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 nonperturbative 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 rigorously probe the saturation regime of the color glass condensate framework in electron-proton collisions at HERA energies and that electron-heavy ion collisions will be essential to access its regime of validity.

• Received 28 June 2018

DOI:https://doi.org/10.1103/PhysRevD.98.034013

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Published by the American Physical Society