Effect of sub-nucleon fluctuations on the DVCS process in proton and nuclear targets at the EIC

The impact of the sub - nucleon fluctuations on the Deeply Virtual Compton Scattering (DVCS) process at the Electron - Ion Collider (EIC) is investigated considering proton and nuclear targets. Assuming the hot - spot model, we estimate the energy dependence of the coherent and incoherent cross - sections for different values of the photon virtuality and atomic number. Predictions for the $t$ - distributions are also presented. We demonstrate that the sub - nucleon fluctuations in the proton, as described by the hot - spot model, implies a turn - over in the energy dependence of the incoherent cross - section, with the position of the maximum being dependent of the photon virtuality. Our results indicate that the ratio between the coherent and incoherent cross - sections increases with energy, atomic numbers and for smaller values of $Q^2$. Moreover, we predict a maximum in the $t$ - distribution of the nuclear incoherent cross - section at a fixed center - of - mass energy, which is dependent on the atomic number and $Q^2$.