Observation of the rare decay $\eta$ $\to$ $\mu^+\mu^-$e$^+$e$^-$

A first observation of the rare decay $\eta$ $\to$ $\mu^+\mu^-$e$^+$e$^-$ is reported by the CMS Collaboration at the CERN LHC. The result is based on a proton-proton collision data sample at $\sqrt{s}$ = 13.6 TeV corresponding to an integrated luminosity of 38.0 fb$^{-1}$, acquired in 2022 using a high-rate dimuon trigger. Using the $\eta$ $\to$ $\mu^+\mu^-\gamma$ decay channel for normalization, the branching fraction is measured to be $\mathcal{B}$($\eta$ $\to$ $\mu^+\mu^-$e$^+$e$^-$) = (2.4 $\pm$ 0.8)$\times$ 10$^{-6}$, with the uncertainty including statistical and systematic sources as well as the $\mathcal{B}$($\eta$ $\to$ $\mu^+\mu^-\gamma$) uncertainty. This result is close to two orders of magnitude smaller than the existing limit, and is consistent with recent theoretical predictions.