Exclusive vector meson production in electron-ion collisions at the EIC, LHeC and FCC-$eh$

The exclusive vector meson production in electron-ion collisions for the energies of the future colliders is investigated. We present predictions for the coherent and incoherent $\phi$ and $J/\psi$ production in $eAu$ collisions considering the possible states of nucleon configurations in the nuclear wave function and taking into account of the non-linear corrections to the QCD dynamics. The cross sections and transverse momentum distributions are estimated assuming the energies of the Electron-Ion Collider (EIC), Large Hadron Electron Collider (LHeC) and Future Circular Collider (FCC-$eh$). Our results indicate that a future experimental analysis of these processes can shed light on the modeling of the gluon saturation effects and constrain the description of the QCD dynamics at high energies.