Exclusive and diffractive quarkonium -- pair production at the LHC and FCC

The production of a quarkonium -- pair in exclusive and diffractive processes in $pp$ collisions at the LHC and FCC energies is investigated. We consider the $J/\Psi J/\Psi$ and $\Upsilon \Upsilon$ production in these processes and present predictions for the transverse momentum and rapidity distributions considering the kinematical ranges expected to be covered by central and forward detectors. Results for the cross sections are also presented. Our results indicate that the double $J/\Psi$ production is dominated by the exclusive process, while the double $\Upsilon$ production receive a large contribution of the diffractive process. The impact of the modelling of the gap survival factor on our predictions is discussed.