Rapidity gap distribution of diffractive small-$x_{I\hspace{-0.3em}P}$ events at HERA and at the EIC

We use the Kovchegov-Levin equation to resum contributions of large invariant mass diffractive final states to diffractive structure functions in the dipole picture of deep inelastic scattering. For protons we use a (modified) McLerran-Venugopalan model as the initial condition for the evolution, with free parameters obtained from fits to the HERA inclusive data. We obtain an adequate agreement to the HERA diffractive data in the moderately high-mass regimes when the proton density profile is fitted to the diffractive structure function data in the low-mass region. The HERA data is found to prefer a proton shape that is steeper than a Gaussian. The initial conditions are generalized to the nuclear case using the optical Glauber model. Strong nuclear modification effects are predicted in diffractive scattering off a nuclear target in kinematics accessible at the future Electron-Ion collider. In particular, the Kovchegov-Levin evolution has a strong effect on the Q 2 -dependence of the diffractive cross section.