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

Proton-proton interactions resulting in final states with two photons are studied in a search for the signature of flavor-changing neutral current interactions of top quarks (t) and Higgs bosons (H). The analysis is based on data collected at a center-of-mass energy of 13 TeV with the CMS detector at the LHC, corresponding to an integrated luminosity of 137 fb$^{-1}$. No significant excess above the background prediction is observed. Upper limits on the branching fractions ($\mathcal{B}$) of the top quark decaying to a Higgs boson and an up (u) or charm quark (c) are derived through a binned fit to the diphoton invariant mass spectrum. The observed (expected) 95% confidence level upper limits are found to be 0.019 (0.031)% for $\mathcal B$(t $\to$ Hu) and 0.073 (0.051)% for $\mathcal{B}$(t $\to$ Hc). These are the strictest upper limits yet determined.

A search for low-mass dilepton resonances in Higgs boson decays is conducted in the four-lepton final state. The decay is assumed to proceed via a pair of beyond the standard model particles, or one such particle and a Z boson. The search uses proton-proton collision data collected with the CMS detector at the CERN LHC, corresponding to an integrated luminosity of 137 fb$^{-1}$, at a center-of-mass energy $\sqrt{s} =$ 13 TeV. No significant deviation from the standard model expectation is observed. Upper limits at 95% confidence level are set on model-independent Higgs boson decay branching fractions. Additionally, limits on dark photon and axion-like particle production, based on two specific models, are reported.

A measurement of the jet mass distribution in hadronic decays of Lorentz-boosted top quarks is presented. The measurement is performed in the lepton+jets channel of top quark pair production ($\mathrm{t\bar{t}}$) events, where the lepton is an electron or muon. The products of the hadronic top quark decay are reconstructed using a single large-radius jet with transverse momentum greater than 400 GeV. The data were collected with the CMS detector at the LHC in proton-proton collisions and correspond to an integrated luminosity of 138 fb$^{-1}$. The differential $\mathrm{t\bar{t}}$ production cross section as a function of the jet mass is unfolded to the particle level and is used to extract the top quark mass. The jet mass scale is calibrated using the hadronic W boson decay within the large-radius jet. The uncertainties in the modelling of the final state radiation are reduced by studying angular correlations in the jet substructure. These developments lead to a significant increase in precision, and a top quark mass of 173.06 $\pm$ 0.84 GeV.

A search for pairs of dijet resonances with the same mass is conducted in final states with at least four jets. Results are presented separately for the case where the four jet production proceeds via an intermediate resonant state and for nonresonant production. The search uses a data sample corresponding to an integrated luminosity of 138 fb$^{-1}$ collected by the CMS detector in proton-proton collisions at $\sqrt{s}$ = 13 TeV. Model-independent limits, at 95% confidence level, are reported on the production cross section of four-jet and dijet resonances. These first LHC limits on resonant pair production of dijet resonances via high mass intermediate states are applied to a signal model of diquarks that decay into pairs of vector-like quarks, excluding diquark masses below 7.6 TeV for a particular model scenario. There are two events in the tails of the distributions, each with a four-jet mass of 8 TeV and an average dijet mass of 2 TeV, resulting in local and global significances of 3.9 and 1.6 standard deviations, respectively, if interpreted as a signal. The nonresonant search excludes pair production of top squarks with masses between 0.50 TeV to 0.77 TeV, with the exception of a small interval between 0.52 and 0.58 TeV, for supersymmetric $R$-parity-violating decays to quark pairs, significantly extending previous limits. Here, the most significant excess above the predicted background occurs at an average dijet mass of 0.95 TeV, for which the local and global significances are 3.6 and 2.5 standard deviations, respectively.

Decays of the Higgs boson into a Z boson and a J/$\psi$ or $\psi$(2S) meson are searched for in four-lepton final states with the CMS detector at the LHC. A data set of proton-proton collisions corresponding to an integrated luminosity of 138 fb$^{-1}$ is used. Using the same data set, decays of the Higgs and Z boson into quarkonium pairs are also searched for. An observation of such decays with this sample would indicate the presence of physics beyond the standard model. No evidence for these decays has been observed and upper limits at the 95% confidence level are placed on the corresponding branching fractions ($\mathcal{B}$). Assuming longitudinal polarization of the Higgs boson decay products, 95% confidence level observed upper limits for $\mathcal{B}$(H $\to$ J/$\psi$) and $\mathcal{B}$(H $\to$ Z$\psi$(2S)) are 1.9$\times$10$^{-3}$ and 6.6$\times$10$^{-3}$, respectively.

A search is presented for vector-like T and B quark-antiquark pairs produced in proton-proton collisions at a center-of-mass energy of 13 TeV. Data were collected by the CMS experiment at the CERN LHC in 2016-2018, with an integrated luminosity of 138 fb$^{-1}$. Events are separated into single-lepton, same-sign charge dilepton, and multilepton channels. In the analysis of the single-lepton channel a multilayer neural network and jet identification techniques are employed to select signal events, while the same-sign dilepton and multilepton channels rely on the high-energy signature of the signal to distinguish it from standard model backgrounds. The data are consistent with standard model background predictions, and the production of vector-like quark pairs is excluded at 95% confidence level for T quark masses up to 1.54 TeV and B quark masses up to 1.56 TeV, depending on the branching fractions assumed, with maximal sensitivity to decay modes that include multiple top quarks. The limits obtained in this search are the strongest limits to date for $\mathrm{T\overline{T}}$ production, excluding masses below 1.48 TeV for all decays to third generation quarks, and are the strongest limits to date for $\mathrm{B\overline{B}}$ production with B quark decays to tW.

A search for a heavy resonance decaying into a top quark and a W boson in proton-proton collisions at $\sqrt{s} =$ 13 TeV is presented. The data analyzed were recorded with the CMS detector at the LHC and correspond to an integrated luminosity of 138 fb$^{-1}$. The top quark is reconstructed as a single jet and the W boson, from its decay into an electron or muon and the corresponding neutrino. A top quark tagging technique based on jet clustering with a variable distance parameter and simultaneous jet grooming is used to identify jets from the collimated top quark decay. The results are interpreted in the context of two benchmark models, where the heavy resonance is either an excited bottom quark b$^*$ or a vector-like quark B. A statistical combination with an earlier search by the CMS Collaboration in the all-hadronic final state is performed to place upper cross section limits on these two models. The new analysis extends the lower range of resonance mass probed from 1.4 down to 0.7 TeV. For left-handed, right-handed, and vector-like couplings, b$^*$ masses up to 3.0, 3.0, and 3.2 TeV are excluded at 95% confidence level, respectively. The observed upper limits represent the most stringent constraints on the b$^*$ model to date.

Production cross sections of the standard model Higgs boson decaying to a pair of W bosons are measured in proton-proton collisions at a center-of-mass energy of 13 TeV. The analysis targets Higgs bosons produced via gluon fusion, vector boson fusion, and in association with a W or Z boson. Candidate events are required to have at least two charged leptons and moderate missing transverse momentum, targeting events with at least one leptonically decaying W boson originating from the Higgs boson. Results are presented in the form of inclusive and differential cross sections in the simplified template cross section framework, as well as couplings of the Higgs boson to vector bosons and fermions. The data set collected by the CMS detector during 2016-2018 is used, corresponding to an integrated luminosity of 138 fb$^{-1}$. The signal strength modifier $\mu$, defined as the ratio of the observed production rate in a given decay channel to the standard model expectation, is measured to be $\mu$ = 0.95 $^{+0.10}_{-0.09}$. All results are found to be compatible with the standard model within the uncertainties.

A search for supersymmetry is presented in events with a single charged lepton, electron or muon, and multiple hadronic jets. The data correspond to an integrated luminosity of 138 fb$^{-1}$ of proton-proton collisions at a center-of-mass energy of 13 TeV, recorded by the CMS experiment at the CERN LHC. The search targets gluino pair production, where the gluinos decay into final states with the lightest supersymmetric particle (LSP) and either a top quark-antiquark ($\mathrm{t\bar{t}}$) pair, or a light-flavor quark-antiquark ($\mathrm{q\bar{q}}$) pair and a virtual or on-shell W boson. The main backgrounds, $\mathrm{t\bar{t}}$ pair and W+jets production, are suppressed by requirements on the azimuthal angle between the momenta of the lepton and of its reconstructed parent W boson candidate, and by top quark and W boson identification based on a machine-learning technique. The number of observed events is consistent with the expectations from standard model processes. Limits are evaluated on supersymmetric particle masses in the context of two simplified models of gluino pair production. Exclusions for gluino masses reach up to 2120 (2050) GeV at 95% confidence level for a model with gluino decay to a $\mathrm{t\bar{t}}$ pair (a $\mathrm{q\bar{q}}$ pair and a W boson) and the LSP. For the same models, limits on the mass of the LSP reach up to 1250 (1070) GeV.

A search for the lepton-flavor violating decay of the Higgs boson and potential additional Higgs bosons with a mass in the range 110-160 GeV to an e$^{\pm}\mu^{\mp}$ pair is presented. The search is performed with a proton-proton collision dataset at a center-of-mass energy of 13 TeV collected by the CMS experiment at the LHC, corresponding to an integrated luminosity of 138 fb$^{-1}$. No excess is observed for the Higgs boson. The observed (expected) upper limit on the e$^{\pm}\mu^{\mp}$ branching fraction for it is determined to be 4.4 (4.7) $\times$ 10$^{-5}$ at 95% confidence level, the most stringent limit set thus far from direct searches. The largest excess of events over the expected background in the full mass range of the search is observed at an e$^{\pm}\mu^{\mp}$ invariant mass of approximately 146 GeV with a local (global) significance of 3.8 (2.8) standard deviations.

The observation of the production of four top quarks in proton-proton collisions is reported, based on a data sample collected by the CMS experiment at a center-of-mass energy of 13 TeV in 2016-2018 at the CERN LHC and corresponding to an integrated luminosity of 138 fb$^{-1}$. Events with two same-sign, three, or four charged leptons (electrons and muons) and additional jets are analyzed. Compared to previous results in these channels, updated identification techniques for charged leptons and jets originating from the hadronization of b quarks, as well as a revised multivariate analysis strategy to distinguish the signal process from the main backgrounds, lead to an improved expected signal significance of 4.9 standard deviations above the background-only hypothesis. Four top quark production is observed with a significance of 5.6 standard deviations, and its cross section is measured to be 17.7 $^{+3.7}_{-3.5}$ (stat) $^{+2.3}_{-1.9}$ (syst) fb, in agreement with the available standard model predictions.

Three searches are presented for signatures of physics beyond the standard model (SM) in $\tau\tau$ final states in proton-proton collisions at the LHC, using a data sample collected with the CMS detector at $\sqrt{s}$ = 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. Upper limits at 95% confidence level (CL) are set on the products of the branching fraction for the decay into $\tau$ leptons and the cross sections for the production of a new boson $\phi$, in addition to the H(125) boson, via gluon fusion (gg$\phi$) or in association with b quarks, ranging from $\mathcal{O}$(10 pb) for a mass of 60 GeV to 0.3 fb for a mass of 3.5 TeV each. The data reveal two excesses for gg$\phi$ production with local $p$-values equivalent to about three standard deviations at $m_\phi$ = 0.1 and 1.2 TeV. In a search for $t$-channel exchange of a vector leptoquark U$_1$, 95% CL upper limits are set on the dimensionless U$_1$ leptoquark coupling to quarks and $\tau$ leptons ranging from 1 for a mass of 1 TeV to 6 for a mass of 5 TeV, depending on the scenario. In the interpretations of the $M_\mathrm{h}^{125}$ and $M_\mathrm{h, EFT}^{125}$ minimal supersymmetric SM benchmark scenarios, additional Higgs bosons with masses below 350 GeV are excluded at 95% CL.

The first observation of the production of W$^\pm$W$^\pm$ bosons from double parton scattering processes using same-sign electron-muon and dimuon events in proton-proton collisions is reported. The data sample corresponds to an integrated luminosity of 138 fb$^{-1}$ recorded at a center-of-mass energy of 13 TeV using the CMS detector at the CERN LHC. Multivariate discriminants are used to distinguish the signal process from the main backgrounds. A binned maximum likelihood fit is performed to extract the signal cross section. The measured cross section for production of same-sign W bosons decaying leptonically is 80.7 $\pm$ 11.2 (stat) $^{+9.5}_{-8.6}$ (syst) $\pm$ 12.1 (model) fb, whereas the measured fiducial cross section is 6.28 $\pm$ 0.81 (stat) $\pm$ 0.69 (syst) $\pm$ 0.37 (model) fb. The observed significance of the signal is 6.2 standard deviations above the background-only hypothesis.

A data sample containing top quark pairs ($\mathrm{t\bar{t}}$) produced in association with a Lorentz-boosted Z or Higgs boson is used to search for signs of new physics using effective field theory. The data correspond to an integrated luminosity of 138 fb$^{-1}$ of proton-proton collisions produced at a center-of-mass energy of 13 TeV at the LHC and collected by the CMS experiment. Selected events contain a single lepton and hadronic jets, including two identified with the decay of bottom quarks, plus an additional large-radius jet with high transverse momentum identified as a Z or Higgs boson decaying to a bottom quark pair. Machine learning techniques are employed to discriminate between $\mathrm{t\bar{t}}$Z or $\mathrm{t\bar{t}}$H events and events from background processes, which are dominated by $\mathrm{t\bar{t}}$ + jets production. No indications of new physics are observed. The signal strengths of boosted $\mathrm{t\bar{t}}$Z and $\mathrm{t\bar{t}}$H production are measured, and upper limits are placed on the $\mathrm{t\bar{t}}$Z and $\mathrm{t\bar{t}}$H differential cross sections as functions of the Z or Higgs boson transverse momentum. The effects of new physics are probed using a framework in which the standard model is considered to be the low-energy effective field theory of a higher energy scale theory. Eight possible dimension-six operators are added to the standard model Lagrangian and their corresponding coefficients are constrained via fits to the data.

An observation is reported of the electroweak production of a W$^+$W$^-$ pair in association with two jets, with both W bosons decaying leptonically. The data sample corresponds to an integrated luminosity of 138 fb$^{-1}$ of proton-proton collisions at $\sqrt{s}$ = 13 TeV, collected by the CMS detector at the CERN LHC. Events are selected by requiring exactly two opposite-sign leptons (electrons or muons) and two jets with large pseudorapidity separation and high dijet invariant mass. Events are categorized based on the flavor of the final-state leptons. A signal is observed with a significance of 5.6 standard deviations (5.2 expected) with respect to the background-only hypothesis. The measured fiducial cross section is 10.2 $\pm$ 2.0 fb and this value is consistent with the standard model prediction of 9.1 $\pm$ 0.6 fb.

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.

A search is presented for long-lived particles produced in pairs in proton-proton collisions at the LHC operating at a center-of-mass energy of 13 TeV. The data were collected with the CMS detector during the period from 2015 through 2018, and correspond to a total integrated luminosity of 140 fb$^{-1}$. This search targets pairs of long-lived particles with mean proper decay lengths between 0.1 and 100 mm, each of which decays into at least two quarks that hadronize to jets, resulting in a final state with two displaced vertices. No significant excess of events with two displaced vertices is observed. In the context of $R$-parity violating supersymmetry models, the pair production of long-lived neutralinos, gluinos, and top squarks is excluded at 95% confidence level for cross sections larger than 0.08 fb, masses between 800 and 3000 GeV, and mean proper decay lengths between 1 and 25 mm.

Measurements of Higgs boson production, where the Higgs boson decays into a pair of $\tau$ leptons, are presented, using a sample of proton-proton collisions collected with the CMS experiment at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. Three analyses are presented. Two are targeting Higgs boson production via gluon fusion and vector boson fusion: a neural network based analysis and an analysis based on an event categorization optimized on the ratio of signal over background events. These are complemented by an analysis targeting vector boson associated Higgs boson production. Results are presented in the form of signal strengths relative to the standard model predictions and products of cross sections and branching fraction to $\tau$ leptons, in up to 16 different kinematic regions. For the simultaneous measurements of the neural network based analysis and the analysis targeting vector boson associated Higgs boson production signal strengths are found to be 0.82 $\pm$ 0.11 for inclusive Higgs boson production, 0.67 $\pm$ 0.19 (0.81 $\pm$ 0.17) for the production mainly via gluon fusion (vector boson fusion), and 1.79 $\pm$ 0.45 for vector boson associated Higgs boson production.

The measurement of the charge asymmetry in top quark pair events with highly Lorentz-boosted top quarks decaying to a single lepton and jets is presented. The analysis is performed using proton-proton collisions at $\sqrt{s}$ = 13 TeV with the CMS detector at the LHC and corresponding to an integrated luminosity of 138 fb$^{-1}$. The selection is optimized for top quarks produced with large Lorentz boosts, resulting in nonisolated leptons and overlapping jets. The top quark charge asymmetry is measured for events with a $\mathrm{t\bar{t}}$ invariant mass larger than 750 GeV and corrected for detector and acceptance effects using a binned maximum likelihood fit. The measured top quark charge asymmetry of (0.42 $_{-0.69}^{+0.64}$)% is in good agreement with the standard model prediction at next-to-next-to-leading order in quantum chromodynamic perturbation theory with next-to-leading-order electroweak corrections. The result is also presented for two invariant mass ranges, 750-900 and $\gt$ 900 GeV.

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 are presented of the B$^0_\mathrm{S}$$\to$$\mu^+\mu^-$ branching fraction and effective lifetime, as well as results of a search for the B$^0$$\to$$\mu^+\mu^-$ decay in proton-proton collisions at $\sqrt{s}$ = 13 TeV at the LHC. The analysis is based on data collected with the CMS detector in 2016-2018 corresponding to an integrated luminosity of 140 fb$^{-1}$. The branching fraction of the B$^0_\mathrm{S}$$\to$$\mu^+\mu^-$ decay and the effective B$^0_\mathrm{S}$ meson lifetime are the most precise single measurements to date. No evidence for the B$^0$$\to$$\mu^+\mu^-$ decay has been found. All results are found to be consistent with the standard model predictions and previous measurements.

A search for decays to invisible particles of Higgs bosons produced in association with a top-antitop quark pair or a vector boson, which both decay to a fully hadronic final state, has been performed using proton-proton collision data collected at $\sqrt{s}$ = 13 TeV by the CMS experiment at the LHC, corresponding to an integrated luminosity of 138 fb$^{-1}$. The 95% confidence level upper limit set on the branching fraction of the 125 GeV Higgs boson to invisible particles, $\mathcal{B}$(H $\to$ inv), is 0.54 (0.39 expected), assuming standard model production cross sections. The results of this analysis are combined with previous $\mathcal{B}$(H $\to$ inv) searches carried out at $\sqrt{s}$ = 7, 8, and 13 TeV in complementary production modes. The combined upper limit at 95% confidence level on $\mathcal{B}$(H $\to$ inv) is 0.15 (0.08 expected).

A search is performed for exclusive high-mass $\gamma\gamma$$\to$ WW and $\gamma\gamma$$\to$ ZZ production in proton-proton collisions using intact forward protons reconstructed in near-beam detectors, with both weak bosons decaying into boosted and merged jets. The analysis is based on a sample of proton-proton collisions collected by the CMS and TOTEM experiments at $\sqrt{s}$ = 13 TeV, corresponding to an integrated luminosity of 100 fb$^{-1}$. No excess above the standard model background prediction is observed, and upper limits are set on the pp $\to$ pWWp and pp $\to$ pZZp cross sections in a fiducial region defined by the diboson invariant mass $m$(VV) $\lt$ 1 TeV (with V = W, Z) and proton fractional momentum loss 0.04 $\lt$$\xi$$\lt$ 0.20. The results are interpreted as new limits on dimension-6 and dimension-8 anomalous quartic gauge couplings.

The measurements of the inclusive and differential fiducial cross sections of the Higgs boson decaying to a pair of photons are presented. The analysis is performed using proton-proton collisions data recorded with the CMS detector at the LHC at a centre-of-mass energy of 13 TeV and corresponding to an integrated luminosity of 137 fb$^{-1}$. The inclusive fiducial cross section is measured to be $\sigma_\mathrm{fid}$ = 73.4 $_{-5.3}^{+5.4}$ (stat) ${}_{-2.2}^{+2.4}$ (syst) fb, in agreement with the standard model expectation of 75.4 $\pm$ 4.1 fb. The measurements are also performed in fiducial regions targeting different production modes and as function of several observables describing the diphoton system, the number of additional jets present in the event, and other kinematic observables. Two double differential measurements are performed. No significant deviations from the standard model expectations are observed.

The dependence of the ratio between the B$_\mathrm{s}^0$ and B$^+$ hadron production fractions, $f_\mathrm{s} / f_\mathrm{u}$, on the transverse momentum ($p_\mathrm{T}$) and rapidity of the B mesons is studied using the decay channels B$_\mathrm{s}^0$$\to$ J$/\psi\,\phi$ and B$^+$$\to$ J$/\psi$ K$^+$. The analysis uses a data 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 61.6 fb$^{-1}$. The $f_\mathrm{s} / f_\mathrm{u}$ ratio is observed to depend on the B $p_\mathrm{T}$ and to be consistent with becoming asymptotically constant at large $p_\mathrm{T}$. No rapidity dependence is observed. The ratio of the B$^0$ to B$^+$ hadron production fractions, $f_\mathrm{d} / f_\mathrm{u}$, measured using the B$^0$$\to$ J$/\psi$ K$^{*0}$ decay channel, is found to be consistent with unity and independent of $p_\mathrm{T}$ and rapidity, as expected from isospin invariance.

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 measurement is presented for the electroweak production of a W boson, a photon ($\gamma$), and two jets (j) in proton-proton collisions. The leptonic decay of the W boson is selected by requiring one identified electron or muon and large missing transverse momentum. The two jets are required to have large invariant dijet mass and large separation in pseudorapidity. The measurement is performed with the data collected by the CMS detector at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. The cross section for the electroweak W$\gamma$jj production is 23.5 $^{+4.9}_{-4.7}$ fb, whereas the total cross section for W$\gamma$jj production is 113 $\pm$ 13 fb. Differential cross sections are also measured with the distributions unfolded to the particle level. All results are in agreement with the standard model expectations. Constraints are placed on anomalous quartic gauge couplings (aQGCs) in terms of dimension-8 effective field theory operators. These are the most stringent limits to date on the aQGCs parameters $f_\mathrm{M,2-5}$$/$$\Lambda^4$ and $f_\mathrm{T,6-7}$$/$$\Lambda^4$.

The production of a top quark-antiquark pair in association with a W boson ($\mathrm{t\bar{t}}$W) is measured in proton-proton collisions at a center-of-mass energy of 13 TeV. The analyzed data was recorded by the CMS experiment at the CERN LHC and corresponds to an integrated luminosity of 138 fb$^{-1}$. Events with two or three leptons (electrons and muons) and additional jets are selected. In events with two leptons, a multiclass neural network is used to distinguish between the signal and background processes. Events with three leptons are categorized based on the number of jets and of jets originating from b quark hadronization, and the lepton charges. The inclusive $\mathrm{t\bar{t}}$W production cross section in the full phase space is measured to be 868 $\pm$ 40 (stat) $\pm$ 51 (syst) fb. The $\mathrm{t\bar{t}}$W$^+$ and $\mathrm{t\bar{t}}$W$^-$ cross sections are also measured as 553 $\pm$ 30 (stat) $\pm$ 30 (syst) and 343 $\pm$ 26 (stat) $\pm$ 25 (syst) fb, respectively, and the corresponding ratio of the two cross sections is found to be 1.61 $\pm$ 0.15 (stat) $^{+0.07}_{-0.05}$ (syst). The measured cross sections are larger than but consistent with the standard model predictions within two standard deviations, and represent the most precise measurement of these cross sections to date.

The production of four top quarks ($\mathrm{t\bar{t}t\bar{t}}$) is studied with LHC proton-proton collision data samples collected by the CMS experiment at a center-of-mass energy of 13 TeV, and corresponding to integrated luminosities of up to 138 fb$^{-1}$. Events that have no leptons (all-hadronic), one lepton, or two opposite-sign leptons (where lepton refers only to prompt electrons or prompt muons) are considered. This is the first $\mathrm{t\bar{t}t\bar{t}}$ measurement that includes the all-hadronic final state. The observed significance of the $\mathrm{t\bar{t}t\bar{t}}$ signal in these final states of 3.9 standard deviations (1.5 expected) provides evidence for $\mathrm{t\bar{t}t\bar{t}}$ production, with a measured cross section of 36 $^{+12}_{-11}$ fb. Combined with earlier CMS results in other final states, the signal significance is 4.0 standard deviations (3.2 expected). The combination returns an observed cross section of 17 $\pm$ 4 (stat) $\pm$ 3 (syst) fb, which is consistent with the standard model prediction.

The charge-parity ($CP$) structure of the Yukawa interaction between the Higgs (H) boson and the top quark is measured in a data sample enriched in the $\mathrm{t\bar{t}}$ and tH associated production, using 138 fb$^{-1}$ of data collected in proton-proton collisions at $\sqrt{s}$ = 13 TeV by the CMS experiment at the CERN LHC. The study targets events where the H boson decays via H $\to$ WW or H $\to$$\tau\tau$ and the top quarks decay via t $\to$ Wb: the W bosons decay either leptonically or hadronically, and final states characterized by the presence of at least two leptons are studied. Machine learning techniques are applied to these final states to enhance the separation of $CP$-even from $CP$-odd scenarios. Two-dimensional confidence regions are set on $\kappa_\mathrm{t}$ and $\tilde{\kappa}_\mathrm{t}$, which are respectively defined as the $CP$-even and $CP$-odd top-Higgs Yukawa coupling modifiers. No significant fractional $CP$-odd contributions, parameterized by the quantity $\lvert{f_{CP}^{\mathrm{Htt}}}\rvert$ are observed; the parameter is determined to be $\lvert{f_{CP}^{\mathrm{Htt}}}\rvert$ = 0.59 with an interval of (0.24, 0.81) at 68% confidence level. The results are combined with previous results covering the H $\to$ ZZ and H $\to$ $\gamma\gamma$ decay modes, yielding two- and one-dimensional confidence regions on $\kappa_\mathrm{t}$ and $\tilde{\kappa}_\mathrm{t}$, while $\lvert{f_{CP}^{\mathrm{Htt}}}\rvert$ is determined to be $\lvert{f_{CP}^{\mathrm{Htt}}}\rvert$ = 0.28 with an interval of $\lvert{f_{CP}^{\mathrm{Htt}}}\rvert$ $\lt$ 0.55 at 68% confidence level, in agreement with the standard model $CP$-even prediction of $\lvert{f_{CP}^{\mathrm{Htt}}}\rvert$ = 0.

The first search for narrow resonances decaying to three well-separated hadronic jets is presented. The search uses proton-proton collision data corresponding to an integrated luminosity of 138 fb$^{-1}$ at $\sqrt{s}$ = 13 TeV, collected at the CERN LHC. No significant deviations from the background predictions are observed between 1.75-9.00 TeV. The results provide the first mass limits on a right-handed boson Z$_{\mathrm{R}}$ decaying to three gluons, an excited quark decaying via a vector boson to three quarks, as well as updated limits on a Kaluza-Klein gluon decaying via a radion to three gluons.

The first search is presented for vector-like leptons (VLLs) in the context of the "4321 model", an ultraviolet-complete model with the potential to explain existing B physics measurements that are in tension with standard model predictions. The analyzed data, corresponding to an integrated luminosity of 96.5 fb$^{-1}$, were recorded in 2017 and 2018 with the CMS detector at the LHC in proton-proton collisions at $\sqrt{s}$ = 13 TeV. Final states with ${\geq}$ 3 b-tagged jets and two third-generation leptons ($\tau\tau$, $\tau\nu_\tau$, or $\nu_\tau\nu_\tau$) are considered. Upper limits are derived on the VLL production cross section in the VLL mass range 500-1050 GeV. The maximum likelihood fit prefers the presence of signal at the level of 2.8 standard deviations, for a representative VLL mass point of 600 GeV. As a consequence, the observed upper limits are approximately double the expected limits.

A search is presented for the Higgs boson decay to a pair of electrons (e$^+$e$^-$) in proton-proton collisions at $\sqrt{s}$ = 13 TeV. The data set was collected with the CMS experiment at the LHC between 2016 and 2018, corresponding to an integrated luminosity of 138 fb$^{-1}$. The analysis uses event categories targeting Higgs boson production via gluon fusion and vector boson fusion. The observed upper limit on the Higgs boson branching fraction to an electron pair is 3.0 $\times$ 10$^{-4}$ (3.0 $\times$ 10$^{-4}$ expected) at the 95% confidence level, which is the most stringent limit on this branching fraction to date.

A search for W' bosons decaying to a top and a bottom quark in final states including an electron or a muon is performed with the CMS detector at the LHC. The analyzed data correspond to an integrated luminosity of 138 fb$^{-1}$ of proton-proton collisions at a center-of-mass energy of 13 Tev. Good agreement with the standard model expectation is observed and no evidence for the existence of the W' boson is found over the mass range examined. The largest observed deviation from the standard model expectation is found for a W' boson mass ($m_\mathrm{W'}$) hypothesis of 3.8 TeV with a relative decay width of 1%, with a local (global) significance of 2.6 (2.0) standard deviations. Upper limits on the production cross sections of W' bosons decaying to a top and a bottom quark are set. Left- and right-handed W' bosons with $m_\mathrm{W'}$ below 3.9 and 4.3 TeV, respectively, are excluded at the 95% confidence level, under the assumption that the new particle has a narrow decay width. Limits are also set for relative decay widths up to 30%. These are the most stringent limits to date on this W' boson decay channel.

A search for new heavy resonances decaying to WW, WZ, ZZ, WH, or ZH boson pairs in the all-jets final state is presented. The analysis is based on proton-proton collision data recorded by the CMS detector in 2016-2018 at a centre-of-mass energy of 13 TeV at the CERN LHC, corresponding to an integrated luminosity of 138 fb$^{-1}$. The search is sensitive to resonances with masses between 1.3 and 6 TeV, decaying to bosons that are highly Lorentz-boosted such that each of the bosons forms a single large-radius jet. Machine learning techniques are employed to identify such jets. No significant excess over the estimated standard model background is observed. A maximum local significance of 3.6 standard deviations, corresponding to a global significance of 2.3 standard deviations, is observed at masses of 2.1 and 2.9 TeV. In a heavy vector triplet model, spin-1 Z' and W' resonances with masses below 4.8 TeV are excluded at the 95% confidence level (CL). These limits are the most stringent to date. In a bulk graviton model, spin-2 gravitons and spin-0 radions with masses below 1.4 and 2.7 TeV, respectively, are excluded at 95% CL. Production of heavy resonances through vector boson fusion is constrained with upper cross section limits at 95% CL as low as 0.1 fb.

A search for a new boson X is presented using CERN LHC proton-proton collision data collected by the CMS experiment at $\sqrt{s}$ = 13 TeV in 2016-2018, and corresponding to an integrated luminosity of 138 fb$^{-1}$. The resonance X decays into either a pair of Higgs bosons HH of mass 125 GeV or an H and a new spin-0 boson Y. One H subsequently decays to a pair of photons, and the second H or Y, to a pair of bottom quarks. The explored mass ranges of X are 260-1000 GeV and 300-1000 GeV, for decays to HH and to HY, respectively, with the Y mass range being 90-800 GeV. For a spin-0 X hypothesis, the 95% confidence level upper limit on the product of its production cross section and decay branching fraction is observed to be within 0.90-0.04 fb, depending on the masses of X and Y. The largest deviation from the background-only hypothesis with a local (global) significance of 3.8 (2.8) standard deviations is observed for X and Y masses of 650 and 90 GeV, respectively. The limits are interpreted using several models of new physics.

A search is presented for high-mass exclusive diphoton production via photon-photon fusion in proton-proton collisions at $\sqrt{s}$ = 13 TeV in events where both protons survive the interaction. The analysis utilizes data corresponding to an integrated luminosity of 103 fb$^{-1}$ collected in 2016-2018 with the central CMS detector and the CMS and TOTEM precision proton spectrometer (PPS). Events that have two photons with high transverse momenta ($p_\mathrm{T}^\gamma > $ 100 GeV), back-to-back in azimuth, and with a large diphoton invariant mass ($m_{\gamma\gamma} \gt$ 350 GeV) are selected. To remove the dominant inclusive diphoton backgrounds, the kinematic properties of the protons detected in PPS are required to match those of the central diphoton system. Only events having opposite-side forward protons detected with a fractional momentum loss between 0.035 and 0.15 (0.18) for the detectors on the negative (positive) side of CMS are considered. One exclusive diphoton candidate is observed for an expected background of 1.1 events. Limits at 95% confidence level are derived for the four-photon anomalous coupling parameters $\lvert\zeta_1\rvert \lt$ 0.073 TeV$^{-4}$ and $\lvert\zeta_2\rvert \lt$ 0.15 TeV$^{-4}$, using an effective field theory. Additionally, upper limits are placed on the production of axion-like particles with coupling strength to photons $f^{-1}$ that varies from 0.03 TeV$^{-1}$ to 1 TeV$^{-1}$ over the mass range from 500 to 2000 GeV.

A search for the rare $\eta$$\to$$\mu^+\mu^-\mu^+\mu^-$ double-Dalitz decay is performed using a sample of proton-proton collisions, collected by the CMS experiment at the CERN LHC with high-rate muon triggers in 2017-2018 and corresponding to an integrated luminosity of 101 fb$^{-1}$. A signal having a statistical significance well in excess of 5 standard deviations is observed. Using the $\eta$$\to$$\mu^+ \mu^-$ decay as normalization, the branching fraction $\mathcal{B}(\eta$$\to$$\mu^+\mu^-\mu^+\mu^-)$ = [5.0 $\pm$ 0.8 (stat) $\pm$ 0.7 (syst) $\pm$ 0.7 ($\mathcal{B}_{2\mu}$)] $\times$ 10$^{-9}$ is measured, where the last term is the uncertainty in the normalization channel branching fraction. This work achieves an improved precision of over five orders of magnitude compared to previous results, leading to the first measurement of this branching fraction, which is found to agree with theoretical predictions.

We search for new massive scalar particles X and Y through the resonant process X $\to$ YH $\to$$\mathrm{b\bar{b}b\bar{b}}$, where H is the standard model Higgs boson. Data from CERN LHC proton-proton collisions are used, collected at a centre-of-mass energy of 13 TeV in 2016-2018 and corresponding to an integrated luminosity of 138 fb$^{-1}$. The search is performed in mass ranges of 0.9-4 TeV for X and 60-600 GeV for Y, where both Y and H are reconstructed as Lorentz-boosted single large-area jets. The results are interpreted in the context of the next-to-minimal supersymmetric standard model and also in an extension of the standard model with two additional singlet scalar fields. The 95% confidence level upper limits for the production cross section vary between 0.1 and 150 fb depending on the X and Y masses, and represent a significant improvement over results from previous searches.

The mass of the top quark is measured in 36.3 fb$^{-1}$ of LHC proton-proton collision data collected with the CMS detector at $\sqrt{s}$ = 13 TeV. The measurement uses a sample of top quark pair candidate events containing one isolated electron or muon and at least four jets in the final state. For each event, the mass is reconstructed from a kinematic fit of the decay products to a top quark pair hypothesis. A profile likelihood method is applied using up to four observables to extract the top quark mass. The top quark mass is measured to be 171.77 $\pm$ 0.37 GeV. This approach significantly improves the precision over previous measurements.

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 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 $\alpha_\mathrm{S}$.

A search for direct production of low-mass dimuon resonances is performed using $\sqrt{s}$ = 13 TeV proton-proton collision data collected by the CMS experiment during the 2017-2018 operation of the CERN LHC with an integrated luminosity of 96.6 fb$^{-1}$. The search exploits a dedicated high-rate trigger stream that records events with two muons with transverse momenta as low as 3 GeV but does not include the full event information. The search is performed by looking for narrow peaks in the dimuon mass spectrum in the ranges of 1.1-2.6 GeV and 4.2-7.9 GeV. No significant excess of events above the expectation from the standard model background is observed. Model-independent limits on production rates of dimuon resonances within the experimental fiducial acceptance are set. Competitive or world's best limits are set at 90% confidence level for a minimal dark photon model and for a scenario with two Higgs doublets and an extra complex scalar singlet (2HDM+S). Values of the squared kinetic mixing coefficient $\varepsilon^2$ in the dark photon model above 10$^{-6}$ are excluded over most of the mass range of the search. In the 2HDM+S, values of the mixing angle $\sin(\theta_\text{H})$ above 0.08 are excluded over most of the mass range of the search with a fixed ratio of the Higgs doublets vacuum expectation $\tan\beta$ = 0.5.

A test of lepton flavor universality in B$^{\pm}$$\to$ K$^{\pm}\mu^+\mu^-$ and B$^{\pm}$$\to$ K$^{\pm}$e$^+$e$^-$ decays, as well as a measurement of differential and integrated branching fractions of a nonresonant B$^{\pm}$$\to$ K$^{\pm}\mu^+\mu^-$ decay are presented. The analysis is made possible by a dedicated data set of proton-proton collisions at $\sqrt{s}$ = 13 TeV recorded in 2018, by the CMS experiment at the LHC, using a special high-rate data stream designed for collecting about 10 billion unbiased b hadron decays. The ratio of the branching fractions $\mathcal{B}$(B$^{\pm}$$\to$ K$^{\pm}\mu^+\mu^-$) to $\mathcal{B}$(B$^{\pm}$$\to$ K$^{\pm}$e$^+$e$^-$) is determined from the measured double ratio $R$(K) of these decays to the respective branching fractions of the B$^\pm$$\to$ J/$\psi$K$^\pm$ with J/$\psi$$\to$$\mu^+\mu^-$ and e$^+$e$^-$ decays, which allow for significant cancellation of systematic uncertainties. The ratio $R$(K) is measured in the range 1.1 $\lt q^2 \lt$ 6.0 GeV$^2$, where $q$ is the invariant mass of the lepton pair, and is found to be $R$(K) = 0.78$^{+0.47}_{-0.23}$, in agreement with the standard model expectation $R$(K) $\approx$ 1. This measurement is limited by the statistical precision of the electron channel. The integrated branching fraction in the same $q^2$ range, $\mathcal{B}$(B$^{\pm}$$\to$ K$^{\pm}\mu^+\mu^-$) = (12.42 $\pm$ 0.68) $\times$ 10$^{-8}$, is consistent with the present world-average value and has a comparable precision.

A measurement of the Higgs boson (H) production via vector boson fusion (VBF) and its decay into a bottom quark-antiquark pair ($\mathrm{b\bar{b}}$) is presented using proton-proton collision data recorded by the CMS experiment at $\sqrt{s}$ = 13 TeV and corresponding to an integrated luminosity of 90.8 fb$^{-1}$. Treating the gluon-gluon fusion process as a background and constraining its rate to the value expected in the standard model (SM) within uncertainties, the signal strength of the VBF process, defined as the ratio of the observed signal rate to that predicted by the SM, is measured to be $\mu^\text{qqH}_\mathrm{Hb\bar{b}}$ = 1.01 $^{+0.55}_{-0.46}$. The VBF signal is observed with a significance of 2.4 standard deviations relative to the background prediction, while the expected significance is 2.7 standard deviations. Considering inclusive Higgs boson production and decay into bottom quarks, the signal strength is measured to be $\mu^\text{incl.}_\mathrm{Hb\bar{b}}$ = 0.99 $^{+0.48}_{-0.41}$, corresponding to an observed (expected) significance of 2.6 (2.9) standard deviations.

A search for the electroweak production of a vector-like quark T$'$, decaying to a top quark and a Higgs boson is presented. The search is based on a sample of proton-proton collision events recorded at the LHC at $\sqrt{s}$ = 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. This is the first T$'$ search that exploits the Higgs boson decay to a pair of photons. For narrow isospin singlet T$'$ states with masses up to 1.1 TeV, the excellent diphoton invariant mass resolution of 1-2% results in an increased sensitivity compared to previous searches based on the same production mechanism. The electroweak production of a T$'$ quark with mass up to 960 GeV is excluded at 95% confidence level, assuming a coupling strength $\kappa_\mathrm{T}$ = 0.25 and a relative decay width $\Gamma/M_{\mathrm{T}'}$ $\lt$ 5%.

The first measurement of the top quark pair ($\mathrm{t\bar{t}}$) production cross section in proton-proton collisions at $\sqrt{s}$ = 13.6 TeV is presented. Data recorded with the CMS detector at the CERN LHC in Summer 2022, corresponding to an integrated luminosity of 1.21 fb$^{-1}$, are analyzed. Events are selected with one or two charged leptons (electrons or muons) and additional jets. A maximum likelihood fit is performed in event categories defined by the number and flavors of the leptons, the number of jets, and the number of jets identified as originating from b quarks. An inclusive $\mathrm{t\bar{t}}$ production cross section of 881 $\pm$ 23 (stat+syst) $\pm$ 20 (lumi) pb is measured, in agreement with the standard model prediction of 924 $^{+32}_{-40}$ pb.

The second-order ($v_2$) and third-order ($v_3$) Fourier coefficients describing the azimuthal anisotropy of prompt and nonprompt (from b-hadron decays) J/$\psi$, as well as prompt $\psi$(2S) mesons are measured in lead-lead collisions at a center-of-mass energy per nucleon pair of $\sqrt{s_\mathrm{NN}}$ = 5.02 TeV. The analysis uses a data set corresponding to an integrated luminosity of 1.61 nb$^{-1}$ recorded with the CMS detector. The J/$\psi$ and $\psi$(2S) mesons are reconstructed using their dimuon decay channel. The $v_2$ and $v_3$ coefficients are extracted using the scalar product method and studied as functions of meson transverse momentum and collision centrality. The measured $v_2$ values for prompt J/$\psi$ mesons are found to be larger than those for nonprompt J/$\psi$ mesons. The prompt J/$\psi$$v_2$ values at high $p_\mathrm{T}$ are found to be underpredicted by a model incorporating only parton energy loss effects in a quark-gluon plasma medium. Prompt and nonprompt J/$\psi$ meson $v_3$ and prompt $\psi$(2S) $v_2$ and $v_3$ values are also reported for the first time, providing new information about heavy quark interactions in the hot and dense medium created in heavy ion collisions.

The polarization of $\tau$ leptons is measured using leptonic and hadronic $\tau$ lepton decays in Z $\to$$\tau^+\tau^-$ events in proton-proton collisions at $\sqrt{s}$ = 13 TeV recorded by CMS at the CERN LHC with an integrated luminosity of 36.3 fb$^{-1}$. The measured $\tau^-$ polarization at the Z boson mass pole is $\mathcal{P}_{\tau}$(Z) = $-$0.144 $\pm$ 0.006 (stat) $\pm$ 0.014 (syst) = $-$0.144 $\pm$ 0.015, in good agreement with the measurement of the $\tau$ lepton asymmetry parameter of $A_{\tau}$ = 0.1439 $\pm$ 0.0043 = $-\mathcal{P}_{\tau}$(Z) at LEP. The $\tau$ polarization depends on the ratio of the vector to axial-vector couplings of the $\tau$ leptons in the neutral current expression, and thus on the effective weak mixing angle $\sin^{2}\theta_\mathrm{W}^{\text{eff}}$, independently of the Z boson production mechanism. The obtained value $\sin^{2}\theta_\mathrm{W}^{\text{eff}}$ = 0.2319 $\pm$ 0.0008 (stat) $\pm$ 0.0018 (syst) = 0.2319 $\pm$ 0.0019 is in good agreement with measurements at e$^+$e$^-$ colliders.