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arxiv: 2605.00666 · v1 · submitted 2026-05-01 · ✦ hep-ph · hep-ex· nucl-th

Recognition: unknown

Stability of parton distributions at high x: impact of nuclear and power corrections

C. Cocuzza , W. Melnitchouk , N. Sato , A. W. Thomas
Authors on Pith no claims yet

Pith reviewed 2026-05-09 18:55 UTC · model grok-4.3

classification ✦ hep-ph hep-exnucl-th
keywords parton distribution functionshigh-x PDFsnuclear correctionshigher twistdeep inelastic scatteringQCD global analysisdeuteron structure functionsoff-shell effects
0
0 comments X

The pith

The u and d quark PDFs remain stable up to x ≈ 0.8 and describe DIS data down to W² = 3.5 GeV² when nuclear and higher-twist corrections are included.

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

This paper performs a global QCD fit of parton distributions using proton, deuteron, and A=3 data that includes the newest high-x measurements from Jefferson Lab. It tests how much the extracted u and d distributions change when the minimum invariant mass W of the final state is lowered, when target-mass and higher-twist terms are added, and when different nuclear wave functions are chosen. The central finding is that the quark distributions and the d/u ratio stay essentially unchanged up to x = 0.8 and still describe the data even at the lowest W and Q values examined. This stability matters because it lets lower-energy experiments tighten the constraints on the large-x region where few other data exist.

Core claim

Within the collinear factorization framework the JAM Bayesian Monte Carlo analysis shows that the u and d quark PDFs and their ratio are relatively stable up to x ≈ 0.8. The distributions continue to describe inclusive DIS data down to W² = 3.5 GeV² and Q² = m_c² once target-mass and higher-twist corrections are fitted. The higher-twist coefficients are positive and largely isospin independent. Nuclear data require nonzero isoscalar and isovector off-shell modifications to the nucleon PDFs, which in turn produce definite predictions for the ratio R_D of deuteron to isoscalar nucleon structure functions.

What carries the argument

The JAM Bayesian Monte Carlo global QCD fit that simultaneously varies the W cut, target-mass corrections, higher-twist coefficients, and nuclear wave functions plus off-shell nucleon PDF modifications for deuteron and A=3 targets.

If this is right

  • The extracted u and d distributions can be used with greater confidence in high-x observables such as Drell-Yan production or neutrino scattering.
  • Positive, isospin-independent higher-twist terms improve the description of DIS data at moderate Q² without spoiling the leading-twist PDFs.
  • The required isoscalar and isovector off-shell corrections give a concrete, testable prediction for R_D that can be checked with future deuteron data.
  • Lower W cuts become viable for PDF fits, allowing more inclusive measurements to constrain the large-x region.

Where Pith is reading between the lines

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

  • The same off-shell mechanism may help quantify the EMC effect in heavier nuclei once the A=3 results are extended.
  • If the stability persists, global fits could incorporate still lower-Q² data from future facilities to reduce uncertainties at x > 0.8.
  • The isospin independence of the higher-twist terms suggests a common dynamical origin that could be tested in separate proton and neutron extractions.

Load-bearing premise

The collinear factorization framework remains valid at the low W and Q values included in the fit, and the chosen nuclear wave functions together with the off-shell PDF modifications capture all relevant nuclear effects without large residual biases.

What would settle it

A new high-precision measurement of the deuteron structure function ratio R_D at x > 0.7 that lies well outside the predicted band from the off-shell contributions, or a clear sign change in the fitted higher-twist coefficients when additional low-W data are added, would falsify the reported stability.

Figures

Figures reproduced from arXiv: 2605.00666 by A. W. Thomas, C. Cocuzza, N. Sato, W. Melnitchouk.

Figure 1
Figure 1. Figure 1: FIG. 1. Reduced view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Structure functions view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. [Top row] Structure function view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Additive higher twist function view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Off-shell functions view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Nucleon off-shell function view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Deuteron EMC ratio view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Neutron to proton structure function ratio view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9 view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Ratios of view at source ↗
read the original abstract

We present a comprehensive new global QCD analysis of unpolarized parton distribution functions (PDFs) based upon proton, deuteron and $A\!=\!3$ data, including the latest inclusive deep-inelastic scattering (DIS) measurements from Jefferson Lab at high Bjorken-$x$. Using the JAM Bayesian Monte Carlo framework, we systematically explore the stability of the PDFs with respect to variations in the cuts on the invariant mass $W$ of the DIS final state, the implementation of target mass and higher twist corrections, as well as on the nuclear wave functions for the $A\!=\!2$ and 3 data. We find the $u$ and $d$ quark PDFs (and the $d/u$ ratio) are relatively stable up to $x \approx 0.8$, and able to describe DIS data down to $W^2=3.5$ GeV$^2$ and $Q^2=m_c^2$. Within the collinear factorization framework, the fitted higher twist corrections to DIS are found to be positive, and largely isospin independent. The description of the nuclear data also requires nonzero isoscalar and isovector nucleon off-shell PDF contributions, which gives specific predictions for the ratio, $R_D$, of deuteron to isoscalar nucleon structure functions.

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

2 major / 2 minor

Summary. The manuscript presents a global QCD analysis of unpolarized PDFs using proton, deuteron, and A=3 data, including recent JLab high-x DIS measurements. Employing the JAM Bayesian Monte Carlo framework, the authors systematically vary kinematic cuts on W, implementations of target-mass and higher-twist corrections, and nuclear wave functions for A=2,3. They report that the u and d quark PDFs (and d/u ratio) remain relatively stable up to x≈0.8 and describe the data down to W²=3.5 GeV² and Q²=m_c². Higher-twist corrections are found to be positive and largely isospin-independent, while nonzero isoscalar and isovector off-shell nucleon PDF modifications are required to fit the nuclear data, yielding predictions for the deuteron-to-isoscalar structure function ratio R_D.

Significance. If the separation of leading-twist PDFs from the fitted power corrections and nuclear effects holds, the work would be significant for high-x PDF phenomenology by enabling reliable inclusion of low-W data in global fits. The systematic Bayesian Monte Carlo exploration of model variations (cuts, nuclear wave functions, off-shell terms) is a clear strength, providing better uncertainty quantification than single-fit approaches. This could impact extractions of the d/u ratio at large x and applications involving nuclear corrections in light nuclei.

major comments (2)
  1. [§4] §4 (results on W² cuts and higher-twist fits): The central claim of PDF stability down to W²=3.5 GeV² rests on the fitted positive, isospin-independent higher-twist corrections fully absorbing deviations from collinear factorization. At these low invariant masses (near the resonance region) and Q²=m_c², resonance contributions and possible target-mass effects beyond the standard implementation could be partially absorbed into the HT coefficients or off-shell parameters, artificially stabilizing the high-x u, d, and d/u distributions. The Bayesian exploration of cuts does not explicitly demonstrate that such degeneracies are ruled out (e.g., via comparison to resonance-subtracted data sets or alternative HT parametrizations).
  2. [§5] §5 (nuclear corrections and R_D prediction): The specific predictions for R_D are generated from the same fitted isoscalar and isovector off-shell PDF contributions used to describe the A=2,3 data. This reduces R_D to a consistency check within the fitted model rather than an independent test, weakening its support for the overall framework's validity at high x.
minor comments (2)
  1. [Abstract] Abstract: The phrase 'relatively stable' is used for the PDFs up to x≈0.8; a quantitative statement (e.g., maximum variation in central values or uncertainty bands across W cuts) would improve clarity.
  2. [Figures] Figure captions (throughout): Several figures comparing PDF bands for different W cuts or nuclear models would benefit from explicit labels indicating the exact parameter variations shown.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below, providing clarifications on our methodology and indicating where revisions will be made.

read point-by-point responses

  1. Referee: [§4] §4 (results on W² cuts and higher-twist fits): The central claim of PDF stability down to W²=3.5 GeV² rests on the fitted positive, isospin-independent higher-twist corrections fully absorbing deviations from collinear factorization. At these low invariant masses (near the resonance region) and Q²=m_c², resonance contributions and possible target-mass effects beyond the standard implementation could be partially absorbed into the HT coefficients or off-shell parameters, artificially stabilizing the high-x u, d, and d/u distributions. The Bayesian exploration of cuts does not explicitly demonstrate that such degeneracies are ruled out (e.g., via comparison to resonance-subtracted data sets or alternative HT parametrizations).

    Authors: We appreciate the referee's concern about possible absorption of resonance or additional target-mass effects into the higher-twist and off-shell parameters. Our Bayesian Monte Carlo analysis systematically varies the W² cuts and HT implementations, showing that the extracted u and d PDFs (and d/u ratio) remain stable up to x≈0.8 across these choices, with the HT corrections remaining positive and largely isospin-independent. The framework quantifies uncertainties from these variations. We agree that explicit resonance-subtracted comparisons or alternative HT forms would provide stronger evidence against degeneracies and will add a dedicated discussion of this limitation, along with suggestions for future checks, in the revised manuscript. revision: partial

  2. Referee: [§5] §5 (nuclear corrections and R_D prediction): The specific predictions for R_D are generated from the same fitted isoscalar and isovector off-shell PDF contributions used to describe the A=2,3 data. This reduces R_D to a consistency check within the fitted model rather than an independent test, weakening its support for the overall framework's validity at high x.

    Authors: We acknowledge that the R_D predictions are derived from the off-shell parameters constrained by the A=2 and A=3 data. However, R_D is not an input to the fit but a specific, falsifiable output of the model for a different observable. This provides a non-trivial consistency test of the extracted isoscalar and isovector off-shell modifications. While we agree that fully independent experimental validation would strengthen the case, the current prediction still offers a concrete benchmark for the framework at high x. revision: no

Circularity Check

1 steps flagged

Fitted off-shell contributions to nuclear data presented as independent predictions for R_D

specific steps
  1. fitted input called prediction [Abstract]
    "The description of the nuclear data also requires nonzero isoscalar and isovector nucleon off-shell PDF contributions, which gives specific predictions for the ratio, R_D, of deuteron to isoscalar nucleon structure functions."

    Off-shell isoscalar and isovector nucleon PDF contributions are fitted parameters adjusted to reproduce the nuclear (deuteron and A=3) DIS data. R_D is the ratio of deuteron to isoscalar nucleon structure functions, which is directly computed from the same fitted nuclear model. Therefore the 'specific predictions' for R_D are the fitted model's output on the input data by construction, not an independent derivation.

full rationale

The paper performs a global QCD fit using JAM Bayesian Monte Carlo, determining u/d PDFs, higher-twist coefficients, and isoscalar/isovector off-shell nucleon PDF modifications simultaneously from proton, deuteron, and A=3 DIS data. The abstract states that nonzero off-shell contributions are required to describe the nuclear data and 'gives specific predictions for the ratio, R_D'. Since R_D is the deuteron-to-isoscalar-nucleon structure function ratio constructed from the same fitted nuclear model, this step reduces to a fitted output rather than an independent test. The core stability claim for PDFs up to x≈0.8 retains some independence through systematic cut variations and isospin-independent HT findings, preventing a higher score. No self-definitional equations or self-citation chains were identified in the provided text.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The analysis rests on the validity of collinear factorization at low scales and introduces fitted higher-twist and off-shell parameters without independent first-principles justification.

free parameters (2)
  • higher-twist corrections
    Fitted positive values, largely isospin independent, to describe DIS data at low W and Q.
  • isoscalar and isovector off-shell PDF contributions
    Nonzero values required to fit nuclear data and generate R_D prediction.
axioms (1)
  • domain assumption Collinear factorization framework holds down to W²=3.5 GeV² and Q²=m_c²
    Invoked to interpret all data within the global fit.

pith-pipeline@v0.9.0 · 5554 in / 1355 out tokens · 52625 ms · 2026-05-09T18:55:40.398277+00:00 · methodology

discussion (0)

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