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 $\mathcal{B}$($\Xi^-$ $\to$ $\Lambda\pi^-$).

The observation of the $\Lambda_\mathrm{b}^0 \to$J/$\psi \Lambda \phi$ decay is reported using proton-proton collision data collected at $\sqrt{s} =$ 13 TeV by the CMS experiment at the LHC in 2018, corresponding to an integrated luminosity of 60 fb$^{-1}$. The ratio of the branching fractions $\mathcal{B}(\Lambda_\mathrm{b}^0 \to$J/$\psi \Lambda \phi)/\mathcal{B}(\Lambda_\mathrm{b}^0\to\psi \Lambda)$ is measured to be (8.26$\pm$0.90 (stat) $\pm$ 0.68 (syst) $\pm$ 0.11 $(\mathcal{B}))\times $10$^{-2}$, where the first uncertainty is statistical, the second is systematic, and the last uncertainty reflects the uncertainties in the world-average branching fractions of $\phi$ and $\psi$(2S) decays to the reconstructed final states.

Measurements are presented of the B$^0_\mathrm{S}$$\to$$\mu^+\mu^-$ branching fraction and effective lifetime, as well as results of a search for the B$^0$$\to$$\mu^+\mu^-$ decay in proton-proton collisions at $\sqrt{s}$ = 13 TeV at the LHC. The analysis is based on data collected with the CMS detector in 2016-2018 corresponding to an integrated luminosity of 140 fb$^{-1}$. The branching fraction of the B$^0_\mathrm{S}$$\to$$\mu^+\mu^-$ decay and the effective B$^0_\mathrm{S}$ meson lifetime are the most precise single measurements to date. No evidence for the B$^0$$\to$$\mu^+\mu^-$ decay has been found. All results are found to be consistent with the standard model predictions and previous measurements.

Measurements of $\mathrm{B}^*_\mathrm{s2}(5840)^0$ and $\mathrm{B}_\mathrm{s1}(5830)^0$ mesons are performed using a data sample of proton-proton collisions corresponding to an integrated luminosity of 19.6 fb$^{-1}$, collected with the CMS detector at the LHC at a centre-of-mass energy of 8 TeV. The analysis studies $P$-wave $\mathrm{B}^0_\mathrm{S}$ meson decays into $\mathrm{B}^{(*)+}\mathrm{K}^-$ and $\mathrm{B}^{(*)0}\mathrm{K}^0_\mathrm{S}$, where the $\mathrm{B}^+$ and $\mathrm{B}^0$ mesons are identified using the decays $\mathrm{B}^+\to\mathrm{J}/\psi\,\mathrm{K}^+$ and $\mathrm{B}^0\to\mathrm{J}/\psi\,\mathrm{K}^*(892)^0$. The masses of the $P$-wave $\mathrm{B}^0_\mathrm{S}$ meson states are measured and the natural width of the $\mathrm{B}^*_\mathrm{s2}(5840)^0$ state is determined. The first measurement of the mass difference between the charged and neutral $\mathrm{B}^*$ mesons is also presented. The $\mathrm{B}^*_\mathrm{s2}(5840)^0$ decay to $\mathrm{B}^0\mathrm{K}^0_\mathrm{S}$ is observed, together with a measurement of its branching fraction relative to the $\mathrm{B}^*_\mathrm{s2}(5840)^0\to\mathrm{B}^+\mathrm{K}^-$ decay.

Using a data sample of proton-proton collisions at $\sqrt{s} =$ 13 TeV, corresponding to an integrated luminosity of 140 fb$^{-1}$ collected by the CMS experiment in 2016-2018, the B$^0_\mathrm{s}$ $\to$ X(3872)$\phi$ decay is observed. Decays into J/$\psi\,\pi^+\pi^-$ and K$^+$K$^-$ are used to reconstruct, respectively, the X(3872) and $\phi$. The ratio of the product of branching fractions $\mathcal{B}($B$^0_\mathrm{s}$ $\to$ X(3872)$\phi)\,\mathcal{B}($X(3872) $\to$ J$/\psi\,\pi^+\pi^-)$ to the product $\mathcal{B}($B$^0_\mathrm{s}$ $\to$ $\psi$(2S)$\phi)\,\mathcal{B}(\psi$(2S) $\to$ J/$\psi\,\pi^+\pi^-)$ is measured to be (2.21 $\pm$ 0.29 (stat) $\pm$ 0.17 (syst))%. The ratio $\mathcal{B}($B$^0_\mathrm{s}$ $\to$ X(3872)$\phi) / \mathcal{B}($B$^{0}$ $\to$ X(3872)K$^0)$ is found to be consistent with one, while the ratio $\mathcal{B}($B$^0_\mathrm{s}$ $\to$ X(3872)$\phi) / \mathcal{B}($B$^+$ $\to$ X(3872)K$^+)$ is two times smaller. This suggests a difference in the production dynamics of the X(3872) in B$^0$ and B$^0_\mathrm{s}$ meson decays compared to B$^+$. The reported observation may shed new light on the nature of the X(3872) particle.

Using a data sample of $\sqrt{s} =$ 13 TeV proton-proton collisions collected by the CMS experiment at the LHC in 2017 and 2018 with an integrated luminosity of 103 fb$^{-1}$, the B$^0$$\to$$\psi$(2S)K$^0_\mathrm{S}$ and B$^0_\mathrm{S}$$\to$$\psi$(2S)K$^0_\mathrm{S}\pi^+\pi^-$ decays are observed with significances exceeding 5 standard deviations. The resulting branching fraction ratios, measured for the first time, correspond to $\mathcal{B}$(B$^0_\mathrm{S}$$\to$$\psi$(2S)K$^0_\mathrm{S}$) / $\mathcal{B}$(B$^0$$\to$$\psi$(2S)K$^0_\mathrm{S}$) = (3.33 $\pm$ 0.69 (stat) $\pm$ 0.11 (syst) $\pm$ 0.34 ($f_\mathrm{s} / f_\mathrm{d}$)) $\times$ 10$^{-2}$ and $\mathcal{B}$(B$^0$$\to$$\psi$(2S)K$^0_\mathrm{S}\pi^+\pi^-$) / $\mathcal{B}$(B$^0$$\to$$\psi$(2S)K$^0_\mathrm{S}$) = 0.480 $\pm$ 0.013 (stat) $\pm$ 0.032 (syst), where the last uncertainty in the first ratio is related to the uncertainty in the ratio of production cross sections of B$^0_\mathrm{s}$ and B$^0$ mesons, $f_\mathrm{s} / f_\mathrm{d}$.

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.