arxiv: 2511.15546 · v1 · 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 2026-05-17 20:37 UTC · model grok-4.3

classification ✦ hep-lat hep-ph

keywords double parton distributionsMellin momentslattice QCDIoffe timeskewness dependencehadronic correlation functionsEuclidean lattice

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The pith

Skewness dependence of hadronic correlation functions must be accounted for when extracting Mellin moments of double parton distributions from lattice data.

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

The paper examines how reconstructing Mellin moments of double parton distributions on the lattice requires integrating over a variable that corresponds to Ioffe time, with its Fourier conjugate acting as kinematic skewness. It discusses the skewness dependence of the underlying hadronic correlation functions and uses several models to quantify how this dependence influences results obtained from existing lattice data. A sympathetic reader would care because double parton distributions encode correlated parton behavior inside nucleons and directly affect predictions for certain high-energy collision processes. If the dependence proves significant and is ignored, extracted moments could carry systematic bias that propagates into phenomenological applications.

Core claim

Reconstructing Mellin moments of double parton distributions from Euclidean lattice calculations requires an integral over an Ioffe-time-like variable whose Fourier conjugate is a kinematic skewness parameter. The relevant hadronic correlation functions depend on this skewness, and model studies show that this dependence affects the numerical values extracted from current lattice data sets.

What carries the argument

The integral transform over the Ioffe-time variable that converts lattice matrix elements into Mellin moments of double parton distributions, with skewness entering as its Fourier conjugate.

If this is right

Extraction procedures for Mellin moments must incorporate a model or parametrization of skewness dependence rather than assuming independence.
Existing lattice data sets may require re-evaluation once skewness dependence is included.
Future lattice simulations should target multiple skewness points to reduce model uncertainty in the extraction.
Phenomenological fits to double parton distributions should treat the lattice-derived moments as having an additional systematic uncertainty from the skewness modeling.

Where Pith is reading between the lines

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

Lattice groups could design future runs with a deliberate scan in the skewness variable to make the extraction less model-dependent.
The same integral-transform approach might be applied to other multi-parton or multi-hadron quantities where an analogous Fourier variable appears.
If the skewness dependence turns out to be weak in the kinematic region of interest, the computational cost of including it could be avoided in future analyses.

Load-bearing premise

The models employed capture the dominant skewness dependence of the relevant hadronic correlation functions in real QCD at the kinematics and lattice spacings of current simulations.

What would settle it

A lattice computation performed at several distinct nonzero values of the skewness parameter that yields moment values deviating substantially from the model-based extrapolations used in the paper.

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.

Desk Editor's Note private letter to a colleague

Model study flags skewness dependence for lattice DPD moments but stays qualitative due to untested model assumptions.

read the letter

The one or two things to know: This paper applies models to study how skewness dependence in correlation functions affects extracting Mellin moments of double parton distributions from lattice data. It concludes that this dependence can have a noticeable impact, but the analysis remains at the level of model estimates rather than direct lattice computations or new data analysis. What the paper does well is to extend the Ioffe-time formalism to the double parton case and to test several models for the skewness behavior. This highlights a potential source of uncertainty that people extracting these moments from existing ensembles should keep in mind. The authors cite relevant prior work and keep the discussion focused on the practical implications for phenomenology. The soft spots are mainly around the model dependence. The central assumption is that the chosen models capture the dominant effects at the Ioffe times and kinematics of current lattice simulations. If higher-twist contributions or other non-perturbative effects play a larger role than the models allow, the estimated impact on the moments could be inaccurate. The paper does not seem to include direct comparisons or fits to actual lattice data points, which makes it harder to assess how robust the findings are. This is not a fatal issue for a model study, but it limits how far the conclusions can be pushed. There is no obvious circularity, as the models are inputs and the lattice data are treated as independent. The work is honest in its scope. This kind of paper is for researchers in lattice hadron structure, particularly those dealing with generalized or double parton distributions. A reader who is planning or analyzing lattice calculations for DPD moments would find it relevant as a warning about an additional systematic. It deserves a serious referee because it addresses a real technical point in an area where lattice results are starting to be used for phenomenology. I recommend sending it to peer review. The authors can likely address the model validation in revisions, and the community would benefit from the discussion.

Referee Report

1 major / 2 minor

Summary. The manuscript examines the skewness dependence of hadronic correlation functions required to reconstruct Mellin moments of double parton distributions (DPDs) from Euclidean lattice QCD calculations. It employs several models to quantify how this dependence influences the extraction of moments from existing lattice data sets, focusing on the integral over the Ioffe-time variable whose Fourier conjugate corresponds to kinematic skewness in the DPDs.

Significance. If the model results hold, the work provides a useful diagnostic for systematic uncertainties arising from skewness in current lattice extractions of DPD Mellin moments. This is relevant for ongoing efforts to compute double parton distributions on the lattice, as it offers a framework to estimate biases without requiring new simulations. The use of multiple models is a strength, allowing cross-checks of the sensitivity.

major comments (1)

[Model studies section] The central claim that the model studies quantify the impact on moment extraction from existing lattice data rests on the models reproducing the leading Ioffe-time and skewness behavior of the relevant matrix elements. The manuscript does not include a direct validation of this assumption against lattice correlators at the momenta and Ioffe times of current simulations (e.g., by comparing model predictions to published lattice data for the relevant hadronic functions).

minor comments (2)

[Introduction] Clarify the precise definition of the Ioffe-time variable and its relation to the skewness parameter in the introductory section to aid readers unfamiliar with the DPD formalism.
[Results] The abstract mentions 'existing lattice data' but the main text would benefit from explicit references to the specific lattice ensembles or publications used for the extraction examples.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive overall assessment and the constructive comment on model validation. We address the major comment below and indicate the revisions we will make.

read point-by-point responses

Referee: [Model studies section] The central claim that the model studies quantify the impact on moment extraction from existing lattice data rests on the models reproducing the leading Ioffe-time and skewness behavior of the relevant matrix elements. The manuscript does not include a direct validation of this assumption against lattice correlators at the momenta and Ioffe times of current simulations (e.g., by comparing model predictions to published lattice data for the relevant hadronic functions).

Authors: We agree that a direct comparison to lattice data at the relevant kinematics would strengthen the support for applying the models to existing simulations. The models employed are based on established frameworks (including light-cone sum rules and phenomenological parametrizations) that are designed to reproduce the leading Ioffe-time dependence and the expected skewness behavior of the relevant matrix elements. Nevertheless, we will revise the manuscript to include an explicit comparison of model predictions against published lattice results for the hadronic correlation functions at comparable momenta and Ioffe times. This addition will be placed in the model studies section and will quantify the level of agreement for the leading behaviors. We will also add a brief discussion of any limitations arising from the comparison. revision: yes

Circularity Check

0 steps flagged

No significant circularity; models and lattice data remain independent inputs

full rationale

The paper's central approach uses external models to examine skewness dependence in hadronic correlation functions and its effect on Mellin-moment extraction from existing lattice data. No load-bearing step reduces by construction to a fitted parameter, self-citation chain, or ansatz smuggled from prior work by the same authors. The models function as independent test inputs, the lattice data are external, and the derivation chain does not equate predictions to inputs via definition or renaming. This is the expected honest non-finding for a model-impact study.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on standard lattice QCD assumptions plus model assumptions about the functional form of skewness dependence; no new particles or forces are introduced.

axioms (1)

domain assumption The Ioffe-time integral can be performed numerically once the skewness dependence of the correlation function is known or modeled.
Stated in the abstract as the central technical step.

pith-pipeline@v0.9.0 · 5374 in / 1147 out tokens · 48045 ms · 2026-05-17T20:37:23.632694+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

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. ... Using several models, we study the impact of this dependence on extracting moments...
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We assume that in the y range ... the ζ and y dependence of I(ζ,y²) factorizes as I_q1q2(ζ,y²)=J_q1q2(ζ)K_q1q2(y²)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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