Quark Orbital Angular Momentum in the MIT Bag Model

TL;DR

This paper investigates quark orbital angular momentum using the MIT bag model, incorporating modifications like Peierls--Yoccoz projection to improve sum rule satisfaction and analyzing related GPDs and their relations.

Contribution

It introduces a modified MIT bag model with Peierls--Yoccoz projection and explores the relation between different definitions of quark orbital angular momentum.

Findings

Sum rule for quark OAM is fulfilled in the modified model.

The model illustrates the relation between two definitions of quark OAM.

Genuine quark-gluon contributions are directly evaluated.

Abstract

We present the results for the Generalized Transverse Momentum Distribution related to quark Orbital Angular Momentum, {\it i.e.} $F_{14}$, in the MIT bag model. This model has been modified to include the Peierls--Yoccoz projection to restore translational invariance. Such a modification allows to fulfill more satisfactorily basic sum rules, that would otherwise be less elegantly carried out with the original version. Using the same model, we have calculated the twist-$3$ GPD that corresponds to Orbital Angular Momentum \`a la Ji, through the Penttinen--Polyakov--Shuvaev--Strikman sum rule. Recently, a new relation between the two definitions of the quark Orbital Angular Momentum at the density level has been proposed, which we illustrate here within the model. The sum rule is fulfilled. Still within the framework of the MIT bag model, we analyze the Wandzura--Wilczek expression for the GPD of interest. The genuine quark-gluon contribution is evaluated directly thanks to the equation of motion of the bag, which allows for a direct control of the kinematical contributions to the twist-3 GPD.