Polarized Gluon Pseudodistributions at Short Distances

TL;DR

This paper develops a pseudo-PDF approach for calculating polarized gluon distributions on the lattice, providing one-loop corrections, evolution properties, and matching relations to connect Euclidean lattice data with light-cone PDFs.

Contribution

It introduces a framework for lattice calculation of polarized gluon PDFs using pseudo-PDFs, including one-loop corrections and matching relations for accurate extraction.

Findings

Derived one-loop corrections for gluonic correlators.

Established evolution properties of matrix elements.

Provided matching relations between Euclidean and light-cone distributions.

Abstract

We formulate the basic points of the pseudo-PDF approach to the lattice calculation of polarized gluon PDFs. We present the results of our calculations of the one-loop corrections for the bilocal $G_{\mu \alpha}(z) \widetilde G_{\lambda \beta}(0)$ correlator of gluonic fields. Expressions are given for a general situation when all four indices are arbitrary, and also for specific combinations of indices corresponding to three matrix elements that contain the twist-2 invariant amplitude related to the polarized PDF. We study the evolution properties of these matrix elements, and derive matching relations between Euclidean and light-cone Ioffe-time distributions. These relations are necessary for extraction of the polarized gluon distributions from the lattice data.