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Coarse-grained binning in Drell-Yan transverse momentum spectra

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The intrinsic sideways motion of quarks can be read from a two-bin ratio of Drell-Yan dilepton momenta, with sensitivity matching the full fine-binned spectrum.

desk verdict A genuinely new two-bin pT-ratio observable for intrinsic-kT extraction, cleanly tested on pseudo-data and CMS data, but the headline systematics advantage rests on a toy detector model and needs a harder look. read the letter →

arxiv 2412.19060 v1 pith:GJWDPB42 submitted 2024-12-26 hep-ph

Wenxiao Zhan , Siqi Yang , Minghui Liu , Francesco Hautmann , Liang Han This is my paper · ORCID
classification hep-ph
keywords intrinsictransversemomentumDrell-YanproductiondileptonTMDpartondistributionsbranchingmethodcoarsebinningLHCphysicsZboson
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that the nonperturbative sideways momentum of quarks and gluons inside the proton—the intrinsic $k_T$—can be pinned down from Drell-Yan lepton-pair data without measuring the finely binned low-$p_T$ spectrum. The proposed observable is a single ratio of the dilepton cross section below a separation momentum $p_s$ to the cross section above it. Pseudo-data tests with parton-branching templates show that this ratio is statistically as sensitive to the intrinsic-$k_T$ width $q_s$ as the full $p_T$ shape, even after 3\% lepton momentum smearing. Applying the ratio to CMS measurements across dilepton masses from 50 GeV to 1 TeV gives $q_s$ values consistent with an earlier fine-binned extraction. Because coarse bins avoid the worst unfolding and momentum-migration systematics, the claim, if right, makes intrinsic-$k_T$ determination cheaper and more robust at the LHC.

What carries the argument

The central object is the $p_T$-ratio of Eq. (3.1), $p_T\text{-ratio} = p_L/p_H$, with $p_L$ the number of events with dilepton $p_T$ below the separation momentum $p_s$ and $p_H$ the number above it. The machine that produces predictions is the parton branching method for transverse-momentum-dependent evolution, whose starting-scale boundary condition is a Gaussian intrinsic-$k_T$ distribution with width $q_s$; seven template samples with different $q_s$ values provide the shapes to fit. Sensitivity is quantified with a least-squares estimator and a covariance matrix, and detector response is modeled by multiplying each dressed lepton's four-momentum by a factor $(1+g)$ with $g$ sampled from a Gaussian of 3\% width. The high-$p_T$ bin acts as a fixed-order reference that makes the ratio sensitive to the relative, not absolute, size of the intrinsic contribution.

What would settle it

Take the same CMS phase space, replace the 3\% Gaussian lepton-smearing model with a full detector simulation with $p_T$-dependent resolution, and re-run the two-bin fit; if the extracted $q_s$ shifts by more than the quoted uncertainty or becomes incompatible with the fine-binned extraction, the central claim is falsified.

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Extended reading notes

Core claim

The authors' central claim is that the information about intrinsic $k_T$ is essentially an overall shift of strength from low to high dilepton $p_T$, so a two-bin ratio $p_L/p_H$—the cross section with $p_T < p_s$ divided by the cross section with $p_T > p_s$—captures the intrinsic-$k_T$ Gaussian width $q_s$ as well as the fine-binned $p_T$ spectrum does. They support this with template samples generated at seven $q_s$ values: the ratio falls monotonically as $q_s$ increases, and least-squares fits to pseudo-data yield uncertainties comparable to fits of binned shapes with bin widths from 0.5 to 3 GeV. With a 3\% Gaussian lepton-momentum smearing meant to model detector resolution, the ratio keeps its sensitivity. An extraction from CMS dilepton $p_T$ data in five mass bins, using $p_s = 2$ GeV, returns $q_s$ values consistent with the earlier parton-branching determination in each mass region.

Load-bearing premise

The load-bearing premise is that detector momentum response is well approximated by a 3\% Gaussian smearing of dressed lepton momenta and that the $p_T > p_s$ bin can serve as a $q_s$-independent reference; if real migration is stronger or correlated differently, the claimed sensitivity and systematic advantage could break down.

Editorial extensions

If this is right

  • The intrinsic-$k_T$ width can be extracted from as few as two $p_T$ bins, so future measurements do not need fine binning in the low-$p_T$ region where lepton efficiency and momentum-resolution systematics are largest.
  • The $p_T$-ratio has statistical sensitivity comparable to the fine-binned $p_T$ shape both at truth level and after 3\% lepton momentum smearing, so no precision is lost by coarse graining.
  • Applying the ratio to existing CMS data reproduces the $q_s$ values from a previous fine-binned parton-branching fit, giving cross-checks on both methods.
  • The separation momentum $p_s$ must be chosen deliberately: too small a $p_s$ dilutes TMD sensitivity, too large a $p_s$ hides the low-$p_T$ information, and the pseudo-data procedure in the paper provides a way to optimize it.
  • The same methodology can be stress-tested with more complex TMD parameterizations and with very small or very large $q_s$ values to ensure the extraction is unbiased.

Reading between the lines

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

  • We infer that the claimed systematic advantage depends on the detector model: a realistic, $p_T$-dependent resolution with non-Gaussian tails could change the optimal $p_s$ or degrade the ratio's sensitivity, so a full-simulation study is the natural next test.
  • The same coarse-ratio logic could be applied to other TMD-sensitive observables, such as angular correlations or event-shape variables, wherever the interesting physics appears as a shift between a low- and high-momentum region.
  • Fixing $p_s = 2$ GeV for all dilepton-mass bins was a practical choice dictated by the published CMS binning; optimizing $p_s$ per mass bin could sharpen the extraction, since the peak of the $p_T$ spectrum moves with $m(ll)$.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper proposes to determine the intrinsic-kT width q_s in the parton-branching TMD approach from a coarse-grained ratio R = sigma(pT<ll><ps)/sigma(pT>ps) rather than from the fine-binned low-pT Drell-Yan spectrum. After reviewing the PB TMD setup (Sec. 2), the authors generate seven MC templates with different q_s, run a pseudo-data closure test (Sec. 3) comparing fit uncertainties from the fine-binned spectrum and from the ratio, with and without a 3% Gaussian lepton-momentum smearing, and apply the method to CMS 13 TeV data in five m_ll bins with fixed ps=2 GeV (Sec. 4). They find that the ratio has sensitivity comparable to fine binning and yields q_s values consistent with Ref. [9], concluding that the ratio is a viable lower-systematics observable for intrinsic-kT determination.

Significance. The proposal is potentially useful for TMD phenomenology: a robust two-bin ratio would ease experimental challenges in the low-pT region and avoid part of the unfolding and systematics burden. The paper's strengths are the clean statistical closure test with large MC samples, explicit covariance propagation in Eqs. (3.2)-(3.3), use of public TMDlib templates and public CMS data, and honest acknowledgment of the need to optimize ps. However, the central claims are stronger than the evidence: the sensitivity comparison is internal to the PB TMD model, the detector-response model is a single Gaussian smearing, and the comparison with Ref. [9] shares the same theoretical framework. With additional validation, the method could become a valuable complement to fine-binned extractions.

major comments (3)
  1. [Section 3, Figs. 3 and 5] The pseudo-data sensitivity test is a closure fit: the 'pseudo-data' and the fitting templates are generated from the same PB TMD model with the same Gaussian parameterization (Eq. (2.2)), so Figs. 3 and 5 quantify the statistical precision of the fit under the model, not the ability of the pT-ratio to determine qs when the true intrinsic-kT distribution has a different functional form or when the evolution model is misspecified. To support the general statement that 'the intrinsic kT can be determined by measuring its overall strength through the pT-ratio', please add a model-mismatch test (e.g., pseudo-data generated with a non-Gaussian intrinsic-kT or from an independent TMD framework) and report the resulting bias in qs.
  2. [Section 3, Eq. (3.4)] The claimed systematics advantage rests on the simplified detector model of Eq. (3.4), a multiplicative 3% Gaussian smearing applied to each dressed lepton. Real LHC momentum resolution is pT- and rapidity-dependent, has asymmetric tails from bremsstrahlung and energy loss, and induces correlated migrations in pT(ll), m(ll), and eta(ll); a single constant smearing does not capture these effects. Figures 4-5 therefore do not establish that the ratio is robust to the 'migration effects' that the paper itself identifies as a dominant systematic. Please validate the migration model against a full detector simulation or against the actual migration matrices used in CMS/ATLAS analyses, or at minimum test a range of pT-dependent smearing and migration scenarios and show that the ratio's sensitivity advantage persists.
  3. [Section 4, Fig. 7] The consistency check against Ref. [9] is partially circular: both analyses use the same PB TMD framework, the same MCatNLO+CASCADE setup, the same CMS data, and overlapping uncertainty treatments, so agreement in Fig. 7 demonstrates internal consistency rather than independent validation. Also, the extraction fixes ps=2 GeV for all five mll bins, and the paper itself notes that the choice of ps 'will need careful investigation' (Sec. 4); without a per-mass-bin optimization or a scan over ps, the claim that the ratio reproduces the reference extraction in every mDY region is not fully supported. A comparison with an independent TMD extraction (e.g., analytic resummation fits in Ref. [8]) or an explicit ps scan would make the validation convincing.
minor comments (4)
  1. [Fig. 1 caption] The generator name appears garbled as 'CRAPHGADM'; it should be 'MCatNLO+CASCADE'.
  2. [Eqs. (3.1)-(3.2)] Please define pL and pH explicitly as integrals of the pT(ll) distribution over the ranges [0,ps] and [ps,pT,max] (or [ps,infinity)) and state whether these are cross sections or event counts, because Eq. (3.2) assumes uncorrelated statistical uncertainties.
  3. [Section 3] The definition of pT,max is ambiguous when comparing the fine-binned fits and the ratio; specify whether events with pT > pT,max are excluded from both the fine-binned and ratio fits.
  4. [Section 4] In the sentence 'For the last two mDY bins, it is not estimated for the lack of statistics', specify which uncertainty source is meant (the pT-range uncertainty) and describe how the variation was performed in Ref. [9].

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the pT-ratio sensitivity study is a self-contained closure test, and the CMS extraction is a feasibility cross-check rather than a prediction built from its own inputs.

full rationale

The central claim is that the two-bin pT-ratio has comparable sensitivity to the fine-binned pT spectrum for determining the intrinsic-kT width qs. This is tested by a pseudo-data closure fit: one PB TMD template with qs = 0.89 is used as pseudo-data, and qs is extracted with the other templates. The resulting fitting uncertainties are compared between the ratio and the fine-binned shape. This is a legitimate statistical sensitivity study, not a circular prediction, because the 'observed' data are explicitly labeled pseudo-data and the exercise measures the statistical precision of the fitting procedure rather than claiming an independent physics result. The CMS extraction in Section 4 is explicitly framed as a feasibility study: 'the purpose of this study is not to carry out a precision extraction of qs, but to perform a feasibility study for the 2-bin pT-ratio.' The comparison with Ref. [9] is a consistency check using the same PB TMD framework and the same CMS data, so the agreement is partly expected; however, it compares two different observables (the ratio versus the full low-pT distribution) and does not reduce the central claim to the fitted input. The Gaussian momentum-smearing model in Eq. (3.4) is a stated modeling assumption, and the paper also notes that 'the choice of ps value will need careful investigation' and that the CMS rebinning restricts the choice of ps. These are limitations on external validity, not circular steps. No equation in the paper defines the pT-ratio in terms of qs itself, and no fitted parameter is renamed as a prediction. The derivation chain is therefore self-contained for its stated purpose, with only minor self-referential benchmarking that is not load-bearing.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The paper's central claim rests on the PB TMD framework and a Gaussian intrinsic-kT ansatz inherited from prior work, plus hand-chosen parameters ps and qs and a simplified resolution model. No new physical entities are introduced.

free parameters (2)
  • intrinsic kT width qs = around 1 GeV per mll bin, see Fig. 7
    Width of the intrinsic kT Gaussian in Eq. (2.2); extracted from CMS data in Section 4 by template fitting. The whole feasibility study concerns how well this parameter can be determined.
  • separation momentum ps = 2 GeV for the CMS extraction; 1.5 to 5 GeV in the pseudo-data scans
    Defines the low and high pT bins in Eq. (3.1); chosen by hand and constrained by CMS binning. The sensitivity of the method depends on this choice.
assumptions (6)
  • domain assumption PB TMD evolution equations with angular-ordered branching and fixed soft-gluon resolution scale provide the correct framework for DY pT spectra.
    Inherited from Refs. [17,18,20,9]; the paper uses PB-NLO-2018 Set2 templates as ground truth for pseudo-data and predictions without rederiving or independently verifying the framework.
  • domain assumption Intrinsic kT distribution is a Gaussian in kT^2 with flavor- and x-independent width qs, Eq. (2.2).
    Central ansatz for the quantity being extracted; the sensitivity of the ratio is to this particular parametrization.
  • domain assumption The high-pT bin pT>ps is insensitive to intrinsic kT and serves as a reference normalization.
    Introduced in Section 3 around Eq. (3.1); the ratio's ability to isolate qs depends on this assumption.
  • ad hoc to paper A 3 percent Gaussian smearing of dressed lepton momenta, Eq. (3.4), represents experimental momentum resolution and migration.
    Simplified model used in Section 3 to claim robustness against migration; no full detector simulation is performed.
  • domain assumption MCatNLO + Cascade + Herwig6 subtraction + Pythia6 final-state shower matching gives reliable NLO TMD predictions.
    Tooling assumption inherited from Refs. [13,45]; not independently validated in this paper.
  • domain assumption Strong coupling uses a pre-confinement alpha_s with qc = 1 GeV.
    Model choice from Refs. [9,20]; affects the shape of the pT spectrum and hence the ratio.

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Cite this review

Pith. "Pith review of Coarse-grained binning in Drell-Yan transverse momentum spectra." pith.science (2026). https://pith.science/paper/GJWDPB42

@misc{pith2026241219060,
  author       = {Pith},
  title        = {Pith review of: Coarse-grained binning in Drell-Yan transverse momentum spectra},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GJWDPB42}},
  note         = {Machine review of arXiv:2412.19060}
}
abstract

We report a study of the determination of the intrinsic transverse momentum of partons, the intrinsic $k_T$, from the dilepton transverse momentum $p_T$ in Drell-Yan (DY) production at hadron colliders. The result shows that a good sensitivity to the intrinsic $k_T$ distribution is achieved by measuring relative ratios between the cross sections of suitably defined low-$p_T$ and high-$p_T$ regions. The study is performed through both a pseudo-data test and an extraction from measurements of the DY process by the CMS collaboration. Since the methodology does not rely on any dedicated partition of bins, this $p_T$-ratio observable requires less special treatment in very low $p_T$ regions, and propagates lower systematic uncertainties induced from unfolding or momentum migration, in contrast with previous proposals of using a fine-binning measurement of the differential cross section.

Figures

Figures reproduced from arXiv: 2412.19060 by the authors.

Figure 1
Figure 1. Transverse momentum distributions from the [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 3
Figure 3. Uncertainties from binned pT and from pT -ratio. The uncertainties from different bin widths of binned pT are drawn in straight lines, while the uncertainties given by pT -ratio are marked and smoothed by curves. The abscissa of each marker is the corresponding ps. In real experiments, momentum resolution causes bin-to-bin migration. Since the migration effect is a dominant systematic uncertainty, it is essential to… view at source ↗
Figure 4
Figure 4. The pT (ll) distributions when the resolution ef￾fect is taken into account. The top plot shows the differ￾ence in the pT (ll) distribution before and after this effect. The bottom plot shows the difference in the relative ratio between the qs = 0.5 GeV and qs = 0.89 GeV cases. 4 Extraction of qs from pT -ratio Having performed a test with pseudo-data in the pre￾vious section, in this section we move on to consider … view at source ↗
Figures from the paper (3 more)
Figure 5
Figure 5. Figure 5: Uncertainties from binned pT and from pT -ratio with 3% energy resolution applied. increases these systematic uncertainties. Given these difficulties in achieving finer binning in the very low pT (ll) range, we next test the pT -ratio methodology of the previous sectio…
Figure 6
Figure 6. Figure 6: Comparison of pT distributions from the PB TMD samples with CMS data [16] in five mll ranges. PB-NLO TMD Set2 with qs = 0.5 GeV, 0.89 GeV and 1.12 GeV are shown in the figure, as well as the measured data. The error bars represent the square root of the diagonal elemen…
Figure 7
Figure 7. Figure 7: Determination of intrinsic kT parameter qs. The upper panel contains the qs values extracted indepen￾dently in different mDY bins, compared with the results in Ref. [9]. The error bars represent the combinations of the corresponding uncertainties in the lower pad. The …

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