Energy dependent nuclear suppression from gluon saturation in exclusive vector meson production

We calculate the exclusive $\mathrm{J}/\psi$ photoproduction cross section at high energies from the Color Glass Condensate approach. The results are compared to the center-of-mass energy dependent $\gamma+A\to\mathrm{J}/\psi+A$ cross sections extracted from measurements in ultra peripheral heavy ion collisions at RHIC and LHC. We predict strong saturation-driven nuclear suppression at high energies, while LHC data prefers even stronger suppression. We explore the effect of nucleon shape fluctuations on the nuclear suppression in the coherent and incoherent cross sections, and show that the most recent measurement of the $|t|$-differential incoherent $\mathrm{J}/\psi$ cross section prefers large event-by-event fluctuations of the nucleon substructure in heavy nuclei, comparable to that found for a free proton.