Charmonium pair production in ultraperipheral collision

We study the exclusive double charmonium ($J/\psi \mbox{-} J/\psi$ and $\eta_c \mbox{-} \eta_c$) production through photon-photon fusion via ultraperipheral collision (UPC) at the HL-LHC and FCC with next-to-leading order (NLO) QCD predictions in the framework of non-relativistic QCD (NRQCD). Numerical results indicate that the NLO corrections for $J/\psi$ pair are large and negative, while positive for $\eta_c$ pair. The total cross section of $J/\psi \mbox{-} J/\psi$ ($\eta_c \mbox{-} \eta_c$) in Pb-Pb UPC is 28.0 (65.1) nb at nucleon-nucleon c.m. energy $\sqrt{s_{NN}} = 5.52$ TeV. Due to the backgrounds from various QCD interactions at UPC are highly suppressed and the event topologies for charmonium pair are easy to tag, the phenomenological studies at the LHC and FCC are feasible. The detailed transverse momentum $p_T$, diphoton invariant mass $m_{\gamma\gamma}$ and the rapidity difference $\Delta y$ distributions are given. The production for X(6900) is also discussed.