Quark Orbital Angular Momentum, piece of the Proton Spin Puzzle

Orbital Angular Momentum (OAM), $L_{q,g}$, is generated inside the proton as a consequence of the quark and gluon transverse motion about the system’s center of momentum. It has been identified as a critical component in the resolution of the proton spin puzzle, which has constituted a central focus of hadron physics since the seminal EMC experiments demonstrated that quark spin alone cannot account for the proton spin. The quark orbital angular momentum component of proton spin, Lq, can be defined in QCD as the integral of a Wigner phase space distribution weighting the cross product of the quark's transverse position and momentum. It can also be independently defined from the operator product expansion for the off-forward Compton amplitude in terms of a twist-three generalized parton distribution. We provide an explicit link between the two definitions, connecting them through their dependence on partonic intrinsic transverse momentum. Connecting the definitions provides the key for correlating direct experimental determinations of Lq, and evaluations through Lattice QCD calculations. We consider model calculations to illustrate both definitions.