Spin-orbit correlation of quarks within quarkonium

Abstract

The spin-orbit correlation (SOC) provides a unique probe into the internal spin structure of hadrons. Defined via the parity-odd (P-odd) energy-momentum tensor (EMT), this observable can remain non-vanishing even in systems where the total angular momentum is zero. In this study, we connect the formal field-theoretical definition of the SOC to a non-perturbative quantum many-body framework utilizing light-front dynamics. Furthermore, we show how the SOC can be extracted directly from the hadronic matrix elements of the P-odd EMT, establishing a pathway to access this observable within the partonic picture. As a practical application, we compute the transverse and longitudinal SOC distributions for charmonium and $B_c$ mesons. While our findings align with rough estimates based on the Clebsch-Gordan decomposition, we demonstrate that these observables yield rich, non-trivial information regarding partonic dynamics.

Comments: 13 pages, 6 figures