In July 2012, the ATLAS and CMS Collaborations at the CERN Large Hadron Collider announced the observation of a Higgs boson at a mass of around 125 GeV. Ten years later, and with the data corresponding to the production of 30 times larger number of Higgs bosons, we have learnt much more about the properties of the Higgs boson. The CMS experiment has observed the Higgs boson in numerous fermionic and bosonic decay channels, established its spin-parity quantum numbers, determined its mass and measured its production cross sections in various modes. Here the CMS Collaboration reports the most up-to-date combination of results on the properties of the Higgs boson, including the most stringent limit on the cross section for the production of a pair of Higgs bosons, on the basis of data from proton-proton collisions at a centre-of-mass energy of 13 TeV. Within the uncertainties, all these observations are compatible with the predictions of the standard model of elementary particle physics. Much evidence points to the fact that the standard model is a low-energy approximation of a more comprehensive theory. Several of the standard model issues originate in the sector of Higgs boson physics. An order of magnitude larger number of Higgs bosons, expected to be examined over the next fifteen years, will help deepen our understanding of this crucial sector.

The polarizations of prompt and non-prompt J$/\psi$ and $\psi$(2S) mesons are measured in proton-proton collisions at $\sqrt{s}$ = 13 TeV, using data samples collected by the CMS experiment in 2017 and 2018, corresponding to a total integrated luminosity of 103.3 fb$^{-1}$. Based on the analysis of the dimuon decay angular distributions in the helicity frame, the polar anisotropy, $\lambda_\theta$, is measured as a function of the transverse momentum, $p_\mathrm{T}$, of the charmonium states, in the 25-120 and 20-100 GeV ranges for the J$/\psi$ and $\psi$(2S), respectively. The non-prompt polarizations agree with predictions based on the hypothesis that, for $p_\mathrm{T}$$\gtrsim$ 25 GeV, the non-prompt J$/\psi$ and $\psi$(2S) are predominantly produced in two-body B meson decays. The prompt results clearly exclude strong transverse polarizations, even for $p_\mathrm{T}$ exceeding 30 times the J$/\psi$ mass, where $\lambda_\theta$ tends to an asymptotic value around 0.3. Taken together with previous measurements, by CMS and LHCb at $\sqrt{s}$ = 7 TeV, the prompt polarizations show a significant variation with $p_\mathrm{T}$, at low $p_\mathrm{T}$.

Diboson production in association with jets is studied in the fully leptonic final states, pp $\to$ (Z$\gamma^*$)(Z/$\gamma^*$)+jets $\to$ 2$\ell$2$\ell'$+jets, ($\ell,\ell'$ = e or $\mu$) in proton-proton collisions at a center-of-mass energy of 13 TeV. The data sample corresponds to an integrated luminosity of 138 fb$^{-1}$ collected with the CMS detector at the LHC. Differential distributions and normalized differential cross sections are measured as a function of jet multiplicity, transverse momentum $p_\mathrm{T}$, pseudorapidity $\eta$, invariant mass and $\Delta\eta$ of the highest-$p_\mathrm{T}$ and second-highest-$p_\mathrm{T}$ jets, and as a function of invariant mass of the four-lepton system for events with various jet multiplicities. These differential cross sections are compared with theoretical predictions that mostly agree with the experimental data. However, in a few regions we observe discrepancies between the predicted and measured values. Further improvement of the predictions is required to describe the ZZ+jets production in the whole phase space.

The production of a $W$ boson in association with a single charm quark is studied using 140 $\mathrm{fb}^{-1}$ of $\sqrt{s} = 13\,\mathrm{TeV}$ proton-proton collision data collected with the ATLAS detector at the Large Hadron Collider. The charm quark is tagged by a charmed hadron, reconstructed with a secondary-vertex fit. The $W$ boson is reconstructed from an electron/muon decay and the missing transverse momentum. The mesons reconstructed are $D^{\pm} \to K^\mp \pi^\pm \pi^\pm$ and $D^{*\pm} \to D^{0} \pi^\pm \to (K^\mp \pi^\pm) \pi^\pm$, where $p_{\text{T}}(e, \mu) > 30\,\mathrm{GeV}$, $|\eta(e, \mu)| < 2.5$, $p_{\text{T}}(D) > 8\,\mathrm{GeV}$, and $|\eta(D)| < 2.2$. The integrated and normalized differential cross-sections as a function of the pseudorapidity of the lepton from the $W$ boson decay, and of the transverse momentum of the meson, are extracted from the data using a profile likelihood fit. The measured fiducial cross-sections are $\sigma^{\mathrm{OS-SS}}_{\mathrm{fid}}(W^{-}{+}D^{+}) = 50.2\pm0.2\,\mathrm{(stat.)}\,^{+2.4}_{-2.3}\,\mathrm{(syst.)}\,\mathrm{pb}$, $\sigma^{\mathrm{OS-SS}}_{\mathrm{fid}}(W^{+}{+}D^{-}) = 48.5\pm0.2\,\mathrm{(stat.)}\,^{+2.3}_{-2.2}\,\mathrm{(syst.)}\,\mathrm{pb}$, $\sigma^{\mathrm{OS-SS}}_{\mathrm{fid}}(W^{-}{+}D^{*+}) = 51.1\pm0.4\,\mathrm{(stat.)}\,^{+1.9}_{-1.8}\,\mathrm{(syst.)}\,\mathrm{pb}$, and $\sigma^{\mathrm{OS-SS}}_{\mathrm{fid}}(W^{+}{+}D^{*-}) = 50.0\pm0.4\,\mathrm{(stat.)}\,^{+1.9}_{-1.8}\,\mathrm{(syst.)}\,\mathrm{pb}$. Results are compared with the predictions of next-to-leading-order quantum chromodynamics calculations performed using state-of-the-art parton distribution functions. The ratio of charm to anti-charm production cross-sections is studied to probe the $s$-$\bar{s}$ quark asymmetry and is found to be $R_c^\pm = 0.971\pm0.006\,\mathrm{(stat.)}\pm0.011\,\mathrm{(syst.)}$.

A search for flavour-changing neutral current (FCNC) events via the coupling of a top quark, a photon, and an up or charm quark is presented using 81 fb$^{-1}$ of proton-proton collision data taken at a centre-of-mass energy of 13 TeV with the ATLAS detector at the LHC. Events with a photon, an electron or muon, a $b$-tagged jet, and missing transverse momentum are selected. A neural network based on kinematic variables differentiates between events from signal and background processes. The data are consistent with the background-only hypothesis, and limits are set on the strength of the $tq\gamma$ coupling in an effective field theory. These are also interpreted as 95% CL upper limits on the cross section for FCNC $t\gamma$ production via a left-handed (right-handed) $tu\gamma$ coupling of 36 fb (78 fb) and on the branching ratio for $t\rightarrow \gamma u$ of $2.8\times 10^{-5}$ ($6.1\times 10^{-5}$). In addition, they are interpreted as 95% CL upper limits on the cross section for FCNC $t\gamma$ production via a left-handed (right-handed) $tc\gamma$ coupling of 40 fb (33 fb) and on the branching ratio for $t\rightarrow \gamma c$ of $22\times 10^{-5}$ ($18\times 10^{-5}$).

A search for excited electrons produced in $pp$ collisions at $\sqrt{s} = 13$ TeV via a contact interaction $q\bar{q} \to ee^*$ is presented. The search uses 36.1 fb$^{-1}$ of data collected in 2015 and 2016 by the ATLAS experiment at the Large Hadron Collider. Decays of the excited electron via a contact interaction into an electron and a pair of quarks ($eq\bar{q}$) are targeted in final states with two electrons and two hadronic jets, and decays via a gauge interaction into a neutrino and a $W$ boson ($\nu W$) are probed in final states with an electron, missing transverse momentum, and a large-radius jet consistent with a hadronically decaying $W$ boson. No significant excess is observed over the expected backgrounds. Upper limits are calculated for the $pp \to ee^* \to eeq\bar{q}$ and $pp \to ee^* \to e\nu W$ production cross sections as a function of the excited electron mass $m_{e^*}$ at 95% confidence level. The limits are translated into lower bounds on the compositeness scale parameter $\Lambda$ of the model as a function of $m_{e^*}$. For $m_{e^*} < 0.5$ TeV, the lower bound for $\Lambda$ is 11 TeV. In the special case of $m_{e^*} = \Lambda$, the values of $m_{e^*} < 4.8$ TeV are excluded. The presented limits on $\Lambda$ are more stringent than those obtained in previous searches.

A search for the production of three massive vector bosons in proton--proton collisions is performed using data at $\sqrt{s}=13\,TeV$ recorded with the ATLAS detector at the Large Hadron Collider in the years 2015--2017, corresponding to an integrated luminosity of $79.8\,\text{fb}^{-1}$. Events with two same-sign leptons $\ell$ (electrons or muons) and at least two reconstructed jets are selected to search for $WWW\to\ell\nu\ell\nu qq$. Events with three leptons without any same-flavour opposite-sign lepton pairs are used to search for $WWW\to\ell\nu\ell\nu\ell\nu$, while events with three leptons and at least one same-flavour opposite-sign lepton pair and one or more reconstructed jets are used to search for $WWZ\to\ell\nu qq \ell\ell$. Finally, events with four leptons are analysed to search for $WWZ\to\ell\nu\ell\nu\ell\ell$ and $WZZ\to qq \ell\ell\ell\ell$. Evidence for the joint production of three massive vector bosons is observed with a significance of 4.0 standard deviations, where the expectation is 3.1 standard deviations.

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 is performed for charged-lepton flavor violating processes in top quark (t) production and decay. The data were collected by the CMS experiment from proton-proton collisions at a center-of-mass energy of 13 TeV and correspond to an integrated luminosity of 138 fb$^{-1}$. The selected events are required to contain one opposite-sign electron-muon pair, a third charged lepton (electron or muon), and at least one jet of which no more than one is associated with a bottom quark. Boosted decision trees are used to distinguish signal from background, exploiting differences in the kinematics of the final states particles. The data are consistent with the standard model expectation. Upper limits at 95% confidence level are placed in the context of effective field theory on the Wilson coefficients, which range between 0.024-0.424 TeV$^{-2}$ depending on the flavor of the associated light quark and the Lorentz structure of the interaction. These limits are converted to upper limits on branching fractions involving up (charm) quarks, t$\to$e$\mu$u (t$\to$e$\mu$c), of 0.032 (0.498)$\times$10$^{-6}$, 0.022 (0.369)$\times$10$^{-6}$, and 0.012 (0.216)$\times$10$^{-6}$ for tensor-like, vector-like, and scalar-like interactions, respectively.

The first search for the Z boson decay to $\tau\tau\mu\mu$ at the CERN LHC is presented, based on data collected by the CMS experiment at the LHC in proton-proton collisions at a center-of-mass energy of 13 TeV and corresponding to an integrated luminosity of 138 fb$^{-1}$. The data are compatible with the predicted background. For the first time, an upper limit at the 95% confidence level of 6.9 times the standard model expectation is placed on the ratio of the Z $\to$ $\tau\tau\mu\mu$ to Z $\to$ 4$\mu$ branching fractions. Limits are also placed on the six flavor-conserving four-lepton effective-field-theory operators involving two muons and two tau leptons, for the first time testing all such operators.