Unraveling sub-leading twist GTMDs of proton using LFQDM

Abstract: This study investigates the sub-leading twist generalized transverse momentum dependent distributions (GTMDs) of a proton within the light-front quark-diquark model (LFQDM) framework. We solve the parametrization equations for the Dirac matrix structure to yield the explicit GTMD expressions for scalar as well as vector diquark configurations for active $u$ and $d$ quarks. This analysis addresses the multi-dimensional nature of GTMDs by exploring their dependencies on one or two variables while keeping others fixed. Additionally, we extract transverse momentum dependent form factors (TMFFs) from GTMDs by integrating over the longitudinal momentum fraction $x$. The study uses $3$-dimensional plots to illustrate the variation of TMFFs with the quark's transverse momentum $p_{\perp}$ and the transverse momentum transfer to the proton $\Delta_{\perp}$.