Study of exclusive photoproduction of charmonium in ultra-peripheral lead-lead collisions

The cross-sections of exclusive (coherent) photoproduction $J\mathrm{/}\psi$ and $\psi (2\mathrm{S})$ mesons in ultra-peripheral PbPb collisions at a nucleon-nucleon centre-of-mass energy of $5.02\mathrm{T}\mathrm{e}\mathrm{V}$ are measured using a data sample corresponding to an integrated luminosity of $228\pm 10{\mu \mathrm{b}}^{-1}$, collected by the LHCb experiment in 2018. The differential cross-sections are measured separately as a function of transverse momentum and rapidity in the nucleus-nucleus centre-of-mass frame for $J\mathrm{/}\psi$ and $\psi (2\mathrm{S})$ mesons. The integrated cross-sections are measured to be \mbox{${\sigma }_{J\mathrm{/}\psi }^{\mathrm{c}\mathrm{o}\mathrm{h}}=5.965\pm 0.059\pm 0.232\pm 0.262\mathrm{m}\mathrm{b}$} and \mbox{${\sigma }_{\psi (2\mathrm{S})}^{\mathrm{c}\mathrm{o}\mathrm{h}}=0.923\pm 0.086\pm 0.028\pm 0.040\mathrm{m}\mathrm{b}$}, where the first listed uncertainty is statistical, the second systematic and the third due to the luminosity determination. The cross-section ratio is measured to be \mbox{${\sigma }_{\psi (2\mathrm{S})}^{\mathrm{c}\mathrm{o}\mathrm{h}}\mathrm{/}{\sigma }_{J\mathrm{/}\psi }^{\mathrm{c}\mathrm{o}\mathrm{h}}=0.155\pm 0.014\pm 0.003$}, where the first uncertainty is statistical and the second is systematic. These results are compatible with theoretical predictions.