A $p_T$-ratio observable for studies of intrinsic transverse momentum of partons from Drell-Yan $p_T$ spectra

Francesco Hautmann; Liang Han; Minghui Liu; Siqi Yang; Wenxiao Zhan

REVIEW 3 major objections 4 minor 2 cited by

A $p_T$-ratio observable for studies of intrinsic transverse momentum of partons from Drell-Yan $p_T$ spectra

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read A ratio of Drell-Yan event counts below and above a separation momentum $p_s$ extracts the intrinsic transverse momentum of partons with sensitivity comparable to the full fine-binned $p_T$ spectrum, while avoiding the hardest systematic…

desk verdict Useful conference summary of an already-published pT-ratio idea; the systematics claim in the abstract outruns what the figures actually show. read the letter →

arxiv 2505.06973 v1 pith:NNUD6OYW submitted 2025-05-11 hep-ph

Wenxiao Zhan , Siqi Yang , Minghui Liu , Liang Han , Francesco Hautmann This is my paper · ORCID

classification hep-ph

keywords p_T-ratiointrinsictransversemomentumDrell-YanTMDpartondistributionsbranchinggaussianwidthq_slow-p_Tspectrum

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

The paper proposes that the intrinsic transverse momentum of partons—the nonperturbative sideways motion of quarks and gluons inside the proton—can be extracted from Drell-Yan lepton-pair production without measuring the finely binned low-$p_T$ spectrum. Instead, one measures only the ratio of events with pair transverse momentum below a separation momentum $p_s$ to events above it. Using Monte Carlo templates, the paper argues that this $p_T$-ratio has sensitivity to the gaussian width $q_s$ of the intrinsic-$k_T$ distribution comparable to that of the full $p_T$ shape, while avoiding the delicate systematic control that fine binning demands. Applied to published collider data, the ratio-based extraction of $q_s$ across dilepton mass bins agrees with an earlier fine-binned determination. If correct, this gives experiments a cheaper, robust observable for transverse-momentum-dependent (TMD) studies.

What carries the argument

The central object is the two-bin $p_T$-ratio, $R(p_s)=p_L/p_H$. It carries the argument because the intrinsic-$k_T$ shift of the spectrum changes the two integrals in opposite directions, amplifying the effect of $q_s$; sensitivity is tuned by $p_s$, since too low a $p_s$ lets soft-gluon splitting transverse momenta fill the upper region, while too high a $p_s$ dilutes the low-$p_T$ information. The templates are generated with next-to-leading-order matrix elements matched to parton-branching TMD showers, giving next-to-leading-logarithmic accuracy in the resummation of the Drell-Yan spectrum, and the fitting procedure compares the $p_T$-ratio against these templates to extract $q_s$.

What would settle it

Take a dataset whose intrinsic-$k_T$ shape is known from an independent method, or generate pseudo-data with a deliberately non-gaussian intrinsic-$k_T$ distribution, then fit $q_s$ using the $p_T$-ratio for several choices of $p_s$; the proposal would fail if the fitted $q_s$ drifts with $p_s$ or disagrees with the known value while the fine-binned fit agrees.

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Extended reading notes

Core claim

In $pp\to Z/\gamma\to l^+l^-$ at 13 TeV, define $p_L$ and $p_H$ as integrated event counts in the regions $p_T(ll)<p_s$ and $p_s<p_T(ll)<p_{T,\mathrm{max}}$. The $p_T$-ratio $p_L/p_H$ decreases monotonically as the gaussian width $q_s$ of the intrinsic-$k_T$ distribution increases, because a wider intrinsic $k_T$ shifts the spectrum from low to high $p_T$. Fitting $q_s$ from this ratio yields statistical uncertainties comparable to fitting the fine-binned $p_T$ shape, and the conclusion survives a 3% lepton momentum smearing that mimics bin-to-bin migration. The same ratio, applied to the measured Drell-Yan $p_T(ll)$ distribution, reproduces the mass-dependent $q_s$ values obtained by the reference fine-binned analysis within uncertainties.

Load-bearing premise

The claim rests on the Monte Carlo model used to generate the templates: the parton-branching TMD shower with a gaussian intrinsic-$k_T$ width must faithfully represent the true nonperturbative low-$p_T$ Drell-Yan spectrum, and the region above $p_s$ must not be contaminated by higher jet multiplicities in a way the model misses.

Editorial extensions

If this is right

Experiments can determine the intrinsic-$k_T$ width from a coarse two-bin measurement, avoiding the most challenging systematic-control burden of fine low-$p_T$ binning.
The method provides a cross-check of fine-binned TMD extractions using the same measured Drell-Yan distribution, with comparable statistical precision.
The dependence on the separation momentum $p_s$ becomes a diagnostic: mapping the fitted $q_s$ and its uncertainty as a function of $p_s$ identifies the $p_T$ range where intrinsic-$k_T$ information is concentrated.
The extension to next-to-next-to-leading-logarithmic accuracy noted in the paper would make the ratio observable more precise for future high-statistics measurements.

Reading between the lines

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

Because the $p_T$-ratio is a ratio of event counts within the same sample, it likely cancels overall luminosity and acceptance normalization uncertainties even more strongly than the paper emphasizes, which could be tested directly on pseudo-data and real data.
A natural testable extension is to generate templates with non-gaussian intrinsic-$k_T$ shapes (for example power-law tails or flavor-dependent widths) and check whether the $p_s$-dependence of the $p_T$-ratio distinguishes shapes that the fine-binned spectrum cannot.
The same ratio idea could be adapted to other TMD-sensitive observables, such as momentum imbalance in Z-plus-jet production or semi-inclusive deep inelastic scattering, where fine binning is similarly costly.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Short version: this is a conference proceedings summary of Ref. [14] (PRD 111, 036018). The pT-ratio observable is genuinely practical, and the paper explains it clearly, but every quantitative result in it is already published. If you need the idea, read Ref. [14]; if you need this paper, you want the Moriond proceedings, not a research article.

What the paper does well: it defines a two-bin pT-ratio with a separation momentum ps, shows with MC templates that the fitted qs uncertainty from the ratio is competitive with fine-binned pT fits, and checks stability under a 3% lepton momentum resolution migration. The writing is honest about the provenance: 'based on our work published in Ref. [14]' appears in the text. The consistency with the earlier CMS-based qs extraction (Ref. [11]) is a useful sanity check.

Soft spots, in proportion. The abstract's claim of 'lower systematic uncertainties' is not established here: Fig. 2 compares statistical fitting uncertainties only. The denominator p_H integrates the pT > ps region, where matching, PDF, scale, and higher-multiplicity uncertainties enter directly, and those are not propagated. The migration test is a single resolution smearing; real detector systematics involve more. The template test is a closure test using the same MC model that defines qs, so it demonstrates self-consistency rather than model independence. No code or data are shipped, so none of the numbers can be reproduced from this manuscript alone. But the paper does not pretend to be a full analysis: it delegates fit details to Ref. [14], and that is the right call for a proceedings.

Who it is for: conference participants or newcomers who want a two-page overview of the observable and its first CMS-based application. Experts in TMD extraction will not find new information.

Recommendation: desk reject if submitted to a research journal; accept as a proceedings contribution if that is the intended venue. A referee would only send the authors back to their own PRD paper.

Referee Report

3 major / 4 minor

Summary. The paper proposes a two-bin 'pT-ratio' observable for Drell-Yan Z/gamma* production, defined as the ratio of event counts in p_T(lep-pair) < p_s and p_T > p_s within a coarse-grained low-p_T region, as an alternative to the fine-binned p_T spectrum for extracting the gaussian width q_s of the intrinsic transverse momentum. Using MCatNLO+CASCADE template samples generated with different q_s values, the authors compare the statistical fitting uncertainty of q_s from the pT-ratio with that from fine-binned p_T fits, including a test with 3% lepton-momentum smearing to model detector migration. They then apply the pT-ratio extraction to the CMS Drell-Yan p_T measurement and report q_s values consistent with the earlier analysis of Ref. [11]. The paper concludes that the pT-ratio has comparable sensitivity to the fine-binned spectrum and lower systematic uncertainties, and can be used directly in experiments.

Significance. If the central claim holds, the pT-ratio would offer a coarse-grained observable for extracting the intrinsic-kT gaussian width q_s from Drell-Yan spectra, potentially reducing the experimental burden of fine-binned measurements. The paper has concrete strengths: a Monte Carlo closure test over a range of q_s, an explicit migration study, and an external-data consistency check against the CMS measurement and Ref. [11]. The novelty lies in repackaging the low-p_T shape information into an integrated ratio and in numerically demonstrating that statistical sensitivity can survive coarse binning. The significance is, however, conditional: the claimed systematic advantage is not quantified, and the demonstration is performed entirely within one Monte Carlo framework, so the result is not yet a validated experimental methodology.

major comments (3)

[Abstract; §'A sensitivity test...' (Fig. 2)] The claim that the pT-ratio observable 'has lower systematic uncertainties' is not demonstrated by the evidence presented. Fig. 2 reports only fitting uncertainties of q_s from template samples; the text does not specify that any systematic term is included, and the uncertainties appear to be statistical. The denominator p_H is the integrated yield above p_s, a region where the authors themselves note that contributions from higher jet multiplicities and the MC@NLO matching/parton-branching scheme are important (Refs. 27-29); theory uncertainties in this region enter the ratio and are not evaluated or propagated to q_s. The 3% lepton-momentum smearing test addresses detector bin-to-bin migration only, and Fig. 3 includes only statistical and scale uncertainties. Thus the paper establishes at most statistical competitiveness, not a reduction in total systematic uncertainty; the abstract should be moderated or the systematics quantified.
[§'Given the difficulties...' and Fig. 3] The consistency between the pT-ratio extraction and Ref. [11] does not by itself validate the method for real data. Both this work and Ref. [11] use the same MCatNLO+CASCADE Monte Carlo model with the same parton-branching TMD input and the same CMS data, so the agreement in Fig. 3 shows internal consistency between two observables within that model, not the absence of model bias. The paper's own caveat that for too low p_s sensitivity may be lost because soft-gluon splitting transverse momenta move into the upper region indicates that the sensitivity is model-dependent. To support the claim that the pT-ratio can be applied directly in experiments, the authors should add a closure test with an alternative intrinsic-kT shape or resummation scheme, or at least quantify the model uncertainty in the extracted q_s.
[§'A sensitivity test...' (Fig. 2) and §'Given the difficulties...' (Fig. 3)] The central quantitative claim that the pT-ratio has comparable sensitivity to the fine-binned p_T shape is not self-contained: all fit details (the definition of the chi-squared, the number and statistical power of the template samples, the treatment of the non-Gaussian uncertainty of a ratio, the number of bins used for the fine-binned fit, and the procedure for the p_T-range uncertainty in Fig. 3) are deferred to Ref. [14]. Without at least a summary of these details, the reader cannot assess whether the comparison in Fig. 2 is fair or whether the error bars quoted for the pT-ratio in Figs. 2 and 3 include the expected asymmetric uncertainties of a ratio of event counts. A concise description of the fitting procedure should be included in this paper.

minor comments (4)

[Title and first paragraph] The text contains OCR-style artifacts such as 'Ap T -ratio' and 'Drell-Y anp T'; these should be corrected.
[Fig. 1 caption and labels] The labels 'PBset2', 'CRAPHGADM-', and 'pT-ratio of the outside plot' are garbled or unclear; the caption should fully define all curves, the inset, and the meaning of the 'outside plot' ratio.
[§'The sensitivity to the intrinsic transverse momentum...'] The dependence of the sensitivity on p_s is discussed only qualitatively; since the paper recommends a 'dedicated study of the separation momentum p_s', it would be useful to provide at least a heuristic criterion or a two-dimensional scan (p_s vs q_s) to guide experimental application.
[§'Given the difficulties...'] The statement that the methodology can be applied directly to experiments assumes that acceptances, efficiencies, and backgrounds cancel in the ratio; the authors should state which experimental systematics are expected to cancel and which are not.

Circularity Check

1 steps flagged · score 3.0 of 10

No definitional circularity; moderate self-citation in the validation chain because the CMS-data check is compared with a same-group, same-model extraction.

self citation load bearing [Section 'Results' and Fig. 3 (CMS data extraction; consistency check with Ref. [11])]
"We here perform an extraction of q_s from this measurement using the pT-ratio. Besides testing the feasibility of the pT-ratio proposal with real data, we also aim to check that the pT-ratio is not biased by the high-pT region, where contributions from higher jet multiplicities are important 27. ... Results are reported in Fig. 3 14. ... We observe consistency with the result of Ref. 11 in every mDY region."

The check that the pT-ratio is not biased by the high-pT region is performed by comparing the q_s extracted with the pT-ratio against q_s from Ref. [11]. Ref. [11] is a prior analysis by overlapping authors that uses the same parton-branching TMD model and the same CMS pT(ll) data. Agreement therefore shows that the two observables return the same q_s inside the same model and data set; it does not establish that the extraction is free of model bias. The validation leg thus reduces to a self-consistency check whose evidentiary weight is carried by a self-citation rather than by an independent external benchmark.

full rationale

The observable is not defined in terms of q_s: pT-ratio = p_L/p_H is a ratio of two integrated event counts, and its sensitivity to the intrinsic-kT gaussian width is a numerical property of the MC-generated spectra, not an algebraic identity. The template fits and the pseudo-data sensitivity test are standard closure tests, so they do not reduce by construction. The CMS-data extraction in Fig. 3 is a genuine fit to external data; however, its validation leg is weakened by the fact that the comparison point, Ref. [11], is a same-group, same-model, same-data extraction, and the model/template procedure itself is anchored in the authors' Refs. [14,20-29]. Thus the paper is not fully self-contained against an independent q_s benchmark; the 'not biased by the high-pT region' conclusion rests on a self-consistency check rather than an external falsification. This raises the score above 0-2 but does not make the central derivation circular: no equation is defined in terms of q_s, and the sensitivity claim would survive as a reproducible Monte Carlo result even if Ref. [11] were absent.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The analysis rests on the PB-TMD Monte Carlo framework and the gaussian intrinsic-kT parametrization; these are domain assumptions inherited from earlier work, not derived in this paper. The only hand-tuned methodological parameters are the separation momentum ps and the integration limit pT,max. No new physical entities are introduced.

free parameters (3)

intrinsic-kT gaussian width q_s = extracted in m_DY bins, see Fig. 3; values not quoted in text
Vary q_s in Monte Carlo templates (0.5 to 1.12 GeV) and fit it to CMS data to demonstrate the observable; it is the physical parameter of the TMD model being studied.
separation momentum p_s
Hand-chosen scale that sets the low and high pT regions; the paper scans p_s from 1.5 to 5 GeV, and sensitivity depends on this choice.
p_T,max integration limit = 10 or 20 GeV, depending on the fit
Choice of upper integration limit for the coarse-grained pT region; varied to estimate uncertainties.

assumptions (4)

domain assumption PB-TMD parton-branching evolution matched to MCatNLO gives an NLL-accurate Drell-Yan pT spectrum.
Used to generate all template spectra; the sensitivity results are conditional on this description of the process.
domain assumption The nonperturbative intrinsic-kT distribution is gaussian with width q_s.
This is the parametrization used in the templates; the paper does not test alternative nonperturbative shapes.
domain assumption The high-pT region p_T > p_s is dominated by fixed-order hard-parton radiation and is not biased by higher jet multiplicities.
The authors state this as a concern and check consistency with Ref. [11], but the assumption is load-bearing for the ratio's interpretation.
ad hoc to paper Detector momentum resolution can be modeled by a 3% smearing of dressed lepton momenta.
The migration test uses this simplified resolution model; real detector effects are more complex and could affect the conclusion.

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Cite this review

Pith. "Pith review of A $p_T$-ratio observable for studies of intrinsic transverse momentum of partons from Drell-Yan $p_T$ spectra." pith.science (2026). https://pith.science/paper/NNUD6OYW

@misc{pith2026250506973,
  author       = {Pith},
  title        = {Pith review of: A $p_T$-ratio observable for studies of intrinsic transverse momentum of partons from Drell-Yan $p_T$ spectra},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NNUD6OYW}},
  note         = {Machine review of arXiv:2505.06973}
}

abstract

The determination of the intrinsic transverse momentum distribution of partons is central both for applications of parton shower Monte Carlo generators and for QCD studies of transverse momentum dependent (TMD) parton densities. Valuable information on this distribution is provided by experimental measurements of Drell-Yan transverse momentum $p_T$, in the region of low transverse momenta, with fine binning in $p_T$. However, such fine-binning measurements are challenging, as they require an extremely delicate control of systematic uncertainties. We suggest a $p_T$ observable based on measuring ratios between cross sections of suitably defined low-$p_T$ and high-$p_T$ regions. This observable does not rely on any dedicated partition of bins and has lower systematic uncertainties, and is shown to provide a good sensitivity to the intrinsic transverse momentum.

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Soft-gluon coupling and the TMD parton branching Sudakov form factor
hep-ph 2024-12 conditional novelty 6.0 of 10

The parton branching TMD framework is upgraded from NLL to NNLL accuracy using the soft-gluon physical coupling, with the Collins-Soper kernel evaluated at NNLL.
Theoretical Summary: Moriond QCD and High-Energy Interactions 2025
hep-ph 2025-06 unverdicted

A conference summary that compiles the main theory results presented at Moriond QCD 2025, spanning hard scattering, precision QCD, flavour, strong coupling, lattice, heavy-ion, and BSM physics.

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