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Comparing theoretical descriptions of Drell-Yan angular coefficients

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Nikita Gramotkov, Oleg Teryaev

High Energy Physics - Phenomenology · Submitted 17 Sep 2026 · 36 references

Pith's verdict: Useful quantitative comparison of three DY angular coefficient models, but the main claim for TMD superiority on A2 is weakened because the Boer-Mulders parameters were fitted to the same data—authors are transparent, but the conclusions need more careful framing.

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arXiv ID2609.20362 (version 1)
Pith IDNZIYDFCP, Pith's permanent record of this paper and its review
CitationNikita Gramotkov, Oleg Teryaev. "Comparing theoretical descriptions of Drell-Yan angular coefficients." arXiv:2609.20362 (2026). https://pith.science/paper/NZIYDFCP
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The paper

The paper claims

TMD factorization best matches low-QT Drell-Yan angular coefficients A0 and A2 among three approaches.

The reading

This paper quantitatively compares three theoretical descriptions—TMD factorization, collinear perturbative QCD (full and leading-power), and a geometrical model—of the Drell-Yan angular coefficients in Z-boson production, using experimental data from ATLAS, CMS, and LHCb. It aims to determine which approach best captures the transverse-momentum dependence of the coefficients A0 and A2, the Lam-Tung relation, and other coefficients (A1, A3, A4) in the low-QT region (QT < 10 GeV). The central finding is that TMD factorization provides the closest agreement with the measured A0 and A2 coefficients in the central rapidity region (|y|<1), as quantified by chi2 per point (1.131 for A0, 2.028 for A2), outperforming both full collinear pQCD (1.963 and 3.862) and the geometrical model (1.288 and 3.403). The differences between approaches are much smaller for A1, A3, and A4, indicating these are less sensitive to transverse-momentum dynamics. If correct, this demonstrates the importance of transverse-momentum-dependent resummation and the Boer-Mulders effect for describing the low-QT angular structure of Drell-Yan events.

What carries the argument

The central object is the TMD factorization framework, specifically the formulation in Ref. [17] that resums kinematic power corrections (KPCs) and incorporates the Boer-Mulders function h⊥1. The KPCs restore gauge and Lorentz invariance while introducing no new nonperturbative functions; the Boer-Mulders function encodes the correlation between quark transverse spin and transverse momentum. These two contributions together generate the violation of the Lam-Tung relation and the shape of A2 at very low QT. The comparison also uses the full collinear pQCD calculation up to NNLP (Ref. [24]) and the geometrical model (Ref. [14]) parametrized by acoplanarity.

Extended reading notes

Core claim

In the central rapidity region (|y|<1) and at low transverse momentum (QT < 10 GeV), the TMD factorization approach, which includes kinematic power corrections (KPCs) and the Boer-Mulders function, predicts the angular coefficients A0 and A2 with significantly smaller chi2 than either full collinear pQCD (including NNLP corrections) or the geometrical model. This advantage is attributed to the all-order resummation of large logarithms ln($Q^{2}$/$QT^{2}$) via TMD factorization and the contribution of the Boer-Mulders function, which violate the Lam-Tung relation and produce the characteristic shape of A2 at very low QT. The Lam-Tung relation itself is also well described by TMD and geometrical approaches in central and intermediate rapidity regions, while at larger rapidities the description deteriorates for both, suggesting higher-twist contributions not captured by the current parametrizations.

Load-bearing premise

The Boer-Mulders function parameters used in the TMD calculation were extracted from the same ATLAS A2 angular coefficient dataset that is used in the comparison (Section 2.2, eq. 25), so the TMD prediction for A2 is not an independent test; it is a fit to one of the datasets being compared.

Editorial extensions

If this is right

  • TMD factorization should be used for phenomenological analyses of Drell-Yan angular distributions in the low-QT regime (QT < 10 GeV) for accurate predictions of A0, A2, and the Lam-Tung relation.
  • The Lam-Tung relation is confirmed as a sensitive test of transverse-momentum dynamics; deviations observed at low QT are consistent with the Boer-Mulders effect and KPCs, not with leading-order collinear expectations.
  • For higher QT (>10 GeV), collinear pQCD becomes more appropriate, suggesting a transition region where different resummation schemes are needed.
  • The A4 coefficient, driven by electroweak couplings, is robust across all approaches, confirming that forward-backward asymmetry is not sensitive to transverse-momentum modeling and can be described by any of the three frameworks.
  • At large rapidities (|y|>2), none of the approaches describes A0 and A2 well, indicating that additional higher-twist contributions or a more refined Boer-Mulders parametrization may be needed for forward kinematics.

Reading between the lines

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

  • Because the Boer-Mulders function parameters used in the TMD calculation were extracted from the same ATLAS A2 angular coefficient dataset that is used in the comparison (Section 2.2, eq. 25), the TMD claim of superiority for A2 is partially circular; a fully independent test would require Boer-Mulders parameters from a different observable or process (e.g., semi-inclusive deep-inelastic scatterin
  • The geometrical model, despite its simplicity, captures the essential kinematic dependencies of A0 and A2 in the low-QT region nearly as well as the more complex TMD calculation (chi2 of 1.288 vs 1.131 for A0). This suggests that the dominant physical effect may be geometric acoplanarity, with the extra TMD dynamics (Boer-Mulders) mainly improving the Lam-Tung relation fit at very low QT.
  • Future experimental measurements of A0 and A2 at very low QT (below 5 GeV) with high statistics could cleanly distinguish between the TMD and geometrical models, as their predictions for the shape of A2 diverge in that region due to the Boer-Mulders peak.
Original abstract

A quantitative comparison of the predictions of three theoretical descriptions (TMD, pQCD and geometrical) of the angular coefficients in Drell-Yan Z-boson production with new experimental data on angular coefficients obtained by the ATLAS, CMS and LHCb collaborations has been performed. In the central rapidity region at low-$Q_T$, the TMD calculation provides a better description of the $A_0$ and $A_2$ coefficients among the descriptions considered. The differences between the approaches are less pronounced for $A_1$,$A_3$ and $A_4$ coefficients. The results identify $A_0$,$A_2$ and the Lam--Tung relation as the most sensitive observables at low-QT and illustrate the domains of applicability of the three descriptions.

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, 2026-09-23: 1 request, 3,741 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.29 · human participants 0.02 · controlled comparison 0.12 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.86 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

A quantitative comparison of the predictions of three theoretical descriptions (TMD, pQCD and geometrical) of the angular coefficients in Drell-Yan Z-boson production with new experimental data on angular coefficients obtained by the ATLAS, CMS and LHCb collaborations has been performed. In the central rapidity region at low-$Q_T$, the TMD calculation provides a better description of the $A_0$ and $A_2$ coefficients among the descriptions considered. The differences between the approaches are less pronounced for $A_1$,$A_3$ and $A_4$ coefficients. The results identify $A_0$,$A_2$ and the Lam--Tung relation as the most sensitive observables at low-QT and illustrate the domains of applicability of the three descriptions.

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 A quantitative comparison of the predictions of three theoretical descriptions (TMD, pQCD and geometrical) of the angular coefficients in Drell-Yan Z-boson production with new experimental data on angular coefficients obtained by the ATLAS, CMS and LHCb collaborations has been performed. contribution 0.98 0.91 0.10 asserted 0.99
s1 In the central rapidity region at low-$Q_T$, the TMD calculation provides a better description of the $A_0$ and $A_2$ coefficients among the descriptions considered. result 1.00 0.87 0.36 asserted 1.00
s2 The differences between the approaches are less pronounced for $A_1$,$A_3$ and $A_4$ coefficients. result 1.00 0.78 0.08 asserted 1.00
s3 The results identify $A_0$,$A_2$ and the Lam--Tung relation as the most sensitive observables at low-QT and illustrate the domains of applicability of the three descriptions. interpretation 0.78 0.91 0.71 asserted 1.00

What kind of paper the classifier reports this is: simulation study 0.46 · evidence from analysis of existing data 0.92.

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. FIG. 1: Collins-Soper reference frame
Figure 2. FIG. 2: Results for
Figure 3. FIG. 3: Results for
Figure 4. FIG. 4: Results for Lam-Tung relation: comparison of theoretical predictions with experimental data
Figure 5. FIG. 5: Results for
Figure 6. FIG. 6: Results for
Figure 7. FIG. 7: Results for

Figures reproduced from arXiv:2609.20362 by the authors.

References

Discussion

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