Lorentz Invariance and QCD Equation of Motion Relations for Generalized Parton Distributions and the Dynamical Origin of Proton Orbital Angular Momentum

TL;DR

This paper derives new Lorentz invariance and equation of motion relations linking measurable twist-three GPDs to the orbital angular momentum of quarks, providing a pathway to experimentally access proton spin structure details.

Contribution

It introduces novel relations between twist-three GPDs and GTMD moments, connecting orbital angular momentum to measurable quantities and expanding understanding of proton spin dynamics.

Findings

Derived relations between twist-three GPDs and GTMD moments.

Connected orbital angular momentum density to measurable twist-three GPDs.

Identified specific spin asymmetries for experimental detection.

Abstract

We derive new Lorentz Invariance and Equation of Motion Relations between twist-three Generalized Parton Distributions (GPDs) and moments in the parton transverse momentum, $k_T$, of twist-two Generalized Transverse Momentum-Dependent Distributions (GTMDs), as a function of the parton longitudinal momentum fraction $x$. Although GTMDs in principle define the observables for partonic orbital motion, experiments that can unambiguously detect them appear remote at present. The relations presented here provide a solution to this impasse in that, e.g., the orbital angular momentum density is connected to directly measurable twist-three GPDs. Out of 16 possible Equation of Motion relations that can be written in the T-even sector, we focus on three helicity configurations that can be detected analyzing specific spin asymmetries: two correspond to longitudinal proton polarization and are associated with quark orbital angular momentum and spin-orbit correlations; the third, obtained for transverse proton polarization, is a generalization of the relation obeyed by the $g_2$ structure function. We also exhibit an additional relation connecting the off-forward extension of the Sivers function to an off-forward Qiu-Sterman term.