Many measurements at the LHC require efficient identification of heavy-flavour jets, i.e. jets originating from bottom (b) or charm (c) quarks. An overview of the algorithms used to identify c jets is described and a novel method to calibrate them is presented. This new method adjusts the entire distributions of the outputs obtained when the algorithms are applied to jets of different flavours. It is based on an iterative approach exploiting three distinct control regions that are enriched with either b jets, c jets, or light-flavour and gluon jets. Results are presented in the form of correction factors evaluated using proton-proton collision data with an integrated luminosity of 41.5 fb$^{-1}$ at $\sqrt{s}$ = 13 TeV, collected by the CMS experiment in 2017. The closure of the method is tested by applying the measured correction factors on simulated data sets and checking the agreement between the adjusted simulation and collision data. Furthermore, a validation is performed by testing the method on pseudodata, which emulate different miscalibration conditions. The calibrated results enable the use of the full distributions of heavy-flavour identification algorithm outputs, e.g. as inputs to machine-learning models. Thus, they are expected to increase the sensitivity of future physics analyses.

The associated production of a W and a Z boson is studied in final states with multiple leptons produced in proton-proton (pp) collisions at a centre-of-mass energy of 13 TeV using 137 fb$^{-1}$ of data collected with the CMS detector at the LHC. A measurement of the total inclusive production cross section yields $\sigma_{\text{tot}}$(pp $\to$ WZ) = 50.6 $\pm$ 0.8 (stat) $\pm$ 1.5 (syst) $\pm$ 1.1 (lumi) $\pm$ 0.5 (theo) pb. Measurements of the fiducial and differential cross sections for several key observables are also performed in all the final-state lepton flavour and charge compositions with a total of three charged leptons, which can be electrons or muons. All results are compared with theoretical predictions computed up to next-to-next-to-leading order in quantum chromodynamics plus next-to-leading order in electroweak theory and for various sets of parton distribution functions. The results include direct measurements of the charge asymmetry and the W and Z vector boson polarization. The first observation of longitudinally polarized W bosons in WZ production is reported. Anomalous gauge couplings are searched for, leading to new constraints on beyond-the-standard-model contributions to the WZ triple gauge coupling.

A search for supersymmetry in events with two or three low-momentum leptons and missing transverse momentum is performed. The search uses proton-proton collisions at $\sqrt{s} =$ 13 TeV collected in the three-year period 2016-2018 by the CMS experiment at the LHC and corresponding to an integrated luminosity of up to 137 fb$^{-1}$. The data are found to be in agreement with expectations from standard model processes. The results are interpreted in terms of electroweakino and top squark pair production with a small mass difference between the produced supersymmetric particles and the lightest neutralino. For the electroweakino interpretation, two simplified models are used, a wino-bino model and a higgsino model. Exclusion limits at 95% confidence level are set on $\widetilde{\chi}^0_2 / \widetilde{\chi}^\pm_1$ masses up to 275 GeV for a mass difference of 10 GeV in the wino-bino case, and up to 205 (150) GeV for a mass difference of 7.5 (3) GeV in the higgsino case. The results for the higgsino are further interpreted using a phenomenological minimal supersymmetric standard model, excluding the higgsino mass parameter $\mu$ up to 180 GeV with the bino mass parameter $M_1$ at 800 GeV. In the top squark interpretation, exclusion limits are set at top squark masses up to 540 GeV for four-body top squark decays and up to 480 GeV for chargino-mediated decays with a mass difference of 30 GeV.

The production cross section of a top quark pair in association with a photon is measured in proton-proton collisions at a center-of-mass energy of 13 TeV. The data set, corresponding to an integrated luminosity of 137 fb$^{-1}$, was recorded by the CMS experiment during the 2016-2018 data taking of the LHC. The measurements are performed in a fiducial volume defined at the particle level. Events with an isolated, highly energetic lepton, at least three jets from the hadronization of quarks, among which at least one is b tagged, and one isolated photon are selected. The inclusive fiducial $\mathrm{t\overline{t}}\gamma$ cross section, for a photon with transverse momentum greater than 20 GeV and pseudorapidity $\lvert \eta\rvert$$\lt$ 1.4442, is measured to be 798 $\pm$ 7 (stat) $\pm$ 48 (syst) fb, in good agreement with the prediction from the standard model at next-to-leading order in quantum chromodynamics. The differential cross sections are also measured as a function of several kinematic observables and interpreted in the framework of the standard model effective field theory (EFT), leading to the most stringent direct limits to date on anomalous electromagnetic dipole moment interactions of the top quark and the photon.

A search is presented for physics beyond the standard model (SM) using electron or muon pairs with high invariant mass. A data set of proton-proton collisions collected by the CMS experiment at the LHC at $\sqrt{s} =$ 13 TeV from 2016 to 2018 corresponding to a total integrated luminosity of up to 140 fb$^{-1}$ is analyzed. No significant deviation is observed with respect to the SM background expectations. Upper limits are presented on the ratio of the product of the production cross section and the branching fraction to dileptons of a new narrow resonance to that of the Z boson. These provide the most stringent lower limits to date on the masses for various spin-1 particles, spin-2 gravitons in the Randall--Sundrum model, as well as spin-1 mediators between the SM and dark matter particles. Lower limits on the ultraviolet cutoff parameter are set both for four-fermion contact interactions and for the Arkani-Hamed, Dimopoulos, and Dvali model with large extra dimensions. Lepton flavor universality is tested at the TeV scale for the first time by comparing the dimuon and dielectron mass spectra. No significant deviation from the SM expectation of unity is observed.

Measurements of the associated production of a W boson and a charm (c) quark in proton-proton collisions at a centre-of-mass energy of 8 TeV are reported. The analysis uses a data sample corresponding to a total integrated luminosity of 19.7 fb$^{-1}$ collected by the CMS detector at the LHC. The W bosons are identified through their leptonic decays to an electron or a muon, and a neutrino. Charm quark jets are selected using distinctive signatures of charm hadron decays. The product of the cross section and branching fraction $\sigma$(pp $\to$ W + c + X) $\mathcal{B}$(W $\to$$\ell\nu$), where $\ell$ = e or $\mu$, and the cross section ratio $\sigma$(pp $\to$ W$^+$ + c + X) / $\sigma$(pp $\to$ W$^-$ + $\mathrm{\bar{c}}$ + X) are measured inclusively and differentially as functions of the pseudorapidity and of the transverse momentum of the lepton from the W boson decay. The results are compared with theoretical predictions. The impact of these measurements on the determination of the strange quark distribution is assessed.

A search for Kaluza-Klein excited vector boson resonances, $W_\mathrm{KK}$, decaying in cascade to three W bosons via a scalar radion $R, W_\mathrm{KK}\to WR \to WWW$, with two or three massive jets is presented. The search is performed with proton-proton collision data recorded at $\sqrt{s} =$ 13 TeV, collected by the CMS experiment at the CERN LHC, during 2016-2018, corresponding to an integrated luminosity of 138 fb$^{-1}$. Two final states are simultaneously probed, one where the two W bosons produced by the R decay are reconstructed as separate, large-radius, massive jets, and one where they are merged in a single large-radius jet. The observed data are in agreement with the standard model expectations. Limits are set on the product of the $W_\mathrm{KK}$ resonance cross section and branching fraction to three W bosons in an extended warped extra-dimensional model and are the first of their kind at the LHC.

The measurement of the cross section for the production of a Z boson, decaying to dielectrons or dimuons, in association with at least one bottom quark jet are performed with proton-proton collision data at $\sqrt{s} =$ 13 TeV. The data sample corresponds to an integrated luminosity of 137 fb$^{-1}$, collected by the CMS experiment at the LHC during 2016-2018. The integrated cross sections for Z + $\ge$ 1 b jet and Z + $\ge$ 2 b jets are reported for the electron, muon, and combined channels. The fiducial cross sections in the combined channel are 6.52 $\pm$ 0.04 (stat) $\pm$ 0.40 (syst) $\pm$ 0.14 (theo) pb for Z + $\ge$ 1 b jet and 0.65 $\pm$ 0.03 (stat) $\pm$ 0.07 (syst) $\pm$ 0.02 (theo) pb for Z + $\ge$ 2 b jets. The differential cross section distributions are measured as functions of various kinematic observables that are useful for precision tests of perturbative quantum chromodynamics predictions. The ratios of integrated and differential cross sections for Z + $\ge$ 2 b jets and Z + $\ge$ 1 b jet processes are also determined. The value of the integrated cross section ratio measured in the combined channel is 0.100 $\pm$ 0.005 (stat) $\pm$ 0.007 (syst) $\pm$ 0.003 (theo). All measurements are compared with predictions from various event generators.

A statistical combination of searches for heavy resonances decaying to pairs of bosons or leptons is presented. The data correspond to an integrated luminosity of 35.9 fb$^{-1}$ collected during 2016 by the CMS experiment at the LHC in proton-proton collisions at a center-of-mass energy of 13 TeV. The data are found to be consistent with expectations from the standard model background. Exclusion limits are set in the context of models of spin-1 heavy vector triplets and of spin-2 bulk gravitons. For mass-degenerate W' and Z' resonances that predominantly couple to the standard model gauge bosons, the mass exclusion at 95% confidence level of heavy vector bosons is extended to 4.5 TeV as compared to 3.8 TeV determined from the best individual channel. This excluded mass increases to 5.0 TeV if the resonances couple predominantly to fermions.

The production of W$^\pm$ bosons is studied in proton-lead (pPb) collisions at a nucleon-nucleon centre-of-mass energy of $\sqrt{s_\mathrm{NN}} =$ 8.16 TeV. Measurements are performed in the W$^\pm$ $\to$ $\mu^\pm\nu_\mu$ channel using a data sample corresponding to an integrated luminosity of 173.4 $\pm$ 8.7 nb$^{-1}$, collected by the CMS Collaboration at the LHC. The number of positively and negatively charged W bosons is determined separately in the muon pseudorapidity region in the laboratory frame $|\eta^\mu_\mathrm{lab}|$ $<$ 2.4 and transverse momentum $p_\mathrm{T}^\mu$ $>$ 25 GeV/$c$. The W$^\pm$ boson differential cross sections, muon charge asymmetry, and the ratios of W$^\pm$ boson yields for the proton-going over the Pb-going beam directions are reported as a function of the muon pseudorapidity in the nucleon-nucleon centre-of-mass frame. The measurements are compared to the predictions from theoretical calculations based on parton distribution functions (PDFs) at next-to-leading-order. The results favour PDF calculations that include nuclear modifications and provide constraints on the nuclear PDF global fits.