For the first time, a search for the rare decay of the W boson to three charged pions has been performed. Proton-proton collision data recorded by the CMS experiment at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 77.3 fb$^{-1}$, have been analyzed. No significant excess is observed above the background expectation. An upper limit of 1.01 $\times$ 10$^{-6}$ is set at 95% confidence level on the branching fraction of the W boson to three charged pions. This provides a strong motivation for theoretical calculations of this branching fraction.

The ratio of the top-quark branching fractions $R = B(t \to Wb)/B(t \to Wq)$, where the denominator includes the sum over all down-type quarks (q = b, s, d), is measured in the $t\bar{t}$ dilepton final state with proton-proton collision data at $\sqrt{s}$ = 8 TeV from an integrated luminosity of 19.7 inverse-femtobarns, collected with the CMS detector. In order to quantify the purity of the signal sample, the cross section is measured by fitting the observed jet multiplicity, thereby constraining the signal and background contributions. By counting the number of b jets per event, an unconstrained value of R = 1.014 $\pm$ 0.003 (stat) $\pm$ 0.032 (syst) is measured, in good agreement with the standard model prediction. A lower limit R greater than 0.955 at the 95% confidence level is obtained after requiring R lower than one, and a lower limit on the Cabibbo-Kobayashi-Maskawa matrix element |$V_tb$| greater than 0.975 is set at 95% confidence level. The result is combined with a previous CMS measurement of the t-channel single-top-quark cross section to determine the top-quark total decay width, $\Gamma_t$ = 1.36 $\pm$ 0.02 (stat)$^{+0.14}_{-0.11}$ (syst) GeV.

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.

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.

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, $f_\mathrm{s} / f_\mathrm{d}$.

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 dependence of $\mathrm{f}_{0}$(980) production on the final-state charged-particle multiplicity in p$-$Pb collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV is reported. The production of $\mathrm{f}_{0}$(980) is measured with the ALICE detector via the $\mathrm{f}_0 (980) \rightarrow \pi^{+}\pi^{-}$ decay channel in a midrapidity region of $-0.5<y<0$. Particle yield ratios of $\mathrm{f}_{0}$(980) to $\pi$ and $\mathrm{K}^{*}$(892)$^{0}$ are found to be decreasing with increasing charged-particle multiplicity. The magnitude of the suppression of the $\mathrm{f}_{0}$(980)/$\pi$ and $\mathrm{f}_{0}$(980)/$\mathrm{K}^{*}$(892)$^{0}$ yield ratios is found to be dependent on the transverse momentum $p_{\mathrm{T}}$, suggesting different mechanisms responsible for the measured effects. Furthermore, the nuclear modification factor $Q_{\mathrm{pPb}}$ of $\mathrm{f}_{0}$(980) is measured in various multiplicity ranges. The $Q_{\mathrm{pPb}}$ shows a strong suppression of the $\mathrm{f}_{0}$(980) production in the $p_{\mathrm{T}}$ region up to about 4 GeV/$c$. The results on the particle yield ratios and $Q_{\mathrm{pPb}}$ for $\mathrm{f}_{0}$(980) may help to understand the late hadronic phase in p$-$Pb collisions and the nature of the internal structure of $\mathrm{f}_{0}$(980) particle.

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.

A measurement of total and fiducial inclusive W and Z boson production cross sections in pp collisions at $\sqrt{s}$ = 8 TeV is presented. Electron and muon final states are analyzed in a data sample collected with the CMS detector corresponding to an integrated luminosity of 18.2 +/- 0.5 inverse-picobarns. The measured total inclusive cross sections times branching fractions are $\sigma(pp \to WX) \times B(W \to l\nu)$ = 12.21 +/- 0.03 (stat) +/- 0.24 (syst) +/- 0.32 (lum) nb, and $\sigma(pp \to ZX) \times B(Z \to l^{+}l^{-})$ = 1.15 +/- 0.01 (stat) +/- 0.02 (syst) +/- 0.03 (lum) nb, for the dilepton mass in the range of 60 to 120 GeV. The measured values agree with next-to-next-to-leading-order QCD cross section calculations. Ratios of cross sections are reported with a precision of 2%. This is the first measurement of inclusive W and Z boson production in proton-proton collisions at $\sqrt{s}$ = 8 TeV.

A search is performed for the rare decay W$^\pm\to\pi^\pm\gamma$ in proton-proton collisions at $\sqrt{s} =$ 13 TeV. Data corresponding to an on W integrated luminosity of 137 fb$^{-1}$ were collected during 2016 to 2018 with the CMS detector. This analysis exploits a novel search strategy based on W boson production in top quark pair events. An inclusive search for the W$^\pm\to\pi^\pm\gamma$ decay is not optimal at the LHC because of the high trigger thresholds. Instead, a trigger selection is exploited in which the W boson originating from one of the top quarks is used to tag the event in a leptonic decay. The W boson emerging from the other top quark is used to search for the W$^\pm\to\pi^\pm\gamma$ signature. Such decays are characterized by an isolated track pointing to a large energy deposit, and by an isolated photon of large transverse momentum. The presence of b quark jets reduces the background from the hadronization of light-flavor quarks and gluons. The W$^\pm\to\pi^\pm\gamma$ decay is not observed. An upper exclusion limit is set to this branching fraction, corresponding to 1.50 $\times$ 10$^{-5}$ at 95% confidence level, whereas the expected upper limit exclusion limit is 0.85 $^{+0.52}_{-0.29}$ $\times$ 10$^{-5}$.