  We investigate whether the Balitsky-Fadin-Kuraev-Lipatov (BFKL) low x
evolution equation is capable to describe the energy dependence of the
exclusive photo-production cross-section of vector mesons J/Psi and Upsilon on
protons. Such cross-sections have been measured by both HERA experiments H1 and
ZEUS in electron-proton collisions and by LHC experiments ALICE, CMS and LHCb
in ultra-peripheral proton-proton and ultra-peripheral proton-lead collisions.
Our approach provides a perturbative description of the rise with energy and
relies only on a fit of the initial transverse momentum profile of the proton
impact factor, which can be extracted from BFKL fits to inclusive HERA data. We
find that BFKL evolution is capable to provide a very good description of the
energy dependence of the current data set, while the available fits of the
proton impact factor require an adjustment in the overall normalization.
