Single spin asymmetries from a single Wilson loop

TL;DR

This paper investigates the behavior of gluon transverse momentum dependent distributions at small longitudinal momentum fractions, revealing a universal origin linked to a single Wilson loop, which advances understanding of gluon contributions to proton spin structure.

Contribution

It demonstrates that at small $x$, all relevant gluon TMDs reduce to a single Wilson loop, the spin-dependent odderon, unifying their origin and implications for spin asymmetry studies.

Findings

At large transverse momentum, gluon TMDs share common dynamical origins.

In the small $x$ limit, only dipole-type gluon TMDs survive and become identical.

All small $x$ gluon TMDs are given by the expectation value of a single Wilson loop.

Abstract

We study the leading-power gluon transverse momentum dependent distributions (TMDs) of relevance to the study of asymmetries in the scattering off transversely polarized hadrons. Next-to-leading-order perturbative calculations of these TMDs show that at large transverse momentum they have common dynamical origins, but that in the limit of small longitudinal momentum fraction $x$ only one origin remains. We find that in this limit only the dipole-type gluon TMDs survive and become identical to each other. At small $x$ they are all given by the expectation value of a single Wilson loop inside the transversely polarized hadron, the so-called spin-dependent odderon. This universal origin of transverse spin asymmetries at small $x$ is of importance to current and future experimental studies, paving the way to a better understanding of the role of gluons in the three-dimensional structure of spin-polarized protons.