Gluon Unpolarized, Polarized, and Transversity GPDs from Lattice QCD: Lorentz-Covariant Parametrization (Part I)

TL;DR

This paper develops a Lorentz-covariant framework to extract gluon generalized parton distributions from lattice QCD, enabling first-principles calculations of nucleon structure relevant to various experimental processes.

Contribution

It introduces a novel Lorentz-covariant parameterization method for gluon GPD matrix elements in lattice QCD, facilitating their separation and determination.

Findings

Established a tensor basis for gluon GPD matrix elements.

Derived components projecting onto invariant amplitudes for gluon GPDs.

Provided a foundation for numerical lattice QCD calculations of gluon GPDs.

Abstract

We identify the matrix elements necessary to determine the leading-twist gluon generalized parton distributions (GPDs) $H_g,~E_g,~\wt{H}_g,~\wt{E}_g,~H^T_g,~E^T_g, \wt{H}^T_g ,~\wt{E}^T_g$ in lattice QCD calculations. We present a method to achieve a Lorentz-covariant parameterization of the matrix elements in terms of a linearly independent basis of tensor structures. This parameterization is crucial for projecting lattice QCD matrix elements onto light cone distributions. For the first time, we determine the corresponding components that project onto the linear combinations of invariant amplitudes, which reduce to the different gluon GPDs in the light cone limit and enable their separation in a lattice QCD calculation for spin-$0$ and spin-$\frac{1}{2}$ hadrons. Hence, this work lays the foundation for the numerical determination of the gluon GPDs from first-principle lattice QCD calculations, directly advancing our understanding of the mass and spin structures and mechanical properties of the nucleon, as well as the physics underlying deeply virtual Compton scattering and deeply virtual meson production in a range of experimental processes.