Transverse Orbital Angular Momentum in the Proton

TL;DR

This paper presents a new method to decompose the proton's transverse angular momentum into spin and orbital parts using QCD equations and Lorentz invariance, linking it to twist-three distributions and transverse momentum.

Contribution

It introduces a more direct decomposition approach for proton transverse angular momentum, connecting it to twist-three distributions and transverse momentum-dependent functions.

Findings

Derived a new decomposition of proton transverse angular momentum.

Expressed orbital component via quark transverse momentum moments.

Linked the decomposition to twist-three generalized parton distributions.

Abstract

Using the equations of motion of QCD and Lorentz invariance relations, we show a new, more direct way of obtaining the decomposition of the proton's quark transverse angular momentum into its spin and orbital components. The new decomposition can be understood as a twist-three relation, with the quark transverse spin described by the parton distribution $g_T$. We find that the orbital component can be expressed in terms of a moment in the quark transverse momentum, $k_T$, of the generalized transverse momentum-dependent distribution $F_{12}$, or alternatively in terms of the twist-three generalized parton distributions $H_{2T}$ and $\widetilde{E}_{2T}$.