Confronting impact parameter dependent JIMWLK evolution with HERA data

The small-$x$ evolution of protons is determined from numerical solutions of the JIMWLK equations, starting from an initial condition at moderate $x$ for a finite size proton. The resulting dipole amplitude is used to calculate the total reduced cross section $\sigma_r$ and charm reduced cross section $\sigma_{rc}$, as well as diffractive vector meson production. We compare results to experimental data from HERA and discuss fundamental problems arising from the regime sensitive to non-perturbative physics. We emphasize that information on the gluonic content of the proton, gluon spatial distributions and correlations over wide ranges in $x$, which can in principle be constrained by our study, are essential ingredients for describing the initial state in proton-proton and proton-ion collisions. Future electron nucleus collisions at an electron-ion collider will provide important additional insight for heavier nuclei. We further demonstrate that it is not possible to probe gluon saturation in electron-proton collision at HERA energies and that electron-heavy ion collisions will be essential to access the saturation regime.