The J/$\psi$$\to$$\mu^+\mu^-\mu^+\mu^-$ decay has been observed with a statistical significance in excess of five standard deviations. The analysis is based on an event sample of proton-proton collisions at a center-of-mass energy of 13 TeV, collected by the CMS experiment in 2018 and corresponding to an integrated luminosity of 33.6 fb${-1}$. Normalizing to the J/$\psi$$\to$$\mu^+\mu^-$ decay mode leads to a branching fraction [10.1$^{+3.3}_{-2.7}$ (stat) $\pm$ 0.4 (syst) ]$\times$ 10$^{-7}$, a value that is consistent with the standard model prediction.
A test of lepton flavor universality in B$^{\pm}$$\to$ K$^{\pm}\mu^+\mu^-$ and B$^{\pm}$$\to$ K$^{\pm}$e$^+$e$^-$ decays, as well as a measurement of differential and integrated branching fractions of a nonresonant B$^{\pm}$$\to$ K$^{\pm}\mu^+\mu^-$ decay are presented. The analysis is made possible by a dedicated data set of proton-proton collisions at $\sqrt{s}$ = 13 TeV recorded in 2018, by the CMS experiment at the LHC, using a special high-rate data stream designed for collecting about 10 billion unbiased b hadron decays. The ratio of the branching fractions $\mathcal{B}$(B$^{\pm}$$\to$ K$^{\pm}\mu^+\mu^-$) to $\mathcal{B}$(B$^{\pm}$$\to$ K$^{\pm}$e$^+$e$^-$) is determined from the measured double ratio $R$(K) of these decays to the respective branching fractions of the B$^\pm$$\to$ J/$\psi$K$^\pm$ with J/$\psi$$\to$$\mu^+\mu^-$ and e$^+$e$^-$ decays, which allow for significant cancellation of systematic uncertainties. The ratio $R$(K) is measured in the range 1.1 $\lt q^2 \lt$ 6.0 GeV$^2$, where $q$ is the invariant mass of the lepton pair, and is found to be $R$(K) = 0.78$^{+0.47}_{-0.23}$, in agreement with the standard model expectation $R$(K) $\approx$ 1. This measurement is limited by the statistical precision of the electron channel. The integrated branching fraction in the same $q^2$ range, $\mathcal{B}$(B$^{\pm}$$\to$ K$^{\pm}\mu^+\mu^-$) = (12.42 $\pm$ 0.68) $\times$ 10$^{-8}$, is consistent with the present world-average value and has a comparable precision.
Using proton-proton collision data corresponding to an integrated luminosity of 140 fb$^{-1}$ collected by the CMS experiment at $\sqrt{s}$ = 13 TeV, the $\Lambda_\text{b}^0$$\to$ J/$\psi\Xi^-$K$^+$ decay is observed for the first time, with a statistical significance exceeding 5 standard deviations. The relative branching fraction, with respect to the $\Lambda_\text{b}^0$$\to$$\psi$(2S)$\Lambda$ decay, is measured to be $\mathcal{B}$($\Lambda_\text{b}^0$$\to$ J/$\psi\Xi^-$K$^+$)/$\mathcal{B}$( $\Lambda_\text{b}^0$$\to$$\psi$(2S)$\Lambda$) = [3.38 $\pm$ 1.02 $\pm$ 0.61 $\pm$ 0.03]%, where the first uncertainty is statistical, the second is systematic, and the third is related to the uncertainties in $\mathcal{B}$($\psi$(2S) $\to$ J/$\psi\pi^+\pi^-$) and $\mathcal{B}$($\Xi^-$ $\to$ $\Lambda\pi^-$).
A search for the lepton flavor violating $\tau$$\to$ 3$\mu$ decay is performed using proton-proton collision events at a center-of-mass energy of 13 TeV collected by the CMS experiment at the LHC in 2017-2018, corresponding to an integrated luminosity of 97.7 fb$^{-1}$. Tau leptons produced in both heavy-flavor hadron and W boson decays are exploited in the analysis. No evidence for the decay is observed. The results of this search are combined with an earlier null result based on data collected in 2016 to obtain a total integrated luminosity of 131 fb$^{-1}$. The observed (expected) upper limits on the branching fraction $\mathcal{B}$($\tau$$\to$ 3$\mu$) at confidence levels of 90 and 95% are 2.9 $\times$ 10$^{-8}$ (2.4 $\times$ 10$^{-8}$) and 3.6 $\times$ 10$^{-8}$ (3.0 $\times$ 10$^{-8}$), respectively.
A search for the rare $\eta$$\to$$\mu^+\mu^-\mu^+\mu^-$ double-Dalitz decay is performed using a sample of proton-proton collisions, collected by the CMS experiment at the CERN LHC with high-rate muon triggers in 2017-2018 and corresponding to an integrated luminosity of 101 fb$^{-1}$. A signal having a statistical significance well in excess of 5 standard deviations is observed. Using the $\eta$$\to$$\mu^+ \mu^-$ decay as normalization, the branching fraction $\mathcal{B}(\eta$$\to$$\mu^+\mu^-\mu^+\mu^-)$ = [5.0 $\pm$ 0.8 (stat) $\pm$ 0.7 (syst) $\pm$ 0.7 ($\mathcal{B}_{2\mu}$)] $\times$ 10$^{-9}$ is measured, where the last term is the uncertainty in the normalization channel branching fraction. This work achieves an improved precision of over five orders of magnitude compared to previous results, leading to the first measurement of this branching fraction, which is found to agree with theoretical predictions.