Transverse spin sum rule of the proton

TL;DR

This paper investigates the transverse spin structure of the proton within QCD, clarifying how transverse angular momentum is defined and related to generalized parton distributions, especially in the infinite momentum frame.

Contribution

It provides a detailed analysis of the transverse spin sum rule of the proton, emphasizing the role of generalized parton distributions in describing transverse orbital angular momentum.

Findings

Transverse angular momentum expectation value grows with particle energy.

Generalized parton distributions H+E encode transverse orbital angular momentum densities.

The transverse spin content is analyzed in the context of QCD angular momentum structure.

Abstract

The transversely-polarized state of a proton with arbitrary momentum is not an eigenstate of transverse angular momentum operator. The latter does not commute with the QCD Hamiltonian. However, the expectation value of the transverse angular momentum in the state is well-defined and grows proportionally to the energy of the particle. The transverse spin content of the proton is analyzed in terms of the QCD angular momentum structure. In particular, we reconfirm that the generalized parton distributions $H+E$ provide transverse orbital angular momentum densities of quarks and gluons in the infinite momentum frame.