Twist analysis of the spin-orbit correlation in QCD

TL;DR

This paper provides a detailed QCD analysis of twist-three parton distribution functions related to spin-orbit correlations in hadrons, deriving identities, sum rules, and physical interpretations.

Contribution

It introduces exact non-perturbative identities decomposing spin-orbit correlations and proposes a new momentum sum rule linked to the Jaffe-Manohar spin sum rule.

Findings

Derived identities for twist-three distributions

Established a novel longitudinal momentum sum rule

Connected sum rule to color Lorentz forces

Abstract

We present a QCD analysis of the twist-three parton distribution functions associated with the spin-orbit correlation of quarks and gluons in spin-$\frac{1}{2}$ and spin-0 hadrons. We derive exact non-perturbative identities decomposing the spin-orbit correlations into the Wandzura-Wilczek part and the genuine twist-three part. In the spin-$\frac{1}{2}$ case, the result is partially related to the kinematical twist-three part of the $g_T(x)$ distribution familiar in the context of transverse spin physics. We use these identities to obtain a novel longitudinal momentum sum rule which may be regarded as the momentum version of the Jaffe-Manohar spin sum rule. We explore the physical interpretation of the sum rule and make a connection to the color Lorentz forces and their associated potential energies.