Associated $\phi$ and $J\mathrm{/}\mathrm{\Psi }$ photoproduction in ultraperipheral $PbPb$ collisions at the Large Hadron Collider and Future Circular Collider

In this paper we analyze the associated $\phi$ and $J\mathrm{/}\mathrm{\Psi }$ photoproduction in ultraperipheral $PbPb$ collisions through the double scattering mechanism for the energies of the Large Hadron Collider (LHC) and Future Circular Collider (FCC). Our results complement a previous analysis for the $\rho \rho$, $J\mathrm{/}\mathrm{\Psi }J\mathrm{/}\mathrm{\Psi }$ and $\rho J\mathrm{/}\mathrm{\Psi }$ production. We present our predictions for the total cross sections and rapidity distributions considering the rapidity ranges covered by the ALICE and LHCb detectors, which indicate that a future experimental analysis of $\phi J\mathrm{/}\mathrm{\Psi }$ final state is feasible. These results point out that the study of the double vector meson photoproduction in heavy ion collisions can be useful to constrain the double scattering mechanism and improve our understanding of the QCD dynamics at high energies.