Justifying the naive partonic sum rule for proton spin

Xiangdong Ji,Jian-Hui Zhang,Yong Zhao

doi:10.1016/j.physletb.2015.02.054

Abstract

We provide a theoretical basis for understanding the spin structure of the proton in terms of the spin and orbital angular momenta of free quarks and gluons in Feynman's parton picture. We show that each term in the Jaffe–Manohar spin sum rule can be related to the matrix element of a gauge-invariant, but frame-dependent operator through a matching formula in large-momentum effective field theory. We present all the matching conditions for the spin content at one-loop order in perturbation theory, which provide a basis to calculate parton orbital angular momentum in lattice QCD at leading logarithmic accuracy.

Highlights

We provide a theoretical basis for understanding the spin structure of the proton in terms of the spin and orbital angular momenta of free quarks and gluons in Feynman’s parton picture
The free-field form of the angular momentum in gauge theories faces a conceptual problem: all terms except the first one are gauge dependent, and it is unclear why the light-cone gauge operator is measurable in physical experiments
When the proton is probed in infinite momentum frame (IMF), some of its physical properties can be understood from simple addition of those of free quarks and gluons

Summary

Introduction

We provide a theoretical basis for understanding the spin structure of the proton in terms of the spin and orbital angular momenta of free quarks and gluons in Feynman’s parton picture. All the four terms are defined to be the proton matrix elements of free-field angular momentum operators (AMOs) in IMF [1]: J= The free-field form of the angular momentum in gauge theories faces a conceptual problem: all terms except the first one are gauge dependent, and it is unclear why the light-cone gauge operator is measurable in physical experiments.

Results

Conclusion