Gluon Wigner Distributions in boost-invariant longitudinal position space

TL;DR

This paper explores gluon Wigner distributions in boost-invariant longitudinal space within a light-front spectator model, revealing diffraction-like patterns and spin-orbit correlations in the proton's internal structure.

Contribution

It introduces a novel model-based analysis of gluon Wigner distributions in boost-invariant space, including diffraction patterns and spin correlations, extending previous theoretical frameworks.

Findings

Gluon Wigner distributions exhibit diffraction-like oscillations.

Distribution patterns are sensitive to momentum fraction x and energy transfer -t.

Gluon spin-orbit correlations are identified and compared with other models.

Abstract

The Wigner distributions (WDs) in boost-invariant longitudinal space for unpolarized, longitudinally polarized and linearly polarized gluons in a proton are presented in the framework of the light-front gluon spectator model inspired by AdS/QCD. The boost-invariant longitudinal space defined by the coordinate $\sigma=\frac{1}{2}b^- P^+$, can be accessed through the Fourier transformation over skewness $\xi$ to the gluon-gluon correlator of generalized transverse momentum dependent distributions (GTMDs). The model results for gluon WDs in $\sigma$-space show an oscillatory behavior analogous to the diffraction scattering of a wave in optics. The diffraction pattern is more sensitive to the momentum fraction $x$ and passively varies with the total energy transfer to the electron-proton scattering $-t$, both of which are analogous to an effective slit-width. The leading-twist gluon WDs in the impact-parameter space and their skewness sensitivity are investigated extensively for unpolarized, longitudinally polarized, and transversely polarized protons. The gluon spin-OAM correlation is also reported and compared with existing models and lattice results.