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Tensor-polarized gluon distribution \texorpdfstring{$h_{1TT}^{g}$}{h1TTg} in the deuteron: QCD evolution and Drell-Yan phenomenology

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Xiupeng Xie, Zhun Lu

High Energy Physics - Phenomenology · Submitted 17 Oct 2026 · 41 references

Pith's verdict: First model-based evolved prediction for tensor-polarized gluon PDF, but the input is fitted to unpolarized data and no lattice check.

T0 · AI review

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arXiv ID2610.24552 (version 1)
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CitationXiupeng Xie, Zhun Lu. "Tensor-polarized gluon distribution \texorpdfstring{$h_{1TT}^{g}$}{h1TTg} in the deuteron: QCD evolution and Drell-Yan phenomenology." arXiv:2610.24552 (2026). https://pith.science/paper/IZMYIODZ
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The paper

The paper claims

Evolved spectator model for deuteron tensor-polarized gluon predicts smaller Drell-Yan asymmetry with stronger Q² drop than earlier benchmark.

The reading

This paper attempts to establish that the tensor-polarized double-helicity-flip gluon distribution $h_{1TT}^g$ in the deuteron, when evolved from a spin-1 spectator model input, leads to a much smaller tensor asymmetry $A_{E_{xy}}$ in proton-deuteron Drell-Yan production than previously estimated using a longitudinally polarized gluon PDF as a proxy. The asymmetry falls rapidly with $Q^2$, dropping from about $10^{-2}$ to $10^{-4}$ over the range studied. The calculation includes model uncertainty from 100 replicas and shows that the asymmetry becomes nearly independent of $\sqrt{s}$ above about 30 GeV. A separate analysis of the longitudinal tensor-polarized distribution $f_{1LL}^g$ finds its effect on the reference cross section to be modest (5–12%).

What carries the argument

The central object is the collinear tensor-polarized double-helicity-flip gluon distribution $h_{1TT}^g(x,Q^2)$, which carries two units of helicity flip and is defined only for spin-1 targets. Its nonperturbative input at $Q_0 = 2\,\mathrm{GeV}$ is obtained by integrating the corresponding transverse-momentum-dependent distribution from a spin-1 spectator model, where the deuteron couples to an off-shell gluon and a spin-1 spectator with form factors and a continuous mass spectrum. The model parameters are fitted to the unpolarized deuteron gluon PDF (nNNPDF1.0). At leading order, $h_{1TT}^g$ evolves autonomously via the splitting function $P_{gg}^{T,(0)}(z)=2C_A[z/(1-z)]_+ + (\beta_0/2)\delta(1-z)$, with no mixing to quarks. The 100 replicas from the fit are evolved independently and propagated through the Drell-Yan convolution to obtain cross-section differences and asymmetries.

Extended reading notes

Core claim

The paper demonstrates that the QCD evolution of the spectator-model $h_{1TT}^g$ produces a tensor asymmetry $|A_{E_{xy}}|$ that decreases much more steeply with $Q^2$ than the earlier benchmark calculation (Ref. [24]) in which $\Delta_T g$ was approximated by the longitudinally polarized gluon PDF. Specifically, at $Q^2 = 50\,\mathrm{GeV}^2$ the evolved asymmetry reaches $10^{-4}$ levels, while the benchmark remains nearly constant. The reduction arises from the combined effects of phase-space shrinkage, running coupling, and the suppression of $h_{1TT}^g$ at moderate $x$ under its autonomous gluon evolution. The paper also shows that at large $\sqrt{s}$ the asymmetry stabilizes to a slowly varying plateau, whereas low $\sqrt{s}$ and high $Q^2$ probe the poorly constrained large-$x_b$ tail of the spectator model. The gluonic $f_{1LL}^g$ correction to the reference cross section is moderate (5–12%) and does not change the qualitative behavior.

Load-bearing premise

The spectator-model input for $h_{1TT}^g$ and $f_{1LL}^g$, fitted only to unpolarized deuteron gluon data (nNNPDF1.0) and lacking direct experimental constraint from tensor-polarized observables, is assumed to be reliable at momentum fractions $x_b < 0.2$, but becomes strongly suppressed and unstable for larger $x_b$ where the Drell-Yan convolution often probes.

Editorial extensions

If this is right

  • Future tensor-polarized deuteron experiments (e.g., at JLab, NICA, or LHC fixed-target) should expect a very small $|A_{E_{xy}}|$ at moderate $Q^2$, typically below $10^{-2}$ and dropping quickly with scale.
  • The asymmetry is nearly flat in $\sqrt{s}$ above about 30 GeV, making the observable robust against beam-energy uncertainties and allowing focused searches at intermediate energies.
  • The weak $Q^2$ dependence of the earlier benchmark is not reproduced by a dynamical model; an observed strong $Q^2$ drop would favor the spectator picture, while a flat trend would disfavor it.
  • The modest $f_{1LL}^g$ correction (5–12% in the reliable region) suggests that the longitudinal tensor-polarized gluon does not significantly contaminate the extraction of $h_{1TT}^g$ from the $E_x-E_y$ cross-section difference.
  • Results at low $\sqrt{s}$ (below 15 GeV) and very small $q_T$ are unreliable with fixed-order treatment; resummation or TMD factorization would be needed for quantitative predictions in those corners.

Reading between the lines

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

  • If high-precision data contradict the strong $Q^2$ drop, the spectator model's assumption that $h_{1TT}^g$ is dominated by a single effective gluon-spectator vertex would be undermined, possibly requiring additional contributions from $\Delta\Delta$, hidden-color, or mesonic components.
  • The autonomous evolution of $h_{1TT}^g$ implies that its small-$x$ rise is weaker than that of the unpolarized gluon PDF; this could be tested at a future Electron-Ion Collider through diffractive or semi-inclusive processes with tensor-polarized deuterons.
  • The 100-replica ensemble provided in this work constitutes a plausible prior for Bayesian reanalyses once experimental limits on $A_{E_{xy}}$ become available, enabling quantitative model discrimination.
  • Analogous calculations for the $f_{1LL}^g$ contribution suggest that tensor-polarized corrections to inclusive cross sections are generally small; future analyses of other tensor-polarized observables (e.g., $b_1$ structure function) may similarly benefit from evolved model inputs.
Original abstract

We study the QCD evolution of the tensor-polarized double-helicity-flip gluon distribution $h_{1TT}^g$ in the deuteron and its impact on proton-deuteron Drell-Yan production. The nonperturbative input is taken from the spin-1 spectator model and evolved at leading order with the autonomous gluon evolution equation. The uncertainty of the model fit is propagated to the tensor-polarized cross-section difference and the asymmetry $A_{E_{xy}}$ using an ensemble of 100 replicas. Compared with the earlier benchmark estimate based on a longitudinally polarized gluon distribution, the evolved spectator-model input gives smaller cross sections in most of the kinematic region and a much stronger decrease of $|A_{E_{xy}}|$ with $Q^2$. At sufficiently large center-of-mass energy, the asymmetry varies only slowly with $\sqrt{s}$, whereas the low-$\sqrt{s}$ and large-$Q^2$ regions probe the poorly constrained large-$x$ tail of the model. We also evolve the tensor-polarized gluon distribution $f_{1LL}^g$ in the coupled singlet-gluon system and assess its contribution to the reference cross-section sum. Its effect remains moderate in the kinematic region where the spectator-model prediction is under reasonable control.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-10-20: 1 request, 5,844 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.88 · human participants 0.01 · controlled comparison 0.75 · randomized assignment 0.01 · states quantitative result 0.45 · compares with prior results 0.98 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We study the QCD evolution of the tensor-polarized double-helicity-flip gluon distribution $h_{1TT}^g$ in the deuteron and its impact on proton-deuteron Drell-Yan production. The nonperturbative input is taken from the spin-1 spectator model and evolved at leading order with the autonomous gluon evolution equation. The uncertainty of the model fit is propagated to the tensor-polarized cross-section difference and the asymmetry $A_{E_{xy}}$ using an ensemble of 100 replicas. Compared with the earlier benchmark estimate based on a longitudinally polarized gluon distribution, the evolved spectator-model input gives smaller cross sections in most of the kinematic region and a much stronger decrease of $|A_{E_{xy}}|$ with $Q^2$. At sufficiently large center-of-mass energy, the asymmetry varies only slowly with $\sqrt{s}$, whereas the low-$\sqrt{s}$ and large-$Q^2$ regions probe the poorly constrained large-$x$ tail of the model. We also evolve the tensor-polarized gluon distribution $f_{1LL}^g$ in the coupled singlet-gluon system and assess its contribution to the reference cross-section sum. Its effect remains moderate in the kinematic region where the spectator-model prediction is under reasonable control.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We study the QCD evolution of the tensor-polarized double-helicity-flip gluon distribution $h_{1TT}^g$ in the deuteron and its impact on proton-deuteron Drell-Yan production. contribution 1.00 0.91 0.09 asserted 0.82
s1 The nonperturbative input is taken from the spin-1 spectator model and evolved at leading order with the autonomous gluon evolution equation. method 1.00 0.80 0.03 asserted 0.99
s2 The uncertainty of the model fit is propagated to the tensor-polarized cross-section difference and the asymmetry $A_{E_{xy}}$ using an ensemble of 100 replicas. method 1.00 0.93 0.04 asserted 0.98
s3 Compared with the earlier benchmark estimate based on a longitudinally polarized gluon distribution, the evolved spectator-model input gives smaller cross sections in most of the kinematic region and a much stronger decrease of $|A_{E_{xy}}|$ with $Q^2$. result 1.00 0.89 0.58 asserted 1.00
s4 At sufficiently large center-of-mass energy, the asymmetry varies only slowly with $\sqrt{s}$, whereas the low-$\sqrt{s}$ and large-$Q^2$ regions probe the poorly constrained large-$x$ tail of the model. interpretation 0.60 0.86 0.15 asserted 0.99
s5 We also evolve the tensor-polarized gluon distribution $f_{1LL}^g$ in the coupled singlet-gluon system and assess its contribution to the reference cross-section sum. contribution 0.84 0.93 0.04 asserted 0.96
s6 Its effect remains moderate in the kinematic region where the spectator-model prediction is under reasonable control. result 0.93 0.88 0.08 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.64 · evidence from simulation or computation 0.99.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. shows the scale dependence of the tensor￾polarized double-helicity-flip gluon distribution. Evolu￾tion redistributes the model input in x and generally suppresses its moderate- and large-x components as the scale increases. Because the evolution is autonomous, the scale dependence and replica uncertainty are deter￾mined entirely by the initial gluon distribution and the double-helicity-flip kernel. No quark input or radiatively generated quark distribution contributes to this evolu￾tion. At large x, the model distributions are strongly sup￾pressed and become more sensitive to the…
Figure 3. FIG. 3. Magnitude of the cross-section difference in the
Figure 4. FIG. 4. Magnitude of the cross-section difference in the
Figure 6. shows the magnitude of the tensor asymmetry. At the lower end of the displayed range, the present results are of order 10−2 , comparable in magnitude to the benchmark estimates, but their scale dependence is markedly different: the benchmark curves remain nearly constant, whereas the present asymmetry decreases to 10 20 30 40 50 60 70 80 10 6 10 5 10 4 10 3 10 2 10 1 Exy A qT=0.2 GeV qT=0.5 GeV qT=1.0 GeV s GeV 2 2 0 0.5 20 GeV y M FIG. 7. The tensor asymmetry |AExy | as a function of √ s for Q 2 = M2 µµ = 20 GeV2 , qT = 0.2, 0.5, and 1.0 GeV, with y = 0.5 and φ = 0. The results…
Figure 7. FIG. 7. The tensor asymmetry
Figure 8. shows the correction as a function of Q2 . At Q2 = 16 GeV2 , the representative values are approxi￾mately 5.4%, 8.5%, and 11.8% for qT = 0.2, 0.5, and 1.0 GeV, respectively. The correction decreases overall with Q2 and is systematically larger at larger qT , reflect￾ing the increasing relative importance of the deuteron￾gluon channel. 10 20 30 40 50 60 70 80 20% 10% 0% 10% 20% 1LL Rf qT=0.2 GeV qT=0.5 GeV qT=1.0 GeV s GeV 2 2 0 0.5 20 GeV y M FIG. 9. Relative f g 1LL correction to AExy as a function of √ s for Q 2 = M2 µµ = 20 GeV2 , qT = 0.2, 0.5, and 1.0 GeV, with y = 0.5 and φ =…

Showing 6 of the paper's 8 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:2610.24552 by the authors.

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