Partons Transverse Momentum and Orbital Angular Momentum Distributions

We discuss the two definitions of partonic orbital angular momentum given by Ji and by Jaffe and Manohar, respectively. While the former connects to the twist two Generalised Transverse Momentum Distribution $F_{14}$, the latter has been shown to connnect to the twist three Generalised Parton Distribution $G_2$. We demonstrate that the two definitions are infact related and differ essentially in their gauge link structure. Starting from nonlocal, $k_T$ unintegrated, off-forward matrix elements, instead of the standard Operator Product Expansion, we show how $G_2$ can be written as the sum of twist two, quark mass, and interaction dependent (twist three) terms, thus emphasizing the role of quark intrinsic transverse momentum and off-shellness. The twist two term in particular is given by the $k^2_T$ moment of $F_{14}$. We therefore uncover a relation/sum rule connecting the two definitions of orbital angular momentum, $F_{14}$ and $G_2$. We explore both the spin and the intrinsic transverse momentum/transverse space correlations as well as the gauge link structure behind the two decomposition frameworks, which are necessary to extract orbital angular momentum from experiment.