Finite-$t$ and target mass corrections for the short-distance expansion of quasi(pseudo) GPDs

Hua-Yu Jiang; Vladimir M. Braun

arxiv: 2606.09732 · v1 · pith:L4ZR5FPEnew · submitted 2026-06-08 · ✦ hep-ph

Finite-t and target mass corrections for the short-distance expansion of quasi(pseudo) GPDs

Vladimir M. Braun , Hua-Yu Jiang This is my paper

Pith reviewed 2026-06-27 15:55 UTC · model grok-4.3

classification ✦ hep-ph

keywords quasi-GPDspseudo-GPDsfinite-t correctionstarget mass correctionsshort-distance expansionlattice QCDgeneralized parton distributionsnucleon structure

0 comments

The pith

Finite-t and target mass corrections are calculated for the short-distance expansion of quasi and pseudo GPDs.

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

This paper computes the corrections proportional to t over P_z squared and nucleon mass squared over P_z squared in the short-distance expansion of nonlocal operators between nucleons of differing momenta. These operators relate at leading twist to moments of generalized parton distributions accessible via lattice QCD. Controlling these kinematic effects reduces a major uncertainty source and broadens the usable range of momentum transfers for mapping the proton's three-dimensional structure. The authors find the corrections sizable under typical lattice conditions.

Core claim

We calculate the ``kinematic'' corrections t/P_z^2 and m_N^2/P_z^2 to the short distance expansion of gauge-invariant nonlocal quark-antiquark operators sandwiched between nucleon states with different momenta. Here t is the momentum transfer, m_N is the nucleon mass and P_z is the momentum component in the direction of the quark-antiquark separation, which is assumed to be large. These matrix elements can be calculated in lattice QCD and, at leading twist, expressed in terms of moments of the generalized parton distrubutions (GPDs). Our results allow one to control one of principal uncertainties in such calculations and extend their region of applicability to larger momentum transfers, whic

What carries the argument

The short-distance expansion of gauge-invariant nonlocal quark-antiquark operators between nucleon states, including finite-t and target-mass corrections.

Load-bearing premise

The matrix elements can be calculated in lattice QCD and at leading twist expressed in terms of moments of the generalized parton distributions.

What would settle it

A lattice computation at fixed P_z where applying the calculated corrections changes the extracted GPD moments by an amount inconsistent with the size predicted in the paper.

read the original abstract

We calculate the ``kinematic'' corrections $t/P_z^2$ and $m_N^2/P_z^2$ to the short distance expansion of gauge-invariant nonlocal quark-antiquark operators sandwiched between nucleon states with different momenta. Here $t$ is the momentum transfer, $m_N$ is the nucleon mass and $P_z$ is the momentum component in the direction of the quark-antiquark separation, which is assumed to be large. These matrix elements can be calculated in lattice QCD and, at leading twist, expressed in terms of moments of the generalized parton distrubutions (GPDs). Our results allow one to control one of principal uncertainties in such calculations and extend their region of applicability to larger momentum transfers, which is important in the quest to access the three-dimension image of the proton. The calculated corrections turn out to be significant for a realistic lattice QCD setup.

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

Braun and Jiang compute explicit O(t/Pz²) and O(mN²/Pz²) corrections to the quasi-GPD short-distance OPE, which look practically useful for lattice work if the formulas hold up.

read the letter

The main new element is the explicit calculation of finite-t and target-mass power corrections in the short-distance expansion of the nonlocal operator matrix elements between moving nucleons. They isolate the t/Pz² and mN²/Pz² terms that enter when relating lattice quasi-GPD matrix elements to GPD moments at leading twist.

This addresses a real limitation: current lattice setups often sit at moderate Pz where these kinematic effects are not tiny, and the paper states they turn out sizable for realistic parameters. That extends the usable range toward higher momentum transfers without changing the underlying lattice computation.

The approach follows the standard OPE treatment for quasi distributions, so the power counting itself is not novel, but spelling out the corrections for nonzero t is the concrete advance. No free parameters or circular fits appear in the abstract.

Soft spots are limited. The abstract gives no sample numbers or full expressions, so the claimed size of the effect needs checking against the actual derivation and any higher-order terms that might mix in. The leading-twist matching assumption is the usual one in the field and does not look strained here.

This is for the lattice GPD and quasi-PDF community. Anyone running or analyzing such calculations would want the formulas if they are presented cleanly. It deserves a serious referee because it supplies a direct, falsifiable correction rather than an assumption.

Referee Report

0 major / 2 minor

Summary. The manuscript calculates the O(t/P_z²) and O(m_N²/P_z²) kinematic corrections to the short-distance OPE of gauge-invariant nonlocal quark-antiquark operators between nucleon states of differing momenta. These matrix elements are to be computed in lattice QCD and matched at leading twist to moments of GPDs; the results are presented as allowing control of a principal uncertainty and extending the usable range of quasi-GPD extractions to larger momentum transfers, with the corrections stated to be numerically significant for realistic lattice parameters.

Significance. If the explicit expansion holds, the work supplies a concrete, calculable handle on power corrections that are otherwise a leading systematic in quasi-GPD lattice studies. This directly supports the goal of accessing three-dimensional nucleon structure and is a positive contribution to the quasi-PDF/GPD literature by performing the indicated OPE rather than treating the corrections as fitted parameters.

minor comments (2)

[Abstract] Abstract: the statement that the corrections 'turn out to be significant for a realistic lattice QCD setup' should be accompanied by at least one concrete numerical example (e.g., the relative size at a quoted P_z value and t) so that readers can immediately judge the practical impact.
[Introduction] The leading-twist matching between the nonlocal operator matrix elements and GPD moments is invoked without an explicit reference to the precise twist-counting or operator definitions used; a short clarifying sentence or citation in the introduction would remove any ambiguity.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript, their recognition of its relevance to controlling power corrections in quasi-GPD lattice studies, and the recommendation for minor revision. No specific major comments are enumerated in the report, so we have no individual points to address below. We will incorporate any editorial or minor suggestions during the revision process.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper performs an explicit calculation of the O(t/P_z²) and O(m_N²/P_z²) kinematic corrections to the short-distance OPE for nonlocal quark operators between nucleon states. This is a direct perturbative expansion of the matrix elements, expressed in terms of GPD moments at leading twist, without any reduction of the output to a fitted parameter, self-defined quantity, or load-bearing self-citation chain. The abstract and scope indicate a standard operator-product expansion whose validity is not assumed from prior author work but derived within the present computation; the result is therefore self-contained against external benchmarks and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based on abstract only; the central claim rests on the leading-twist relation between nonlocal operators and GPD moments plus the validity of the short-distance expansion at large P_z.

axioms (2)

domain assumption At leading twist the matrix elements are expressed in terms of moments of GPDs
Invoked when stating that the operators relate to GPD moments and that the corrections control uncertainties in lattice extractions.
domain assumption Short-distance expansion applies when P_z is large
Underlying premise for the expansion whose corrections are being calculated.

pith-pipeline@v0.9.1-grok · 5689 in / 1300 out tokens · 21856 ms · 2026-06-27T15:55:04.187891+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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