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

M Engelhardt,J R Green,S Meinel,J Negele,A Pochinsky,S Krieg,N Hasan,S Syritsyn

doi:10.1103/physrevd.102.074505

Abstract

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 removes a significant numerical bias that had been seen to afflict results of a previous study. In particular, the value obtained for Ji quark orbital angular momentum is reconciled with the one obtained independently via Ji's sum rule, validating the GMTD approach. Since GTMDs simultaneously contain information about the quark impact parameter and transverse momentum, they permit a direct evaluation of the cross product of the latter. They are defined through proton matrix elements of a quark bilocal operator containing a Wilson line; the choice in Wilson line path allows one to continuously interpolate from Ji to Jaffe-Manohar quark orbital angular momentum. The latter is seen to be significantly enhanced in magnitude compared to Ji quark orbital angular momentum, confirming previous results.

Highlights

The manner in which the spin of the proton arises from the spins and orbital angular momenta of its quark and gluon constituents has been the object of sustained study
Considering initially the special case of a straight Wilson line, η 1⁄4 0, corresponding to Ji quark orbital angular momentum, Fig. 2 displays the results obtained in the isovector case at the three available values of ζ
The introduction of this method has led to a reliable quantitative computation of the needed derivative, with respect to momentum transfer, of the relevant generalized transverse momentum-dependent parton distributions (GTMDs) matrix element

Summary

Introduction

The manner in which the spin of the proton arises from the spins and orbital angular momenta of its quark and gluon constituents has been the object of sustained study. The sum rule relates the total quark angular momentum J to specific moments of generalized parton distributions (GPDs), and by combining this with a calculation of the quark spin S [4,5], one can isolate the quark orbital angular momentum L 1⁄4 J − S [6,7,8,9,10,11,12].

Methods

Results

Conclusion