A search is performed for the central exclusive production of pairs of charmonia produced in protonproton collisions. Using data corresponding to an integrated luminosity of $3{\rm\ fb}^{1}$ collected at centreofmass energies of 7 and 8 TeV, $J/\psi J/\psi$ and $J/\psi\psi(2S)$ pairs are observed, which have been produced in the absence of any other activity inside the LHCb acceptance that is sensitive to charged particles in the pseudorapidity ranges $(3.5,1.5)$ and $(1.5,5.0)$. Searches are also performed for pairs of Pwave charmonia and limits are set on their production. The crosssections for these processes, where the dimeson system has a rapidity between 2.0 and 4.5, are measured to be $$ \begin{array}{rl} \sigma^{J/\psi J/\psi} &= 58\pm10{(\rm stat)} \pm 6{(\rm syst)} {\rm\ pb} , \\ \sigma^{J/\psi\psi(2S)} &= 63 ^{+27}_{18}{(\rm stat)}\pm 10{(\rm syst)} {\rm\ pb} , \\ \sigma^{\psi(2S)\psi(2S)} &< 237 {\rm\ pb}, \\ \sigma^{\chi_{c0}\chi_{c0}} &< 69 {\rm\ nb}, \\ \sigma^{\chi_{c1}\chi_{c1}} &< 45 {\rm\ pb}, \\ \sigma^{\chi_{c2}\chi_{c2}} &< 141 {\rm\ pb}, \\ \end{array} $$ where the upper limits are set at the 90% confidence level. The measured $J/\psi J/\psi$ and $J/\psi\psi(2S)$ crosssections are consistent with theoretical expectations.
Representative Feynman diagrams for pairs of charmonia produced through double pomeron exchange. In the left, one $t$channel gluon is much softer than the other while in the right, they are similar. 
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Left: Invariant masses of pairs of oppositely charged muons in events with exactly four tracks. Of the two possible ways of combining the muons per event, the one with the higher value for the lowermass pair is plotted. Right: Invariant mass of the second pair of tracks where the first pair has a mass consistent with the $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ or $\psi {(2S)}$ meson. When both masses are consistent with a charmonium, only the candidate with the higher mass is displayed. The curve shows an exponential fit in the region below 2500 $\mathrm{ Me V}$ . 
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Invariant mass of the fourmuon system in (left) $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} $ and (right) $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \psi {(2S)} $ events. 
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Number of tracks passing the $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} $ exclusive selection after having removed the requirement that there be no additional charged tracks or photons. The shaded histogram is the expected feeddown from exclusive $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \psi {(2S)} $ events. 
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Transverse momentum squared distribution of candidates for exclusively produced (left) $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} $ and (right) dimuons whose invariant mass is between 6 and 9 $\mathrm{ Ge V}$ . The curves are fits to the data as described in the text. 
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Animated gif made out of all figures. 
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Summary of numbers entering the crosssection calculation. 
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Percentage uncertainties on the quantities entering the denominator of Eq. (2). 
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Supplementary material full pdf 
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Created on 11 January 2020.