Probing Composite Structure and Spin-Orbit Coupling with GPDs in ${}^{4}$He

Abstract

In this work, we extend the Impulse Approximation for the generalized parton distributions (GPDs) of a spin-0 composite hadron with spin-$\tfrac{1}{2}$ constituents to manifestly incorporate the symmetries of the target wave function. The method utilizes a light-front Wigner function representation instead of a spectral density and a basis of Pauli matrices for the spin. It exploits the boost invariance of the light front and rotational invariance in the rest frame to parameterize the Wigner density in terms of only 3 structures. In addition to the isotropic term and a term describing $\vec{L} \cdot \vec{S}$ coupling previously observed for transverse momentum dependent parton distributions (TMDs), we also identify a novel coupling $\Delta\vec{L}\cdot\vec{S}$ to the angular momentum \textit{transfer} which is unique to the case of GPDs. We then apply the framework to a composite ${}^4$He target with simple phenomenological models to identify qualitative experimental signatures of composite-structure effects in light nuclei. The framework we have constructed here can be readily extended to the case of generalized TMDs (GTMDs), while the phenomenological framework is applicable both to analyses of light nucleus data and as training input for AI-assisted applications.