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 search for long-lived heavy neutrinos (N) in the decays of \PB mesons produced in proton-proton collisions at $\sqrt{s}$ = 13 TeV is presented. The data sample corresponds to an integrated luminosity of 41.6 fb$^{-1}$ collected in 2018 by the CMS experiment at the CERN LHC, using a dedicated data stream that enhances the number of recorded events containing B mesons. The search probes heavy neutrinos with masses in the range 1 $\lt$$m_\mathrm{N}$$\lt$ 3 GeV and decay lengths in the range 10$^{-2}$$\lt$$c\tau$$\lt$ 10$^{4}$ mm, where $\tau_\mathrm{N}$ is the N proper mean lifetime. Signal events are defined by the signature B $\to$$\ell_\mathrm{B}$NX; N $\to$$\ell^{\pm} \pi^{\mp}$, where the leptons $\ell_\mathrm{B}$ and $\ell$ can be either a muon or an electron, provided that at least one of them is a muon. The hadronic recoil system, X, is treated inclusively and is not reconstructed. No significant excess of events over the standard model background is observed in any of the $\ell^{\pm}\pi^{\mp}$ invariant mass distributions. Limits at 95% confidence level on the sum of the squares of the mixing amplitudes between heavy and light neutrinos, $\vert V_\mathrm{N}\vert^2$, and on $c\tau$ are obtained in different mixing scenarios for both Majorana and Dirac-like N particles. The most stringent upper limit $\vert V_\mathrm{N}\vert^2$ $\lt$ 2.0$\times$10$^{-5}$ is obtained at $m_\mathrm{N}$ = 1.95 GeV for the Majorana case where N mixes exclusively with muon neutrinos. The limits on $\vert V_\mathrm{N}\vert^2$ for masses 1 $\lt$ $m_\mathrm{N}$ $\lt$ 1.7 GeV are the most stringent from a collider experiment to date.

Production cross sections of $\Upsilon$(1S), $\Upsilon$(2S), and $\Upsilon$(3S) states decaying into $\mu^+\mu^-$ in proton-lead (pPb) collisions are reported using data collected by the CMS experiment at $\sqrt{s_\mathrm{NN}} =$ 5.02 TeV. A comparison is made with corresponding cross sections obtained with pp data measured at the same collision energy and scaled by the Pb nucleus mass number. The nuclear modification factor for $\Upsilon$(1S) is found to be $R_\mathrm{pPb}(\Upsilon(1S))$ = 0.806 $\pm$ 0.024 (stat) $\pm$ 0.059 (syst). Similar results for the excited states indicate a sequential suppression pattern, such that $R_\mathrm{pPb}(\Upsilon(1S))$$\gt$$R_\mathrm{pPb}(\Upsilon(2S))$$\gt$$R_\mathrm{pPb}(\Upsilon(3S))$. The suppression is much less pronounced in pPb than in PbPb collisions, and independent of transverse momentum $p_\mathrm{T}^\Upsilon$ and center-of-mass rapidity $y_\mathrm{CM}^\Upsilon$ of the individual $\Upsilon$ state in the studied range $p_\mathrm{T}^\Upsilon$$\lt$ 30 GeV$/c$ and $\vert y_\mathrm{CM}^\Upsilon\vert$$\lt$ 1.93. Models that incorporate sequential suppression of bottomonia in pPb collisions are in better agreement with the data than those which only assume initial-state modifications.

The spectra measurements of charged hadrons produced in the shower of a parton originating in the same hard scattering with a leptonically decaying Z boson, are reported in lead-lead (PbPb) and proton-proton (pp) collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV. Both PbPb and pp data sets are recorded by the CMS experiment at the LHC, and correspond to an integrated luminosity of 1.7 nb$^{-1}$ and 320 pb$^{-1}$, respectively. Hadronic collision data with one reconstructed Z boson candidate with the transverse momentum $p_\mathrm{T}$$\gt$ 30 GeV/$c$ are analyzed. The Z boson constrains the initial energy and direction of the associated parton. In heavy ion events, azimuthal angular distributions of charged hadrons with respect to the direction of a Z boson are sensitive to modifications of the in-medium parton shower and medium response. Compared to reference data from pp interactions, the results for central PbPb collisions indicate a modification of the angular correlations. The measurements of the fragmentation functions and $p_\mathrm{T}$ spectra of charged particles in Z boson events, which are sensitive to medium modifications of the parton shower longitudinal structure, are also reported. Significant modifications in central PbPb events compared to pp reference data are also found for these observables.

Differential cross sections for the Drell-Yan process, including Z boson production, using the dimuon decay channel are measured in proton-lead (pPb) collisions at a nucleon-nucleon centre-of-mass energy of 8.16 TeV. A data sample recorded with the CMS detector at the LHC is used, corresponding to an integrated luminosity of 173 nb$^{-1}$. The differential cross section as a function of the dimuon mass is measured in the range 15-600 GeV, for the first time in proton-nucleus collisions. It is also reported as a function of dimuon rapidity over the mass ranges 15-60 GeV and 60-120 GeV, and ratios for the p-going over the Pb-going beam directions are built. In both mass ranges, the differential cross sections as functions of the dimuon transverse momentum $p_\mathrm{T}$ and of a geometric variable $\phi^*$ are measured, where $\phi^*$ highly correlates with $p_\mathrm{T}$ but is determined with higher precision. In the Z mass region, the rapidity dependence of the data indicate a modification of the distribution of partons within a lead nucleus as compared to the proton case. The data are more precise than predictions based upon current models of parton distributions.

The strong Coulomb field created in ultrarelativistic heavy ion collisions is expected to produce a rapidity-dependent difference ($\Delta v_2$) in the second Fourier coefficient of the azimuthal distribution (elliptic flow, $v_2$) between $\mathrm{D}^0$ ($\mathrm{\bar{u}c}$) and $\overline{\mathrm{D}}^0$ ($\mathrm{u\bar{c}}$) mesons. Motivated by the search for evidence of this field, the CMS detector at the LHC is used to perform the first measurement of $\Delta v_2$. The rapidity-averaged value is found to be $\langle\Delta v_2 \rangle =$ 0.001 $\pm$ 0.001 (stat) $\pm$ 0.003 (syst) in PbPb collisions at $\sqrt{s_\mathrm{NN}} =$ 5.02 TeV. In addition, the influence of the collision geometry is explored by measuring the $\mathrm{D}^0$ and $\overline{\mathrm{D}}^0$ mesons $v_2$ and triangular flow coefficient ($v_3$) as functions of rapidity, transverse momentum ($p_\mathrm{T}$), and event centrality (a measure of the overlap of the two Pb nuclei). A clear centrality dependence of prompt $\mathrm{D}^0$ meson $v_2$ values is observed, while the $v_3$ is largely independent of centrality. These trends are consistent with expectations of flow driven by the initial-state geometry.

The differential cross section and charge asymmetry for inclusive W boson production at $\sqrt{s} =$ 13 TeV is measured for the two transverse polarization states as a function of the W boson absolute rapidity. The measurement uses events in which a W boson decays to a neutrino and either a muon or an electron. The data sample of proton-proton collisions recorded with the CMS detector at the LHC in 2016 corresponds to an integrated luminosity of 35.9 fb$^{-1}$. The differential cross section and its value normalized to the total inclusive W boson production cross section are measured over the rapidity range $|y_\mathrm{W}|$ $\lt$ 2.5. In addition to the total fiducial cross section, the W boson double-differential cross section, d$^2\sigma$/d$p^\ell_\mathrm{T}$d$|\eta|$ and the charge asymmetry are measured as functions of the charged lepton transverse momentum and pseudorapidity. The precision of these measurements is used to constrain the parton distribution functions of the proton using the next-to-leading order NNPDF3.0 set.

The dependence of inclusive jet production in proton-proton collisions with a center-of-mass energy of 13 TeV on the distance parameter $R$ of the anti-$k_\mathrm{T}$ algorithm is studied using data corresponding to integrated luminosities up to 35.9 fb$^{-1}$ collected by the CMS experiment in 2016. The ratios of the inclusive cross sections as functions of transverse momentum $p_\mathrm{T}$ and rapidity $y$, for $R$ in the range 0.1 to 1.2 to those using $R = $ 0.4 are presented in the region 84 $\lt$ $p_\mathrm{T}$ $\lt$ 1588 GeV and $|y|$ $\lt$ 2.0. The results are compared to calculations at leading and next-to-leading order in the strong coupling constant using different parton shower models. The variation of the ratio of cross sections with $R$ is well described by calculations including a parton shower model, but not by a leading-order quantum chromodynamics calculation including nonperturbative effects. The agreement between the data and the theoretical predictions for the ratios of cross sections is significantly improved when next-to-leading order calculations with nonperturbative effects are used.

Measurements of production cross sections of WZ and same-sign WW boson pairs in association with two jets in proton-proton collisions at $\sqrt{s} =$ 13 TeV at the LHC are reported. The data sample corresponds to an integrated luminosity of 137 fb$^{-1}$, collected with the CMS detector during 2016-2018. The measurements are performed in the leptonic decay modes W$^\pm$Z $\to$ $\ell^\pm\nu\ell'^\pm\ell'^\mp$ and WW $\to$ $\ell^\pm\nu\ell'^\pm\nu$, where $\ell, \ell' = $ e, $\mu$. Differential fiducial cross sections as functions of the invariant masses of the jet and charged lepton pairs, as well as of the leading-lepton transverse momentum, are measured for WW production and are consistent with the standard model predictions. The dependence of differential cross sections on the invariant mass of the jet pair is also measured for WZ production. An observation of electroweak production of WZ boson pairs is reported with an observed (expected) significance of 6.8 (5.3) standard deviations. Constraints are obtained on the structure of quartic vector boson interactions in the framework of effective field theory.

The first direct, model-independent measurement is presented of the modulus of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements $|V_\mathrm{tb}|$, $|V_\mathrm{td}|$, and $|V_\mathrm{ts}|$, in final states enriched in single top quark $t$-channel events. The analysis uses proton-proton collision data from the LHC, collected during 2016 by the CMS experiment, at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. Processes directly sensitive to these matrix elements are considered at both the production and decay vertices of the top quark. In the standard model hypothesis of CKM unitarity, a lower limit of $|V_\mathrm{tb}|$ $>$ 0.970 is measured at the 95% confidence level. Several theories beyond the standard model are considered, and by releasing all constraints among the involved parameters, the values $|V_\mathrm{tb}| =$ 0.988 $\pm$ 0.024, and $|V_\mathrm{td}|^2 + |V_\mathrm{ts}|^2 =$ 0.06 $\pm$ 0.06, where the uncertainties include both statistical and systematic components, are measured.