Gauge-independence of gluon spin in the nucleon and its evolution

TL;DR

This paper proves that the gauge-invariant decomposition of nucleon spin, including the gluon spin component, evolves independently of gauge choice, aligning with known polarized distribution evolution equations.

Contribution

It explicitly demonstrates the gauge-independence of the gluon spin operator's evolution in nucleons, resolving previous ambiguities about gauge dependence.

Findings

Gluon spin operator evolution is gauge-independent.

Reproduces the Altarelli-Parisi evolution equations.

Supports gauge-invariant nucleon spin decomposition.

Abstract

In recent papers, we have established the existence of gauge-invariant decomposition of nucleon spin, each term of which can be related to known high-energy deep-inelastic-scattering observables. A subtlety remains, however, for the intrinsic spin part of gluons at the quantum level. In fact, it was sometimes claimed that the evolution of gluon spin depends on the gauge choice and its physical interpretation makes sense only in the light-cone gauge. In the present paper, we will demonstrate explicitly that the gluon spin operator appearing in our decomposition evolves gauge-independently and that it properly reproduces the familiar evolution equation for the 1st moments of polarized quark and gluon distributions obtained with the Altarelli-Parisi method, which cannot directly be checked by the standard operator expansion method.