Nuclear geometry at high energy from exclusive vector meson production

We show that when saturation effects are included one obtains a good description of the exclusive $\mathrm{J}/\psi$ production spectra in ultra peripheral lead-lead collisions as recently measured by the ALICE Collaboration at the LHC. As exclusive spectra are sensitive to the spatial distribution of nuclear matter at small Bjorken-$x$, this implies that gluon saturation effects modify the impact parameter profile of the target as we move towards small $x$. In addition to saturation effects, we find a preference for larger nuclear strong-interaction radii compared to the typical charge radius. We demonstrate the role of finite photon transverse momentum and the interference between the cases for which the role of photon emitter and target are switched between the nuclei. We show that these effects are comparable to the experimental precision for $p_T$-differential cross sections and as such need to be included when comparing to LHC data. Finally, the integrated $\mathrm{J}/\psi$ production cross sections from the LHC and preliminary transverse momentum spectra from RHIC are shown to prefer calculations with fluctuating nucleon substructure, although these datasets would require even stronger saturation effects than predicted from our framework.