# Quark transverse spin-orbit correlations

## TL;DR

This paper explores the transverse spin-orbit correlations of quarks in nucleons, introducing new theoretical insights and sum rules, supported by lattice calculations indicating negative correlations for up and down quarks.

## Contribution

It extends the understanding of quark spin-orbit correlations to transverse polarization, introduces a new correlation, and provides the first Wandzura-Wilczek expression for twist-3 transversity GPDs.

## Key findings

- Quark transverse spin-orbit correlation is negative for up and down flavors.
- Introduces a new transverse correlation between quark transversity and orbital angular momentum.
- Provides the first Wandzura-Wilczek expression for the second Mellin moment of twist-3 transversity GPDs.

## Abstract

We extend the study of quark spin-orbit correlations in the nucleon to the case of transverse polarization. At the leading-twist level, this completes the spin structure of the quark kinetic energy-momentum tensor. In particular, we revisit the transversity decomposition of angular momentum proposed a decade ago by Burkardt and introduce a new transverse correlation, namely between quark transversity and orbital angular momentum. We also provide for the first time the Wandzura-Wilczek expression for the second Mellin moment of twist-3 transversity generalized parton distributions, along with a new sum rule. Based on lattice calculation results, we conclude that the quark transverse spin-orbit correlation is negative for both up and down flavors, just like in the longitudinal case.