Hunting the Gluon Orbital Angular Momentum at the Electron-Ion Collider

Applying the connection between the parton Wigner distribution and orbital angular momentum (OAM), we investigate the probe of the gluon OAM in hard scattering processes at the planned electron-ion collider. We show that the single longitudinal target-spin asymmetry in the hard diffractive dijet production is very sensitive to the gluon OAM distribution. The associated spin asymmetry leads to a characteristic azimuthal angular correlation of $\sin ({\varphi }_q-{\varphi }_{\mathrm{\Delta }})$, where ${\varphi }_{\mathrm{\Delta }}$ and ${\varphi }_q$ are the azimuthal angles of the proton momentum transfer and the relative transverse momentum between the quark-antiquark pair. This study will enable a first measurement of the gluon OAM in the proton spin sum rule.