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REVIEW 4 major objections 4 minor 38 references

Relative difference between up and down quark structure of the proton

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The down-to-up quark ratio in the proton, extracted from the Drell-Yan forward-backward asymmetry at the LHC, deviates from current PDF predictions in both its value and its x-dependence.

desk verdict A credible AFB-based extraction of d/u at lower x, but the new x-dependence claim rests on weak low-|Y| bins and CT18-fixed Delta terms; the high-x excess is solid and D0-consistent. read the letter →

arxiv 2505.17608 v1 pith:YITN7PAB submitted 2025-05-23 hep-ph

Mingzhe Xie , Siqi Yang , Wenhao Ma , Minghui Liu , Liang Han , C.-P. Yuan This is my paper · ORCID
classification hep-ph
keywords forward-backwardasymmetryDrell-YanprocesspartondistributionfunctionsupanddownquarksvalencequarkratioprotonstructureflavorseparationLHC
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 reports a direct measurement of the ratio of down-quark to up-quark contributions inside the proton, using the forward-backward asymmetry of Drell-Yan lepton pairs at the LHC. Unlike most cross-section measurements, this asymmetry can be factorized so that the up and down quark components appear separately, and their ratio is nearly free of contamination from strange, charm, and bottom quarks. The authors extract this ratio from CMS data at 13 TeV (138 $fb^{-1}$) and re-analyze the earlier 8 TeV data. They find that the ratio is significantly larger than current PDF predictions for momentum fractions x > 0.05, consistent with a previous D0 measurement, and smaller than predictions around x ~ 0.01. These deviations point to a different x-dependence of the light-quark distributions than current global fits allow.

What carries the argument

The central object is the factorization of AFB into Cu and Cd (measured as bin-averaged Pu and Pd) multiplying hard-process asymmetries Au_FB and Ad_FB, with R = Cd/Cu. The hard-process asymmetries are computed with ResBos at approximate NNLO+N3LL, and the small kinematic dependences within each |Y| bin (Delta_u, Delta_d) are fixed using the CT18 NNLO PDF. This factorization cancels the contributions of s, c, and b quarks in R, so that R probes the d and u quark distributions almost without mixing.

What would settle it

Perform a global PDF fit that includes the CMS 13 TeV and 8 TeV AFB data with a free d/u ratio; if the best-fit d/u does not move to the high values found here for x > 0.05 and the lower value at x ~ 0.01, the claimed deviation is not reproducible. Alternatively, redo the extraction with Delta_u and Delta_d computed from MSHT20 and NNPDF4.0 instead of CT18; if R shifts by more than the quoted uncertainty, the result depends on the assumed kinematics.

Watch

Extended reading notes

Core claim

The paper claims that the ratio R = Pd/Pu, where Pu and Pd are structure parameters that factorize the forward-backward asymmetry AFB(Y,M,QT) for pp -> Z/gamma* -> l+l- into separate up-quark and down-quark contributions, is a nearly pure observable for the valence ratio dV(x1)/uV(x1) in the region x1 > 0.01. Using the latest CMS 13 TeV AFB data and a re-analysis of the CMS 8 TeV data with the weak mixing angle fixed, the measured R is found to be significantly above the predictions of CT18, MSHT20, and NNPDF4.0 for x > 0.05, while at x ~ 0.01 it lies below the predictions. The authors take this as evidence that the x-dependence of the light-quark PDFs, in particular the d/u and anti-d/anti-u ratios, is different from what current global fits assume.

Load-bearing premise

The extraction assumes that the small kinematic dependences within each rapidity bin, computed with the CT18 PDF, correctly describe how the up and down structure parameters vary; if the true light-quark distributions differ from CT18 inside a bin, the fit could absorb that difference into Pu and Pd and bias R toward the CT18 prediction.

Editorial extensions

If this is right

  • If the deviation is real, PDF global fits must include Drell-Yan AFB data to constrain the d/u and anti-d/anti-u ratios, which are currently only weakly constrained.
  • The observed higher R at x > 0.05 implies either a larger d/u valence ratio or a suppressed anti-d/anti-u asymmetry in that region.
  • The sign change at x ~ 0.01 indicates that current PDF parameterizations have the wrong x-dependence for the light-quark flavor separation.
  • Because R is nearly insensitive to heavier quarks, the measurement provides a clean test for non-perturbative models of the proton sea.

Reading between the lines

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

  • One could extend the same method to lower x using forward rapidity coverage (e.g., LHCb) to see whether the downward deviation persists below x = 0.01.
  • If confirmed, the x-dependence mismatch would feed into electroweak precision measurements at the LHC, since the Z rapidity distribution depends on light-quark flavor separation.
  • The cancellation of sea-quark contributions in R relies on the assumption u(x2) ~ d(x2) at x2 ~ 10^-3; the method itself could test this by comparing extractions in different rapidity bins, where x2 varies.
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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

4 major / 4 minor

Summary. The paper extracts the ratio R = P_d/P_u of down-type to up-type structure parameters from the forward-backward asymmetry in pp → Z/γ* → ℓ+ℓ− events, using the CMS 13 TeV 138 fb⁻¹ measurement and re-analyzing the CMS 8 TeV data with sin²θ_eff fixed. In each |Y| bin, P_u and P_d are fitted while the kinematic dependences Δ_u and Δ_d are fixed using the CT18 NNLO PDF. The authors report that R is significantly higher than current PDF predictions for x > 0.05, consistent with the D0 measurement, and lower than predictions at x ≈ 0.01, claiming a different x-dependence of the light-quark PDFs.

Significance. If the result holds, the paper offers a genuinely novel flavor-separated constraint on the d/u valence ratio, complementary to inclusive Drell-Yan and DIS measurements, and the high-x excess provides independent corroboration of the D0 anomaly. The use of public CMS data and the explicit separation of experimental and Δ-induced uncertainties are strengths. However, the low-x reversal, which is the truly new part of the claim, is statistically fragile and depends on the fixed CT18 shapes; the paper does not yet establish that reversal at the level claimed in the abstract. With a closure test, a significance quantification, and a goodness-of-fit report, this would be a valuable contribution.

major comments (4)
  1. [Section 3, Eq. (4) and the paragraph beginning 'The fixed Δ_u and Δ_d...'] The central claim of a changed x-dependence is not robust to the way Δ_u and Δ_d are fixed. In Eq. (4), C_u and C_d are decomposed into bin-constant P_u, P_d plus Δ_u, Δ_d, and the fit adjusts only P_u and P_d, with Δ_u, Δ_d taken from CT18 NNLO. If the true kinematic dependence inside a |Y| bin differs from CT18, that difference is absorbed into P_u and P_d, biasing R toward the CT18 prediction. The quoted Δ uncertainties (the second parentheses in Tables I and II) sample only the CT18 error sets; they do not cover an alternative x-dependence of the light-quark distributions. The paper's statement that MSHT20 and NNPDF4.0 give consistent Δ values validates the central shapes but not the sensitivity of the final R to those shapes. Please add a closure test in which pseudo-data are generated with a modified input d/u ratio and the extraction is repeated, and report the change in R when Δ_u, Δ_d are recomputed from MSHT20 or NNPDF4.0 instead of CT18.
  2. [Table I and the paragraph beginning 'The most important results...'] The claimed low-x reversal at x ≈ 0.01 is statistically weak. In the lowest |Y| bin (0–0.4), P_d = −0.0012 ± 0.0052, consistent with zero; in the next bin (0.4–0.8), P_d = 0.0138 ± 0.0054. No significance is quoted for the downward deviation of R from CT18, MSHT20, or NNPDF4.0, and the large relative uncertainty on P_d in these bins means the ratio R is not well determined. Please report the significance of the deviation from each PDF prediction in each |Y| bin, and the combined significance of the two low-|Y| bins for a reversal. If the combined significance is below about 3σ, the abstract and conclusions should be softened to state a 'tendency' rather than a 'significant' reversal.
  3. [Eq. (6) and Section 3] The paper defines a χ² but never reports its minimum value or the number of degrees of freedom for any of the fits. Without this information the reader cannot judge whether the factorized model of Eqs. (1) and (4) actually describes the CMS AFB data; a poor global fit would undermine the interpretation of the extracted P_u, P_d. Please include the minimum χ² per |Y| interval (and for the combined 13 TeV and 8 TeV fits), together with the number of mass bins used in each fit.
  4. [Figures 1–2 and the abstract] The abstract claims 'significant deviations in both the value and x-dependence of this ratio compared to predictions from current parton distribution functions'. The value deviation at x > 0.05 is supported by the D0 measurement and by the 8 TeV re-analysis, but the x-dependence reversal rests on the low-|Y| bins discussed above, and the statistical significance is not quantified anywhere. Please state the quantitative significance for each claimed deviation, and ensure the abstract's wording matches the reported precision. Also note that the 8 TeV low-|Y| bins (|Y| < 1.25) are consistent with predictions, so the reversal is driven by the 13 TeV low-|Y| bins; this asymmetry in evidence should be acknowledged.
minor comments (4)
  1. [Abstract and references] There is a typo in the abstract: 'presen' should be 'present'; also, reference [32] contains 'Electronweak' instead of 'Electroweak'.
  2. [Equation (5)] Equation (5) writes the angular distribution as 1 + cosθ* + A4 cosθ*, which appears to omit the cos²θ* term; please check against the CMS convention and correct the formula.
  3. [Tables I–II and Figures 1–2] Tables I and II give correlation factors ρ, but no numerical values for R = P_d/P_u with their uncertainties; since R is the central observable, please provide a table of R with total uncertainties and correlation information, or state explicitly that the plotted R error bars include the correlated treatment.
  4. [Section 3] The phrase 'mass window not wider than 100 GeV around the Z pole' is vague; please specify the exact mass bins used in the fit and how the index i in Eq. (6) runs over them.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the extraction uses CT18 only for fixed bin-shape corrections, and the claimed deviations are compared against external PDFs and D0, so the result is not forced by construction.

full rationale

The derivation chain is not circular. The measured AFB distributions are the input; Pu and Pd are obtained by a chi-square fit (Eq. 6) with Au_FB and Ad_FB computed independently by ResBos, and the ratio R=Pd/Pu is then compared with CT18, MSHT20 and NNPDF4.0. The only place a PDF enters the extraction is the fixed Delta_u and Delta_d in Eq. (4), taken from CT18 ("The fixed Delta_u and Delta_d ... are predicted from the CT18 NNLO PDF"). This is not a fitted parameter renamed as a prediction: Delta_u/d are fixed shape corrections defined to integrate to zero, and the two free constants Pu, Pd are adjusted to the data. If the CMS AFB data agreed exactly with CT18, the fit would return CT18's R, so a measured deviation is a data-driven offset, not an input recycled as an output. The CT18-dependence of the corrections is a genuine systematic caveat (the Delta-induced error is sampled only from CT18 error sets, not from alternative x-dependences), but it biases the extraction toward CT18 if anything and cannot manufacture the observed deviations. Self-citations [23,24] supply the factorization formula and a previous application of the method; both are published, parameter-free derivations/analyses, and the present conclusions are additionally benchmarked against the external D0 measurement and two non-CT18 PDF sets. No step reduces to its own input by definition.

Assumptions & free parameters 26 free parameters · 6 assumptions · 0 invented entities

The central claim rests on a chain of theoretical inputs: the AFB factorization of Ref [23], ResBos predictions for hard asymmetries, fixed Delta terms from CT18, and the sea-symmetry assumption at low x2. The per-bin Pu and Pd are 26 fitted parameters that define the measured R values. No new particles or forces are introduced.

free parameters (26)
  • P_u (13TeV, bin 0-0.4) = 0.0242
    Fitted to CMS 13 TeV AFB data via chi2 minimization (Eq. 6).
  • P_d (13TeV, bin 0-0.4) = -0.0012
    Fitted to CMS 13 TeV AFB data via chi2 minimization (Eq. 6).
  • P_u (13TeV, bin 0.4-0.8) = 0.0651
    Fitted to CMS 13 TeV AFB data via chi2 minimization (Eq. 6).
  • P_d (13TeV, bin 0.4-0.8) = 0.0138
    Fitted to CMS 13 TeV AFB data via chi2 minimization (Eq. 6).
  • P_u (13TeV, bin 0.8-1.2) = 0.1054
    Fitted to CMS 13 TeV AFB data via chi2 minimization (Eq. 6).
  • P_d (13TeV, bin 0.8-1.2) = 0.0460
    Fitted to CMS 13 TeV AFB data via chi2 minimization (Eq. 6).
  • P_u (13TeV, bin 1.2-1.6) = 0.1574
    Fitted to CMS 13 TeV AFB data via chi2 minimization (Eq. 6).
  • P_d (13TeV, bin 1.2-1.6) = 0.0720
    Fitted to CMS 13 TeV AFB data via chi2 minimization (Eq. 6).
  • P_u (13TeV, bin 1.6-2.0) = 0.2307
    Fitted to CMS 13 TeV AFB data via chi2 minimization (Eq. 6).
  • P_d (13TeV, bin 1.6-2.0) = 0.0956
    Fitted to CMS 13 TeV AFB data via chi2 minimization (Eq. 6).
  • P_u (13TeV, bin 2.0-2.4) = 0.2966
    Fitted to CMS 13 TeV AFB data via chi2 minimization (Eq. 6).
  • P_d (13TeV, bin 2.0-2.4) = 0.1423
    Fitted to CMS 13 TeV AFB data via chi2 minimization (Eq. 6).
  • P_u (13TeV, bin 2.4-2.7) = 0.3159
    Fitted to CMS 13 TeV AFB data via chi2 minimization (Eq. 6).
  • P_d (13TeV, bin 2.4-2.7) = 0.2054
    Fitted to CMS 13 TeV AFB data via chi2 minimization (Eq. 6).
  • P_u (13TeV, bin 2.7-3.0) = 0.4503
    Fitted to CMS 13 TeV AFB data via chi2 minimization (Eq. 6).
  • P_d (13TeV, bin 2.7-3.0) = 0.1907
    Fitted to CMS 13 TeV AFB data via chi2 minimization (Eq. 6).
  • P_u (13TeV, bin 3.0-3.4) = 0.4656
    Fitted to CMS 13 TeV AFB data via chi2 minimization (Eq. 6).
  • P_d (13TeV, bin 3.0-3.4) = 0.2993
    Fitted to CMS 13 TeV AFB data via chi2 minimization (Eq. 6).
  • P_u (8TeV, bin 0-1.0) = 0.1216
    Fitted to CMS 8 TeV AFB data via chi2 minimization (Eq. 6).
  • P_d (8TeV, bin 0-1.0) = 0.0439
    Fitted to CMS 8 TeV AFB data via chi2 minimization (Eq. 6).
  • P_u (8TeV, bin 1.0-1.25) = 0.2743
    Fitted to CMS 8 TeV AFB data via chi2 minimization (Eq. 6).
  • P_d (8TeV, bin 1.0-1.25) = 0.1025
    Fitted to CMS 8 TeV AFB data via chi2 minimization (Eq. 6).
  • P_u (8TeV, bin 1.25-1.5) = 0.3205
    Fitted to CMS 8 TeV AFB data via chi2 minimization (Eq. 6).
  • P_d (8TeV, bin 1.25-1.5) = 0.1636
    Fitted to CMS 8 TeV AFB data via chi2 minimization (Eq. 6).
  • P_u (8TeV, bin 1.5-2.4) = 0.4609
    Fitted to CMS 8 TeV AFB data via chi2 minimization (Eq. 6).
  • P_d (8TeV, bin 1.5-2.4) = 0.2056
    Fitted to CMS 8 TeV AFB data via chi2 minimization (Eq. 6).
assumptions (6)
  • domain assumption Factorized form of AFB into u and d contributions, Eq. (1), from Ref [23], valid to all orders in QCD.
    The entire extraction of Pu and Pd from the observed AFB relies on this factorization being exact. The paper does not derive it; it cites the authors' earlier work. The D0 collaboration has applied the same method, giving some external validation.
  • domain assumption Hard-process asymmetries A_u_FB and A_d_FB are precisely predicted by ResBos at approximate NNLO plus N3LL with electroweak corrections.
    Any error in these theoretical asymmetries propagates directly into the extracted Pu and Pd. The paper uses the ResBos package without an independent cross-check of its accuracy in the relevant phase space.
  • domain assumption Delta_u and Delta_d, the kinematic dependence of the structure parameters within each |Y| bin, are fixed to predictions from the CT18 NNLO PDF, with uncertainties estimated from CT18 error sets.
    The fit in Eq. (6) assumes this fixed shape. If the true shape differs, the extracted Pu and Pd can be biased. The uncertainty estimate covers only within-CT18 variations, not a different x dependence of the light-quark distributions.
  • domain assumption At x2 around 0.002 to 0.005, the light sea quarks are approximately equal: u(x2) ~ bar u(x2) ~ d(x2) ~ bar d(x2).
    This assumption underlies the interpretation R approximately equals dV(x1)/uV(x1). It is most fragile at the lower x1 values where the sea contribution is not negligible and where the paper reports a reversal of the trend.
  • domain assumption The strange, charm and bottom quark contributions cancel in R, assuming q(x,Q0) = bar q(x,Q0) at the initial scale Q0 around 1 GeV.
    This is a standard assumption in PDF analyses, but it is an input that the paper invokes to claim R cleanly reflects only up and down quark information.
  • domain assumption The bin-by-bin correlations of the experimental uncertainties in the CMS AFB measurement are negligible.
    The chi2 definition in Eq. (6) treats the measurements as uncorrelated. If the neglected correlations are non-negligible, the extracted parameters and their uncertainties would change. The paper cites the CMS report for this claim.

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Pith. "Pith review of Relative difference between up and down quark structure of the proton." pith.science (2026). https://pith.science/paper/YITN7PAB

@misc{pith2026250517608,
  author       = {Pith},
  title        = {Pith review of: Relative difference between up and down quark structure of the proton},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YITN7PAB}},
  note         = {Machine review of arXiv:2505.17608}
}
read the original abstract

We presen a novel determination of the down-to-up composition ratio using the forward-backward asymmetry observed in the proton-proton collisions at the LHC. This method offers unique insights into the flavor-specific difference between down and up quarks, which are difficult to isolate in traditional cross-section measurements due to the inherent mixing of contributions from both flavors. In this study, we systematically measure the down-to-up quark ratio over a broad momentum fraction (x) range of 0.01 to 0.1, utilizing the sensitivity of the forward-backward asymmetry to quark-level couplings. Our findings reveal significant deviations in both the value and x-dependence of this ratio compared to predictions from current parton distribution functions (PDFs). These discrepancies highlight potential limitations in existing PDF parameterization and emphasize the importance of flavor-separated measurements for advancing our understanding of proton structure.

Figures

Figures reproduced from arXiv: 2505.17608 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

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Reviewed August 7, 2026 · model on record in the stance chip above.