Gluon Wigner Distributions in boost-invariant longitudinal position space

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 $σ=\frac{1}{2}b^- P^+$, can be accessed through the Fourier transformation over skewness $ξ$ to the gluon-gluon correlator of generalized transverse momentum dependent distributions (GTMDs). The model results for gluon WDs in $σ$-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.