Subleading Twist-3 Gluon Generalized Parton Distributions in the Light-Front Model

TL;DR

This paper presents the first systematic calculation of twist-3 gluon generalized parton distributions (GPDs) in the proton within a light-front two-body gluon–spectator model, with light-front wave functions derived from soft-wall AdS/QCD. The authors derive the twist-3 gluon GPDs at zero skewness, express them via an overlap of light-front wave functions, and compute their behavior across a broad range of $x$ and transverse momentum transfer, including their Fourier-transformed impact-parameter space distributions. They analyze the associated gluon kinetic orbital angular momentum (OAM) via the gluon energy–momentum tensor and Ji-type sum rules, finding a negative total gluon OAM consistent with prior twist-2 results, while highlighting the distinct twist-3 contributions. The study provides new insights into subleading gluon spin–orbit correlations and sets the stage for future phenomenology and lattice studies of twist-3 gluon structure and OAM in hadrons.

Abstract

We present a calculation of the twist-3 generalized parton distributions (GPDs) for gluons in the proton. Our analysis is performed within a light-front constituent model where the proton is treated as a two-body state of a spin-1 gluon and a spin-1/2 spectator system. The requisite light-front wave functions are derived from the soft-wall AdS/QCD correspondence. We compute the complete set of twist-3 gluon GPDs over a broad kinematic range. The corresponding distributions in impact parameter space are obtained via Fourier transform, revealing the transverse spatial distribution of gluons. Furthermore, we evaluate the contribution of these GPDs to the gluon kinetic orbital angular momentum (OAM) and compare our findings with other theoretical predictions.

Figures (6)

• Figure 1: The twist-3 GPDs $x {G}_{g,3}(x,\boldsymbol{\Delta}_T^2)$,$x{\tilde{G}}_{g,1}(x,\boldsymbol{\Delta}_T^2)$,$x{\tilde{G}}_{g,2}(x,\boldsymbol{\Delta}_T^2)$ and $x{\tilde{G}}_{g,4}(x,\boldsymbol{\Delta}_T^2)$ are plotted with respect to $x$ and $\boldsymbol{\Delta}_T^2[\text{GeV}^2]$ in the kinematic range $x\in[0.05,0.6]$ and $\boldsymbol{\Delta}_T^2\in[0.01,2] \ \text{GeV}^2$.
• Figure 2: The twist-3 GPDs $x {G}_{g,3}(x,\boldsymbol{\Delta}_T^2)$,$x{\tilde{G}}_{g,1}(x,\boldsymbol{\Delta}_T^2)$,$x{\tilde{G}}_{g,2}(x,\boldsymbol{\Delta}_T^2)$ and $x{\tilde{G}}_{g,4}(x,\boldsymbol{\Delta}_T^2)$ are plotted with respect to $x$ in the kinematic range $x\in[0.05,0.8]$ at fixed of $\boldsymbol{\Delta}_T^2=0.1(\text{blue}) \ [\text{GeV}^2],0.5(\text{red})\ [\text{GeV}^2]$ and $\boldsymbol{\Delta}_T^2=1.2 \ [\text{GeV}^2](\text{black})$.
• Figure 3: The twist-3 IPDPDFs $x \mathcal{G}_{g,3}(x,b_T)$,$x\mathcal{\tilde{G}}_{g,1}(x,b_T)$,$x\mathcal{\tilde{G}}_{g,2}(x,b_T)$ and $x\mathcal{\tilde{G}}_{g,4}(x,b_T)$ are plotted with respect to $x$ and $b_T [\text{GeV}^{-1}]$ in the kinematic range $x\in[0.05,0.8]$ and $b_T\in[0.01,4]$.
• Figure 4: The twist-3 IPDPDFs $x \mathcal{G}_{g,3}(x,b_T)$,$x\mathcal{\tilde{G}}_{g,1}(x,b_T)$,$x\mathcal{\tilde{G}}_{g,2}(x,b_T)$ and $x\mathcal{\tilde{G}}_{g,4}(x,b_T)$ are plotted with respect to $b_T[fm]$ in the kinematic range $b_T\in[0.01,10]$ at fixed of $x=0.05(\text{blue}),0.10(\text{red})$ and $x=0.20(\text{black})$.
• Figure 5: The twist-3 IPDPDFs $x \mathcal{G}_{g,3}(x,b_T)$,$x\mathcal{\tilde{G}}_{g,1}(x,b_T)$,$x\mathcal{\tilde{G}}_{g,2}(x,b_T)$ and $x\mathcal{\tilde{G}}_{g,4}(x,b_T)$ are plotted with respect to $b_x$ and $b_y$ at fixed value of $x=0.05$.