Exclusive Photo-production of J/Ψ and Ψ(2s) as a tool to explore the transition to high and saturated gluon densities at the LHC.

We study the energy dependence of the cross-section for exclusive photo-production of vector mesons J/Ψ and Ψ(2s) and search for signs for the onset of non-linear QCD dynamics in this observable. Our study is based on two dipole models: the Golec-Biernat, Wuesthoff Model (GBW) and the Bartels, Golec-Biernat, Kowal- ski Model (BGK). We find that differences between linear and non-linear implementations of these models are relatively small in the kinematic region probed by both HERA and LHC experiments if the energy dependence of the photo-production cross-section is being considered. We however find that the ratio of both cross-sections grows with energy in the presence of non-linear effects, while it remains approximately constant in the linearized case. The ratio of photo-production cross-sections might therefore provide a suitable tool to characterize the size of non-linear QCD effects at current collider energies.