Accessing gluon parton distributions in large momentum effective theory

TL;DR

This paper develops a method to calculate gluon parton distribution functions directly from lattice QCD using large momentum effective theory, by identifying renormalized quasi-PDFs that handle divergences and operator mixing.

Contribution

It identifies specific multiplicatively renormalizable gluon quasi-PDF correlators for unpolarized and helicity distributions, enabling direct lattice calculations of gluon PDFs.

Findings

Four independent quasi-PDF correlators for unpolarized gluons.

Three independent quasi-PDF correlators for helicity gluons.

A LaMET factorization formula for extracting gluon PDFs.

Abstract

Gluon parton distribution functions (PDFs) in the proton can be calculated directly on Euclidean lattices using large momentum effective theory (LaMET). To realize this goal, one has to find renormalized gluon quasi-PDFs in which power divergences and operator mixing are thoroughly understood. For the unpolarized distribution, we identify four independent quasi-PDF correlators that can be multiplicatively renormalized on the lattice. Similarly, the helicity distribution can be derived from three independent multiplicatively renormalizable quasi-PDFs. We provide a LaMET factorization formula for these renormalized quasi-PDFs from which one can extract the gluon PDFs.