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 measurement is presented of a ratio observable that provides a measure of the azimuthal correlations among jets with large transverse momentum $p_\mathrm{T}$. This observable is measured in multijet events over the range of $p_\mathrm{T}$ = 360-3170 GeV based on data collected by the CMS experiment in proton-proton collisions at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 134 fb$^{-1}$. The results are compared with predictions from Monte Carlo parton-shower event generator simulations, as well as with fixed-order perturbative quantum chromodynamics (pQCD) predictions at next-to-leading-order (NLO) accuracy obtained with different parton distribution functions (PDFs) and corrected for nonperturbative and electroweak effects. Data and theory agree within uncertainties. From the comparison of the measured observable with the pQCD prediction obtained with the NNPDF3.1 NLO PDFs, the strong coupling at the Z boson mass scale is $\alpha_\mathrm{S}(m_\mathrm{Z})$ = 0.1177 $\pm$ 0.0013 (exp) $_{-0.0073}^{+0.0116}$ (theo) = 0.1177$_{-0.0074}^{+0.0117}$, where the total uncertainty is dominated by the scale dependence of the fixed-order predictions. A test of the running of $\alpha_\mathrm{S}(m_\mathrm{Z})$ in the TeV region shows no deviation from the expected NLO pQCD behaviour.

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$^{-5}$.

A measurement of inclusive four-jet production in proton-proton collisions at a center-of-mass energy of 13\TeV is presented. The transverse momenta of jets within $\lvert\eta\rvert \lt$ 4.7 reach down to 35, 30, 25, and 20 GeV for the first-, second-, third-, and fourth-leading jet, respectively. Differential cross sections are measured as functions of the jet transverse momentum, jet pseudorapidity, and several other observables that describe the angular correlations between the jets. The measured distributions show sensitivity to different aspects of the underlying event, parton shower, and matrix element calculations. In particular, the interplay between angular correlations caused by parton shower and double-parton scattering contributions is shown to be important. The double-parton scattering contribution is extracted by means of a template fit to the data, using distributions for single-parton scattering obtained from Monte Carlo event generators and a double-parton scattering distribution constructed from inclusive single-jet events in data. The effective double-parton scattering cross section is calculated and discussed in view of previous measurements and of its dependence on the models used to describe the single-parton scattering background.

The dependence of the ratio between the B$_\mathrm{s}^0$ and B$^+$ hadron production fractions, $f_\mathrm{s} / f_\mathrm{u}$, on the transverse momentum ($p_\mathrm{T}$) and rapidity of the B mesons is studied using the decay channels B$_\mathrm{s}^0$$\to$ J$/\psi\,\phi$ and B$^+$$\to$ J$/\psi$ K$^+$. The analysis uses a data 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 61.6 fb$^{-1}$. The $f_\mathrm{s} / f_\mathrm{u}$ ratio is observed to depend on the B $p_\mathrm{T}$ and to be consistent with becoming asymptotically constant at large $p_\mathrm{T}$. No rapidity dependence is observed. The ratio of the B$^0$ to B$^+$ hadron production fractions, $f_\mathrm{d} / f_\mathrm{u}$, measured using the B$^0$$\to$ J$/\psi$ K$^{*0}$ decay channel, is found to be consistent with unity and independent of $p_\mathrm{T}$ and rapidity, as expected from isospin invariance.

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.

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.

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 the differential production cross-sections of prompt and non-prompt $J/\psi$ and $\psi(2$S$)$ mesons with transverse momenta between 8 and 360 GeV and rapidity in the range $|y|<2$ are reported. Furthermore, measurements of the non-prompt fractions of $J/\psi$ and $\psi(2$S$)$, and the prompt and non-prompt $\psi(2$S$)$-to-$J/\psi$ production ratios, are presented. The analysis is performed using 140 fb$^{-1}$ of $\sqrt{s}=13$ TeV $pp$ collision data recorded by the ATLAS detector at the LHC during the years 2015-2018.