Relativistic spatial distributions of transverse angular momentum

RESUMO

In our previous work [C. Lorcé et al., Phys. Lett. B 868 (2025) 139792], we investigated the 2D spatial distributions of transverse total angular momentum, including orbital angular momentum and intrinsic spin, relative to the canonical center (or center of spin). In the present work, we extend this analysis in two directions. First, we study the corresponding transverse boost distributions relative to the canonical center. Second, since the definition of generalized angular momentum density depends crucially on the choice of pivot, we analyze how the spatial distributions of transverse total angular momentum and boost are modified when they are defined relative to different relativistic centers, viz.~the relativistic centers of mass, energy, and spin. Considering spin-1/2 targets, we derive the corresponding 2D spatial distributions in the transverse plane, and further investigate how the spatial patterns evolve under longitudinal Lorentz boosts. Additionally, we provide the corresponding light-front distributions in the transverse plane, establishing a clear connection between the instant-form and light-front descriptions of transverse angular momentum and boost.