Gluon Generalized TMD signatures at the EIC from exclusive heavy (axial-)vector meson production

Potential experimental signatures of gluon generalized transverse momentum-dependent distributions (GTMDs) are proposed via exclusive heavy (axial-)vector meson production in lepton-proton collisions. Within the framework of collinear twist-3 factorization, we show that specific azimuthal-angle-dependent observables can provide sensitivity to the gluon GTMDs $F_{1,4}^g$ and $G_{1,1}^g$, which are related to partonic orbital angular momentum and spin-orbit correlations, respectively. These functions represent a unique sector of nucleon structure with no counterparts in the generalized parton distribution or transverse-momentum-dependent frameworks. We show that interference between different virtual-photon polarizations leads to distinct azimuthal modulations, including the polarization-independent $\cos 2\phi$ and polarization-dependent $\sin 2\phi$ terms, with $\phi$ defined as the angle between the lepton scattering plane and the hadron production plane. These observables provide signatures of the elusive gluon GTMDs $F_{1,4}^g$ and $G_{1,1}^g$, opening a new channel to access the spin structure of the nucleon at the future Electron-Ion Collider.