Justifying the Naive Partonic Sum Rule for Proton Spin

TL;DR

This paper establishes a theoretical framework linking the proton's spin structure to gauge-invariant operators of quarks and gluons, enabling lattice QCD calculations of orbital angular momentum.

Contribution

It provides the first one-loop matching conditions for the spin sum rule terms, connecting them to gauge-invariant operators in a frame-dependent manner.

Findings

Derived all one-loop matching conditions for spin operators.

Linked spin sum rule terms to gauge-invariant, frame-dependent operators.

Enabled lattice QCD calculations of orbital angular momentum at leading logarithmic accuracy.

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.