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 gT (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.
