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 $\alpha_\text{s}(m_Z)= 0.1170^{+ 0.0021}_{-0.0018}$.

Three rare decay processes of the Higgs boson to a $\rho$(770)$^0$, $\phi$(1020), or K$^{*}$(892)$^0$ meson and a photon are searched for using $\sqrt{s}$ = 13 TeV proton-proton collision data collected by the CMS experiment at the LHC. Events are selected assuming the mesons decay into a pair of charged pions, a pair of charged kaons, or a charged kaon and pion, respectively. Depending on the Higgs boson production mode, different triggering and reconstruction techniques are adopted. The analyzed data sets correspond to integrated luminosities up to 138 fb$^{-1}$, depending on the reconstructed final state. After combining various data sets and categories, no significant excess above the background expectations is observed. Upper limits at 95% confidence level on the Higgs boson branching fractions into $\rho$(770)$^0$$\gamma$, $\phi$(1020)$\gamma$, and K$^{*}$(892)$^0\gamma$ are determined to be 3.7 $\times$ 10$^{-4}$, 3.0 $\times$ 10$^{-4}$, and 3.0 $\times$ 10$^{-4}$, respectively. In case of the $\rho$(770)$^0$$\gamma$ and $\phi$(1020)$\gamma$ channels, these are the most stringent experimental limits to date.

A pioneering machine-learning-based flavor-tagging algorithm combining same-side and opposite-side tagging is used to obtain the equivalent of 27$\,$000 tagged B$^0_\mathrm{s}$$\to$ J/$\psi\, \phi$(1020) decays from pp collisions at $\sqrt{s} =$ 13 TeV, collected by the CMS experiment and corresponding to an integrated luminosity of 96.5 fb$^{-1}$. A time- and flavor-dependent angular analysis of the $\mu^+\mu^-$K$^+$K$^-$ final state is used to measure parameters of the $\mathrm{B}^0_\mathrm{s}$-$\overline{\mathrm{B}}^0_\mathrm{s}$ system. The weak phase is measured to be $\phi_\mathrm{s}$ = $-$73 $\pm$ 23 (stat) $\pm$ 7 (syst) mrad, which, combined with a $\sqrt{s}$ = 8 TeV CMS result, gives $\phi_\mathrm{s}$ = $-$74 $\pm$ 23 mrad. This value differs from zero by 3.2 standard deviations, providing evidence for $CP$ violation in B$^0_\mathrm{s}$$\to$ J/$\psi\,\phi$(1020) decays. All measured physics parameters are found to agree with standard model predictions where available.

A search for heavy neutral gauge bosons (Z') decaying into a pair of tau leptons is performed in proton-proton collisions at $\sqrt{s}$ = 13 TeV at the CERN LHC. The data were collected with the CMS detector and correspond to an integrated luminosity of 138 fb$^{-1}$. The observations are found to be in agreement with the expectation from standard model processes. Limits at 95% confidence level are set on the product of the Z' production cross section and its branching fraction to tau lepton pairs for a range of Z' boson masses. For a narrow resonance in the sequential standard model scenario, a Z' boson with a mass below 3.5 TeV is excluded. This is the most stringent limit to date from this type of search.

A full set of optimized observables is measured in an angular analysis of the decay B$^0$$\to$ K$^*$(892)$^0\mu^+\mu^-$ using a sample of proton-proton collisions at $\sqrt{s}$ = 13 TeV, collected with the CMS detector at the LHC, corresponding to an integrated luminosity of 140 fb$^{-1}$. The analysis is performed in six bins of the squared invariant mass of the dimuon system, $q^2$, over the range 1.1 $\lt$$q^2$$\lt$ 16 GeV$^2$. The results are among the most precise experimental measurements of the angular observables for this decay and are compared to a variety of predictions based on the standard model. Some of these predictions exhibit tension with the measurements.

The first search for a heavy neutral spin-1 gauge boson (Z') with nonuniversal fermion couplings produced via vector boson fusion processes and decaying to tau leptons or W bosons is presented. The analysis is performed using LHC data at $\sqrt{s}$ = 13 TeV, collected from 2016 to 2018 and corresponding to an integrated luminosity of 138 fb$^{-1}$. The data are consistent with the standard model predictions. Upper limits are set on the product of the cross section for production of the Z' boson and its branching fraction to $\tau\tau$ or WW. The presence of a Z' boson decaying to $\tau^+\tau^-$ (W$^+$W$^-$) is excluded for masses up to 2.45 (1.60) TeV, depending on the Z' boson coupling to SM weak bosons, and assuming a Z' $\to$$\tau^+\tau^-$ (W$^+$W$^-$) branching fraction of 50%.

The polarization of the $\Lambda$ and $\overline{\Lambda}$ hyperons along the beam direction has been measured in proton-lead (pPb) collisions at a center-of-mass energy per nucleon pair of 8.16 TeV. The data were obtained with the CMS detector at the LHC and correspond to an integrated luminosity of 186.0 $\pm$ 6.5 nb$^{-1}$. A significant azimuthal dependence of the hyperon polarization, characterized by the second-order Fourier sine coefficient $P_{z,s2}$, is observed. The $P_{z,s2}$ values decrease as a function of charged particle multiplicity, but increase with transverse momentum. A hydrodynamic model that describes the observed $P_{z,s2}$ values in nucleus-nucleus collisions by introducing vorticity effects does not reproduce either the sign or the magnitude of the pPb results. These observations pose a challenge to the current theoretical implementation of spin polarization in heavy ion collisions and offer new insights into the origin of spin polarization in hadronic collisions at LHC energies.

Entanglement is an intrinsic property of quantum mechanics and is predicted to be exhibited in the particles produced at the Large Hadron Collider. A measurement of the extent of entanglement in top quark-antiquark ($\mathrm{t\bar{t}}$) events produced in proton-proton collisions at a center-of-mass energy of 13 TeV is performed with the data recorded by the CMS experiment at the CERN LHC in 2016, and corresponding to an integrated luminosity of 36.3 fb$^{-1}$. The events are selected based on the presence of two leptons with opposite charges and high transverse momentum. An entanglement-sensitive observable $D$ is derived from the top quark spin-dependent parts of the $\mathrm{t\bar{t}}$ production density matrix and measured in the region of the $\mathrm{t\bar{t}}$ production threshold. Values of $D$$\lt$$-$1/3 are evidence of entanglement and $D$ is observed (expected) to be $-$0.480 $^{+0.026}_{-0.029}$$(-$0.467 $^{+0.026}_{-0.029})$ at the parton level. With an observed significance of 5.1 standard deviations with respect to the non-entangled hypothesis, this provides observation of quantum mechanical entanglement within $\mathrm{t\bar{t}}$ pairs in this phase space. This measurement provides a new probe of quantum mechanics at the highest energies ever produced.

Measurements are presented of inclusive and differential cross sections for Z boson associated production of top quark pairs ($\mathrm{t\bar{t}}$Z) and single top quarks (tZq or tWZ). The data were recorded in proton-proton collisions at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. Events with three or more leptons, electrons or muons, are selected and a multiclass deep neural network is used to separate three event categories, the $\mathrm{t\bar{t}}$Z and tWZ processes, the tZq process, and the backgrounds. A profile likelihood approach is used to unfold the differential cross sections, to account for systematic uncertainties, and to determine the correlations between the two signal categories in one global fit. The inclusive cross sections for a dilepton invariant mass between 70 and 110 GeV are measured to be 1.14 $\pm$ 0.07 pb for the sum of $\mathrm{t\bar{t}}$Z and tWZ, and 0.81 $\pm$ 0.10 pb for tZq, in good agreement with theoretical predictions.

The discovery of the Higgs boson has led to new possible signatures for heavy resonance searches at the LHC. Since then, search channels including at least one Higgs boson plus another particle have formed an important part of the program of new physics searches. In this report, the status of these searches by the CMS Collaboration is reviewed. Searches are discussed for resonances decaying to two Higgs bosons, a Higgs and a vector boson, or a Higgs boson and another new resonance. All analyses use proton-proton collision data collected at $\sqrt{s}$ = 13 TeV in the years 2016-2018. A combination of the results of these searches is presented together with constraints on different beyond-the-standard model scenarios, including scenarios with extended Higgs sectors, heavy vector bosons and extra dimensions. Studies are shown for the first time by CMS on the validity of the narrow-width approximation in searches for the resonant production of a pair of Higgs bosons. The potential for a discovery at the High Luminosity LHC is also discussed.