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 $$ begin{array}{rcl} sigma_{J/psirightarrowmu^+mu^-}&=&435 pm 18 pm 17 pm 16 {rm pb}, sigma_{psi(2S)rightarrowmu^+mu^-}&=&11.1 pm 1.1 pm 0.3 pm 0.4 {rm pb}. end{array} $$ 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.
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