Wigner Distributions For Gluons

TL;DR

This paper calculates gluon Wigner distributions for various polarized states of a quark-gluon target at one loop, providing new insights into spin and angular momentum distributions in momentum and impact parameter space.

Contribution

It introduces the first calculation of gluon Wigner distributions for transversely polarized targets and linearly polarized gluons, improving numerical convergence over previous studies.

Findings

First calculation of gluon Wigner distribution for transversely polarized targets.

Analysis of spin densities in momentum and impact parameter space.

Investigation of helicity and orbital angular momentum distributions at small-x.

Abstract

We investigate the gluon Wigner distributions for unpolarized, longitudinally polarized and transversely polarized target state. Instead of a nucleon, we take the target state to be a quark dressed with a gluon at one loop and investigate the gluon Wigner distributions at leading twist. Better numerical convergence is obtained compared to an earlier study, that removes the regulator dependence of the results. We present a first calculation of the Wigner distribution for the transversely polarized target and linearly polarized gluon. We study the spin densities in momentum and impact parameter space. We also investigate the quark and gluon helicity and orbital angular momentum distributions at small-$x$.