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. It is by now established that the two definitions are described by the same generalized transverse momentum distribution, $F_{14}$, while they differ through their gauge link structure. They can also be both described in terms of a twist three generalized parton distribution, $G_2$ which can be measured in DVCS type experiments. Here, starting from nonlocal, $k_T$ unintegrated, off-forward matrix elements, instead of the standard OPE, 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 $k_T^2$ 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.