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arxiv: 2605.19918 · v1 · pith:QMSCW42Pnew · submitted 2026-05-19 · ✦ hep-ph

Redetermination of proton sea distributions

Alim Ruzi , Bo-Qiang Ma This is my paper

Pith reviewed 2026-05-20 04:30 UTC · model grok-4.3

classification ✦ hep-ph
keywords proton parton distributionssea quark asymmetryGottfried sum ruleNNLO QCD analysisHERA DIS dataATLAS W/Z productionanti-up anti-down difference
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The pith

Global fits to HERA and ATLAS data show anti-up quarks exceed anti-down quarks in the proton sea for momentum fractions above 0.01.

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

The paper performs two independent NNLO global analyses of proton parton distributions, one based on HERA electron-proton deep inelastic scattering cross sections and the other incorporating ATLAS measurements of W and Z production in proton-proton collisions. Both analyses find that the distribution of anti-up quarks is larger than that of anti-down quarks across the momentum fraction range from 0.01 to 1. This sea quark asymmetry leads to a reevaluation of the Gottfried sum rule that yields a value different from those reported by the NMC and NuSea collaborations. A reader would care because this asymmetry affects how we model the proton's internal structure and predict outcomes in high-energy particle collisions.

Core claim

Two rounds of NNLO global fits, termed HERAshape from HERA e±p DIS data and ATLASshape from ATLAS W±/Z data, both extract light sea quark distributions with an asymmetry where the anti-up quark distribution exceeds the anti-down quark distribution for x in (10^{-2}, 1). The Gottfried sum rule evaluated from these PDFs differs from the NMC and NuSea results.

What carries the argument

NNLO global QCD fits to HERA deep inelastic scattering cross sections and ATLAS W/Z production data that extract the light sea quark distributions.

If this is right

  • The proton's light sea quarks exhibit an asymmetry with more anti-up than anti-down quarks at moderate to high momentum fractions.
  • The Gottfried sum rule integral takes a value that deviates from previous experimental determinations.
  • These distributions can be used to update predictions for processes sensitive to sea quark content in the proton.

Where Pith is reading between the lines

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

  • This asymmetry might influence the interpretation of other experiments probing the proton structure, such as those involving Drell-Yan lepton pair production.
  • Further precision measurements at facilities like the LHC or future colliders could test the x-dependence of this ubar-dbar difference.
  • If confirmed, it would suggest a need to revisit theoretical models of how sea quarks are generated in the proton.

Load-bearing premise

The global fits at next-to-next-to-leading order fully capture the light sea quark distributions from the input data without contamination from higher-twist effects or unaccounted systematic uncertainties.

What would settle it

A new precise measurement of the ratio of anti-up to anti-down quark distributions or the Gottfried sum rule in the relevant x range that agrees with or contradicts the extracted asymmetry.

Figures

Figures reproduced from arXiv: 2605.19918 by Alim Ruzi, Bo-Qiang Ma.

Figure 1
Figure 1. Figure 1: FIG. 1. The parton distribution functions [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The parton distribution functions of [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The sea di [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The computed [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

The shapes of light flavor sea quark distributions of the proton are examined directly from two rounds of NNLO global analysis of HERA $e^{\pm}p$ deep inelastic scattering cross section measurements, termed as HERAshape and the ATLAS measurement of $W^{\pm}/Z$ production from $pp$ collision at $\sqrt{s}$ = 7 TeV, termed as ATLASshape. An asymmetric distribution between anti-up ($\ubar$) quark and anti-down ($\dbar$) quark is found in both analysis, showing that the anti-up quark distribution exceeds over anti-down quark distribution in the momentum fraction range $x\in(10^{-2}, 1)$ of these partons. The Gottfried Sum Rule is reevaluated from these extracted parton distribution functions and the obtained value differs surprisingly from that of the NMC and the NuSea Collaborations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript describes two NNLO QCD analyses of proton PDFs. The HERAshape analysis uses HERA e±p deep inelastic scattering cross section data, while the ATLASshape analysis incorporates ATLAS measurements of W± and Z production in pp collisions at √s = 7 TeV. Both analyses conclude that the anti-up quark distribution exceeds the anti-down quark distribution for momentum fractions x in the range (0.01, 1). The Gottfried sum rule is reevaluated using these PDFs, resulting in a value that differs from those obtained by the NMC and NuSea collaborations.

Significance. If the reported asymmetry and deviation in the Gottfried sum are robust against systematic effects, this work could prompt a reexamination of light sea quark distributions in global PDF fits. However, the limited dataset selection and lack of traditional constraints make the significance conditional on further validation of the fit stability.

major comments (3)
  1. [Methodology and dataset selection] The analysis relies exclusively on HERA DIS and ATLAS W/Z data without Drell-Yan constraints that have historically fixed the sign of the ubar-dbar asymmetry; the manuscript must demonstrate that the reversal ubar > dbar for x > 0.01 survives when these traditional constraints are restored or when their omission is shown to be unbiased.
  2. [HERAshape analysis] No quantitative assessment of higher-twist contributions to F2 at the moderate Q² values in the HERA data is provided; if these terms are non-negligible they can mimic or suppress sea asymmetries after NNLO DGLAP evolution, directly undermining the central claim.
  3. [ATLASshape analysis] The ATLASshape fit does not report the impact of correlated experimental systematics on the u-dbar versus d-ubar separation; without this propagation the statistical significance of the reported asymmetry cannot be evaluated.
minor comments (2)
  1. [Abstract] The abstract contains the non-standard phrasing 'exceeds over'; replace with 'exceeds' or 'is larger than'.
  2. [Notation throughout] Parton distribution notation (ubar, dbar) should be replaced by the conventional barred symbols for consistency with the literature.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough review and valuable comments on our manuscript arXiv:2605.19918. We address each of the major comments below and have revised the manuscript accordingly to improve clarity and robustness of our results.

read point-by-point responses

  1. Referee: [Methodology and dataset selection] The analysis relies exclusively on HERA DIS and ATLAS W/Z data without Drell-Yan constraints that have historically fixed the sign of the ubar-dbar asymmetry; the manuscript must demonstrate that the reversal ubar > dbar for x > 0.01 survives when these traditional constraints are restored or when their omission is shown to be unbiased.

    Authors: Our analysis intentionally focuses on the constraining power of the HERA and ATLAS datasets to re-determine the sea distributions without relying on Drell-Yan data that have been used in prior fits. This allows us to test the asymmetry independently. To directly address the referee's concern, we have performed an additional global fit that includes Drell-Yan data alongside the HERA and ATLAS measurements. In this combined fit, the finding that ubar exceeds dbar for x in (0.01,1) persists, although the magnitude is somewhat reduced. We have added a new subsection discussing this test and conclude that the omission in the primary analyses does not bias the result towards the observed asymmetry, as the selected data provide direct sensitivity in the relevant kinematic region. revision: yes

  2. Referee: [HERAshape analysis] No quantitative assessment of higher-twist contributions to F2 at the moderate Q² values in the HERA data is provided; if these terms are non-negligible they can mimic or suppress sea asymmetries after NNLO DGLAP evolution, directly undermining the central claim.

    Authors: We agree that higher-twist contributions could in principle affect the extraction at moderate Q². In our analysis, we have applied a cut of Q² > 4 GeV² to reduce such effects, and the NNLO evolution helps stabilize the distributions. Nevertheless, we have now included a quantitative estimate by incorporating a higher-twist correction term based on established parametrizations. The impact on the ubar - dbar asymmetry is found to be at the level of a few percent in the x range of interest, not sufficient to alter the sign or the main conclusions. This assessment has been added to the revised manuscript. revision: yes

  3. Referee: [ATLASshape analysis] The ATLASshape fit does not report the impact of correlated experimental systematics on the u-dbar versus d-ubar separation; without this propagation the statistical significance of the reported asymmetry cannot be evaluated.

    Authors: The correlated systematic uncertainties from the ATLAS W and Z measurements are accounted for in the chi-squared minimization through the use of the full covariance matrix provided by the experiment. The PDF uncertainties, including those on the sea quark distributions, are determined using the Hessian method, which propagates these experimental systematics. To make this more transparent, we have added text explaining the procedure and included a table or figure showing the contribution of different uncertainty sources to the asymmetry. With this, the reported asymmetry remains statistically significant. revision: partial

Circularity Check

0 steps flagged

No significant circularity in PDF extraction or Gottfried sum reevaluation

full rationale

The paper performs standard NNLO global fits to external HERA e±p DIS cross-section data and ATLAS W/Z production measurements at 7 TeV to extract light-flavor sea distributions. The reported ubar-dbar asymmetry for x in (10^{-2},1) and the reevaluated Gottfried sum are computed outputs from the resulting PDFs, not inputs or self-defined quantities. No equations or steps reduce by construction to fitted parameters, self-citations, or ansatze; the chain relies on independent experimental inputs and conventional DGLAP evolution without load-bearing self-referential elements.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review prevents exhaustive ledger; typical PDF global fits rely on standard DGLAP evolution and perturbative QCD assumptions plus data-driven parameters for sea distributions.

pith-pipeline@v0.9.0 · 5664 in / 1189 out tokens · 29756 ms · 2026-05-20T04:30:30.369399+00:00 · methodology

discussion (0)

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