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.

Figures (19)

• Figure 1: The Wigner distribution $\rho^Z_{UY}$, (Y = U, L, T; Z = R, L) for unpolarized proton in the boost invariant longitudinal position space $\sigma$ for different values of $-t$ in GeV$^2$ at fixed $x=0.2$, ${\bf p}_{\perp}^2=0.3$ GeV$^2$ and ${\bf \Delta}_{\perp}\perp{\bf p}_{\perp}$.
• Figure 2: The Wigner distribution $\rho^Z_{LY}$, (Y = U, L, T; Z = R, L) for longitudinally polarized proton in the boost invariant longitudinal position space $\sigma$ for different values of $-t$ in GeV$^2$ at fixed $x=0.2$, ${\bf p}_{\perp}^2=0.3$ GeV$^2$ and ${\bf \Delta}_{\perp}\perp{\bf p}_{\perp}$.
• Figure 3: The Wigner distribution $\rho^Z_{TY}$, (Y = U, L, T; Z = R, L) for transversely polarized proton in the boost invariant longitudinal position space $(\sigma)$ for different values of $-t$ in GeV$^2$ at fixed $x=0.2$, ${\bf p}_{\perp}^2=0.3$ GeV$^2$ and ${\bf \Delta}_{\perp}\perp{\bf p}_{\perp}$.
• Figure 4: The longitudinal momentum fraction $(x)$ sensitivity to Wigner distribution $\rho^Z_{UY}$, (Y = U, L, T; Z = R, L) for unpolarized proton in the boost invariant longitudinal position space $\sigma$ at fixed $-t=0.20$ GeV$^2$, ${\bf p}_{\perp}^2=0.30$ GeV$^2$ and ${\bf \Delta}_{\perp}\perp{\bf p}_{\perp}$.
• Figure 5: The longitudinal momentum fraction $(x)$ sensitivity to Wigner distribution $\rho^Z_{LY}$, (Y = U, L, T; Z = R, L) for longitudinally polarized proton in the boost invariant longitudinal position space $\sigma$ at fixed $-t=0.20$ GeV$^2$, ${\bf p}_{\perp}^2=0.30$ GeV$^2$ and ${\bf \Delta}_{\perp}\perp{\bf p}_{\perp}$.