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.

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 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.

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 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.

The $p_{\rm T}$-differential production cross sections of prompt D$^{0}$, $\Lambda_{\rm c}^{+}$, and $\Sigma_{\rm c}^{0,++}(2455)$ charmed hadrons are measured at midrapidity ($|y| < 0.5$) in pp collisions at $\sqrt{s} = 13$ TeV. This is the first measurement of $\Sigma_{\rm c}^{0,++}$ production in hadronic collisions. Assuming the same production yield for the three $\Sigma_{\rm c}^{0,+,++}$ isospin states, the baryon-to-meson cross section ratios $\Sigma_{\rm c}^{0,+,++}/{\rm D}^{0}$ and $\Lambda_{\rm c}^{+}/{\rm D}^{0}$ are calculated in the transverse momentum ($p_{\rm T}$) intervals $2 < p_{\rm T} < 12$ GeV/$c$ and $1 < p_{\rm T} < 24$ GeV/$c$. Values significantly larger than in e$^{+}$e$^{-}$ collisions are observed, indicating for the first time that baryon enhancement in hadronic collisions also extends to the $\Sigma_{\rm c}$. The feed-down contribution to $\Lambda_{\rm c}^{+}$ production from $\Sigma_{\rm c}^{0,+,++}$ is also reported and is found to be larger than in e$^{+}$e$^{-}$ collisions. The data are compared with predictions from event generators and other phenomenological models, providing a sensitive test of the different charm-hadronisation mechanisms implemented in the models.

Two-particle azimuthal correlations are measured with the ALICE apparatus in pp collisions at $\sqrt{s} = 13$ TeV to explore strangeness- and multiplicity-related effects in the fragmentation of jets and the transition regime between bulk and hard production, probed with the condition that a strange meson (K$^{0}_{\rm S}$) or baryon ($\Lambda$) with transverse momentum $p_{\rm T} > 3$ GeV/c is produced. Azimuthal correlations between kaons or $\Lambda$ hyperons with other hadrons are presented at midrapidity for a broad range of the trigger ($3 < p_{\rm T}^{\rm trigg} < 20$ GeV/$c$) and associated particle $p_{\rm T}$ (1 GeV/$c$$< p_{\rm T}^{\rm assoc} < p_{\rm T}^{\rm trigg}$), for minimum-bias events and as a function of the event multiplicity. The near- and away-side peak yields are compared for the case of either K$^{0}_{\rm S}$ or $\Lambda$($\overline{\Lambda}$) being the trigger particle with that of inclusive hadrons (a sample dominated by pions). In addition, the measurements are compared with predictions from PYTHIA 8 and EPOS LHC event generators.

Cross-sections for the production of a $Z$ boson in association with two photons are measured in proton$-$proton collisions at a centre-of-mass energy of 13 TeV. The data used correspond to an integrated luminosity of 139 fb$^{-1}$ recorded by the ATLAS experiment during Run 2 of the LHC. The measurements use the electron and muon decay channels of the $Z$ boson, and a fiducial phase-space region where the photons are not radiated from the leptons. The integrated $Z(\rightarrow\ell\ell)\gamma\gamma$ cross-section is measured with a precision of 12% and differential cross-sections are measured as a function of six kinematic variables of the $Z\gamma\gamma$ system. The data are compared with predictions from MC event generators which are accurate to up to next-to-leading order in QCD. The cross-section measurements are used to set limits on the coupling strengths of dimension-8 operators in the framework of an effective field theory.

Differential cross-sections are measured for the production of four charged leptons in association with two jets. These measurements are sensitive to final states in which the jets are produced via the strong interaction as well as to the purely-electroweak vector boson scattering process. The analysis is performed using proton-proton collision data collected by ATLAS at $\sqrt{s}=13$ TeV and with an integrated luminosity of 140 fb$^{-1}$. The data are corrected for the effects of detector inefficiency and resolution and are compared to state-of-the-art Monte Carlo event generator predictions. The differential cross-sections are used to search for anomalous weak-boson self-interactions that are induced by dimension-six and dimension-eight operators in Standard Model effective field theory.