Interplay of intrinsic motion of partons and soft gluon emissions in Drell-Yan production studied with PYTHIA

H. Jung; I. Bubanja; N. Raicevic; S. Taheri Monfared

REVIEW 3 major objections 8 minor 1 cited by

Interplay of intrinsic motion of partons and soft gluon emissions in Drell-Yan production studied with PYTHIA

T0 review · 3 major / 8 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The energy growth of the intrinsic-$k_T$ width in PYTHIA is caused by soft gluon emissions, not by a change in partons' internal motion.

desk verdict The paper pins down a clear empirical trend—sigma rises with pT0Ref—but the soft-gluon interpretation is plausible rather than proven; send to review. read the letter →

arxiv 2412.05221 v2 pith:DT6JP4AA submitted 2024-12-06 hep-ph hep-ex

I. Bubanja , H. Jung , N. Raicevic , S. Taheri Monfared This is my paper · ORCID

classification hep-phhep-ex

keywords intrinsictransversemomentumDrell-YanproductionpartonshowersoftgluonemissionsSudakovformfactorPYTHIAspectrumnon-perturbativeQCD

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 asks why the intrinsic transverse momentum width fitted in PYTHIA grows with collision energy, reaching values that seem unphysical. The answer it argues for is that the width is not a clean measure of partons' internal motion: it also absorbs non-perturbative soft gluon emissions. Using Drell-Yan pair production at low transverse momentum, where these effects dominate, the authors fit the Gaussian width sigma at several center-of-mass energies and values of the initial-state-radiation cutoff pT0Ref. They find that sigma increases approximately linearly with pT0Ref in the range 0.5-2.0 GeV, so the energy dependence enters through the Sudakov no-emission probability rather than through intrinsic motion. If correct, this resolves a longstanding puzzle in parton-shower modeling and tells generators how to separate the two non-perturbative contributions.

What carries the argument

The load-bearing object is the PYTHIA initial-state parton shower with its non-perturbative regulator pT0Ref, which suppresses small-transverse-momentum emissions by a factor $pT^{2}$/($pT^{2}$ + $pT0Ref^{2}$). The Sudakov form factor, the probability of no radiation between two scales, depends on this cutoff, so changing pT0Ref changes how many soft gluons are emitted and thus how much transverse momentum the intrinsic Gaussian distribution must provide to describe the measured low-pT Drell-Yan spectrum. The argument is carried by the fitted $\sigma$ as a function of pT0Ref and $\sqrt$(s), together with the dependence of $\sigma$ on the DY invariant mass, which probes the scale dependence of the Sudakov form factor.

What would settle it

Extract the intrinsic-kT width from low-pT Drell-Yan data using a TMD calculation whose Sudakov form factor is computed analytically (rather than through a shower cutoff), and compare the fitted sigma across sqrt(s) = 38.8 GeV, 200 GeV, 1.96 TeV and 13 TeV. The paper's claim implies the TMD-extracted width is roughly energy-independent; if it grows with energy, the claim is falsified.

Watch

Extended reading notes

Core claim

The central claim is that the sqrt(s)-dependence of the intrinsic-kT width sigma observed in PYTHIA 8 arises from the interplay between two non-perturbative processes: the internal transverse motion of partons and soft gluon emissions. By fitting sigma to measured Drell-Yan transverse momentum spectra at sqrt(s) = 38.8 GeV, 200 GeV, 1.96 TeV and 13 TeV, and repeating the fit for three values of the ISR cutoff pT0Ref (0.5, 1.0 and 2.0 GeV), the paper shows that at fixed energy sigma rises nearly linearly with pT0Ref, and at fixed pT0Ref sigma rises with energy. Since lowering pT0Ref unsuppresses soft gluon emissions, the fitted width must be understood as a combined observable: the part of the low-pT spectrum that the shower does not generate through soft radiation is compensated by a larger intrinsic Gaussian width. The paper therefore concludes that the energy scaling in PYTHIA is a compensation mechanism for soft gluon emissions, not a property of intrinsic transverse momentum.

Load-bearing premise

The argument assumes that changing PYTHIA's pT0Ref parameter alters only the non-perturbative soft-gluon part of the shower, so that the fitted Gaussian width sigma cleanly separates intrinsic motion from soft-gluon effects and does not absorb other model deficiencies.

Editorial extensions

If this is right

Fitted intrinsic-kT widths from parton-shower generators should not be interpreted as direct measurements of intrinsic transverse momentum; they are effective parameters that also encode soft-gluon physics.
At fixed collision energy, sigma can be changed by nearly 1 GeV by moving pT0Ref from 0.5 to 2.0 GeV, so the low-pT DY spectrum alone does not fix both parameters; the two must be tuned together.
The energy dependence reported by previous studies disappears once the soft-gluon contribution is accounted for, meaning intrinsic transverse motion could be roughly energy-independent as the parton-branching method suggests.
Soft gluon effects grow with collision energy and are largest at low DY mass, so low-mass Drell-Yan measurements are the most sensitive place to constrain the non-perturbative Sudakov form factor.

Reading between the lines

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

If the paper is right, other event generators with different soft-gluon regulators should show a different sigma-versus-energy pattern, so comparing the same data across generators would test whether the effect is universal or regulator-specific.
A practical extension would be to replace the Gaussian intrinsic-kT model with a TMD distribution that already contains the Sudakov suppression, in which case the fitted sigma should become independent of pT0Ref; this is a testable prediction of the paper's interpretation.
Because sigma absorbs soft-gluon effects, the unphysical high-energy widths are not a failure of the generator but a sign that the Gaussian ansatz is being pushed to cover two distinct physics effects; a two-component fit separating both contributions would be more physical.
The near-linear sigma-pT0Ref relation could serve as a tuning rule: once pT0Ref is chosen, sigma is determined by the requirement that the total low-pT spectrum matches data, turning a puzzling energy dependence into a known compensation.

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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

Two things to know about arXiv:2412.05221. First, it pins down something concrete: in PYTHIA 8 the fitted Gaussian width sigma of the intrinsic-kT distribution rises almost linearly with the ISR cutoff pT0Ref, across four collision energies. That is a new observation, and it directly speaks to a known puzzle—why sigma appears to grow with sqrt(s) in parton-shower MCs. Second, the paper's interpretation of that trend, that sigma is compensating for suppressed non-perturbative soft gluon emissions, is plausible but not proven. The evidence supports the trend; the causal story is stronger than the evidence.

The paper does several things well. It builds an 'intrinsic kT-optimized tune' with pT0Ref = 0.5 GeV and shows it describes DY data from 38.8 GeV to 13 TeV with reasonable chi2. The fitting procedure is transparent: chi2 minimization in pT(ll), with the sigma uncertainty from delta-chi2 = 1 quoted. It also checks the mDY dependence and shows that the pT0Ref effect on sigma is larger at low mDY, which is qualitatively consistent with soft emissions at low scales. That is a nice cross-check.

The soft spots are real but not load-bearing. The stress-test concern is valid: pT0Ref enters as a smooth suppression factor pT^2/(pT^2+pT0^2), not a hard cut, so lowering it changes emission rates across the whole pT spectrum. The paper itself notes that 'soft emissions can appear at all scales Q2.' That means the sigma(pT0Ref) trend does not cleanly isolate non-perturbative soft gluons; it could partly absorb shifted perturbative emissions or other model deficiencies. The optimized tune also adjusts alpha_s, so the attribution is not unique. Figure 6 has no error bars on sigma, and the linear trend uses only three points per energy. These are presentation and evidence issues, not fatal flaws: the qualitative pattern—steeper sigma(pT0Ref) at higher sqrt(s), flatter at low energy—would likely survive better uncertainty handling.

Who benefits: people who tune PYTHIA or interpret intrinsic-kT in TMD and DY contexts. It is a practical, reproducible study, but not a first-principles derivation. It deserves a serious referee. If I were handling it, I would send it out and ask for explicit error bars in Fig. 6, a test of whether the sigma shift is driven by emissions below a genuine non-perturbative scale, and a discussion of how much the alpha_s adjustment alters the conclusion. My bottom line: engage with this paper, but treat the soft-gluon claim as a working hypothesis rather than a settled result.

Referee Report

3 major / 8 minor

Summary. This paper investigates the origin of the collision-energy dependence of the Gaussian intrinsic transverse-momentum width σ (PYTHIA 8 parameter BeamRemnants:primodialkThard) that is required when fitting low-pT Drell-Yan data. Using an 'intrinsic kT-optimized tune' (a Monash-2013-based setting with an adjusted αs for ISR/FSR), the authors fit σ to measurements at √s = 38.8, 200, 1960, and 13000 GeV for three values of the ISR cutoff SPACESHOWER:pT0Ref (0.5, 1.0, 2.0 GeV) via χ² minimization (Section 3, Eq. 1). Figure 6 shows that σ increases approximately linearly with pT0Ref, with a stronger slope at TeV-scale energies; the paper attributes the √s-dependence of σ to soft, non-perturbative gluon emissions controlled by the Sudakov form factor (Section 4, Eq. 2) and supports this with the observed mDY-dependence of σ (Section 4.2, Figs. 7–9). The central conclusion is that σ reflects the interplay of two non-perturbative processes: intrinsic parton motion and soft gluon emission.

Significance. If the central attribution holds, this paper provides a physical explanation for a long-standing generator-tuning puzzle: parton-shower generators such as PYTHIA and HERWIG require an intrinsic-kT width that grows with √s, whereas PB-TMD fits yield an essentially energy-independent σ. The study contains several useful falsifiable statements, including a small dσ/dpT0Ref slope at low energies with a growing slope at high energy, and a weak mDY-dependence of σ at 13 TeV with a visible dependence at low mDY. Credit is due for the transparent methodology (public data, MCatNLO+PYTHIA, Rivet, explicit χ² definition) and for the strong diagnostic in Fig. 5(right), where the σ tuned at pT0Ref = 0.5 GeV fails catastrophically at pT0Ref = 2 GeV (χ²/n = 70.14), demonstrating that the pT0Ref effect is large and not a small correction. The main weakness is that the Sudakov form factor is discussed qualitatively but never evaluated to make a quantitative prediction, and the key evidence (Fig. 6) is presented without uncertainties. The paper is therefore best read as a well-motivated interpretive study of a Monte-Carlo artifact rather than a quantitative derivation of the energy dependence.

major comments (3)

[Section 4.1 / Fig. 6] The σ values in Fig. 6 are plotted without any uncertainty bars, even though Section 3 defines a Δχ² = 1 uncertainty on each tuned value (Fig. 4, left). Consequently the 'approximately linear' increase of σ with pT0Ref, and in particular the comparison of the slopes at 13 TeV and 1.96 TeV, cannot be quantitatively assessed. The problem is compounded by the fact that the fit at pT0Ref = 2 GeV for the CMS 13 TeV data has χ²/n = 2.34 (Fig. 5, left), which is not a good description even at the best-fit σ. Please provide the numerical values σ ± δσ for all points (as a table or as error bars in the figure) and explicitly comment on the reliability of the pT0Ref = 2 GeV extraction.
[Section 4.1 / Eq. (2)] The attribution of the σ(pT0Ref) trend specifically to non-perturbative soft gluon emission is not established by the presented analysis. In the PYTHIA shower, the pT0Ref cutoff enters not as a hard separation but as the smooth suppression factor pT²/(pT²+pT0²) multiplying the splitting probability at all transverse momenta (Section 4, Ref. [9]); lowering pT0Ref from 2 GeV to 0.5 GeV changes that factor from 0.5 to 0.94 even at pT = 2 GeV, so perturbative-region emissions are also modified. The manuscript provides no decomposition showing that the σ shift is driven by emissions below a genuinely non-perturbative scale. A concrete test would be to evaluate the Sudakov form factor of Eq. (2) with and without the pT0-suppression and compare the resulting low-pT(ℓℓ) predictions with the fitted σ values, thereby predicting σ(pT0Ref) and σ(√s) rather than reading them from the fits.
[Section 2.2] The definition of the 'intrinsic kT-optimized tune' is incomplete: the text states that 'by changing the value of αs(mZ) = 0.130 in the Monash tune, an excellent description is achieved. In the following, we take this value,' but the adopted αs value (and whether it applies to ISR, FSR, or both) is never specified. Since αs strongly affects the 2–5 GeV region shown in Fig. 2, and σ is subsequently fitted with αs held fixed, a possible degeneracy between σ and αs should be checked, for example by a two-dimensional χ² scan or by refitting αs at each pT0Ref. Without such a check, part of the σ shift in Fig. 6 could be absorbing the αs adjustment rather than the soft-gluon cutoff.

minor comments (8)

[Figure 1 caption] The caption reads '√s = 13 GeV' but should read '√s = 13 TeV' for the proton-proton collision energy.
[Section 3] The parameter name 'primodialkThard' is misspelled throughout the manuscript (it should be 'primordialkThard'); please standardize the spelling.
[Section 3] The text defines NDF as equal to the number of bins, which is non-standard (normally NDF = number of bins − number of fitted parameters); please clarify this convention or rename the quantity.
[Section 2.2, footnote] The footnote contains a typo: 'higher order αs contribtuins' should be 'higher order αs contributions'.
[Section 4.1] The sentence 'a significantly larger fraction of soft gluon contribution is removed when when the ISR cutoff parameter is increased' contains a duplicated 'when'.
[Abstract and Section 1] The phrase 'soft gluon effects become increasingly prominent with rising collision energy—contrary to initial expectations' is confusing, because an increasing role of soft emissions with increasing phase space is precisely the standard Sudakov expectation; please rephrase or justify what expectation is being contrasted.
[Section 3] The fit range for the χ² calculation is stated as '8 GeV when applicable', but the actual fitted pT(ℓℓ) ranges for the CDF, PHENIX, and E605 datasets are not given; please list them for each dataset.
[Section 3] The description of the χ² scan does not state the number of σ-grid points or the step size used for the cubic spline interpolation; please provide these details for reproducibility.

Circularity Check

1 steps flagged · score 4.0 of 10

The sigma-vs-pT0Ref relation is presented as evidence for soft-gluon interplay, but it is a compensation effect of the fitting procedure rather than an independent Sudakov prediction.

fitted input called prediction [Section 4.1, Figure 6; Section 5 Conclusion]
"Figure 6 shows the width σ obtained from χ2 minimization as a function of the cut-off parameter, pT0Ref, at different values of √s. ... In the examined region 0.5 < pT0Ref < 2.0 GeV, the value of σ increases nearly linearly with pT0Ref, as indicated by the linear fits applied to the points for visual guidance."

σ is not measured independently: it is the χ2-minimizing value of BeamRemnants:primodialkThard (Eq. 1) for each generator setting. pT0Ref is, by the paper's own description, the parameter that dynamically suppresses non-perturbative soft emissions. Hence the rise of σ with pT0Ref is the fit compensating for the removal of shower soft emissions so that the same data are still described; the 'interplay' is largely a property of the fitting setup. The Sudakov form factor (Eq. 2) is quoted but never used to compute σ, so the causal attribution of the trend to soft gluons is not independently derived and the conclusion partly restates the definition of the varied parameter.

full rationale

The paper is not wholly circular: the sigma values are fitted to external Drell-Yan data at several collision energies (CMS, CDF, PHENIX, E605), and the cross-check in Fig. 5(right) shows that a sigma optimized for one pT0Ref fails when used with another, which gives the fitted relation some empirical content. However, the central explanatory claim—that the sqrts-dependence of sigma arises from the interplay with soft, non-perturbative gluon emissions—is inferred from the behaviour of the only parameter the authors vary to control soft emissions. Since sigma is defined by chi2 minimization and pT0Ref is defined as the soft-emission suppression parameter, the observed sigma(pT0Ref) trend is partly a built-in compensation of the fit, not a prediction from the Sudakov form factor. The paper never computes sigma from Eq. (2), so the strength of the causal conclusion exceeds what the analysis establishes. This is partial circularity in the interpretation, but not a tautology and not a self-citation chain, hence score 4.

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

The central claim rests on several unvalidated model assumptions: the Gaussian ansatz for intrinsic kT, the PYTHIA shower's separation of soft gluon emissions via pT0Ref, and the reliability of the fitted sigma as a measure of non-perturbative effects. No external prediction is made.

free parameters (3)

intrinsic kT width sigma (BeamRemnants:primodialkThard) = 1.43 to 2.05 GeV depending on pT0Ref and sqrt(s); e.g., 1.43 GeV at pT0Ref=0.5 and 13 TeV, 2.05 GeV at pT0Ref=2.0 and…
Fitted to DY pT(ll) data via chi2 minimization at each energy and pT0Ref value.
pT0Ref (SPACESHOWER:pT0Ref) = 0.5, 1.0, 2.0 GeV (scanned, not fitted)
Chosen by hand to scan the soft gluon cutoff; central to the observed linear relation with sigma.
alpha_s(mZ) for ISR/FSR in the intrinsic kT-optimized tune = 0.130 (inferred from text)
Set to 0.130 to achieve a good description of the 13 TeV data; not systematically fitted and the exact change is described ambiguously.

assumptions (4)

domain assumption PYTHIA 8's parton shower correctly implements the Sudakov form factor and its pT0Ref suppression factor.
The paper relies on this to connect sigma to soft gluon emissions (Section 4, Eq. 2 and surrounding text).
domain assumption The intrinsic kT distribution is Gaussian and convolves with the shower to produce the DY pT spectrum.
Used in all fits; no test of alternative shapes is presented.
domain assumption The experimental data from CMS, CDF, PHENIX, and E605 are reliable and the binning choices are appropriate.
Fits treat these data as ground truth; no systematic uncertainty breakdown is used.
domain assumption MCatNLO plus PYTHIA matching is accurate for low pT DY and missing higher-order alpha_s corrections do not affect the region used for sigma extraction.
The paper notes higher-order terms matter at higher pT, but the fitted region still relies on the shower's accuracy at low pT.

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Cite this review

Pith. "Pith review of Interplay of intrinsic motion of partons and soft gluon emissions in Drell-Yan production studied with PYTHIA." pith.science (2026). https://pith.science/paper/DT6JP4AA

@misc{pith2026241205221,
  author       = {Pith},
  title        = {Pith review of: Interplay of intrinsic motion of partons and soft gluon emissions in Drell-Yan production studied with PYTHIA},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DT6JP4AA}},
  note         = {Machine review of arXiv:2412.05221}
}

abstract

Understanding the intrinsic transverse momentum (intrinsic-$k_T$) of partons within colliding hadrons, typically modeled with a Gaussian distribution characterized by a specific width (the intrinsic-$k_T$ width), has been an extremely challenging issue. This difficulty arises because event generators like Pythia require an intrinsic-$k_T$ width that unexpectedly varies with collision energy, reaching unphysical values at high energies. This paper investigates the underlying physics behind this energy dependence in Pythia, revealing that it arises from an interplay between two non-perturbative processes: the internal transverse motion of partons and non-perturbative soft gluon emissions. These contributions are most constrained in the production of Drell-Yan pairs with very low transverse momentum, where soft gluon effects become increasingly prominent with rising collision energy-contrary to initial expectations. Through a detailed analysis of the non-perturbative Sudakov form factor and its influence on intrinsic-$k_T$ width, we clarify the observed energy scaling behavior in Pythia, providing insight into a longstanding issue in parton shower modeling.

Figures

Figures reproduced from arXiv: 2412.05221 by the authors.

**Figure 1.** illustrates the impact of intrinsic-kT on the transverse momentum distribution of DY pairs, pT(ℓℓ), in the Z-peak region obtained from proton-proton collisions at 13 TeV using the default settings from PYTHIA8 for the two values of ISR cutoff parameter: the default one, pT0Ref=2 GeV, and pt0Ref=0.5 GeV (all other parameters are set to the Monash 2013 tune [17]). As shown in the figure, the impact of intrinsic-kT is … view at source ↗

**Figure 2.** Comparison of the LHC DY cross-section measurement as a function of [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Comparison of the DY cross section measurement as a function of [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (6 more)

**Figure 4.** Figure 4: χ 2 (primodialkThard) − χ 2 min distribution obtained from the comparison of CMS measurements at √ s = 13 TeV [18] with the intrinsic kT-optimized tune prediction for pT0Ref = 2 GeV(left). The green line represents the result of the fit using a cubic spline function in…

**Figure 5.** Figure 5: The cross section as a function of pT(ℓℓ) in the Z-peak region, obtained from protonproton collisions at √ s = 13 TeV [18], compared with intrinsic kT-optimized tune. (Left): Predictions using different pT0Ref values, with the intrinsic-kT width adjusted accordingly. …

**Figure 6.** Figure 6: Dependence of the intrinsic-kT width, σ, on the ISR cut-off parameter pT0Ref used in intrinsic kT-optimized tune, obtained from comparison with the measurements at different collision center of mass energies listed in [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

**Figure 7.** Figure 7: Intrinsic-kT width, σ, as a function of the DY pair invariant mass, obtained from the comparison of data at √ s = 13 TeV [18] (left) and at √ s = 38.8 GeV [22] (right) with PYTHIA8 with pT0Ref = 2.0 GeV. In order to study the impact of the scale-dependence of the soft …

**Figure 8.** Figure 8: Measurement of the ratio of the cross section as a function of [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]

**Figure 9.** Figure 9: The ratio of the cross section as a function of [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]

Discussion (0). Continue with ORCID to comment.

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2025 arXiv

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [9]

A comprehensive guide to the physics and usage of PYTHIA 8.3

C. Bierlich et al., “A comprehensive guide to the physics and usage of PYTHIA 8.3”, SciPost Phys. Codeb. 2022 (2022) 8, arXiv:2203.11601

arXiv 2022

[2] [1]

The small kTregion in Drell–Yan production at next-to-leading order with the parton branching method

I. Bubanja et al., “The small kTregion in Drell–Yan production at next-to-leading order with the parton branching method”, Eur. Phys. J. C 84 (2024) 154, arXiv:2312.08655

arXiv 2024

[3] [2]

Center-of-mass energy dependence of intrinsic- kT distributions obtained from Drell–Yan production

I. Bubanja et al., “Center-of-mass energy dependence of intrinsic- kT distributions obtained from Drell–Yan production”, Eur. Phys. J. C 85 (2025) 278, arXiv:2404.04088

arXiv 2025

[4] [3]

Energy-scaling behavior of intrinsic transverse momentum parameters in Drell-Yan simulation

CMS Collaboration, “Energy-scaling behavior of intrinsic transverse momentum parameters in Drell-Yan simulation”, CMS-GEN-22-001, CERN-EP-2024-216 (09, 2024) arXiv:2409.17770. 13

arXiv 2024

[5] [4]

Collinear and TMD quark and gluon densities from Parton Branching solution of QCD evolution equations

F. Hautmann et al., “Collinear and TMD quark and gluon densities from Parton Branching solution of QCD evolution equations”, JHEP 01 (2018) 070, arXiv:1708.03279

arXiv 2018

[6] [5]

Soft-gluon resolution scale in QCD evolution equations

F. Hautmann et al., “Soft-gluon resolution scale in QCD evolution equations”, Phys. Lett. B 772 (2017) 446, arXiv:1704.01757

arXiv 2017

[7] [6]

Production of Z-bosons in the parton branching method

A. Bermudez Martinez et al., “Production of Z-bosons in the parton branching method”, Phys. Rev. D 100 (2019) 074027, arXiv:1906.00919

arXiv 2019

[8] [7]

The transverse momentum spectrum of low mass Drell–Yan production at next-to-leading order in the parton branching method

A. Bermudez Martinez et al., “The transverse momentum spectrum of low mass Drell–Yan production at next-to-leading order in the parton branching method”, Eur. Phys. J. C 80 (2020) 598, arXiv:2001.06488

arXiv 2020