Measurement of exclusive $J/\psi$ and $\psi(2S)$ production at $\sqrt{s}=13$ TeV

Measurements are presented of the cross-section for the central exclusive production of $J/\psi\to\mu^+\mu^-$ and $\psi(2S)\to\mu^+\mu^-$ processes in proton-proton collisions at $\sqrt{s} = 13 $ TeV with 2016-2018 data. They are performed by requiring both muons to be in the LHCb acceptance (with pseudorapidity $2<\eta_{\mu^\pm} < 4.5$) and mesons in the rapidity range $2.0 < y < 4.5$. The integrated cross-section results are \begin{equation*} \sigma_{J/\psi\to\mu^+\mu^-}(2.0<y_{J/\psi}<4.5,2.0<\eta_{\mu^\pm} < 4.5) = 400 \pm 2 \pm 5 \pm 12 \,{\rm pb}\,, \end{equation*} \begin{equation*} \sigma_{\psi(2S)\to\mu^+\mu^-}(2.0<y_{\psi(2S)}<4.5,2.0<\eta_{\mu^\pm} < 4.5) = 9.40 \pm 0.15 \pm 0.13 \pm 0.27 \,{\rm pb}\,, \end{equation*} where the uncertainties are statistical, systematic and due to the luminosity determination. In addition, a measurement of the ratio of \psi(2S) and J/\psi cross-sections, at an average photon-proton centre-of-mass energy of 1 TeV, is performed, giving \begin{equation*} \frac{\sigma_{\psi(2S)}}{\sigma_{J/\psi}} = 0.1763 \pm 0.0029 \pm 0.0008 \pm 0.0039 \,, \end{equation*} where the first uncertainty is statistical, the second systematic and the third due to the knowledge of the involved branching fractions. For the first time, the dependence of the $J/\psi$ and $\psi(2S)$ cross-sections on the total transverse momentum transfer is determined in $pp$ collisions and is found consistent with the behaviour observed in electron-proton collisions.