  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 generalizing the proton matrix elements of
quark bilocal operators which define transverse momentum-dependent parton
distributions (TMDs); the transverse momentum information is supplemented with
transverse position information by introducing an additional nonzero momentum
transfer. A gauge connection between the quarks must be specified in the quark
bilocal operators; the staple-shaped gauge link path used in TMD calculations
yields the Jaffe-Manohar definition of orbital angular momentum, whereas a
straight path yields the Ji definition. An exploratory lattice calculation,
performed at the pion mass m_pi = 518 MeV, is presented which
quasi-continuously interpolates between the two definitions and demonstrates
that their difference can be clearly resolved. The resulting Ji orbital angular
momentum is confronted with traditional evaluations based on Ji's sum rule.
Jaffe-Manohar orbital angular momentum is enhanced in magnitude compared to its
Ji counterpart.
