Quark orbital dynamics in the proton from Lattice QCD -- from Ji to Jaffe-Manohar orbital angular momentum

TL;DR

This paper uses lattice QCD to explore quark orbital angular momentum in the proton, demonstrating how different gauge link paths relate Ji and Jaffe-Manohar definitions and quantifying their differences.

Contribution

It provides the first lattice QCD calculation interpolating between Ji and Jaffe-Manohar orbital angular momentum definitions using a generalized Wigner distribution.

Findings

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

The difference between the two definitions can be clearly resolved.

The lattice calculation at m_pi=518 MeV successfully interpolates between the definitions.

Abstract

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.