Deciphering Twist-3 Chiral-Even GPDs in the Light-Front Quark-Diquark Model

We investigate quantum chromodynamics (QCD) in this study by computing chiral-even generalized parton distributions (GPDs) at twist-$3$ using the light-front quark-diquark model (LFQDM), particularly when the longitudinal momentum transfer is zero. We provide a detailed analysis of the twist-$3$ chiral-even GPD's dependence on the longitudinal momentum fraction ($x$) and the momentum transfer ($t$) by illustrating their behavior through extensive two-dimensional ($2$-D) and three-dimensional ($3$-D) visualizations. Our investigation also reveals the intricate relationships between these GPDs and other distribution functions (DFs) such as generalized transverse-momentum dependent distributions (GTMDs), transverse momentum-dependent parton distributions (TMDs), and parton distribution functions (PDFs). Our study also includes the connected form factors (FFs) which are crucial in understanding the internal structure of hadrons. Additionally, we provide impact parameter GPD plots to offer insights into the spatial distribution of partons.