Spin structure of hadrons and minimum energy of bound systems

TL;DR

This paper explores how the spin of composite particles like hadrons is formed from their constituents' angular momenta, examining different composition patterns and their relation to the system's minimal energy, especially in the context of proton spin.

Contribution

It introduces a hierarchical approach to angular momentum composition in multi-constituent systems and discusses energy considerations influencing preferred spin configurations in hadrons.

Findings

Multiple composition patterns can produce the same total spin.

Energy minimization can favor specific constituent arrangements.

The role of gluons and orbital angular momentum in proton spin is emphasized.

Abstract

The spin of a composite particle, like a nucleus or a hadron, is generated by the composition of angular moments (consisting of spins and orbital angular moments) of the constituents. The composition of two angular moments is done by the standard way with the use of Clebsch-Gordan coefficients. However, if there are more than two constituents, the composition must be done in a hierarchical way, which admits more ways leading to the same resulting spin state |J, J_{z}>. Different composition patterns can generate states with the same spin quantum numbers, but which may vary in the contributions of different kinds of the constituents. We will discuss which composition patterns could be preferred in the hadrons from the viewpoint of minimal energy of the bound system. In this context, particular attention is paid to the role of gluons or quark orbital angular momentum in the proton spin.