Twist-4 proton GTMDs in the light-front quark-diquark model

TL;DR

This paper calculates twist-4 generalized transverse-momentum dependent parton distributions (GTMDs) for the proton using a light-front quark-diquark model, providing explicit equations and exploring their physical implications.

Contribution

It introduces the first detailed derivation of twist-4 GTMDs within the light-front quark-diquark model, including their dependence on multiple variables and connections to TMDs and Wigner distributions.

Findings

Derived explicit equations for twist-4 GTMDs for scalar and vector diquarks.

Obtained transverse-momentum dependent form factors from GTMDs.

Established the relation between twist-4 GTMDs and T-even TMDs.

Abstract

By integrating across the light-cone energy, totally unintegrated, off-diagonal quark-quark generalized parton correlation functions (GPCFs) can yield generalized transverse-momentum dependent parton distributions (GTMDs). We have obtained the twist-4 GTMDs for the case of proton in the light-front quark-diquark model (LFQDM). We have decoded the quark-quark GTMD correlator for proton and solved the parametrization equations for Dirac matrix structure at twist-4. We have derived the explicit equations of GTMDs for the diquark being scalar or vector leading to the results for the struck quark being a $u$ or $d$ quark. Being a multidimensional function, the dependence is studied with two variables at a time, keeping the others fixed. Transverse-momentum dependent form factors (TMFFs) have been obtained from GTMDs via integration over the longitudinal momentum fraction $x$ of the quark. We have debated over the possibility to specify the initial and final state polarizations of the smacked quark and the nucleon in twist-4 GTMDs as well as the Wigner distributions. Additionally, from twist-4 GTMDs, we have deduced the twist-4 T-even TMDs and found its synchronization with the already published results.