Dynamical gluon effects in twist-3 generalized parton distributions of the proton

TL;DR

This work addresses the nonperturbative structure of subleading, twist-3 GPDs of the proton by extending Basis Light-Front Quantization (BLFQ) to include the first two Fock sectors $|qqq\rangle$ and $|qqqg\rangle$. By diagonalizing the light-front Hamiltonian and forming overlap representations with the resulting LFWFs, the authors compute twist-3 GPDs in the zero-skewness limit ($\xi=0$) and separate the results into non-genuine and genuine (quark–quark–gluon) contributions. They find that eight twist-3 GPDs vanish at $\xi=0$, while four nonzero GPDs ($\tilde{E}_{2T}$, $H_{2T}'$, $E_{2T}'$, $\tilde{H}_{2T}'$) receive sizable but modest genuine components, with nonvalence gluon effects driving small-$x$ features. The study also evaluates related twist-3 observables, including quark orbital angular momentum and the quark spin–orbit correlation, finding results that are qualitatively consistent with other model approaches and offering nonperturbative input for future DVCS measurements at the EIC and EicC. Looking ahead, extensions to nonzero skewness and to gluon/sea twist-3 distributions are planned to sharpen predictions for twist-3 DVCS amplitudes and spin structure studies.

Abstract

Within the Basis Light-Front Quantization framework, we systematically investigate the subleading-twist (twist-3) generalized parton distributions (GPDs) of the proton's valence quarks beyond the Wandzura--Wilczek (WW) approximation. The twist-3 GPDs are not independent; through the equations of motion they decompose into a non-genuine contribution and a genuine twist-3 term. The latter encodes quark--quark--gluon correlations and involves interference between the light-front Fock sectors |qqq> and |qqqg>, which are typically neglected in the WW approximation. Using light-front wave functions obtained from diagonalizing the proton light-front Hamiltonian for its |qqq> and |qqqg> Fock components, we compute these GPDs via their overlap representations. To further explore their physical implications, we also evaluate several twist-3--related quantities, including the quark orbital angular momentum, the total quark spin contribution, and the quark spin--orbit correlation. Our results provide new nonperturbative input on higher-twist dynamics particularly multi-parton interference effects relevant for future measurements at the EicC and the EIC.

Figures (4)

• Figure 1: 3D Plots of the twist-3 quark GPDs $x\tilde{E}_{2T}, xH_{2T}^\prime, xE_{2T}^\prime,$ and $x\tilde{H}_{2T}^\prime$ in the proton, evaluated with $N_{\mathrm{max}}=9$ and $K=16.5$. The left column panels {(a), (c), (e), (g)} correspond to the $u$ quark and the right column panels {(b), (d), (f), (h)} correspond to the $d$ quark on the flavor level. The flavor level distributions are given by $X_{flavor}^u =2 X_{quark}^u$ and $X_{flavor}^d=X_{quark}^d$, where $X$ stands for all the GPDs.
• Figure 2: 2D Plots of the twist-3 quark GPDs $x\tilde{E}_{2T}, xH_{2T}^\prime, xE_{2T}^\prime,$ and $x\tilde{H}_{2T}^\prime$ in the proton at fixed $-t=0.25$ GeV$^2$, evaluated with $N_{\mathrm{max}}=9$ and $K=16.5$. The left column panels {(a), (c), (e), (g)} correspond to the $u$ quark and the right column panels {(b), (d), (f), (h)} correspond to the $d$ quark on the flavor level. The flavor level distributions are given by $X_{flavor}^u =2 X_{quark}^u$ and $X_{flavor}^d=X_{quark}^d$, where $X$ stands for all the GPDs.
• Figure 3: 2D Plots of the twist-3 quark GPDs $x\tilde{E}_{2T}, xH_{2T}^\prime, xE_{2T}^\prime,$ and $x\tilde{H}_{2T}^\prime$ in the proton at fixed $x=2.5/16.5$, evaluated with $N_{\mathrm{max}}=9$ and $K=16.5$. The left column panels {(a), (c), (e), (g)} correspond to the $u$ quark and the right column panels {(b), (d), (f), (h)} correspond to the $d$ quark on the flavor level. The flavor level distributions are given by $X_{flavor}^u =2 X_{quark}^u$ and $X_{flavor}^d=X_{quark}^d$, where $X$ stands for all the GPDs.
• Figure 4: Plots of the twist-3 FFs $\tilde{A}_q, \tilde{C}_q$ and $\tilde{F}_q$ in the proton, evaluated with $N_{\mathrm{max}}=9$ and $K=16.5$. The blue circle solid line corresponds to the $u$ quark and the red square dotted line corresponds to the $d$ quark on the quark level.