Gluon contribution to the angular momentum distribution of a dressed quark state

TL;DR

This paper calculates the gluonic contribution to the angular momentum distribution in a dressed quark state using light-front techniques, comparing different decompositions and verifying the spin sum rule.

Contribution

It provides a detailed analysis of gluon contributions to angular momentum in a simple quark-gluon system, using light-front formalism and impact parameter space.

Findings

Gluonic contributions to angular momentum are quantified in a dressed quark model.

Different angular momentum decompositions are compared at the density level.

The spin sum rule is verified for the dressed quark state.

Abstract

We compute the contribution of the gluonic component of the energy-momentum tensor (EMT) to the angular momentum density in various decompositions. We use the light-front Hamiltonian technique, and a two-component formalism in light-front gauge, where the constrained degrees of freedom are eliminated. Instead of a nucleon, we consider a simple composite spin-$1/2$ state, namely a quark dressed with a gluon. We present two dimensional light-front distributions in transverse impact parameter space, and compare the different angular momentum decompositions at the density level. Incorporating also the contribution coming from the quark part of the EMT, we verify the spin sum rule for such a state.