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

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 $Δ\vec{L}\cdot\vec{S}$ 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.

💡 Research Summary

In this paper the authors develop a novel theoretical framework for describing the generalized parton distributions (GPDs) of a spin‑zero composite system whose constituents carry spin‑½, with a particular focus on the helium‑4 nucleus. The work builds on the traditional impulse approximation (IA) but replaces the usual spectral‑density representation with a light‑front Wigner‑function formalism. By exploiting the boost invariance of the light‑front and the rotational invariance of the target rest frame, the Wigner distribution is constrained to three independent structures: an isotropic term, a familiar orbital‑angular‑momentum–spin (L·S) coupling that also appears in transverse‑momentum‑dependent distributions (TMDs), and a newly identified ΔL·S term that couples the transferred orbital angular momentum ΔL to the constituent spin. The ΔL·S structure is unique to GPDs because it involves the non‑zero momentum transfer Δ inherent in exclusive processes.

The authors first derive a master convolution formula for the composite GPD in terms of constituent GPDs and the parameterized Wigner function. They introduce a Pauli‑matrix decomposition for the spin degrees of freedom and impose explicit parity, time‑reversal, and rotational symmetries, which leads to a compact expression (Eq. 37) where the three Wigner‑function coefficients (denoted A, B, C) multiply the constituent GPDs. The coefficient B encodes the conventional L·S correlation, while C encodes the novel ΔL·S correlation.

To illustrate the physical implications, a simple phenomenological model of the ⁴He nucleus is constructed. The nuclear light‑front wave function is taken to be Gaussian in the transverse direction and symmetric in the longitudinal momentum fractions, while the constituent quark GPDs are supplied by a perturbative quark‑target model. Within this model the authors evaluate the impact of each Wigner structure on the observable GPD H(x, ξ, t). They find that the ΔL·S term produces a pronounced asymmetry in the t‑dependence, especially at larger momentum transfer, and modifies the ξ‑dependence in a non‑linear way. These effects translate into measurable signatures in deeply virtual Compton scattering (DVCS) observables, such as beam‑spin asymmetries and cross‑section harmonics that are sensitive to the interference between the Bethe‑Heitler and DVCS amplitudes.

The paper also discusses the connection to short‑range correlations and the EMC effect. Because the ΔL·S term is most significant in regions of high internal momentum (short distances), it offers a possible mechanism linking three‑dimensional nuclear modifications to the longstanding EMC puzzle. Moreover, the authors point out that the same formalism can be straightforwardly generalized to generalized transverse‑momentum‑dependent distributions (GTMDs), where the full dependence on both transverse momentum and momentum transfer is retained.

Finally, the authors provide a ready‑to‑use parameterization and a numerical implementation that can serve as training data for AI‑assisted phenomenology, exemplified by the EXCLAIM collaboration. This positions the framework to be directly applicable to upcoming high‑precision data from Jefferson Lab (e.g., experiment E12‑17‑012 with the ALERT detector) and the future Electron‑Ion Collider, where exclusive measurements on light nuclei will become routine.

In summary, the work delivers a symmetry‑driven, Wigner‑function based extension of the impulse approximation, identifies a new ΔL·S spin‑orbit coupling unique to GPDs, and demonstrates how this coupling can be probed experimentally in light nuclei. The methodology opens a pathway to more accurate three‑dimensional imaging of composite hadrons and provides a solid theoretical foundation for future experimental and AI‑driven analyses.