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REVIEW 5 major objections 5 minor 57 references

A recoil fix makes the PDF2ISR shower reproduce the PB-TMD intrinsic-kT width and exposes alpha_s-transition sensitivity in low-pT Drell-Yan.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-02 22:13 UTC pith:IKIEUOJE

load-bearing objection The recoil-mode fix is solid and the a-priori q_s test is legitimate, but the paper overclaims energy independence and the arXiv abstract contradicts the body. the 5 major comments →

arxiv 2602.17533 v2 pith:IKIEUOJE submitted 2026-02-19 hep-ph

Non-perturbative effects and soft-gluon dynamics in low-p_T Drell-Yan production

D. Suboti\'c , H. Jung , A. V. Kotikov , N. Rai\v{c}evi\'c This is my paper
classification hep-ph
keywords Drell-Yan productionlow transverse momentumintrinsic transverse momentumparton showerParton Branching methodsoft-gluon radiationstrong coupling constantnon-perturbative QCD
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper tries to establish that the low-transverse-momentum Drell-Yan spectrum is fully explained by two complementary non-perturbative ingredients: a universal, energy-independent intrinsic transverse momentum of partons inside the proton, and soft-gluon radiation generated during initial-state evolution. The key technical claim is an improved recoil treatment (primordialKTRecoilMode) in the PYTHIA-based PDF2ISR shower that preserves the intrinsic kT of hard initiators, so the input Gaussian width maps directly to the observed spectrum. With this fix, the same width q_s = 1.04 GeV used in the PB/CASCADE approach describes measurements from a fixed-target experiment at 38.8 GeV up to CMS at 13 TeV, demonstrating that the width is independent of collision energy. The paper also claims that at high energy the low-pT spectrum is sensitive to how the strong coupling alpha_s is tamed in the perturbative-to-non-perturbative transition region, so Drell-Yan data can constrain that transition. This matters because it turns the low-pT Drell-Yan spectrum into a clean probe of proton structure and the infrared behavior of the strong coupling.

Core claim

The central discovery is that, once the PYTHIA default recoil-sharing step is modified so that only beam remnants carry the transverse-momentum compensation (primordialKTRecoilMode), the PDF2ISR shower yields the same intrinsic-kT width as the PB-TMD approach, and that width is energy-independent. Applied to Drell-Yan data from E605 at sqrt(s)=38.8 GeV, PHENIX at 200 GeV, CDF at 1.96 TeV, and CMS at 13 TeV, the universal value q_s=1.04 GeV gives chi^2/NDF values between 0.16 and 0.67. The paper further finds that at 13 TeV the low-pT Z-boson spectrum discriminates between different infrared treatments of alpha_s: hard freezing (option A) and running gluon mass (option C) both describe the da

What carries the argument

The load-bearing mechanism is the recoil-preserving primordial-kT scheme, labelled BeamRemnants:primordialKTRecoilMode, which enforces transverse-momentum conservation by letting beam remnants absorb the full compensating kick, sum(kT initiators + kT remnants) = 0, leaving the hard initiators' kT untouched. This makes the effective Gaussian width equal the input width, sigma_eff = sigma, and enables a direct mapping between the shower's primordial kT and the PB-TMD boundary condition A(x,k,mu0^2)=f0(x,mu0^2)G(sigma,kT) with G a Gaussian. A second ingredient is the backward-evolution ansatz of eq. (8), where the Gaussian is applied unevolved at the starting scale; the paper explicitly notes t

Load-bearing premise

The universality claim rests on the assumption that the proton's intrinsic transverse momentum is exactly a single Gaussian of width sigma, applied unevolved at the starting scale of the backward shower; if the true kT is non-Gaussian or the unevolved-input bias is not small at the lowest-energy bin that anchors the claim, the energy-independent q_s is an artifact of that ansatz.

What would settle it

Fit q_s independently to the E605, PHENIX, CDF, and CMS datasets and check for a trend with sqrt(s) or invariant mass; or compare the 7-8 GeV, 38.8 GeV spectrum against a forward-evolved TMD at the same q_s—if per-energy widths drift or a non-Gaussian intrinsic kT fits that bin significantly better, the universality claim fails.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The same intrinsic-kT width q_s = 1.04 GeV describes Drell-Yan data from sqrt(s) = 38.8 GeV to 13 TeV, establishing that the width is independent of collision energy.
  • Intrinsic kT and soft-gluon radiation play complementary, non-substitutable roles: the Gaussian sets the overall non-perturbative width while ISR shapes the spectrum and the transition region.
  • At 13 TeV the low-pT Z spectrum discriminates between infrared treatments of alpha_s: hard freezing and running gluon mass describe the data, fixed gluon mass does not.
  • A large intrinsic width cannot rescue the failing alpha_s option, confirming that inaccurate soft-gluon modeling cannot be compensated by intrinsic kT.
  • The modified recoil prescription is process-independent and can be applied to other final states.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • We infer that the extracted q_s is an effective width: because the backward shower applies the Gaussian unevolved, the 'small bias' conceded in the paper could be sizable at the lowest mass and energy, so the true non-perturbative kT distribution might be narrower or non-Gaussian.
  • We infer that the demonstrated alpha_s sensitivity at 13 TeV implies high-statistics Z-peak data could be added to global alpha_s fits as a constraint on the transition region, a step the paper does not itself take.
  • We infer that the recoil-preserving scheme could be tested in W or Higgs production at the LHC, where the same universal intrinsic width should appear if the picture is correct.
  • We infer that the energy-independence claim would be strengthened or weakened by fitting q_s separately to each experiment and propagating correlated systematics; the quoted chi^2 values assume uncorrelated uncertainties.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 5 minor

Summary. The paper studies low-transverse-momentum Drell-Yan production in the PDF2ISR framework, a PYTHIA-based initial-state shower constructed to be consistent with PB collinear/TMD parton densities. It introduces a modified recoil scheme ('primordialKTRecoilMode') in which the intrinsic transverse momentum of the hard initiators is preserved and transverse-momentum conservation is carried entirely by beam remnants, so that the effective Gaussian width equals the input width. Using the value q_s = 1.04 GeV previously obtained in the PB framework, the paper compares PDF2ISR predictions with E605, PHENIX, CDF, and CMS data and reports acceptable chi-square values over a wide range of center-of-mass energies. It further compares three infrared treatments of alpha_s (hard freezing, fixed gluon mass, running gluon mass) and argues that the low-pT DY spectrum at high sqrt(s) is sensitive to the perturbative-to-non-perturbative transition region of alpha_s.

Significance. If the claims hold, the paper provides a valuable cross-check between a PYTHIA-based shower and the PB-TMD formalism, and the recoil prescription is a useful technical improvement that makes the intrinsic-kT input in a Monte Carlo shower directly interpretable. The use of a fixed q_s from an independent implementation as an a-priori input is a genuinely falsifiable test, and the comparison across four experiments is a strength. The demonstration that low-pT DY at high sqrt(s) is sensitive to the alpha_s transition region is also interesting and, if confirmed, opens a new observable for infrared-QCD studies. However, the paper's central universality claim is weakened by an unresolved internal inconsistency between the abstract and the conclusions, and by the absence of a direct extraction of q_s(sqrt(s)) within PDF2ISR.

major comments (5)
  1. [Abstract vs. §2.2 and §4] The abstract states that the authors 'determine the width of the intrinsic-kT distribution and find a sqrt(s) dependence that is steeper than in PB, but much flatter than in PYTHIA.' The body and conclusion, however, state the opposite: §2.2 concludes the width is 'independent of sqrt(s)', and §4 calls it 'universal and energy independent.' No per-√s extraction of q_s is reported anywhere in the paper. This is not a presentation nuance; the two claims describe different physics. The abstract must be reconciled with the analysis, or actual per-√s fits must be provided.
  2. [§2.2, Table 2] The energy-independence claim is not actually extracted. Table 2 reports chi^2/NDF for a single value q_s = 1.04 GeV taken from Ref. [7]; no PDF2ISR-specific fit of q_s per dataset is shown. A fixed value that describes all datasets is a valid prediction test, but by itself it does not demonstrate that the width is √s-independent, since a mild √s dependence could be compatible with the same fixed input within uncertainties. Please provide, at minimum, a scan or profile fit of q_s for each experiment, with uncertainties, and state clearly whether the extracted q_s(√s) is flat. If this is not intended, the conclusion should be softened to 'consistent with a universal q_s within current uncertainties.'
  3. [§2.1, Eq. (8) vs. Eq. (7)] The paper acknowledges that the backward-shower implementation adds the intrinsic Gaussian only at the end of the backward cascade, so that this Gaussian does not experience the Sudakov suppression and angular ordering of the forward PB evolution in Eq. (7). The text calls the resulting bias 'small,' but no quantification is provided. Because q_s = 1.04 GeV is the PB value used as an a-priori input, the effective q_s in PDF2ISR need not equal the PB q_s; a √s-dependent offset could be masked by fixing q_s. This is particularly important for the E605 low-mass, low-√s bin where the intrinsic component dominates. Please quantify the bias as a function of √s and DY mass (e.g., from a comparison like Fig. 4 but with the extracted shift), or fit the PDF2ISR effective q_s directly.
  4. [Fig. 1, §2.1] The central validation of the modified recoil scheme is Fig. 1, which compares input σ and 'extracted σ.' The extraction procedure is not described (from which observable? which fit range? with what statistical treatment?), and no uncertainties are shown on the extracted values. Without this information, the claimed σ_ext = σ_in for the remnant-only recoil mode is not quantitatively established. Please specify the extraction method and include at least MC statistical uncertainties.
  5. [Table 2, §2.2] The chi-square values in Table 2 treat all experimental uncertainties as uncorrelated, following Ref. [6]. This assumption is not tested or justified. Since these chi-square values are the only quantitative evidence for the universality claim, correlated systematic uncertainties (normalization, luminosity, bin-to-bin correlated systematics) could materially change the conclusions. Please estimate the impact of correlated uncertainties or explicitly state this as a limitation of the quantitative comparison.
minor comments (5)
  1. [Abstract] The abstract provided with the arXiv record and the abstract inside the full text are inconsistent: the former claims a determined √s-dependent width, while the latter does not. Please align them with the actual analysis and with each other.
  2. [References] References [14] and [16] appear to be the same paper; please remove the duplicate.
  3. [Fig. 8 caption] In Fig. 8, the parameter varied is q_min for Option A but m0 for Options B and C. Please state this explicitly in the caption to avoid confusion.
  4. [§2.2] Before Table 2, the text refers to 'as explained in the text' but does not define the pT and invariant-mass fit range used for the chi-square computation. Please define it explicitly.
  5. [§3, Eqs. (10)-(12)] The parameters of Option C are chosen to 'best reproduce' Option A. This should be emphasized in the main text, not only in the list of parameters, so that the agreement between Options A and C is not interpreted as an independent confirmation.

Circularity Check

0 steps flagged

No significant circularity: the q_s value is an imported input from a prior external fit, and the paper's central test is a parameter-transfer check against independent experimental data.

full rationale

The derivation chain is not circular. In Sect. 2.2 the paper states: 'For comparison with data at all √s, we apply q_s = 1.04 GeV, as obtained in Ref. [7] with the PB method.' The width is therefore an input imported from a prior, externally validated PB fit, not a parameter fitted in this paper. The subsequent comparison to CMS, CDF, PHENIX and E605 data (Table 2) is a genuine predictive consistency test of a different shower implementation (PDF2ISR) with that fixed value; no q_s value is re-fitted per dataset, so the agreement is not forced by construction. The modified recoil scheme does make σ_eff = σ by design (Table 1), but that only ensures the mapping between the input Gaussian and the extracted width is transparent; the physical test remains the external data comparison. The α_s options are also contrasted with the same external data, and the running-gluon-mass parameters are explicitly said to be 'chosen to best reproduce option A', i.e., tuned to an existing prescription rather than to the data, so no fitted-input-is-called-prediction pattern applies. The paper itself acknowledges a limitation of its backward-shower ansatz (Sect. 2.1: 'any extraction of q_s from a backward shower ... must be understood as containing a small bias'), which is a modeling caveat, not a circular reduction. There is an internal inconsistency: the Abstract claims 'we determine the width ... and find a √s dependence', while the body applies a fixed q_s and the Conclusion asserts the width 'can be taken to be universal and energy independent'. This is an overclaim/underdetermination issue (no per-energy fits are reported), but it does not make the derivation circular. The self-citation of Refs. [6,7] for q_s is load-bearing as an input, but because that cited work is an independent published fit to Drell-Yan data and the present paper compares an independent implementation to external measurements, it counts as real evidence rather than a circular self-reference.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The paper contributes no new physical entities: the 'gluon mass' in Options B/C is an infrared regulator borrowed from Refs. [24,27,37], and primordialKTRecoilMode is a technical Monte-Carlo setting, not a physical object. The physical claims rest on inputs inherited from the same PB collaboration — the PDFs (Ref. [11]), the framework (Ref. [5]), and the universal width q_s (Refs. [6,7]) — tested against external data (CMS, CDF, PHENIX, E605). The main assumption is the Gaussian factorization ansatz for intrinsic kT, which the paper itself flags as biased in backward evolution.

free parameters (4)
  • q_s (intrinsic-kT Gaussian width) = 1.04 GeV
    Inherited from the PB fit of Ref. [7] (overlapping authors) and applied a priori in PDF2ISR. Not fitted here, but the whole universality comparison and all data predictions depend on this value.
  • q_min (hard-freezing scale, Option A) = 1.0 GeV
    Scale at which alpha_s is frozen in PB-NLO-2018 Set2 (Ref. [11]); the baseline for the alpha_s comparison. The 0.5/1.0/1.5 GeV scan serves as the 7-point uncertainty estimate.
  • m0 (fixed/running gluon mass, Options B and C) = 1.0 GeV
    Mass parameter in eqs. (10)-(12); chosen to reproduce Option A, not fitted to data.
  • Lambda_m and gamma (running-gluon-mass shape) = Lambda_m = 0.67 GeV, gamma = 1.96
    Parameters of eq. (12); 'chosen to best reproduce option A' (sect. 3).
axioms (5)
  • standard math DGLAP evolution with Sudakov form factors (eqs. 1-3) correctly describes initial-state parton evolution.
    Standard QCD factorization framework, used as the background for both PB and PDF2ISR.
  • domain assumption Angular ordering + NLO DGLAP splitting functions + zM -> 1 in PDF2ISR yields the same effective TMD as PB-NLO-2018.
    This consistency is the founding result of Ref. [5] (overlapping author) and is inherited, not re-derived here.
  • domain assumption The intrinsic-kT distribution is a single Gaussian of width sigma (eq. 4), factorized at the starting scale and pasted unevolved in the backward shower (eq. 8).
    The non-perturbative shape is assumed; the paper concedes the backward-unevolved treatment introduces a 'small bias' in q_s extractions (sect. 2.1).
  • domain assumption Experimental uncertainties can be treated as uncorrelated for the chi^2 evaluation.
    Stated in sect. 2.2; if correlations matter, the Table 2 chi^2 values are not meaningful evidence for universality.
  • ad hoc to paper The infrared behavior of alpha_s can be represented by one of three ad-hoc schemes with parameters tuned to match Option A.
    Options A-C (eqs. 9-12) are phenomenological regulators; the sensitivity conclusion is conditional on these choices.

pith-pipeline@v1.3.0-alltime-deepseek · 17965 in / 24623 out tokens · 224617 ms · 2026-08-02T22:13:01.804655+00:00 · methodology

0 comments
read the original abstract

The transverse-momentum spectrum of Drell--Yan lepton pairs at small \ptll\ probes non-perturbative QCD effects, including intrinsic partonic transverse momentum and initial-state soft-gluon radiation. The novel \pythiaPB\ approach, which implements the Parton Branching (\PB ) framework in \pythia\ while employing the same evolution ingredients, is used to study this spectrum in the low-\ptll\ region. This framework is particularly well suited for such investigations, as it allows for a systematic treatment of the dominant non-perturbative effects and their interplay. We examine in detail the implementation of primordial transverse momentum in \pythiaPB . With an improved recoil treatment, we determine the width of the intrinsic-\kt\ distribution and find a \sqrts\ dependence that is steeper than in \PB , but much flatter than in \pythia . We identify the origin of these differences. Furthermore, different treatments of the strong coupling at low scales are investigated and confronted with available experimental data. We find that, at the highest centre-of-mass energy considered, the low-\ptll\ Drell--Yan spectrum becomes sensitive to the transition between the perturbative and non-perturbative regimes.

Figures

Figures reproduced from arXiv: 2602.17533 by A. V. Kotikov, D. Suboti\'c, H. Jung, N. Rai\v{c}evi\'c.

Figure 1
Figure 1. Figure 1: Comparison of input σ to the extracted one as a function of the centre-of-mass energy √ s obtained from PYTHIA-default (left) and the modified recoil treatment (right). In the standard PYTHIA 8 approach, a recoil-sharing step enforces exact conservation of the transverse momentum of the beam system. This compensation redistributes the net transverse momentum among all beam-related partons, including the ha… view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of pT(ℓℓ) for the DY pairs with invariant mass 7 ≤ m(ℓℓ) ≤ 8 GeV produced at √ s = 38.8 GeV for two different intrinsic-kT widths in PDF2ISR and PB (CASCADE): qs = 0.5 GeV (left) and qs = 1.0 GeV (right). For comparison the prediction of PDF2ISR with the default recoil scheme is shown. The uncertainty bands show the 7-point theoretical uncertainties. (Please note that the difference at pT(ℓℓ) ≥ … view at source ↗
Figure 3
Figure 3. Figure 3: Comparison between PB (CASCADE) and PDF2ISR predictions obtained with parton shower and TMD evolution (without intrinsic kT) for pT(ℓℓ) of DY pairs with invariant mass 7 ≤ m(ℓℓ) ≤ 8 GeV produced at √ s = 38.8 GeV (left) and for DY pairs in the Z-peak region produced at √ s = 13 TeV (right). The uncertainty bands show the 7-point theoretical uncertainties. undergoes full perturbative evolution to the scale … view at source ↗
Figure 4
Figure 4. Figure 4: Comparison between PB (CASCADE) and PDF2ISR predictions obtained with an intrinsic￾kT width of qs = 1 GeV and with parton shower and TMD evolution for pT(ℓℓ) of DY pairs with invariant mass 7 ≤ m(ℓℓ) ≤ 8 GeV produced at √ s = 38.8 GeV (left) and for DY pairs in the Z-peak region produced at √ s = 13 TeV (right). For comparison the prediction of PDF2ISR with the default recoil scheme is also shown. The unce… view at source ↗
Figure 5
Figure 5. Figure 5: shows the prediction of the PDF2ISR approach, together with measurements of CMS [19] at the highest centre-of-mass energy, √ s = 13 TeV, for the three invariant-mass bins indicated in the figure, focusing on the region of small pT(ℓℓ). b b b b b b b b b b b b b b b b b Data PDF2ISR qs = 1.04 GeV 1 CMS, 13 TeV, Z/γ ∗ → ℓ+ℓ−, 50 < mℓℓ < 76 GeV d σ/d pT(ℓℓ) [pb/GeV] b b b b b b b b b b b b b b b b 1 10 1 0.5 … view at source ↗
Figure 6
Figure 6. Figure 6: Transverse-momentum distributions of DY lepton pairs at √ s = 38.8 GeV (left), √ s = 200 GeV (middle), and √ s = 1.96 TeV (right), obtained with the PDF2ISR approach using PB-NLO￾2018-Set2, compared to measurements [21–23]. The invariant-mass ranges of the DY pairs are indi￾cated above the histograms, and the uncertainty bands show the 7-point theoretical uncertainties. The dependence of χ 2 on the centre-… view at source ↗
Figure 7
Figure 7. Figure 7: αs as a function of the scale µ 2 , with experimental measurements [38–58] and predictions at NLO, for Hard Freezing (Option A), Fixed Gluon Mass (Option B), and Running Gluon Mass (Option C), with the parameters given in the text. b b b b b b b b b bbb bb b b b b b b b b b b b b b b b b b b b b b b b b Data m0 = 0.5 GeV m0 = 1.0 GeV m0 = 1.5 GeV Option A 10 1 CMS, 13 TeV, Z/γ ∗ → ℓ+ℓ−, 76 < mℓℓ < 106 GeV … view at source ↗
Figure 8
Figure 8. Figure 8: Transverse-momentum distributions of DY lepton pairs at √ s = 13 TeV, obtained with the PDF2ISR approach, using three different ways of taming αs and three values of the m0 parameter, compared to measurements [19]. The uncertainty bands show the 7-point theoretical uncertainties. 11 [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Transverse-momentum distributions of DY lepton pairs at √ s = 38.8 GeV (left), √ s = 200 GeV (middle), and √ s = 1.96 TeV (right), obtained with the PDF2ISR approach, us￾ing three different ways of taming αs with m0 = 1 GeV, compared to measurements [21–23]. The invariant-mass ranges of the DY pairs are indicated above the histograms. The uncertainty bands show the 7-point theoretical uncertainties. Due to… view at source ↗
Figure 10
Figure 10. Figure 10: Transverse momentum distributions of DY lepton pairs at √ s = 13 TeV (left) and √ s = 38.8 GeV (right), obtained with the PDF2ISR approach, using the Fixed Gluon Mass taming (Option B), with qs = 2.0 GeV, compared to measurements [19, 21]. The invariant-mass ranges of the DY pairs are indicated above the histograms. The uncertainty bands show the 7-point theoretical uncertainties. 4 Conclusion We have app… view at source ↗

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