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A Lattice QCD approach to quark orbital angular momentum in the proton basedon generalized transverse momentum-dependent parton distributions (GTMDs) isenhanced methodologically by incorporating a direct derivative technique. Thisimprovement removes a significant numerical bias that had been seen to afflictresults of a previous study. In particular, the value obtained for Ji quarkorbital angular momentum is reconciled with the one obtained independently viaJi's sum rule, validating the GMTD approach. Since GTMDs simultaneously containinformation about the quark impact parameter and transverse momentum, theypermit a direct evaluation of the cross product of the latter. They are definedthrough proton matrix elements of a quark bilocal operator containing a Wilsonline; the choice in Wilson line path allows one to continuously interpolatefrom Ji to Jaffe-Manohar quark orbital angular momentum. The latter is seen tobe significantly enhanced in magnitude compared to Ji quark orbital angularmomentum, confirming previous results.

From Ji to Jaffe-Manohar orbital angular momentum in Lattice QCD using a direct derivative method