LHC and DIS experimental data in the CT18(Z) global QCD analysis

Bo-Ting Wang; Carl Schmidt; C.-P. Yuan; Dan Stump; Ibrahim Sitiwaldi; Joey Huston; Jon Pumplin; Jun Gao; Keping Xie; Marco Guzzi

REVIEW 4 major objections 4 minor 17 references

LHC and DIS experimental data in the CT18(Z) global QCD analysis

T0 review · 4 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The CT18Z global QCD analysis shows that a tuned x-dependent factorization scale, $\mu_{F,x}^2=0.82(Q^2+0.3\,\mathrm{GeV}^2/x^{0.3})$, cuts the NNLO HERA inclusive-DIS $\chi^2$ by more than 50 units and reproduces the improvement…

desk verdict A solid proceedings writeup of the CT18 PDF family, but the resummation-mimicry claim rests on a scale tuned in-sample and needs an out-of-sample check. read the letter →

arxiv 1909.00001 v1 pith:DYZH2RXS submitted 2019-08-29 hep-ph

Tie-Jiun Hou , Keping Xie , Jun Gao , Sayipjamal Dulat , Marco Guzzi , T. J. Hobbs , Joey Huston , Pavel Nadolsky

show 6 more authors

Jon Pumplin Carl Schmidt Ibrahim Sitiwaldi Dan Stump Bo-Ting Wang C.-P. Yuan

This is my paper · ORCID

classification hep-ph

keywords CT18PDFspartondistributionfunctionsNNLOQCDglobalanalysisHERAI+IIinclusiveDISx-dependentfactorizationscalelow-xresummationLHCdatastrangenessPDF

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 presents four new families of next-to-next-to-leading-order parton distribution functions---CT18, CT18A, CT18X, and CT18Z---produced in a global QCD analysis that adds eleven LHC data sets. Its central claim is that a fitted x-dependent factorization scale, $\mu_{F,x}^2 = 0.82(Q^2 + 0.3\,\mathrm{GeV}^2/x^{0.3})$, lowers the NNLO $\chi^2$ of the combined HERA I+II inclusive deep-inelastic-scattering data by more than 50 units, matching the gain previously attributed to low-$x$ resummation. A sympathetic reader would care because the scale choice changes the small-$x$ gluon and strangeness PDFs and therefore shifts NNLO predictions for LHC observables, while also offering a fixed-order alternative to resummation. The four ensembles are designed to bracket the PDF uncertainty coming from data selection and scale choice rather than to give a single answer.

What carries the argument

The load-bearing object is the x-dependent factorization scale $\mu_{F,x}^2 = 0.82(Q^2+0.3\,\mathrm{GeV}^2/x^{0.3})$, a saturation-inspired one-scale ansatz whose coefficients were chosen to minimize the HERA DIS $\chi^2$. At small $x$, the added $0.3/x^{0.3}$ term raises the scale above $Q^2$, effectively absorbing a class of enhanced power logarithms that would otherwise be treated by low-$x$ resummation; at larger $x$ it reduces to a constant factor $0.82$ times $Q^2$. The same machinery also includes fast impact-analysis programs to select eleven new LHC data sets and a parallelized fitting code with fast grid interfaces, but the scale ansatz is what carries the central claim about matching resummation.

What would settle it

Take the fitted $\mu_{F,x}$ scale into a predictor outside the fitted HERA kinematics, for example forward charm or Drell-Yan production at the LHC at small $x$, or HERA data with $Q$ below 2 GeV, and compare CT18Z predictions with data and with a resummed PDF set. If the CT18Z predictions agree with data at resummation quality, the scale is a valid proxy; if the >50-unit improvement disappears or the predictions deviate once kinematics change, the ansatz is tuned rather than physical.

Watch

Extended reading notes

Core claim

On its own terms, the paper establishes that the conventional fixed-order NNLO description of HERA data can be substantially improved without resummation by evaluating DIS cross sections with the tuned scale $\mu_{F,x}^2=0.82(Q^2+0.3\,\mathrm{GeV}^2/x^{0.3})$ instead of $\mu_F^2=Q^2$. In the region $Q>2$ GeV, $x>10^{-5}$, this reduces $\chi^2(\mathrm{HERA\ I+II})$ by more than 50 units, a quality of improvement the paper describes as comparable to that reported by resummed analyses. The resulting CT18X and CT18Z fits show reduced $u$ and $d$ (anti-)quark PDFs and increased gluon and strangeness at $x<10^{-2}$, with compensating changes at $x>0.5$ to preserve valence and momentum sum rules. In CT18Z, removal of CDHSW nuclear data and inclusion of ATLAS 7 TeV W/Z data combine to reduce the NNLO gluon-fusion Higgs cross section by about 1% relative to CT14 and CT18.

Load-bearing premise

The premise is that a scale whose two coefficients were tuned to the HERA data can genuinely reproduce the small-$x$ logarithms that resummation computes explicitly, so its benefit should persist for unmeasured kinematics rather than being an in-sample artifact.

Editorial extensions

If this is right

At NNLO, the small-$x$ behavior of the gluon and strangeness PDFs in CT18X/Z differs from CT18; quantities such as the gluon-fusion Higgs cross section shift by about 1%, altering the central value that precision electroweak and Higgs analyses compare with.
The reported >50-unit $\chi^2$ drop means the combined HERA data do not, by themselves, force low-$x$ resummation: a fixed-order fit with the tuned scale is an equally good description, so resummed PDFs and scale-shifted PDFs should both be used for uncertainty bands.
Because CT18, A, X, and Z are generated under different data-selection and scale assumptions, the spread among them gives a practical systematic uncertainty on NNLO predictions for LHC processes beyond the one-sigma Hessian error.
Including the ATLAS 7 TeV W/Z rapidity data raises the tension with the strangeness-sensitive dimuon data from CCFR and NuTeV; the elevated goodness-of-fit variables in CT18Z show that the strangeness PDF is constrained by competing data sets, not uniquely by either.

Reading between the lines

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

A natural extension not drawn by the paper: the same scale ansatz could be lifted into nuclear PDF fits or future electron-ion collider projections, where the small-$x$ regime is scanned directly; if it holds there, the saturation-inspired wording gains predictive content.
An explicit overlap test would fit with both the tuned scale and a resummed theory simultaneously and see whether the scale loses its benefit; if it does, the two mechanisms are not independent alternatives but overlapping ways of absorbing the same logarithms.
The tuned coefficients 0.82 and 0.3 depend on the data set; one could attempt to derive them from a first-principles saturation momentum and re-fit newer datasets to see whether the same functional form recurs, rather than being a one-off adjustment.

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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 punchline: this is a competent proceedings writeup of the CT18 family, and the four new PDF ensembles are real new objects. But the claim that the x-dependent scale reproduces the effect of low-x resummation is not backed by an out-of-sample check, because the scale coefficients were tuned to the same HERA data whose chi-square improvement is quoted. That specific claim should be treated as conditional until tested on unmeasured kinematics or on LHC observables.

What's genuinely good: the paper is transparent about tensions. The SE distribution figure and the discussion of why the ATLAS W/Z data elevate the dimuon chi-square is honest. The use of PDFSense and ePump to preselect data, the cross-validation of APPLgrid tables, and the acknowledgment that the CDHSW data were removed because they prefer a harder gluon are all the right kind of methodological candor. The paper also does a service by pointing to the companion full CT18 paper for the actual fit details.

The soft spots, in order. First, the x-dependent scale. The text says explicitly the coefficients 0.82, 0.3 GeV^2, and 0.3 are "chosen to minimize chi-square for the HERA DIS data." With three parameters free, an in-sample improvement of more than 50 chi-square units on a large correlated data set is exactly what you'd expect from tuning; it is not evidence that the scale captures the physics of resummation. The comparison to resummed fits is also indirect: they cite the resummation papers but don't show a quantitative side-by-side. Second, the PDF changes at small x from the scale choice have no uncertainty bands shown, so it's unclear whether the gluon shift is demanded by data or is an artifact of the ansatz. That's a presentation gap, minor in a proceedings but relevant to anyone who wants to use CT18Z. Third, the global fit itself has the usual selection-after-inspection issue: data sets are added or removed after looking at fit quality. They are open about it, and it's standard practice, but it means the quoted chi-squares are not a rigorous measure of global fitness.

None of this sinks the paper. The CT18 family is a credible incremental update of an established program, and the four ensembles are useful tools for exploring scale and data-selection sensitivity. The resummation-mimicry claim is the part I'd want to see pinned down with a genuine prediction before I'd bank on it.

Who gets value: anyone doing NNLO phenomenology at the LHC who wants up-to-date PDFs with controlled variations; PDF fitters will go to the companion paper. I'd take this to my reading group and cite it, but I'd also flag the scale-tuning issue to my students.

Recommendation: yes, send it to peer review. It's a legitimate contribution, and referees should push for an out-of-sample check of the x-dependent scale.

Referee Report

4 major / 4 minor

Summary. This proceedings contribution from the CTEQ-TEA collaboration reports on the implementation of HERA I+II and LHC data in the new CT18 global QCD analysis. The paper presents four NNLO (and corresponding NLO) PDF families: CT18, CT18A, CT18X, and CT18Z, which differ in data selection and in the factorization scale used for DIS. The main physics claim is that using an x-dependent factorization scale mu_F,x^2 = 0.82(Q^2 + 0.3 GeV^2/x^0.3) in fixed-order NNLO DIS calculations reduces the HERA I+II inclusive DIS chi-square by more than 50 units, an improvement described as comparable to that obtained with low-x resummation in Refs. [6,7]. The paper also discusses tensions among HERA, Tevatron, and LHC data sets, the use of PDFSense and ePump for data selection, and the impact of the alternative scales on PDFs and on the NNLO Higgs cross section.

Significance. If the central claim is correct, CT18Z and its siblings provide a systematic family of NNLO PDFs that span a range of plausible scale and data-selection choices, and the x-dependent scale idea could offer a practical fixed-order alternative to small-x resummation for global fits. The paper is valuable for its candid discussion of data tensions, its explicit statement that the x-dependent scale coefficients are tuned to minimize the HERA chi-square, and its use of modern fast-interfacing and reweighting tools. However, the key quantitative evidence for the resummation-mimicry claim is currently in-sample: the scale is fitted to the same HERA data whose chi-square improvement is reported, and no out-of-sample test or uncertainty analysis is provided. The significance of CT18X/Z therefore rests on validation that is not presented in this manuscript.

major comments (4)

[Combined HERA I+II DIS data and an x-dependent factorization scale] The sentence defining mu_F,x^2 states that the numerical coefficients are chosen to minimize chi-square for the HERA DIS data. The subsequent claim that this scale produces a reduction of more than 50 chi-square units and a 'comparable quality of improvement' to low-x resummation is therefore an in-sample fit statistic, not independent evidence of physical equivalence. The manuscript should provide an out-of-sample validation: for example, fix the coefficients using a training subset of HERA data or a HERA-only fit, then evaluate the held-out HERA bins and LHC observables sensitive to the small-x gluon. The improved chi-square reported for charm SIDIS and H1 FL in Fig. 1(right) does not resolve this issue because these data sets are part of the same fit.
[Figure 1] Figure 1(left) shows ratios of CT18 PDFs obtained with the x-dependent and standard scales, but no PDF uncertainty bands or chi-square decomposition are provided. Without error bands and per-data-set chi-square values, the reader cannot determine whether the enhanced small-x gluon and altered quark distributions are statistically required or are an artifact of the tuned scale. The manuscript should show the uncertainties of CT18 and CT18Z and report the chi-square per data set for both scale choices.
[Combined HERA I+II DIS data and an x-dependent factorization scale] The comparison with low-x resummation in Refs. [6,7] is not apples-to-apples as presented: the data selections, kinematic cuts, chi-square definitions, and perturbative orders differ between the CT18 fit and the resummed fits. The claim that the improvement is 'comparable' requires a table specifying the data sets, Q and x cuts, and chi-square definitions used in each comparison. Without this, the >50 unit improvement cannot be interpreted as equivalent to the resummation effect.
[Selection of new LHC experiments] The abstract and body present CT18, A, X, and Z as four new PDF families, but this proceedings contribution does not provide the defining criteria for each family beyond brief descriptions: no LHAPDF names, no complete input data lists, no central chi-square values, and no error sets are given. Since these definitions are load-bearing for the paper's central claim, the manuscript should either include a compact table summarizing the data sets and scale choices for each family or explicitly refer to a publicly available companion document where these details are given.

minor comments (4)

[Combined HERA I+II DIS data and an x-dependent factorization scale] There are typographical errors in this section: 'thee+p and e−p' should be 'the e+p and e−p', 'with e HERA' should be 'with HERA', and 'multi-prone' should be 'multi-pronged'.
[Figure 1] The left panel's caption contains a garbled formula, 'a (x,Q)/f (2)a f', which appears to be an attempt to write the ratio of PDFs; it should be cleaned up to something like f_a^{(1)}(x,Q)/f_a^{(2)}(x,Q).
[Combined HERA I+II DIS data and an x-dependent factorization scale] The phrase 'unconstrained region x > 0.5' is imprecise: the valence quark region is constrained by sum rules, so it would be clearer to say 'a region less tightly constrained by the fitted data' or to specify what is meant by 'unconstrained'.
[Figure 2] The caption labels 'CT18 NNLO' and 'CT18Z NNLO' but the text refers to 'CT14HERA2' in the upper panel; the notation and the relationship between the two panels should be clarified.

Circularity Check

1 steps flagged · score 4.0 of 10

The x-dependent scale is tuned to the same HERA chi-square that is then quoted as evidence of resummation-level improvement.

fitted input called prediction [Section 'Combined HERA I+II DIS data and an x-dependent factorization scale' (pp. 1-2), inline definition of mu_F,x and first-figure discussion]
"In our analysis, we observe that, by evaluating the DIS cross sections at NNLO with an x-dependent factorization scale, such as a tuned scale μ2F,x = 0.82(Q2 + 0.3 GeV2/x0.3), instead of the conventional choice μ2F = Q2, we achieve a comparable quality of improvement ... Namely, the χ2(HERA I+II) reduces by > 50 units ... and the numerical coefficients in μ2F,x are chosen to minimize χ2 for the HERA DIS data."

The three coefficients of μ2F,x are explicitly fitted to minimize χ2 for the HERA I+II inclusive DIS data, and the same χ2 reduction (>50 units) is then reported as evidence that this scale choice matches the improvement attributed to low-x resummation. This is an in-sample fit improvement, not an independent prediction: three free parameters tuned to a large precise data set are expected to reduce its χ2, so the comparison to fixed-scale resummation is not a controlled out-of-sample test. The paper even labels the scale 'tuned' and states that its coefficients are chosen to minimize the very χ2 that is quoted.

full rationale

The CT18, CT18A, CT18X, and CT18Z PDFs are produced by a standard global QCD fit to many independent data sets (HERA, Tevatron, LHC jets, W/Z and top production, dimuon production, etc.), so the analysis as a whole is not circular and is benchmarked against external data. The self-citations to the companion CT18 paper, CT14HERA2, ePump, and PDFSense are methodological and not load-bearing in a circular way. The one genuine circular element is the x-dependent factorization scale: its numerical constants are chosen to minimize the HERA I+II DIS chi-square, and the resulting in-sample chi-square gain is then used to claim equivalence to small-x resummation. This is a fitted input being presented as evidence for a physics conclusion without an out-of-sample check or uncertainty quantification for the resulting PDF changes. Because this affects only the specific 'mimics resummation' claim and not the central PDF-determination machinery, the overall circularity score is moderate rather than severe.

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

The central fit rests on standard QCD factorization and on the fitted x-dependent scale ansatz; the scale is the main non-standard input. No new particles, forces, or entities are introduced. The PDF shape coefficients are standard fit parameters of the method.

free parameters (4)

0.82 prefactor in x-dependent scale = 0.82
Chosen to minimize HERA DIS chi-square; directly sets the magnitude of the claimed 50-unit improvement.
0.3 GeV^2 offset in x-dependent scale = 0.3 GeV^2
Chosen to minimize HERA DIS chi-square; part of the tuned ansatz that mimics small-x logarithms.
0.3 exponent of x in x-dependent scale = 0.3
Chosen to minimize HERA DIS chi-square; controls the small-x growth of the scale.
PDF parametrization coefficients (Bernstein polynomial)
All coefficients of the input PDF shapes are fitted in the global analysis; they are standard internal parameters of the CTEQ-TEA method rather than newly introduced constants.

assumptions (4)

domain assumption NNLO collinear factorization is valid for all included DIS and LHC observables.
The global fit relies on NNLO pQCD kernels and factorization theorems; this is the standard working assumption of the CTEQ-TEA program.
ad hoc to paper The x-dependent scale ansatz can reproduce the effect of small-x resummation.
No derivation is given for the ansatz; the coefficients are fitted to the HERA data whose chi-square is quoted as evidence, making the assumption load-bearing for the improvement claim.
domain assumption The HERA I+II combined data provide unbiased constraints on quark and gluon PDFs.
HERA data dominate the fit, and the paper acknowledges unresolved e+p versus e-p tensions that are not conclusively explained.
domain assumption The Hessian error PDF methodology and tolerance criteria are valid.
The analysis uses Hessian error sets and statistical tolerance tests without rederiving their validity.

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Cite this review

Pith. "Pith review of LHC and DIS experimental data in the CT18(Z) global QCD analysis." pith.science (2026). https://pith.science/paper/DYZH2RXS

@misc{pith2026190900001,
  author       = {Pith},
  title        = {Pith review of: LHC and DIS experimental data in the CT18(Z) global QCD analysis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DYZH2RXS}},
  note         = {Machine review of arXiv:1909.00001}
}

read the original abstract

We discuss implementation of the LHC experimental data sets in the new CT18 global analysis of quantum chromodynamics (QCD) at the next-to-next-leading order of the QCD coupling strength. New methodological developments in the fitting methodology are discussed. Behavior of the CT18 NNLO PDFs for the conventional and "saturation-inspired" factorization scales in deep-inelastic scattering is reviewed. Four new families of (N)NLO CTEQ-TEA PDFs are presented: CT18, A, X, and Z.

Figures

Figures reproduced from arXiv: 1909.00001 by the authors.

**Figure 2.** The effective Gaussian variable (Sn) distribution of all (a) CT18 data sets, and (b) CT18Z data sets. Two squares and two stars indicate the Sn values for the NuTeV dimuon and CCFR dimuon data, respectively. costs grow quickly with the number of experimental data sets at NNLO. Poorly fitted experiments would increase, not decrease, the final PDF uncertainty. The generation of one error PDF set took several days of C… view at source ↗

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Reference graph

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Pith tools

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

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arXiv 2016

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T.-J. Hou, S. Dulat, J. Gao, M. Guzzi, J. Huston, P. Nadolsky et al., CTEQ-TEA parton distribution functions and HERA Run I and II combined data, Phys. Rev. D95 (2017) 034003 [1609.07968]

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