattering dominates over double-parton scattering.
    Stated in Section 3: 'single-parton scattering is assumed to dominate.' At COMPASS energies, DPS is checked to be at most 8% [9], but at LHC energies this is not explicitly verified.

pith-pipeline@v1.1.0-glm · 11807 in / 2959 out tokens · 392654 ms · 2026-07-09T14:26:02.126936+00:00 · methodology

0 comments
read the original abstract

We present new results for double quarkonium production in (un)polarized hadronic collisions at fixed-target experiments. Our approach incorporates the transverse momentum dependent factorization in combination with the Color-Singlet Model. We present new analytical expressions for the angular structure of the cross section for the $q\bar q$-induced channel, and provide predictions for the unpolarized cross section and transverse single-spin asymmetries for present and future fixed-target experiments at CERN and the LHC.

Figures

Figures reproduced from arXiv: 2607.07312 by Carlo Flore, Cristian Pisano.

Figure 1
Figure 1. Figure 1: Left: comparison with COMPASS data [9] of the unpolarized cross section for di-𝐽/𝜓 production in 𝜋 − 𝑝 scattering, as a function of the transverse momentum of the 𝐽/𝜓-pair, 𝑞𝑇, at √ 𝑠 = 18.9 GeV. Right: prediction for the Sivers asymmetry 𝐴 sin(𝜙𝑇 −𝜙𝑆 ) 𝑈𝑇 in 𝜋 − 𝑝 ↑ collisions at the same energy, assuming the Sivers sign change and adopting the same 𝑞𝑇-binning as for the unpolarized cross section. and 𝑝: … view at source ↗
Figure 2
Figure 2. Figure 2: Predictions for double quarkonium production (di-𝐽/𝜓, di-𝜓(2𝑆) and di-Υ) at the LHC fixed￾target experiments, for different values of √ 𝑠 and in different 𝑌Q Q, 𝑧 and 𝑀Q Q ranges. Top: quark-induced unpolarized cross section based on the MAP22 TMDs. Bottom: quark-induced Sivers asymmetry, assuming the Sivers sign change w.r.t. SIDIS. References [1] F. Halzen, Cvc for Gluons and Hadroproduction of Quark Fla… view at source ↗

discussion (0)

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