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arxiv: 2511.15546 · v2 · pith:SMOMBGQ7new · submitted 2025-11-19 · ✦ hep-lat · hep-ph

Extracting Mellin moments of double parton distributions from lattice data

Markus Diehl , Oskar Grocholski , Daniel Reitinger , Andreas Sch\"afer , Christian Zimmermann This is my paper

Pith reviewed 2026-05-21 18:15 UTC · model grok-4.3

classification ✦ hep-lat hep-ph
keywords double parton distributionsMellin momentslattice QCDIoffe timekinematic skewnesscorrelation functionsparton distributions
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The pith

Reconstructing Mellin moments of double parton distributions from lattice data requires accounting for skewness in correlation functions.

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

The paper explores the challenges in extracting Mellin moments of double parton distributions using Euclidean lattice QCD calculations. It identifies that this reconstruction involves an integral over a variable equivalent to Ioffe time, with the Fourier conjugate corresponding to kinematic skewness. Several models are applied to evaluate how this skewness dependence affects the extraction from currently available lattice data.

Core claim

Reconstructing the Mellin moments requires taking an integral over the Ioffe-time variable. The Fourier conjugate of this variable is the kinematic skewness, and the skewness dependence of the hadronic correlation functions has a significant impact on the extraction of the moments from existing lattice data.

What carries the argument

The integral over the Ioffe time variable with its Fourier conjugate being the kinematic skewness in double parton distributions.

Load-bearing premise

The models employed sufficiently accurately represent the skewness dependence in the lattice QCD correlation functions for double parton distributions.

What would settle it

Computing the hadronic correlation functions on the lattice at multiple values of skewness and observing whether they match the model predictions or deviate in a way that alters the extracted moments.

read the original abstract

Reconstructing Mellin moments of double parton distributions from calculations on a Euclidean lattice requires taking an integral over a variable that may be regarded as a Ioffe time. The Fourier conjugate of this variable plays the role of a kinematic skewness in the double parton distributions. We discuss the skewness dependence of the relevant hadronic correlation functions. Using several models, we study the impact of this dependence on extracting moments of double parton distributions from existing lattice data.

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 examines the reconstruction of Mellin moments of double parton distributions from Euclidean lattice QCD. It emphasizes that this requires an integral over a variable interpretable as Ioffe time, whose Fourier conjugate is the kinematic skewness, and analyzes the skewness dependence of the relevant hadronic correlation functions. Several models are used to assess the impact of this dependence on moment extraction from existing lattice data.

Significance. If the model-based assessment holds, the work identifies a relevant systematic consideration for lattice extractions of DPD moments, which could inform the design of future calculations and improve control over kinematic effects in multi-parton observables. The focus on an often-overlooked integral transform aspect provides a useful conceptual clarification for the field.

major comments (2)
  1. [§3] §3 (model definitions): The skewness dependence is parameterized via several external models, yet no direct comparison or cross-check is presented against lattice correlation functions computed at multiple fixed values of skewness while holding other kinematics constant. This assumption is load-bearing for the central claim about quantitative impact on moment extraction.
  2. [§4] §4 (impact analysis): The reported effects on existing lattice data are described qualitatively without accompanying numerical estimates, error propagation, or sensitivity plots showing how variations in the skewness profile alter the extracted Mellin moments; this weakens the ability to judge the practical size of the correction.
minor comments (2)
  1. [§2] The definition of the Ioffe-time variable and its relation to the lattice operator could be stated more explicitly in the introductory formalism section to aid readers unfamiliar with the double-parton context.
  2. Figure captions should include the specific model names and parameter choices used for each curve to improve reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive comments, which help clarify the presentation of our results. We address each major comment below and indicate the revisions we will make to strengthen the manuscript.

read point-by-point responses

  1. Referee: [§3] §3 (model definitions): The skewness dependence is parameterized via several external models, yet no direct comparison or cross-check is presented against lattice correlation functions computed at multiple fixed values of skewness while holding other kinematics constant. This assumption is load-bearing for the central claim about quantitative impact on moment extraction.

    Authors: We thank the referee for highlighting this point. Direct lattice QCD results for the relevant hadronic correlation functions at multiple fixed values of skewness (with other kinematics held constant) are not available in the existing literature for double parton distributions; this is precisely why the manuscript employs several independent phenomenological models to quantify the potential effect. The models serve to demonstrate that the skewness dependence can introduce a non-negligible systematic in moment extraction and to motivate future lattice studies that vary skewness explicitly. In the revised manuscript we will expand the discussion in §3 to include a clearer statement of the current absence of such lattice data and to outline how future calculations could perform the suggested cross-checks. revision: partial

  2. Referee: [§4] §4 (impact analysis): The reported effects on existing lattice data are described qualitatively without accompanying numerical estimates, error propagation, or sensitivity plots showing how variations in the skewness profile alter the extracted Mellin moments; this weakens the ability to judge the practical size of the correction.

    Authors: We agree that the impact analysis would benefit from greater quantitative detail. In the revised version we will augment §4 with explicit numerical estimates of the bias induced in the extracted Mellin moments for each model considered. We will also add sensitivity plots that display the variation of the moments as a function of the assumed skewness profile, together with a discussion of how uncertainties in the skewness dependence propagate to the final results (within the limitations inherent to a model-based study). These additions will make the practical size of the correction more transparent to readers. revision: yes

Circularity Check

0 steps flagged

No circularity: model-based assessment of skewness impact is independent of lattice inputs

full rationale

The paper discusses skewness dependence of hadronic correlation functions and employs several models to quantify its effect on extracting Mellin moments from existing lattice data. This constitutes an external-model assessment rather than any derivation that reduces a result to a fitted parameter by construction, a self-definitional loop, or a load-bearing self-citation chain. No equations or steps in the abstract or description exhibit the specific reductions required for a circularity finding; the central claim remains an evaluation of model sensitivity and is therefore self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard lattice QCD methodology for correlation functions and on the representativeness of the chosen models for skewness dependence; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • standard math Standard assumptions of lattice QCD for computing hadronic correlation functions and of perturbative QCD for parton distributions
    The reconstruction procedure and model application presuppose established lattice techniques and parton-distribution frameworks.

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