Quark Orbital Angular Momentum in the Proton from a Twist-3 Generalized Parton Distribution

Quark orbital angular momentum in the proton is evaluated via a Lattice QCDcalculation of the second Mellin moment of the twist-3 generalized partondistribution E_2T in the forward limit. The connection betweenthis approach to quark orbital angular momentum and approaches previouslyutilized in Lattice QCD calculations, via generalized transversemomentum-dependent parton distributions and via Ji's sum rule, is reviewed.This connection can be given in terms of Lorentz invariance and equation ofmotion relations. The calculation of the second Mellin moment ofE_2T proceeds via a finite-momentum proton matrix element of aquark bilocal operator with a straight-line gauge connection and separation inboth the longitudinal and transverse directions. The dependence on the formercomponent serves to extract the second Mellin moment, whereas the dependence onthe latter component provides a transverse momentum cutoff for the matrixelement. Furthermore, a derivative of the matrix element with respect tomomentum transfer in the forward limit is required, which is obtained using adirect derivative method. The calculation utilizes a clover fermion ensemble atpion mass 317 MeV. The resulting quark orbital angular momentum is consistentwith previous evaluations through alternative approaches, albeit with greaterstatistical uncertainty using a comparable number of samples.