Quark spin-orbit correlations in the pion meson in light-cone quark model

TL;DR

This paper investigates the quark spin-orbit correlation within the pion meson using light-cone quark models, revealing an anti-aligned correlation and demonstrating consistency between GPD and GTMD approaches.

Contribution

It provides analytical and numerical analysis of the pion's quark spin-orbit correlation using both GPD and GTMD frameworks within a light-cone quark model.

Findings

The spin-orbit correlation in the pion is anti-aligned.

GPD and GTMD approaches yield consistent results.

Numerical analysis confirms the anti-aligned correlation.

Abstract

We study the correlation between the quark spin and orbital angular momentum inside the pion meson. Similar to the case inside the nucleon, the longitudinal spin-orbit correlation $C_z^{q/\pi}$ in pion meson can be expressed in terms of the corresponding generalized parton distributions (GPDs) and generalized transverse momentum distributions (GTMDs). This provides new information about the spin structure of the pion. Using the wavefunctions of the pion in the light-cone quark model and the overlap representation for GPDs and GTMDs, we present the analytical results for the quark longitudinal spin-orbit correlation. We find that the GPD approach and the GTMD approach lead to the same results. The numerical results is also obtained, showing that the correlation in pion is anti-aligned. In addition, we compare $C_z^{q/\pi}$ from the GPD approach and the GTMD approach, with $x$ and the transverse momentum $k_T$ unintegrated.