Gluon Transverse-Momentum-Dependent Distributions from Large-Momentum Effective Theory

TL;DR

This paper proposes a method to extract gluon transverse-momentum-dependent parton distribution functions (TMDPDFs) from lattice QCD calculations using large-momentum effective theory, providing a perturbative matching formula and scheme conversion guidance.

Contribution

It introduces a novel approach to compute gluon TMDPDFs from lattice data via LaMET, including a one-loop hard matching kernel and scheme independence insights.

Findings

Derived a matching formula connecting LaMET and TMDPDFs.

Provided a one-loop calculation of the hard matching kernel.

Showed scheme independence of the perturbative results.

Abstract

We demonstrate that gluon transverse-momentum-dependent parton distribution functions (TMDPDFs) can be extracted from lattice calculations of appropriate Euclidean correlations in large-momentum effective theory (LaMET). Based on perturbative calculations of gluon unpolarized and helicity TMDPDFs, we present a matching formula connecting them and their LaMET counterparts, where the latter are renormalized in a scheme facilitating lattice calculations and converted to the $\overline{\rm MS}$ scheme. The hard matching kernel is given up to one-loop level. We also show that the perturbative result is independent of the prescription used for the pinch-pole singularity in the relevant correlations. Our results offer a guidance for the extraction of gluon TMDPDFs from lattice simulations, and have the potential to greatly facilitate perturbative calculations of the hard matching kernel.