Gluon pseudo-distributions at short distances

TL;DR

This paper develops a theoretical framework for extracting gluon parton distribution functions from lattice QCD calculations using the pseudo-PDF approach, including one-loop calculations and a matching relation.

Contribution

It identifies the relevant gluon correlator functions, performs gauge-invariant one-loop calculations, and derives a matching relation linking lattice data to the gluon PDF.

Findings

Ultraviolet terms cancel in the reduced Ioffe-time distribution

Derived a kernel-based matching relation between lattice data and gluon PDF

Provided a gauge-invariant coordinate-space formulation for gluon PDFs

Abstract

We present the results that are necessary in the ongoing lattice calculations of the gluon parton distribution functions (PDFs) within the pseudo-PDF approach. We identify the two-gluon correlator functions that contain the invariant amplitude determining the gluon PDF in the light-cone $z^2 \to 0$ limit, and perform one-loop calculations in the coordinate representation in an explicitly gauge-invariant form. Ultraviolet (UV) terms, which contain $\ln (-z^2)$-dependence cancel in the reduced Ioffe-time distribution (ITD), and we obtain the matching relation between the reduced ITD and the light-cone ITD. Using a kernel form, we get a direct connection between lattice data for the reduced ITD and the normalized gluon PDF.