  The exclusive photoproduction of vector mesons ($J/\psi$ and $\phi$) are
investigated by taking into account the next-to-leading order corrections in
the framework of Color Glass Condensate. We confront the next-to-leading order
modified dipole amplitude with the HERA data finding good agreement. Our
studies show that the $\chi^2/d.o.f$ from leading order, running coupling and
collinearly improved next-to-leading order dipole amplitudes are 2.159, 1.097,
and 0.932 for the elastic cross section, and 2.056, 1.449, and 1.357 for
differential cross section. The outcomes indicate that the higher-order
corrections have a significant contribution to the vector meson productions and
the description of the experimental data is dramatically improved once the
higher order corrections are included. We extend the next-to-leading order
exclusive vector meson production model to LHC energies by using the same
parameters obtained from HERA. We find that our model can also give a rather
good description of the $J/\psi$ and $\phi$ data in proton-proton collision at
7 TeV and 13 TeV at LHCb experiments.

High Energy Physics - Phenomenology