Deeply virtual Compton scattering at small-$x$ in future Electron - Ion Colliders

The study of exclusive processes in the future electron-ion ($eA$) colliders will be an important tool to investigate the QCD dynamics at high energies as they are in general driven by the gluon content of the target which is strongly subject to parton saturation effects. In this paper we compute the coherent and incoherent cross sections for the deeply virtual Compton scattering (DVCS) process relying on the color dipole approach and considering different models for the dipole - proton scattering amplitude. The dependencies of the cross sections with the energy, photon virtuality, nuclear mass number and squared momentum transfer are analysed in detail. We demonstrate that the ratio between the incoherent and coherent cross sections decreases at smaller values of $Q^2$ and increases at smaller values of $A$. We show that the coherent cross section dominates at small $t$ and exhibits the typical diffractive pattern, with the number of dips in the range $|t| \le 0.3$ GeV$^2$ increasing with the mass atomic number. Our results indicate that the position of the dips are independent of the model used to treat the dipole - proton interaction as well as of the center-of-mass energy.