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

TL;DR

This paper introduces a direct derivative method in Lattice QCD to accurately compute quark orbital angular momentum, bridging Ji and Jaffe-Manohar definitions, and confirms that Jaffe-Manohar angular momentum is notably larger.

Contribution

The paper develops a direct derivative technique in Lattice QCD for calculating quark orbital angular momentum, improving accuracy and validating the connection between Ji and Jaffe-Manohar definitions.

Findings

Ji quark orbital angular momentum matches previous results with the new method

Jaffe-Manohar orbital angular momentum is significantly larger than Ji's

The direct derivative method removes numerical biases in Lattice QCD calculations

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.