The double differential cross sections of the Drell-Yan lepton pair ($\ell^+\ell^-$, dielectron or dimuon) production are measured as functions of the invariant mass $m_{\ell\ell}$, transverse momentum $p_\mathrm{T}(\ell\ell)$, and $\phi^*_\eta$. The $\phi^*_\eta$ observable, derived from angular measurements of the leptons and highly correlated with $p_\mathrm{T}(\ell\ell)$, is used to probe the low-$p_\mathrm{T}(\ell\ell)$ region in a complementary way. Dilepton masses up to 1 TeV are investigated. Additionally, a measurement is performed requiring at least one jet in the final state. To benefit from partial cancellation of the systematic uncertainty, the ratios of the differential cross sections for various $m_{\ell\ell}$ ranges to those in the Z mass peak interval are presented. The collected data correspond to an integrated luminosity of 36.3 fb$^{-1}$ of proton-proton collisions recorded with the CMS detector at the LHC at a centre-of-mass energy of 13 TeV. Measurements are compared with predictions based on perturbative quantum chromodynamics, including soft-gluon resummation.

Multijet events at large transverse momentum ($p_\mathrm{T}$) are measured at $\sqrt{s}$ = 13 TeV using data recorded with the CMS detector at the LHC, corresponding to an integrated luminosity of 36.3 fb$^{-1}$. The multiplicity of jets with $p_\mathrm{T}$$>$ 50 GeV that are produced in association with a high-$p_\mathrm{T}$ dijet system is measured in various ranges of the $p_\mathrm{T}$ of the jet with the highest transverse momentum and as a function of the azimuthal angle difference $\Delta\phi_{1,2}$ between the two highest $p_\mathrm{T}$ jets in the dijet system. The differential production cross sections are measured as a function of the transverse momenta of the four highest $p_\mathrm{T}$ jets. The measurements are compared with leading and next-to-leading order matrix element calculations supplemented with simulations of parton shower, hadronization, and multiparton interactions. In addition, the measurements are compared with next-to-leading order matrix element calculations combined with transverse-momentum dependent parton densities and transverse-momentum dependent parton shower.

We report a measurement of the $e^+e^- \to \pi^+\pi^-\pi^0$ cross section in the energy range from 0.62 to 3.50 GeV using an initial-state radiation technique. We use an $e^+e^-$ data sample corresponding to 191 $\text{fb}^{-1}$ of integrated luminosity, collected at a center-of-mass energy at or near the $\Upsilon{(4S)}$ resonance with the Belle II detector at the SuperKEKB collider. Signal yields are extracted by fitting the two-photon mass distribution in $e^+e^- \to \pi^+\pi^-\pi^0\gamma$ events, which involve a $\pi^0 \to \gamma\gamma$ decay and an energetic photon radiated from the initial state. Signal efficiency corrections with an accuracy of 1.6% are obtained from several control data samples. The uncertainty on the cross section at the $\omega$ and $\phi$ resonances is dominated by the systematic uncertainty of 2.2%. The resulting cross sections in the 0.62-1.80 GeV energy range yield $ a_\mu^{3\pi} = [48.91 \pm 0.23~(\mathrm{stat}) \pm 1.07~(\mathrm{syst})] \times 10^{-10} $ for the leading-order hadronic vacuum polarization contribution to the muon anomalous magnetic moment. This result differs by $2.5$ standard deviations from the most precise current determination.

Measurements of the inclusive and normalised differential cross sections are presented for the production of single top quarks in association with a W boson in proton-proton collisions at a centre-of-mass energy of 13 TeV. The data used were recorded with the CMS detector at the LHC during 2016-2018, and correspond to an integrated luminosity of 138 fb$^{-1}$. Events containing one electron and one muon in the final state are analysed. For the inclusive measurement, a multivariate discriminant, exploiting the kinematic properties of the events is used to separate the signal from the dominant $\mathrm{t\bar{t}}$ background. A cross section of 79.2 $\pm$ 0.9 (stat) $^{+7.7}_{-8.0}$ (syst) $\pm$ 1.2 (lumi) pb is obtained, consistent with the predictions of the standard model. For the differential measurements, a fiducial region is defined according to the detector acceptance, and the requirement of exactly one jet coming from the fragmentation of a bottom quark. The resulting distributions are unfolded to particle level and agree with the predictions at next-to-leading order in perturbative quantum chromodynamics.

Measurements of inclusive and normalized differential cross sections of the associated production of top quark-antiquark and bottom quark-antiquark pairs, ttbb, are presented. The results are based on data from proton-proton collisions collected by the CMS detector at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. The cross sections are measured in the lepton+jets decay channel of the top quark pair, using events containing exactly one isolated electron or muon and at least five jets. Measurements are made in four fiducial phase space regions, targeting different aspects of the ttbb process. Distributions are unfolded to the particle level through maximum likelihood fits, and compared with predictions from several event generators. The inclusive cross section measurements of this process in the fiducial phase space regions are the most precise to date. In most cases, the measured inclusive cross sections exceed the predictions with the chosen generator settings. The only exception is when using a particular choice of dynamic renormalization scale, $\mu_\mathrm{R}=\frac{1}{2} \prod_{i = \mathrm{t, \bar{t}, b, \bar{b}}} m_{\mathrm{T},i}^{1/4}$, where $m_{\mathrm{T}, i}^2 = m_i^2 + p^2_{\mathrm{T}, i}$ are the transverse masses of top and bottom quarks. The differential cross sections show varying degrees of compatibility with the theoretical predictions, and none of the tested generators with the chosen settings simultaneously describe all the measured distributions.

A measurement is presented of a ratio observable that provides a measure of the azimuthal correlations among jets with large transverse momentum $p_\mathrm{T}$. This observable is measured in multijet events over the range of $p_\mathrm{T}$ = 360-3170 GeV based on data collected by the CMS experiment in proton-proton collisions at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 134 fb$^{-1}$. The results are compared with predictions from Monte Carlo parton-shower event generator simulations, as well as with fixed-order perturbative quantum chromodynamics (pQCD) predictions at next-to-leading-order (NLO) accuracy obtained with different parton distribution functions (PDFs) and corrected for nonperturbative and electroweak effects. Data and theory agree within uncertainties. From the comparison of the measured observable with the pQCD prediction obtained with the NNPDF3.1 NLO PDFs, the strong coupling at the Z boson mass scale is $\alpha_\mathrm{S}(m_\mathrm{Z})$ = 0.1177 $\pm$ 0.0013 (exp) $_{-0.0073}^{+0.0116}$ (theo) = 0.1177 $_{-0.0074}^{+0.0117}$, where the total uncertainty is dominated by the scale dependence of the fixed-order predictions. A test of the running of $\alpha_\mathrm{S}(m_\mathrm{Z})$ in the TeV region shows no deviation from the expected NLO pQCD behaviour.

A study of the anomalous couplings of the Higgs boson to vector bosons, including $CP$-violation effects, has been conducted using its production and decay in the WW channel. This analysis is performed on proton-proton collision data collected with the CMS detector at the CERN LHC during 2016-2018 at a center-of-mass energy of 13 TeV, and corresponds to an integrated luminosity of 138 fb$^{-1}$. The different-flavor dilepton (e$\mu$) final state is analyzed, with dedicated categories targeting gluon fusion, electroweak vector boson fusion, and associated production with a W or Z boson. Kinematic information from associated jets is combined using matrix element techniques to increase the sensitivity to anomalous effects at the production vertex. A simultaneous measurement of four Higgs boson couplings to electroweak vector bosons is performed in the framework of a standard model effective field theory. All measurements are consistent with the expectations for the standard model Higgs boson and constraints are set on the fractional contribution of the anomalous couplings to the Higgs boson production cross section.

Energy correlators that describe energy-weighted distances between two or three particles in a jet are measured using an event sample of $\sqrt{s}$ = 13 TeV proton-proton collisions collected by the CMS experiment and corresponding to an integrated luminosity of 36.3 fb$^{-1}$. The measured distributions are consistent with the trends in the simulation that reveal two key features of the strong interaction: confinement and asymptotic freedom. By comparing the ratio of the measured three- and two-particle energy correlator distributions with theoretical calculations that resum collinear emissions at approximate next-to-next-to-leading logarithmic accuracy matched to a next-to-leading order calculation, the strong coupling is determined at the Z boson mass: $\alpha_\mathrm{S}(m_\mathrm{Z})$ = 0.1229 $^{+0.0040}_{-0.0050}$, the most precise $\alpha_\mathrm{S}(m_\mathrm{Z})$ value obtained using jet substructure observables.

A search for signatures of a dark analog to quantum chromodynamics is performed. The analysis targets long-lived dark mesons that decay into standard-model particles, with a high branching fraction of the dark mesons decaying into muons. The dark mesons are formed by the hadronisation of dark partons, which are produced by a decay of the Higgs boson. The search is performed using a data set corresponding to an integrated luminosity of 41.6 fb$^{-1}$, which was collected in proton-proton collisions at $\sqrt{s}$ = 13 TeV by the CMS experiment at the CERN LHC in 2018 using non-prompt muon triggers. The search is based on resonant muon pair signatures. Machine-learning techniques are employed in the analysis, utilising boosted decision trees to discriminate between signal and background. No significant excess is observed above the standard model expectation. Upper limits on the branching fraction of the Higgs boson decaying to dark partons are determined to be as low as 10$^{-4}$ at 95% confidence level, surpassing and extending the existing limits on models with dark $\tildeω$ mesons for mean proper decay lengths of less than 500 mm and for $\tildeω$ masses down to 0.3 GeV. First limits are set for extended dark-shower models with two dark flavours that contain dark photons, probing their masses down to 0.33 GeV.

A first search for beyond the standard model physics in jet multiplicity patterns of multilepton events is presented, using a data sample corresponding to an integrated luminosity of 138 fb$^{-1}$ of 13 TeV proton-proton collisions recorded by the CMS detector at the LHC. The search uses observed jet multiplicity distributions in one-, two-, and four-lepton events to explore possible enhancements in jet production rate in three-lepton events with and without bottom quarks. The data are found to be consistent with the standard model expectation. The results are interpreted in terms of supersymmetric production of electroweak chargino-neutralino superpartners with cascade decays terminating in prompt hadronic $R$-parity violating interactions.