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We introduced a generalized Wilson line gauge link that reproduces both staple and near straight links in different limits. We then studied the gauge-invariant bi-local orbital angular momentum operator with such a general gauge link, in the framework of Chen et. al. decomposition of gauge fields. At the appropriate combination of limits, the operator reproduces both Jaffe-Manohar and Jis operator structure and offers a continuous analytical interpolation between the two in the small-$x$ limit. We also studied the potential OAM which is defined as the difference between the two, and how it depends on the geometry or orientation of the gauge links.
A Lattice QCD approach to quark orbital angular momentum in the proton based on generalized transverse momentum-dependent parton distributions (GTMDs) is enhanced methodologically by incorporating a direct derivative technique. This improvement remov
Given a Wigner distribution simultaneously characterizing quark transverse positions and momenta in a proton, one can directly evaluate their cross-product, i.e., quark orbital angular momentum. The aforementioned distribution can be obtained by gene
We determine the small Bjorken $x$ asymptotics of the quark and gluon orbital angular momentum (OAM) distributions in the proton in the double-logarithmic approximation (DLA), which resums powers of $alpha_s ln^2 (1/x)$ with $alpha_s$ the strong coup
We present a general analysis of the orbital angular momentum (OAM) distribution of gluons $L_g(x)$ inside the nucleon with particular emphasis on the small-$x$ region. We derive a novel operator representation of $L_g(x)$ in terms of Wilson lines an
A general consensus now is that there are two physically inequivalent complete decompositions of the nucleon spin, i.e. the decomposition of the canonical type and that of mechanical type. The well-known Jaffe-Manohar decomposition is of the former t