The growth with energy of vector meson photo-production cross-sections and low $x$ evolution

We investigate the energy dependence of the exclusive photo-production cross-sections of vector mesons $J/\Psi$ and $\Upsilon$ on protons. In particular we are interested in the question whether their energy dependence has a description in terms of perturbative low $x$ (i.e. BFKL) evolution. As an update to the original publication [1] we include recent LHCb 13 TeV results in our comparison with data.