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A search for the rare $\eta$ $\to$ $\mu^+\mu^-\mu^+\mu^-$ double-Dalitz decayis performed using a sample of proton-proton collisions, collected by the CMSexperiment at the CERN LHC with high-rate muon triggers in 2017-2018 andcorresponding to an integrated luminosity of 101 fb$^{-1}$. A signal having astatistical significance well in excess of 5 standard deviations is observed.Using the $\eta$ $\to$ $\mu^+ \mu^-$ decay as normalization, the branchingfraction $\mathcal{B}(\eta$ $\to$ $\mu^+\mu^-\mu^+\mu^-)$ = [5.0 $\pm$ 0.8(stat) $\pm$ 0.7 (syst) $\pm$ 0.7 ($\mathcal{B}_{2\mu}$)] $\times$ 10$^{-9}$ ismeasured, where the last term is the uncertainty in the normalization channelbranching fraction. This work achieves an improved precision of over fiveorders of magnitude compared to previous results, leading to the firstmeasurement of this branching fraction, which is found to agree withtheoretical predictions.

Observation of the rare decay of the $\eta$ meson to four muons