Kinematic twist-three contributions to pseudo- and quasi-GPDs and translation invariance

TL;DR

This paper derives explicit tree-level twist-three contributions to nucleon matrix elements of gauge-invariant operators, restoring translation invariance in lattice GPD calculations and highlighting their logarithmic enhancement and discontinuities at specific kinematic points.

Contribution

It provides the first explicit expressions for kinematic twist-three contributions to gauge-invariant nonlocal quark-antiquark operators relevant for lattice GPD studies.

Findings

Restores translation invariance up to higher twist four.

Reveals logarithmic enhancement of twist-three corrections.

Identifies discontinuities at specific kinematic points.

Abstract

We present explicit expressions for the tree-level "kinematic" twist-three contributions to the nucleon matrix elements of gauge-invariant nonlocal quark-antiquark operators which can be used in lattice calculations of generalized parton distributions (GPDs). These contributions in particular restore the translation invariance of the results up to higher twist four. The calculated twist-three corrections are logarithmically enhanced as compared to the leading twist, and are discontinuous at the kinematic points $x=\pm\xi$.