Studies of $CP$ violation and anomalous couplings of the Higgs boson to vector bosons and fermions are presented. The data were acquired by the CMS experiment at the LHC and correspond to an integrated luminosity of 137 fb$^{-1}$ at a proton-proton collision energy of 13 TeV. The kinematic effects in the Higgs boson's four-lepton decay H $\to$ 4$\ell$ and its production in association with two jets, a vector boson, or top quarks are analyzed, using a full detector simulation and matrix element techniques to identify the production mechanisms and to increase sensitivity to the Higgs boson tensor structure of the Higgs boson interactions. A simultaneous measurement is performed of up to five Higgs boson couplings to electroweak vector bosons (HVV), two couplings to gluons (Hgg), and two couplings to top quarks (Htt). The $CP$ measurement in the Htt interaction is combined with the recent measurement in the H $\to$$\gamma\gamma$ channel. The results are presented in the framework of anomalous couplings and are also interpreted in the framework of effective field theory, including the first study of $CP$ properties of the Htt and effective Hgg couplings from a simultaneous analysis of the gluon fusion and top-associated processes. The results are consistent with the standard model of particle physics.

A combination of measurements of the inclusive top-quark pair production cross-section performed by ATLAS and CMS in proton-proton collisions at centre-of-mass energies of 7 and 8 TeV at the LHC is presented. The cross-sections are obtained using top-quark pair decays with an opposite-charge electron-muon pair in the final state and with data corresponding to an integrated luminosity of about 5 fb$^{-1}$ at $\sqrt{s}=7$ TeV and about 20 fb$^{-1}$ at $\sqrt{s}=8$ TeV for each experiment. The combined cross-sections are determined to be $178.5 \pm 4.7$ pb at $\sqrt{s}=7$ TeV and $243.3^{+6.0}_{-5.9}$ pb at $\sqrt{s}=8$ TeV with a correlation of 0.41, using a reference top-quark mass value of 172.5 GeV. The ratio of the combined cross-sections is determined to be $R_{8/7}= 1.363\pm 0.032$. The combined measured cross-sections and their ratio agree well with theory calculations using several parton distribution function (PDF) sets. The values of the top-quark pole mass (with the strong coupling fixed at 0.118) and the strong coupling (with the top-quark pole mass fixed at 172.5 GeV) are extracted from the combined results by fitting a next-to-next-to-leading-order plus next-to-next-to-leading-log QCD prediction to the measurements. Using a version of the NNPDF3.1 PDF set containing no top-quark measurements, the results obtained are $m_t^\text{pole} = 173.4^{+1.8}_{-2.0}$ GeV and $\alpha_\text{s}(m_Z)= 0.1170^{+ 0.0021}_{-0.0018}$.

The cross section for W or Z boson production in association with two photons is measured in proton-proton collisions at a centre-of-mass energy of 13 TeV. The data set corresponds to an integrated luminosity of 137 fb$^{-1}$ collected by the CMS experiment at the LHC. The W $\to$$\ell\nu$ and Z $\to$$\ell\ell$ decay modes (where $\ell =$ e, $\mu$) are used to extract the W$\gamma\gamma$ and Z$\gamma\gamma$ cross sections in a phase space defined by electron (muon) with transverse momentum larger than 30 GeV and photon transverse momentum larger than 20 GeV. All leptons and photons are required to have absolute pseudorapidity smaller than 2.5. The measured cross sections in this phase space are $\sigma$(W$\gamma\gamma$) = 13.6 $^{+1.9}_{-1.9}$ (stat) ${}^{+4.0}_{-4.0}$ (syst) $\pm$ 0.08 (PDF + scale) fb and $\sigma$(Z$\gamma\gamma$) = 5.41 $^{+0.58}_{-0.55}$ (stat) ${}^{+0.64}_{-0.70}$ (syst) $\pm$ 0.06 (PDF + scale) fb. Limits on anomalous quartic gauge couplings are set in the framework of an effective field theory with dimension-8 operators.

A generic search is presented for the associated production of a Z boson or a photon with an additional unspecified massive particle X, pp $\to$ pp + Z/$\gamma$ + X, in proton-tagged events from proton-proton collisions at $\sqrt{s}$ = 13 TeV, recorded in 2017 with the CMS detector and the CMS-TOTEM precision proton spectrometer. The missing mass spectrum is analysed in the 600-1600 GeV range and a fit is performed to search for possible deviations from the background expectation. No significant excess in data with respect to the background predictions has been observed. Model-independent upper limits on the visible production cross section of pp $\to$ pp + Z/$\gamma$ + X are set.

The inclusive jet cross section is measured as a function of jet transverse momentum $p_\mathrm{T}$ and rapidity $y$. The measurement is performed using proton-proton collision data at $\sqrt{s}$ = 5.02 TeV, recorded by the CMS experiment at the LHC, corresponding to an integrated luminosity of 27.4 pb$^{-1}$. The jets are reconstructed with the anti-$k_\mathrm{T}$ algorithm using a distance parameter of $R$ = 0.4, within the rapidity interval $\lvert y\rvert$$\lt$ 2, and across the kinematic range 0.06 $\lt$$p_\mathrm{T}$$\lt$ 1 TeV. The jet cross section is unfolded from detector to particle level using the determined jet response and resolution. The results are compared to predictions of perturbative quantum chromodynamics, calculated at both next-to-leading order and next-to-next-to-leading order. The predictions are corrected for nonperturbative effects, and presented for a variety of parton distribution functions and choices of the renormalization / factorization scales and the strong coupling $\alpha_\mathrm{S}$.

The results of a search for Higgs boson pair (HH) production in the WW*WW*, WW*$\tau\tau$, and $\tau\tau\tau\tau$ decay modes are presented. The search uses 138 fb$^{-1}$ of proton-proton collision data recorded by the CMS experiment at the LHC at a center-of-mass energy of 13 TeV from 2016 to 2018. Analyzed events contain two, three, or four reconstructed leptons, including electrons, muons, and hadronically decaying tau leptons. No evidence for a signal is found in the data. Upper limits are set on the cross section for nonresonant HH production, as well as resonant production in which a new heavy particle decays to a pair of Higgs bosons. For nonresonant production, the observed (expected) upper limit on the cross section at 95% confidence level (CL) is 21.3 (19.4) times the standard model (SM) prediction. The observed (expected) ratio of the trilinear Higgs boson self-coupling to its value in the SM is constrained to be within the interval $-$6.9 to 11.1 ($-$6.9 to 11.7) at 95% CL, and limits are set on a variety of new-physics models using an effective field theory approach. The observed (expected) limits on the cross section for resonant HH production range from 0.18 to 0.90 (0.08 to 1.06) pb at 95% CL for new heavy-particle masses in the range 250-1000 GeV.

The strange quark content of the proton is probed through the measurement of the production cross section for a W boson and a charm (c) quark in proton-proton collisions at a center-of-mass energy of 13 TeV. The analysis uses a data sample corresponding to a total integrated luminosity of 138 fb$^{-1}$ collected with 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 jets are tagged using the presence of a muon or a secondary vertex inside the jet. The W+c production cross section and the cross section ratio $R^\pm_\text{c}$ = $\sigma$(W$^+$+$\bar{\text{c}}$) / $\sigma$(W$^-$+$\text{c}$) are measured inclusively and differentially as functions of the transverse momentum and the pseudorapidity of the lepton originating from the W boson decay. The precision of the measurements is improved with respect to previous studies, reaching 1% in $R^\pm_\text{c}$. The precision of the measurements is improved with respect to previous studies, reaching 1% in $R^\pm_\text{c}$ = 0.950 $\pm$ 0.005 (stat) $\pm$ 0.010 (syst). The measurements are compared with theoretical predictions up to next-to-next-to-leading order in perturbative quantum chromodynamics.

A search for W$\gamma$ resonances in the mass range between 0.7 and 6.0 TeV is presented. The W boson is reconstructed via its hadronic decays, with the final-state products forming a single large-radius jet, owing to a high Lorentz boost of the W boson. The search is based on proton-proton collision data at $\sqrt{s} =$ 13 TeV, corresponding to an integrated luminosity of 137 fb$^{-1}$, collected with the CMS detector at the LHC in 2016-2018. The W$\gamma$ mass spectrum is parameterized with a smoothly falling background function and examined for the presence of resonance-like signals. No significant excess above the predicted background is observed. Model-specific upper limits at 95% confidence level on the product of the cross section and branching fraction to the W$\gamma$ channel are set. Limits for narrow resonances and for resonances with an intrinsic width equal to 5% of their mass, for spin-0 and spin-1 hypotheses, range between 0.17 fb at 6.0 TeV and 55 fb at 0.7 TeV. These are the most restrictive limits to date on the existence of such resonances over a large range of probed masses. In specific heavy scalar (vector) triplet benchmark models, narrow resonances with masses between 0.75 (1.15) and 1.40 (1.36) TeV are excluded for a range of model parameters. Model-independent limits on the product of the cross section, signal acceptance, and branching fraction to the W$\gamma$ channel are set for minimum W$\gamma$ mass thresholds between 1.5 and 8.0 TeV.

A search for long-lived particles decaying in the outer regions of the CMS silicon tracker or in the calorimeters is presented. The search is based on a data sample of proton-proton collisions at $\sqrt{s}$ = 13 TeV recorded with the CMS detector at the LHC in 2016-2018, corresponding to an integrated luminosity of 138 fb$^{-1}$. A novel technique, using trackless and out-of-time jet information combined in a deep neural network discriminator, is employed to identify decays of long-lived particles. The results are interpreted in a simplified model of chargino-neutralino production, where the neutralino is the next-to-lightest supersymmetric particle, is long-lived, and decays to a gravitino and either a Higgs or Z boson. This search is most sensitive to neutralino proper decay lengths of approximately 0.5 m, for which masses up to 1.18 TeV are excluded at 95% confidence level. The current search is the best result to date in the mass range from the kinematic limit imposed by the Higgs mass up to 1.8 TeV.

A search is reported for high-mass hadronic resonances that decay to a parton and a Lorentz-boosted resonance, which in turn decays into a pair of partons. The search is based on data collected with the CMS detector at the LHC in proton-proton collisions at $\sqrt{s} =$ 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. The boosted resonance is reconstructed as a single wide jet with substructure consistent with a two-body decay. The high-mass resonance is thus considered as a dijet system. The jet substructure information and the kinematic properties of cascade resonance decays are exploited to disentangle the signal from the large quantum chromodynamics multijet background. The dijet mass spectrum is analyzed for the presence of new high-mass resonances, and is found to be consistent with the standard model background predictions. Results are interpreted in a warped extra dimension model where the high-mass resonance is a Kaluza-Klein gluon, the boosted resonance is a radion, and the final state partons are all gluons. Limits on the production cross section are set as a function of the Kaluza-Klein gluon and radion masses. These limits exclude at 95% confidence level models with Kaluza-Klein gluon masses in the range from 2.0 to 4.3 TeV and radion masses in the range from 0.20 to 0.74 TeV. By exploring a novel experimental signature, the observed limits on the Kaluza-Klein gluon mass are extended by up to about 1 TeV compared to previous searches.