Observation of the Rare Decay of the $\eta $ Meson to Four Muons

A search for the rare $\eta \to {\mu }^{+}{\mu }^{-}{\mu }^{+}{\mu }^{-}$ double-Dalitz decay is performed using a sample of proton-proton collisions, collected by the CMS experiment at the CERN LHC with high-rate muon triggers during 2017 and 2018 and corresponding to an integrated luminosity of $101\text{}\text{}{\mathrm{fb}}^{-1}$. A signal having a statistical significance well in excess of 5 standard deviations is observed. Using the $\eta \to {\mu }^{+}{\mu }^{-}$ decay as normalization, the branching fraction $B\left(\eta \to {\mu }^{+}{\mu }^{-}{\mu }^{+}{\mu }^{-}\right)=\left[5.0±0.8\left(\mathrm{stat}\right)±0.7\left(\mathrm{syst}\right)±0.7\left({B}_{2\mu }\right)\right]×{10}^{-9}$ is measured, where the last term is the uncertainty in the normalization channel branching fraction. This work achieves an improved precision of over 5 orders of magnitude compared to previous results, leading to the first measurement of this branching fraction, which is found to agree with theoretical predictions.