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REVIEW 3 major objections 5 minor 5 cited by

Progress in the CTEQ-TEA NNLO global QCD analysis

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

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Pith's one-line read The CT18 global analysis claims that an x-dependent factorization scale reproduces the HERA-data improvement attributed to low-x resummation.

desk verdict CT18 is a solid public PDF update, but the x-dependent scale improvement is fitted on the same HERA data it is then used to describe. read the letter →

arxiv 1908.11394 v1 pith:4ZEDTC7Y 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 5 more authors
Jon Pumplin Carl Schmidt Ibrahim Sitiwaldi Dan Stump C.-P. Yuan
This is my paper · ORCID
classification hep-ph
keywords QuantumchromodynamicspartondistributionfunctionsglobalQCDanalysisnext-to-next-to-leadingorderHessianmethoddeep-inelasticscatteringfactorizationscaleLHCdata
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 introduces the CT18 family of parton distribution functions, the new NNLO global QCD analysis based on 3681 data points with a default chi-squared per point of 1.17. The new PDFs include a wide range of LHC measurements—W and Z production, Drell-Yan, jets, and top-quark pairs—and replace the earlier CT14 set. The central physics claim is that an x-dependent factorization scale, $\mu^2_{F,x}=0.82(Q^2+0.3\,\mathrm{GeV}^2/x^{0.3})$, improves the fixed-order NNLO description of the combined HERA deep-inelastic data by more than 50 units of chi-squared, comparable to what low-x resummation was previously reported to achieve. If this is correct, standard NNLO tools can describe small-x DIS without explicit resummation, and the small-x gluon and sea-quark shapes in CT18 shift accordingly. Because the ATLAS 7 and 8 TeV W/Z data cannot be fitted together with the rest of the world data, four PDF families—CT18, CT18A, CT18X, CT18Z—are provided to bracket the resulting ambiguity.

What carries the argument

The central mechanism is the $x$-dependent factorization scale $\mu^2_{F,x}=0.82\,(Q^2+0.3\,\mathrm{GeV}^2/x^{0.3})$, used in place of the conventional $\mu_F^2=Q^2$ when evaluating NNLO DIS cross sections. It is intended as a fixed-order proxy for enhanced low-$x$ logarithms; the paper reports that it lowers $\chi^2$ for the HERA I+II inclusive data by more than 50 units in the stated region, matching the improvement attributed to resummation. The supporting apparatus is the Hessian global-fit machinery: fast grid interfaces (APPLgrid and fastNLO) for cross sections, the PDFSense and ePump programs for deciding which data sets constrain the fit, Lagrange Multiplier scans for PDF constraints, and flexible Bernstein-polynomial parametrizations tested over more than 90 functional forms.

What would settle it

Take the tuned scale $\mu^2_{F,x}$ with its published coefficients and apply it, without refitting, to independent low-x DIS data not included in the CT18 fit, such as future EIC structure-function measurements; if the out-of-sample improvement is not comparable to the reported >50-unit gain on HERA, the scale is absorbing fit noise rather than the low-x logarithms it is claimed to reproduce.

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Extended reading notes

Core claim

The paper claims that the CT18 family of NNLO parton distribution functions, fitted to 3681 data points with $\chi^2/N_{\mathrm{pt}}=1.17$ in the default set, supersede CT14 and CT14HERA2 for LHC phenomenology. Its central physics result is that an $x$-dependent factorization scale in fixed-order NNLO deep-inelastic scattering reproduces the HERA-data improvement previously attributed to low-$x$ resummation, a reduction of more than 50 units of $\chi^2$ in the kinematic region $Q>2$ GeV and $x>10^{-5}$, while also moving the small-$x$ gluon and sea quarks. Because the high-precision ATLAS $W/Z$ measurements cannot be accommodated together with the rest of the world data, four PDF families (CT18, CT18A, CT18X, CT18Z) are presented; the spread among them is the paper's estimate of the present ambiguity in NNLO PDFs.

Load-bearing premise

The x-dependent scale's coefficients are chosen to minimize chi-squared on the HERA data that are then quoted as the improvement, so the small-x physics claim rests on that scale being a genuine theoretical proxy for resummation rather than a flexible fit.

Editorial extensions

If this is right

  • The default CT18 set becomes the reference NNLO PDF ensemble for LHC calculations, replacing CT14 and CT14HERA2, with Hessian error sets for uncertainty propagation.
  • If the tuned scale is equivalent to low-x resummation for inclusive DIS, fixed-order NNLO calculations can be used in kinematic regions where explicit resummation was previously thought necessary.
  • The four CT18 families quantify the range of NNLO PDF behavior consistent with current data; using only the default set would understate the ambiguity revealed by the ATLAS W/Z tension.
  • CT18Z, the variant that includes the ATLAS W/Z data, removes CDHSW, adopts a saturation-inspired DIS scale, and reduces the NNLO gluon-fusion Higgs cross section by about 1% relative to CT14 and CT18.
  • The new parametrization, with an SU(3)-symmetric strange sea at x->0 and a d/u ratio free at x->1, changes strange-quark and high-x d-quark predictions relevant to W-mass and new-physics analyses.

Reading between the lines

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

  • Beyond the paper, the central claim is directly testable out of sample: take the fixed coefficients of $\mu^2_{F,x}$ and apply them to low-x DIS data not used in the fit; the paper reports no such held-out test.
  • The claimed equivalence with resummation is demonstrated only for inclusive HERA data; a natural extension would be to check charm and bottom structure functions or transverse-momentum distributions, where resummation and a scale change can diverge.
  • If the tuned scale is instead a phenomenological knob, then the spread across CT18, A, X, and Z would be the honest statement of current small-x uncertainty, and future precision data would be needed to break the degeneracy between scale choice and resummation.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The manuscript presents the CTEQ-TEA collaboration's new CT18 global QCD analysis at NNLO, which is offered as the successor to CT14. Four PDF families are released (CT18, CT18A, CT18X, CT18Z), based on a global fit to 3681 data points for the default set with chi^2/Npt = 1.17 at NNLO. The paper describes the inclusion of new LHC data on jets, W/Z, Drell-Yan, and top-quark pair production, along with methodological advances (PDFSense, ePump, parallelized fitting). A central feature is an x-dependent factorization scale mu_F,x^2 = 0.82(Q^2 + 0.3 GeV^2 / x^0.3) used for DIS, which is reported to reduce the HERA I+II chi^2 by more than 50 units relative to the conventional scale mu_F^2 = Q^2, an improvement described as comparable to the inclusion of low-x resummation. The paper also compares PDF luminosities at the 13 TeV LHC with other groups and presents Lagrange Multiplier scans for the gluon and strangeness PDFs.

Significance. If the CT18 analysis is sound, it represents a valuable update to a widely used PDF set, incorporating a large body of new LHC data and improved fitting methodology. The public availability of the PDF grids and the careful comparisons with other groups are clear strengths. The x-dependent scale observation is intriguing: if it were shown to be a theoretically legitimate proxy for low-x resummation, it would be an important result for small-x phenomenology. However, the evidence presented in the manuscript does not currently establish that claim, because the scale's coefficients are tuned on the same HERA data used to demonstrate the chi^2 improvement. The four-family spread is also presented as a way to explore PDF uncertainty, but the selection of the alternative variants is driven by post-hoc data choices, so this spread is not a calibrated uncertainty band. These issues do not undermine the basic existence of the CT18 fit, but they do affect the strength of the paper's central 'progress' claims.

major comments (3)
  1. [Sec. II, 'Combined HERA I+II DIS data and an x-dependent factorization scale'] The paper states that the numerical coefficients in mu_F,x^2 = 0.82(Q^2 + 0.3 GeV^2 / x^0.3) are 'chosen to minimize chi^2 for the HERA DIS data', and then uses the same HERA I+II data to report a chi^2 reduction of more than 50 units. This is an in-sample, fitted improvement, not an out-of-sample validation. The comparison with the resummed fits of Refs. [15,16] is therefore a comparison of two tuned descriptions of the same data, and it does not by itself establish that the x-dependent scale is a legitimate proxy for low-x resummation. I request either an out-of-sample test (for example, fitting the scale parameters to a subset of the data and evaluating on a held-out subset, or checking consistency against independent low-x data sets not used in the tuning) or an explicit reframing of this result as an exploratory observation that does not carry the weight of a validation of resummation mimicry.
  2. [Sec. I and Sec. II, data set selection (ATLAS 7 TeV W/Z, CDHSW)] The decision to exclude the ATLAS 7 TeV W/Z data from the default CT18 fit and include it only in CT18Z, and to remove CDHSW in CT18Z, is made after examining the tension indicators (the SE distribution in Fig. 8). Such post-hoc choices mean that the spread among CT18, CT18A, CT18X, and CT18Z is not a systematically defined PDF uncertainty band. The quoted chi^2/Npt values are conditional on these decisions. If the four families are intended to 'explore the full range of PDF behavior consistent with the available hadronic data', the manuscript should either specify selection criteria that are defined before inspecting the data or clearly label the family spread as a sensitivity study rather than an uncertainty envelope. As written, the claim is too strong for the presented methodology.
  3. [General (Sections I and II)] Several details that are essential for independently assessing the CT18 determination are deferred to an upcoming publication: the complete list of fitted data sets with their kinematic cuts and treatment of correlated systematic uncertainties, the explicit functional forms of the PDF parametrizations (beyond the mention of Bernstein polynomials), the precise definition of chi^2 including normalization penalties, and the exact source of the '0.5% uncorrelated error'. For a paper that proposes CT18 as a replacement for CT14, these are load-bearing for reproducibility. If this is intended as a preliminary proceedings contribution, that status should be stated clearly and the full record should be made permanently accessible, for example in a public repository, so that the CT18 result can be independently validated rather than resting on the upcoming publication.
minor comments (5)
  1. [Sec. II, 'Advancements in fitting methodology'] The phrase 'multi-prone effort' should be 'multi-pronged effort'.
  2. [Throughout] The typesetting of chi^2 as 'χ2' is inconsistent; the exponential form 'χ²' would be clearer.
  3. [Sec. II, Fig. 7 caption] The sentence 'The right Fig. 7 shows the χ2/Npt values' should be 'The right panel of Fig. 7 shows...' for clarity.
  4. [Sec. II, x-dependent scale equation] The formula for mu_F,x is given in the text without an equation number; adding a numbered equation would aid referencing in the discussion.
  5. [Sec. I, description of CT18Z variants] The phrase 'take charm pole mass to be 1.4 GeV, instead of the nominal value of 1.3 GeV' could be made more precise by stating whether this is the pole mass in the MS-bar scheme or a specific threshold parameter; a brief definition would avoid ambiguity.

Circularity Check

1 steps flagged · score 6.0 of 10

The x-dependent factorization scale is tuned on the HERA DIS data it is then claimed to improve, so the resummation-mimicry result is in-sample rather than a prediction.

  1. fitted input called prediction [Section II (Combined HERA I+II DIS data and an x-dependent factorization scale), text defining µ2F,x = 0.82 (Q2 + 0.3 GeV2/x0.3)]
    "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 in the description of the HERA DIS data set by the fixed-order NNLO theoretical prediction as the inclusion of the low-x resummation in [15, 16]."

    The same section states that 'the numerical coefficients in µ2F,x are chosen to minimize χ2 for the HERA DIS data.' Reporting a >50-unit χ2(HERA I+II) improvement for the very dataset used to tune those coefficients is an in-sample description of the minimized objective, not an independent validation. Consequently, the claim that the x-dependent scale mimics low-x resummation is not established: the comparison with resummed fits of Refs. [15,16] compares a tuned fixed-order scale against resummation, rather than testing a prediction. The small-x gluon and sea-quark changes in the CT18X/Z variants inherit this in-sample character insofar as they are cited as evidence of progress.

full rationale

The core CT18 global analysis is a standard Hessian PDF fit: parton distributions are parameterized and then adjusted to reproduce 3681 data points, which is parameter estimation rather than circular reasoning. The one genuinely circular element is the treatment of the x-dependent factorization scale in Section II. The coefficients 0.82 and 0.3 in µ2F,x are explicitly chosen to minimize χ2 for the HERA DIS data, and the same HERA DIS data are then quoted as showing a large χ2 improvement when this scale is used. That makes the 'comparable quality of improvement ... as the inclusion of the low-x resummation' claim an in-sample fitted result, not a prediction or independent confirmation. The paper itself is transparent about the tuning, but the load-bearing comparison to resummation rests on that tuned scale, so the resummation-mimicry claim partially reduces to its own input. No other circular step was found: the selection of new LHC data via PDFSense/ePump, the Lagrange-multiplier scans, and the comparisons of PDF luminosities are all data-driven analyses that do not presuppose their conclusions. Self-citations to CT14 and CT14HERA2 are normal references to the group's own previous fits, and they are not used to forbid alternatives or to import an unverified uniqueness theorem.

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

The central output is a fit, so the fitted PDF shape parameters are legitimate estimation parameters rather than hidden assumptions. The main added freedom is the x-dependent scale, whose coefficients are tuned to the HERA data it then describes; this is the largest unaccounted-for flexibility in the analysis.

free parameters (3)
  • x-dependent scale coefficients = 0.82, 0.3 GeV^2, 0.3
    mu^2_F,x = 0.82 (Q^2 + 0.3 GeV^2 / x^0.3); coefficients chosen to minimize chi-squared for HERA DIS data (Section II).
  • Charm pole mass = 1.3 GeV nominal; 1.4 GeV in CT18Z
    Used as a theoretical input in the fit; CT18Z varies it.
  • PDF parametrization parameters = not listed in this report
    Bernstein polynomial coefficients for each flavor at Q0 = 1.3 GeV, fitted to data; exact values deferred to the full paper.
assumptions (4)
  • domain assumption Perturbative QCD factorization at NNLO holds for all fitted processes.
    The entire analysis computes NNLO predictions with K-factors; no proof or nonperturbative correction beyond PDFs is provided.
  • domain assumption The Hessian method approximates PDF uncertainties as Gaussian around a global minimum.
    All uncertainties are reported as 90% C.L. Hessian eigenvector sets; this assumes a quadratic chi-squared near the minimum.
  • ad hoc to paper SU(3) symmetry of the sea quark PDFs is assumed as x approaches 0.
    CT18 assumes (s+sbar)/(ubar+dbar) approaches 1 at x to 0 through the s-PDF parametrization, a new assumption not present in CT14.
  • ad hoc to paper Tensions between ATLAS W/Z data and DIS data are attributed to incomplete theory rather than an unknown systematic.
    This motivates separating PDF families instead of including the data in a single fit.

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Cite this review

Pith. "Pith review of Progress in the CTEQ-TEA NNLO global QCD analysis." pith.science (2026). https://pith.science/paper/4ZEDTC7Y

@misc{pith2026190811394,
  author       = {Pith},
  title        = {Pith review of: Progress in the CTEQ-TEA NNLO global QCD analysis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4ZEDTC7Y}},
  note         = {Machine review of arXiv:1908.11394}
}
abstract

We present the new CTEQ-TEA global analysis of quantum chromodynamics (QCD). In this analysis, parton distribution functions (PDFs) of the nucleon are determined within the Hessian method at the next-to-next-to-leading order (NNLO) in perturbative QCD, based on the most recent measurements from the Large Hadron Collider (LHC) and a variety of world collider data. Because of difficulties in fitting both the ATLAS 7 and 8 TeV $W$ and $Z$ vector boson production cross section data, we present four families of (N)NLO CTEQ-TEA PDFs, named CT18, A, X and Z PDFs, respectively. We study the impact of the CT18 family of PDFs on the theoretical predictions of standard candle cross sections at the LHC.

Figures

Figures reproduced from arXiv: 1908.11394 by the authors.

Figure 1
Figure 1. FIG. 1. A comparison of 90% C.L. PDF uncertainties from CT18 (red curve), CT18Z (green [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. A comparison of 90% C.L. uncertainties on the ratio [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. A comparison of 90% C.L. uncertainties on the ratios [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The Lagrange Multiplier scan of gluon PDF at [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. The Lagrange Multiplier scan of [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Comparison of various PDF luminosities at the 13 TeV LHC. [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Left: The ratios of the candidate CT18 NNLO PDFs obtained with the [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. The effective Gaussian variable ( [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]

Discussion (0). Continue with ORCID to comment.

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