nCTEQ PDFs at the LHC: Vector boson production in heavy ion collisions

A. Kusina; C. Keppel; E. Godat; F. I. Olness; F. Lyonnet; I. Schienbein; J.F. Owens; J.G. Morfin; J. Kent; J. Y. Yu

REVIEW 3 major objections 5 minor 15 references

nCTEQ PDFs at the LHC: Vector boson production in heavy ion collisions

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Adding LHC proton-lead W/Z data to a nuclear PDF fit raises the lead strange quark distribution by about 40 percent, and the authors ask whether this shift is physical or a fitting artifact.

desk verdict A candid progress report whose headline strange shift is likely a byproduct of a restricted parameterization; the framework work is solid and worth a look. read the letter →

arxiv 1909.00452 v1 pith:5IO7JHKT submitted 2019-09-01 hep-ph

The nCTEQ Collaboration: D. B. Clark , E. Godat , T. J. Hobbs , T. Ježo , J. Kent , C. Keppel , M. Klasen , K. Kovarík

show 7 more authors

A. Kusina F. Lyonnet J.G. Morfin F. I. Olness J.F. Owens I. Schienbein J. Y. Yu

This is my paper · ORCID

classification hep-ph

keywords nuclearpartondistributionfunctionsstrangequarkPDFW/Zbosonproductionproton-leadcollisionsglobalQCDfitnCTEQNLOLHCheavy-iondata

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 claims that the long-standing puzzle of the strange quark parton distribution can be attacked with LHC vector-boson data from proton-lead collisions, and that the new data materially change the extracted nuclear strange PDF. Using a new C++ implementation of the nCTEQ global fit, the authors include NLO W±/Z production data in a preliminary fit alongside the usual DIS and Drell-Yan data. With no normalization shifts allowed, the fit improves the overall $\chi^2$ per degree of freedom from 992/816 to 828/816 and pulls the lead strange PDF up by about 40% at the $x$ values probed by W/Z production. When normalization shifts of up to 1σ are allowed, that strange-quark increase is roughly halved. The authors state the question directly: are the data telling us the strange sea is larger, or is the fit exploiting the least constrained flavor?

What carries the argument

The central object is nCTEQ++, a modular C++ rewrite of the nCTEQ nuclear-PDF global-fitting code. It integrates HOPPET for DGLAP evolution, APPLgrid for precomputed NLO coefficient grids, and MCFM for the W/Z matrix elements, and it exports fits in YAML for analysis. The key technical step is validation that the MCFM-generated ApplGrids are sufficiently PDF-independent that proton and nuclear PDF grids can be interchanged inside the fitting loop. The fit described here uses a deliberately limited parameter set—12 parameters instead of nCTEQ15’s 16—so that the strange PDF, normally fixed, is free to move; this restricted setup is what lets the authors attribute changes in $s(x)$ to the new LHC data.

What would settle it

Perform the same restricted fit with the three W/Z data sets that need roughly 3σ normalization shifts either removed or forced to zero shift; if the strange PDF returns to its nCTEQ15 value and the remaining W/Z $\chi^2$ stays far above 1, the 40% increase is a normalization artifact, not a physical signal.

Watch

Extended reading notes

Core claim

On its own terms, the paper's central result is that LHC pPb W±/Z data are a new, independent handle on flavor separation in nuclear parton distributions, and specifically that they prefer an enhanced strange PDF in lead. In a restricted fit that frees only 12 parameters—three for $s+\bar{s}$ and nine for the other fitted flavors—the NLO W/Z data pull $s(x)$ upward by roughly 40% in the $x$ region relevant to vector-boson production, while improving the fit to the W/Z data sets. The same exercise with a 1σ normalization shift cuts that increase roughly in half, which the authors take as a sign that the size of the strange-sea enhancement is entangled with the treatment of data normalization. The paper deliberately stops short of claiming the enhancement is physical; its stated question is whether the shift is dictated by nature or is the fit exploiting $s(x)$ because it is one of the least constrained flavors.

Load-bearing premise

The load-bearing assumption is that the normalization shifts allowed for a few LHC data sets—up to about 3σ—are genuine experimental uncertainties rather than a way to absorb theoretical or nuclear-correction errors.

Editorial extensions

If this is right

If the result holds, LHC proton-lead W/Z measurements become a usable constraint on the strange quark PDF in nuclei, complementing fixed-target neutrino-dimuon data.
The extracted strange PDF depends strongly on the assumed normalization uncertainties: without shifts it rises about 40%, with 1σ shifts about half that, so future fits must quote the normalization treatment alongside the PDF.
Including heavy-ion vector-boson data can improve proton PDFs by reducing the reliance on nuclear corrections applied to heavy-target DIS data.
With normalization shifts of up to about 3σ for a few data sets, a $\chi^2$/dof near 1 is achievable for all W/Z data, meaning the data are not mutually incompatible once normalizations are free.

Reading between the lines

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

If the 40% strange enhancement survives a full 16-parameter fit and the inclusion of ALICE, LHCb, and the second CMS run, it would imply that nuclear shadowing at small $x$ is weaker than nCTEQ15 assumes; the paper does not make this claim, but its own rapidity comparison points in that direction.
A direct cross-check would be to fit neutrino-DIS dimuon data and LHC pPb W/Z data together; if the strange PDF preferred by the two data sets disagree, the tension would locate the problem in nuclear corrections rather than in the strange flavor itself.
The near-3σ normalization shifts on a few data sets could be absorbing missing higher-order QCD corrections or underestimated theory uncertainties; under that reading the physical strange enhancement would be closer to the 1σ-shift result, roughly 20%.

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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

The one thing to know: this is an honest progress report, not a physics result. The nCTEQ collaboration has built a new C++ harness (nCTEQ++) that can include LHC W/Z observables in nuclear PDF fits, and they've run a first, deliberately restricted fit with pPb data. The eye-catching 40% rise in the lead strange PDF is fragile: it depends on both the fit's limited parameter count and on whether normalization shifts are allowed. The authors say this themselves, which is to their credit.

What is actually new: the modular C++ implementation with HOPPET/APPLgrid/MCFM integration, and the first attempt to constrain nPDFs with LHC pPb W/Z data inside the nCTEQ framework. They checked that the APPLgrids are sufficiently PDF-independent, which is a necessary validation. The chi-square improvement from 992/816 to 828/816 is not surprising — you're fitting something and it's better than not fitting — but the fact that the W/Z data pull toward a larger strange sea is worth noting.

Where it's soft: the fit uses only 12 parameters, with 9 for g, uV, dV, ubar+dbar, compared with 16 in nCTEQ15 for those same flavors. If the data want to move in those freed directions, the fit can compensate through the strange distribution, which is the least constrained. That's a direct confound for the 40% claim, and the paper doesn't test it. The normalization story is also wobbly: with a 1 sigma shift the effect halves, and they allow a few data sets to move up to 3 sigma. Without a proper treatment of the likelihood including normalization penalties, the quoted improvement is not evidence for a physical strange enhancement. There is also no uncertainty band on the 40% shift.

I'd say the right reading is: new tool, promising pipeline, one preliminary observation that needs a full 16-parameter fit and honest treatment of normalization before it means anything. The paper is candid about its limits, and the authors explicitly ask whether the fit is exploiting s(x). That kind of self-assessment deserves a fair referee.

Recommendation: send it to review as a proceedings-style contribution, but the referee should hold the authors to a clear statement that the strange shift is not a determination until they run the full basis.

Referee Report

3 major / 5 minor

Summary. This proceedings contribution from the nCTEQ collaboration describes a new C++ implementation of the nuclear PDF fitting framework (nCTEQ++) that integrates HOPPET, APPLgrid, and MCFM, and its first application: a preliminary NLO global fit that adds LHC pPb W±/Z vector-boson production data to the existing DIS and Drell-Yan data sets of nCTEQ15. The fit uses 12 parameters, three of which describe the strange-plus-antistrange distribution. The central phenomenological result is that, when no normalization shifts are allowed for the LHC data, the fit raises the lead strange PDF by about 40% at the x values probed by W/Z production; allowing normalization shifts of up to 1σ roughly halves this shift. The paper explicitly asks whether the strange increase is dictated by nature or is an artifact of fitting one of the least constrained flavors, and states that a complete analysis with additional parameters and data is in progress.

Significance. If the reported strange-PDF shift were robust, it would be an interesting hint that LHC pPb W/Z data, together with nuclear corrections, can discriminate strange flavor in a way complementary to neutrino-DIS dimuon production. The paper has real strengths: it introduces a modular, maintainable fitting code (nCTEQ++) with validated APPLgrid-based NLO calculations, and it is admirably candid in identifying the normalization-shift dependence and the question of whether s(x) is simply being exploited as a least-constrained flavor. However, the analysis is explicitly preliminary and the central 40% figure is not accompanied by an uncertainty estimate, is obtained from a deliberately restricted parameter basis, and depends strongly on the normalization treatment. The significance of the claim is therefore conditional: the framework and the questions posed are valuable, but the quantitative conclusion is not yet established.

major comments (3)

[Sec. 4, Fig. 4] The 40% increase of the lead strange PDF is quoted as a single number with no uncertainty. The paper advertises nCTEQ nPDFs with uncertainties, and the nCTEQ15 baseline has an uncertainty band; the fitted s(x) should be compared with that band at the relevant x values. Without such a comparison, the reader cannot tell whether a 40% shift is statistically significant or consistent with the prior uncertainty, and the abstract and conclusion currently present the number without this qualification.
[Sec. 4, footnote 3] The restricted parameterization is a load-bearing confound for the central claim. The fit uses 12 parameters (3 for s+sbar and 9 for the remaining flavors), whereas nCTEQ15 uses 16 parameters for the non-strange set. Because the non-strange directions that are frozen here could absorb some of the LHC W/Z data's pull, the 40% strange shift may be an artifact of the reduced basis rather than a property of the data. The paper itself voices this concern in Sec. 4, but it does not provide a test, such as a fit with the full 16-parameter non-strange basis or a fit that frees the gluon and strange parameters separately, to determine how much of the shift survives.
[Sec. 4, Fig. 3] The no-normalization fit, which produces the 40% strange shift, has an overall chi2/dof of 828/816, but the figure shows that several individual W/Z data sets have unacceptable chi2 values. The paper notes that allowing up to 1-sigma normalization shifts reduces the strange shift by roughly half. Since the headline number is taken from a fit that does not adequately describe the new data, the central claim is not robust to the normalization treatment; at minimum, the paper should give the shift with a systematic uncertainty reflecting the choice of whether and how normalization shifts are allowed.

minor comments (5)

[Abstract] The abstract uses the word “impact” for the effect of the LHC W/Z data, but the reported chi2 numbers and PDF shifts are results of a fit that includes those data, not predictions made before the fit; a qualifier noting that the result is a preliminary fit would be appropriate in the abstract.
[Sec. 2] There is a typo in the abstract, “strucure” for “structure,” and in Sec. 2 “Y AML” appears where “YAML” is intended; these should be corrected.
[Fig. 3 caption] The caption contains the typos “Prelimnary” and “unconstrainted,” and the phrase “w/o Norm Penalty” should be explained, since the body text describes the shifts as constrained by luminosity uncertainties rather than by a penalty term.
[Sec. 4, status table] The status table lists CMS Z (6235) and CMS_II W± (6232, 6234) as “grids finished not validated,” while the text says several data sets are “fully included”; the paper should specify explicitly which of the listed LHC data sets enter the reported fit and which are only shown as comparisons.
[Fig. 4] The vertical magenta line is described only as “the central x value for pPb W±/Z production”; stating the x range or value, and the Q scale used for the PDFs, would make the plot more informative.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the 40% strange shift is a fit output, not a prediction; the paper explicitly flags the fit-artifact possibility.

full rationale

The paper's central result is a standard PDF re-fit: nCTEQ++ adds LHC pPb W±/Z data to the existing nCTEQ15 global fit and reports the resulting changes in χ² and in the strange PDF. This is not circular because the strange PDF is an output of the fit, not an input used to construct the data or the theory predictions. The χ² improvement from 992/816 to 828/816 is the expected consequence of adding freedom to describe newly included data, and the paper does not present this improvement as an independent prediction. The 40% increase in s(x) at the W/Z x-region is a sensitivity result, explicitly conditional on the chosen 12-parameter fit basis and on the treatment of normalization shifts; the authors themselves ask whether the fit is 'simply exploiting s(x) because that is one of the least constrained flavors.' That caveat is a limitation or model-dependence, not a logical circularity. The derivation chain relies on external inputs (LHC data, MCFM/APPLgrid/HOPPET, nCTEQ15 baseline) and makes a genuine comparison between fits with and without the new data. Self-citations to prior nCTEQ work provide the code and baseline, but the load-bearing quantitative results are computed in this paper. No equation or result is shown to reduce by construction to its own input, and no fitted parameter is renamed as a prediction. The reduced non-strange parameter basis is a legitimate methodological restriction, not a circular step.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The central analysis rests on standard QCD factorization and the validity of NLO calculations from MCFM, plus the nCTEQ15 nuclear corrections. It introduces no invented entities. The main free parameters are the 12 PDF shape parameters and the data normalization shifts.

free parameters (2)

12 PDF shape parameters (3 for s+sbar, 9 for {g,uV,dV,ubar+dbar}) = not reported
These parameters are fitted to the global dataset; no values or uncertainties are given in the proceedings.
Normalization shifts for LHC W/Z data sets = up to ~3σ for a few data sets
Applied in the fit to improve χ²; the paper does not quote the fitted shift values.

assumptions (3)

domain assumption Collinear QCD factorization and DGLAP evolution are valid for pPb W/Z production at NLO.
Standard framework used via HOPPET and MCFM in Section 2.
domain assumption MCFM APPLgrids are sufficiently PDF-independent to allow interchanging proton and nuclear PDFs.
Explicitly stated as an important validation step in Section 2.
ad hoc to paper The nCTEQ15 nuclear correction parameterization provides an adequate baseline, with 12 free parameters sufficient to capture the impact of the new data.
The fit uses only 12 parameters and the paper acknowledges the result may be an artifact of limited freedom.

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Cite this review

Pith. "Pith review of nCTEQ PDFs at the LHC: Vector boson production in heavy ion collisions." pith.science (2026). https://pith.science/paper/5IO7JHKT

@misc{pith2026190900452,
  author       = {Pith},
  title        = {Pith review of: nCTEQ PDFs at the LHC: Vector boson production in heavy ion collisions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5IO7JHKT}},
  note         = {Machine review of arXiv:1909.00452}
}

read the original abstract

Extraction of the strange quark PDF is a long-standing puzzle. We use the nCTEQ nPDFs with uncertainties to study the impact of the LHC W/Z production data on both the flavor differentiation and nuclear corrections; this complements the information from neutrino-DIS data. As the proton flavor determination is dependent on nuclear corrections (from heavy target DIS, for example), LHC heavy ion measurements can also help improve proton PDFs. We introduce a new implementation of the nCTEQ code (nCTEQ++) based on C++ which has a modular strucure and enables us to easily integrate programs such as HOPPET, APPLgrid, and MCFM. Using ApplGrids generated from MCFM, we use nCTEQ++ to perform a preliminary fit including the pPb LHC W/Z vector boson data.

Figures

Figures reproduced from arXiv: 1909.00452 by the authors.

**Figure 1.** Comparison of LHC W boson production in p-Pb processes vs. rapidity. The lighter (yellow) band uses CT10 with no nuclear corrections, and the darker (blue) band uses the nCTEQ15 PDFs; this data is not included in the nCTEQ15 fit [11]. In a previous study we compared our predictions for the production of W±/Z bosons with available LHC data for proton-lead collisions [11]. This process is an ideal QCD “laboratory” as … view at source ↗

**Figure 2.** a) Theory predictions for Run II CMS W− production (ID:6232), and b) for Run I CMS W+ production (ID:6233) in pPb. The data are the blue squares and the theory are the red points. For comparison, we also display the theory predictions in b) with a 5% normalization shift (cyan). 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** χ 2/do f for individual data sets of the (restricted) nCTEQ+LHC fit; data set ID’s are given in Ref. [11]. The LHC W±/Z data is displayed in green. Prelimnary results are shown for i) no normalization shift, ii) a shift of up to 1σ, iii) an unconstrainted (optimal) shift. In [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Resulting nPDFs for lead (Pb) at Q = 2 GeV for the a) strange and b) gluon. The vertical line (magenta) represents the central x value for pPb W±/Z production. indicates the central x value for pPb W±/Z production. Compared to the nCTEQ15 result, we see the [NO NORM] f…

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

nCTEQ15 - Global analysis of nuclear parton distributions with uncertain- ties in the CTEQ framework

K. Kovarik et al. “nCTEQ15 - Global analysis of nuclear parton distributions with uncertain- ties in the CTEQ framework”. In: Phys. Rev. D93.8 (2016), p. 085037. arXiv: 1509.00792 [hep-ph]

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Nuclear parton distributions from lepton-nucleus scattering and the impact of an electron-ion collider

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Strange Quark PDFs and Implications for Drell-Yan Boson Production at the LHC

A. Kusina et al. “Strange Quark PDFs and Implications for Drell-Yan Boson Production at the LHC”. In: Phys. Rev. D85 (2012), p. 094028. arXiv: 1203.1290 [hep-ph]

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A. M. Cooper-Sarkar and K. Wichmann. “QCD analysis of the ATLAS and CMSW± and Z cross-section measurements and implications for the strange sea density”. In: Phys. Rev. D98.1 (2018), p. 014027. arXiv: 1803.00968 [hep-ex]

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M. Hirai, S. Kumano, and T. H. Nagai. “Determination of nuclear parton distribution functions and their uncertainties in next-to-leading order”. In: Phys. Rev. C76 (2007), p. 065207. arXiv: 0709.3038 [hep-ph]

arXiv 2007

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Daniel de Florian et al. “Global Analysis of Nuclear Parton Distributions”. In:Phys. Rev. D85 (2012), p. 074028. arXiv: 1112.6324 [hep-ph]

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A Higher Order Perturbative Parton Evolution Toolkit (HOPPET)

Gavin P. Salam and Juan Rojo. “A Higher Order Perturbative Parton Evolution Toolkit (HOPPET)”. In: Comput. Phys. Commun. 180 (2009), pp. 120–156. arXiv: 0804.3755 [hep-ph]

arXiv 2009