Generalized Parton Distributions from Lattice QCD with Asymmetric Momentum Transfer: Unpolarized Quarks at Nonzero Skewness

TL;DR

This paper develops a lattice QCD framework for calculating unpolarized generalized parton distributions with nonzero skewness, enabling comprehensive mapping of GPDs across various kinematic regimes.

Contribution

It extends the asymmetric frame formalism to include nonzero skewness, facilitating the extraction of GPDs from lattice data with broader kinematic coverage.

Findings

Successfully extracted GPD amplitudes in coordinate space.

Reconstructed quasi-distributions and performed matching to light cone.

Identified key challenges for nonzero skewness GPD calculations.

Abstract

We extend the formalism of asymmetric frames of reference for generalized parton distributions (GPDs) to the case of nonzero skewness, i.e., including longitudinal momentum transfer. The framework, based on Lorentz-invariant amplitudes and previously developed and numerically implemented for unpolarized, helicity and transversity GPDs at zero skewness, gives efficient access to a broad range of kinematics, making full mapping of GPDs from the lattice realistic. The general-skewness formalism is tested using lattice data with both transverse and longitudinal or only longitudinal momentum transfer, the latter being a special case with a reduced number of independent amplitudes. We extract the amplitudes in coordinate space and express the GPDs $H$ and $E$ in terms of these amplitudes. This is followed by reconstruction of quasi-distributions and their matching to the light cone. We further identify and discuss the principal challenges for nonzero skewness GPDs.