Central exclusive production of $J/\psi$ and $\psi(2S)$ mesons in $pp$ collisions at $\sqrt{s}=13~$TeV.

Measurements are reported of the central exclusive production of \jpsi and \psitwos mesons in $pp$ collisions at a centre-of-mass energy of 13 TeV. Backgrounds are significantly reduced compared to previous measurements made at lower energies through the use of new forward shower counters. The products of the cross-sections and the branching fractions for the decays to dimuons, where both muons are within the pseudorapidity range $2.0<\eta<4.5$, are measured to be $$ \begin{array}{rcl} \sigma_{J/\psi\rightarrow\mu^+\mu^-}&=&399 \pm 16 \pm 10 \pm 16 {\rm \ pb},\\ \sigma_{\psi(2S)\rightarrow\mu^+\mu^-}&=&10.2 \pm 1.0 \pm 0.3 \pm 0.4 {\rm \ pb}.\\ \end{array} $$ The first uncertainties are statistical, the second are systematic, and the third are due to the luminosity determination. The cross-sections are also measured differentially for meson rapidities between 2.0 and 4.5. Good agreement is observed with theoretical predictions. Photoproduction cross-sections are derived and compared to previous experiments, and a deviation from a pure power-law extrapolation of lower energy data is observed.