New relation between transverse angular momentum and generalized parton distributions

TL;DR

This paper establishes a precise relation between the transverse angular momentum of quarks in a nucleon and generalized parton distributions, extending Ji's relation to transverse polarization with clarified notation.

Contribution

It derives a new rigorous relation linking transverse angular momentum expectation value to GPDs H and E, enhancing understanding of nucleon spin structure.

Findings

Derived a relation between <J_T> and GPDs H and E.

Extended Ji's relation to transverse polarization.

Clarified the notation and meaning of terms in the relations.

Abstract

I derive a rigorous relation between the expectation value of the transverse component of the angular momentum <J_T> of a quark in a transversely polarized nucleon in terms of the Generalized Parton Distributions H and E, namely <J_T(quark)> = 1/2M [P_0 \int dx x E_q(x,0,0) + M \int dx x H_q(x,0,0)] where P_0 is the energy of the nucleon and where "quark" implies the sum of quark and antiquark of a given flavor. A similar relation holds for gluons. The result is remarkably similar to Ji's relation for the case of longitudinal polarization. In this revised version, I have rectified some misleading statements, introduced a more precise notation and specified mpre clearly the meaning of the terms in both the Ji and the new tranverse relation.