Gluon and Wilson loop TMDs for hadrons of spin $\leq$ 1

TL;DR

This paper develops a detailed parametrization of gluon TMD correlators, including Wilson loop TMDs, and explores their behavior at small x for various polarized hadronic targets, relevant for future collider experiments.

Contribution

It introduces a new parametrization framework for Wilson loop TMDs and relates them to small-x dipole gluon TMDs, extending understanding of gluon distributions in polarized hadrons.

Findings

Wilson loop correlators parametrized in terms of Wilson loop TMDs.

Identification of leading and suppressed gluon TMDs at small x.

Relevance for polarized deuteron studies at future Electron-Ion Colliders.

Abstract

In this paper we consider the parametrizations of gluon transverse momentum dependent (TMD) correlators in terms of TMD parton distribution functions (PDFs). These functions, referred to as TMDs, are defined as the Fourier transforms of hadronic matrix elements of nonlocal combinations of gluon fields. The nonlocality is bridged by gauge links, which have characteristic paths (future or past pointing), giving rise to a process dependence that breaks universality. For gluons, the specific correlator with one future and one past pointing gauge link is, in the limit of small $x$, related to a correlator of a single Wilson loop. We present the parametrization of Wilson loop correlators in terms of Wilson loop TMDs and discuss the relation between these functions and the small-$x$ `dipole' gluon TMDs. This analysis shows which gluon TMDs are leading or suppressed in the small-$x$ limit. We discuss hadronic targets that are unpolarized, vector polarized (relevant for spin-$1/2$ and spin-$1$ hadrons), and tensor polarized (relevant for spin-$1$ hadrons). The latter are of interest for studies with a future Electron-Ion Collider with polarized deuterons.