Accessing gluon orbital angular momentum and spin-orbit correlations at the Electron-Ion Collider

Since the discovery of the “spin crisis”, studies of proton spin structure have grown into a vibrant field aimed at disentangling the role of quarks and gluons in generating the proton’s spin. A key but unknown component of the proton spin sum rule is the contribution from the gluon orbital angular momentum. We present a novel observable to access gluon orbital angular momentum, which is obtainable through exclusive production of heavy mesons in electron-proton collisions. We also identify observables sensitive to correlations between the gluon’s spin and its orbital motion, which remain largely unexplored. Our results highlight the potential for future measurements at the upcoming Electron–Ion Collider in the United States to provide, for the first time, direct access to these fundamental gluon contributions, thereby advancing our understanding of proton spin structure.