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The observation of the $\mathrm{Z}$ boson rare decay to a $\psi$ meson andtwo oppositely charged same-flavour leptons, $\ell^+ \ell^-$, where $\psi$represents the sum of $\mathrm{J}/\psi$ and$\psi(\mathrm{2S})\to\mathrm{J}/\psi\, X$, and $\ell=\mu,\mathrm{e}$, ispresented. The data sample used corresponds to an integrated luminosity of$35.9\,\mathrm{fb}^{-1}$ of proton-proton collisions at a center-of-mass energyof $13\,\mathrm{TeV}$ accumulated by the CMS experiment at the LHC. The signalis observed with a significance in excess of 5 standard deviations. Removingcontributions from $\psi(\mathrm{2S})$ decays to $\mathrm{J}/\psi$, the signalis interpreted as being entirely from$\mathrm{Z}\to\mathrm{J}/\psi\,\ell^+\ell^-$, with its fiducial branchingfraction relative to that of the decay $\mathrm{Z}\to\mu^+\mu^-\mu^+\mu^-$measured to be$$\frac{\mathcal{B}(\mathrm{Z}\to\mathrm{J}/\psi\,\ell^+\ell^-)}{\mathcal{B}(\mathrm{Z}\to\mu^+\mu^-\mu^+\mu^-)}=0.70\pm0.18\, \mathrm{(stat)} \pm 0.05\, \mathrm{(syst)}.$$ This result is obtainedwith the assumption of no $\mathrm{J}/\psi$ polarisation, where extremepolarisation scenarios can create $-24\%$ to $+22\%$ variations.

Observation of the decay $\mathrm{Z}\to\psi\,\ell^+\ell^-\to\mu^+\mu^-\ell^+\ell^-$ with the CMS detector