Wigner Distributions for Gluons in Light-front Dressed Quark Model

TL;DR

The paper addresses how gluons contribute to nucleon spin by computing gluon Wigner distributions in a simple light-front dressed quark model, using a quark–gluon Fock sector and light-front Hamiltonian perturbation theory. It derives gluon GTMDs, notably F_{1,4}^g and G_{1,1}^g, and uses them to obtain canonical OAM l^g_z and spin–orbit C^g_z, with kinetic OAM L^g_z given via Ji's relation involving gluon GPDs. Numerically, it reveals characteristic Wigner-space distortions and shows that canonical and kinetic OAM differ in magnitude, while gauge-link dependence remains absent at order α_s. These results illuminate gluon spin–OAM structure in a controllable model and test the GTMD–GPD/TMD connections in a gluon-enabled framework.

Abstract

We present a calculation of Wigner distributions for gluons in light-front dressed quark model. We calculate the kinetic and canonical gluon orbital angular momentum and spin-orbit correlation of the gluons in this model.

Figures (5)

• Figure 1: (Color online) 3D plots of the Wigner distributions $W^{UU}$. Plots (a) and (b) are in $b$ space with $k_\perp = 0.4$ GeV. Plots (c) and (d) are in $k$ space with $b_\perp = 0.4$$\mathrm{GeV}^{-1}$. Plots (e) and (f) are in mixed space where $k_x$ and $b_y$ are integrated. All the plots on the left panel (a,c,e) are for $\Delta_{max} = 1.0$ GeV. Plots on the right panel (b,d,f) are for $\Delta_{max} = 5.0$ GeV. For all the plots we kept $m = 0.33$ GeV, integrated out the $x$ variable and we took $\vec{k_\perp} = k \hat{j}$ and $\vec{b_\perp} = b \hat{j}$.
• Figure 2: (Color online) 3D plots of the Wigner distributions $W^{LU}$. Plots (a) and (b) are in $b$ space with $k_\perp = 0.4$ GeV. Plots (c) and (d) are in $k$ space with $b_\perp = 0.4$$\mathrm{GeV}^{-1}$. Plots (e) and (f) are in mixed space where $k_x$ and $b_y$ are integrated. All the plots on the left panel (a,c,e) are for $\Delta_{max} = 1.0$ GeV. Plots on the right panel (b,d,f) are for $\Delta_{max} = 5.0$ GeV. For all the plots we kept $m = 0.33$ GeV, integrated out the $x$ variable and we took $\vec{k_\perp} = k \hat{j}$ and $\vec{b_\perp} = b \hat{j}$.
• Figure 3: (Color online) 3D plots of the Wigner distributions $W^{UL}$. Plots (a) and (b) are in $b$ space with $k_\perp = 0.4$ GeV. Plots (c) and (d) are in $k$ space with $b_\perp = 0.4$$\mathrm{GeV}^{-1}$. Plots (e) and (f) are in mixed space where $k_x$ and $b_y$ are integrated. All the plots on the left panel (a,c,e) are for $\Delta_{max} = 1.0$ GeV. Plots on the right panel (b,d,f) are for $\Delta_{max} = 5.0$ GeV. For all the plots we kept $m = 0.33$ GeV, integrated out the $x$ variable and we took $\vec{k_\perp} = k \hat{j}$ and $\vec{b_\perp} = b \hat{j}$.
• Figure 4: (Color online) 3D plots of the Wigner distributions $W^{LL}$. Plots (a) and (b) are in $b$ space with $k_\perp = 0.4$ GeV. Plots (c) and (d) are in $k$ space with $b_\perp = 0.4$$\mathrm{GeV}^{-1}$. Plots (e) and (f) are in mixed space where $k_x$ and $b_y$ are integrated. All the plots on the left panel (a,c,e) are for $\Delta_{max} = 1.0$ GeV. Plots on the right panel (b,d,f) are for $\Delta_{max} = 5.0$ GeV. For all the plots we kept $m = 0.33$ GeV, integrated out the $x$ variable and we took $\vec{k_\perp} = k \hat{j}$ and $\vec{b_\perp} = b \hat{j}$.
• Figure 5: (Color online) Plots of OAM (a) $l^{g}_z$ and (b) $L^{g}_z$ vs $m_q$ (GeV) for different values of $Q$ (GeV).