Double vector meson production in $\gamma \gamma$ interactions at hadronic colliders

In this paper we revisit the double vector meson production in $\gamma \gamma$ interactions at heavy ion collisions and present, by the first time, predictions for the $\rho\rho$ and $J/\Psi J/\Psi$ production in proton -- nucleus and proton -- proton collisions. In order to obtain realistic predictions for rapidity distributions and total cross sections for the double vector production in ultra peripheral hadronic collisions we take into account of the description of $\gamma \gamma \rightarrow VV$ cross section at low energies as well as its behaviour at large energies, associated to the gluonic interaction between the color dipoles. Our results demonstrate that the double $\rho$ production is dominated by the low energy behaviour of the $\gamma \gamma \rightarrow VV$ cross section. In contrast, for the double $J/\Psi$ production, the contribution associated to the description of the QCD dynamics at high energies contributes significantly, mainly in $pp$ collisions. Predictions for the RHIC, LHC, FCC and CEPC - SPPC energies are shown.