This paper presents the measurement of fiducial and differential cross sections for both the inclusive and electroweak production of a same-sign $W$-boson pair in association with two jets ($W^\pm W^\pm jj$) using 139 fb$^{-1}$ of proton-proton collision data recorded at a centre-of-mass energy of $\sqrt{s}=13$ TeV by the ATLAS detector at the Large Hadron Collider. The analysis is performed by selecting two same-charge leptons, electron or muon, and at least two jets with large invariant mass and a large rapidity difference. The measured fiducial cross sections for electroweak and inclusive $W^\pm W^\pm jj$ production are $2.92 \pm 0.22\, \text{(stat.)} \pm 0.19\, \text{(syst.)}$ fb and $3.38 \pm 0.22\, \text{(stat.)} \pm 0.19\, \text{(syst.)}$ fb, respectively, in agreement with Standard Model predictions. The measurements are used to constrain anomalous quartic gauge couplings by extracting 95% confidence level intervals on dimension-8 operators. A search for doubly charged Higgs bosons $H^{\pm\pm}$ that are produced in vector-boson fusion processes and decay into a same-sign $W$ boson pair is performed. The largest deviation from the Standard Model occurs for an $H^{\pm\pm}$ mass near 450 GeV, with a global significance of 2.5 standard deviations.

The first evidence for the Higgs boson decay to a $Z$ boson and a photon is presented, with a statistical significance of 3.4 standard deviations. The result is derived from a combined analysis of the searches performed by the ATLAS and CMS Collaborations with proton-proton collision data sets collected at the CERN Large Hadron Collider (LHC) from 2015 to 2018. These correspond to integrated luminosities of around 140 fb$^{-1}$ for each experiment, at a center-of-mass energy of 13 TeV. The measured signal yield is $2.2\pm0.7$ times the Standard Model prediction, and agrees with the theoretical expectation within 1.9 standard deviations.

A search for an exotic decay of the Higgs boson to a Z boson and a light pseudoscalar particle (a), decaying to a pair of leptons and a pair of photons, respectively, is presented. The search is based on proton-proton collision data at a center-of-mass energy of $\sqrt{s}$ = 13 TeV, collected with the CMS detector and corresponding to an integrated luminosity of 138 fb$^{-1}$. The analysis probes pseudoscalar masses $m_\mathrm{a}$ between 1 and 30 GeV, leading to two pairs of well-isolated leptons and photons. Upper limits at 95% confidence level are set on the Higgs boson production cross section times its branching fraction to two leptons and two photons. The observed (expected) limits are in the range of 1.1-17.8 (1.7-17.9) fb within the probed $m_\mathrm{a}$ interval. An excess of data above the expected standard model background with a local (global) significance of 2.6 (1.3) standard deviations is observed for a mass hypothesis of $m_\mathrm{a}$ = 3 GeV. Limits on models involving axion-like particles, formulated as an effective field theory, are also reported.

A search for a new charged particle X with mass between 0.3 and 2.0 TeV decaying to a W boson and a photon is presented, using proton-proton collision data at a center-of-mass energy of 13 TeV, collected by the CMS experiment and corresponding to an integrated luminosity of 138 fb$^{-1}$. Particle X has electric charge $\pm$ 1 and is assumed to have spin 0. The search is performed using the electron and muon decays of the W boson. No significant excess above the predicted background is observed. The upper limit at 95% confidence level on the product of the production cross section of the X and its branching fraction to a W boson and a photon is found to be 94 (137) fb for a 0.3 TeV resonance and 0.75 (0.81) fb for a 2.0 TeV resonance, for an X width-to-mass ratio of 0.01% (5%). This search presents the most stringent constraints to date on the existence of such resonances across the probed mass range. A statistical combination with an earlier study based on the hadronic decay mode of the W boson is also performed, and the upper limit at 95% confidence level for a 2.0 TeV resonance is reduced to 0.50 (0.63) fb for an X width-to-mass ratio of 0.01% (5%).

A search for nonresonant new physics phenomena in high-mass dilepton events produced in association with b-tagged jets is performed using proton-proton collision data collected in 2016$-$2018 by the CMS experiment at the CERN LHC, at a center-of-mass energy of 13 TeV corresponding to an integrated luminosity of 138 fb$^{-1}$. The analysis considers two effective field theory models with dimension-six operators; involving four-fermion contact interactions between two leptons ($\ell\ell$, electrons or muons) and b or s quarks (bb$\ell\ell$ and bs$\ell\ell$). Two lepton flavor combinations (ee and $μμ$) are required and events are classified as having 0, 1, and $\geq$2 b-tagged jets in the final state. No significant excess is observed over the standard model backgrounds. Upper limits are set on the production cross section of the new physics signals. These translate into lower limits on the energy scale $Λ$ of 6.9 to 9.0 TeV in the bb$\ell\ell$ model, depending on model parameters, and on the ratio of energy scale and effective coupling, $Λ/g_*$, of 2.0 to 2.6 TeV in the bs$\ell\ell$ model. The latter represent the most stringent limits on this model to date. Lepton flavor universality is also tested by comparing the dielectron and dimuon mass spectra for different b-tagged jet multiplicities. No significant deviation from the standard model expectation of unity is observed.

A search for dark matter particles produced in association with a Higgs boson decaying into a pair of $\tau$ leptons is performed using data collected in proton-proton collisions at a center-of-mass energy of 13 TeV with the CMS detector. The analysis is based on a data set corresponding to an integrated luminosity of 101 fb$^{-1}$ collected in 2017$-$2018. No significant excess over the expected standard model background is observed. This result is interpreted within the frameworks of the 2HDM+a and baryonic Z$'$ benchmark simplified models. The 2HDM+a model is a type-II two-Higgs-doublet model featuring a heavy pseudoscalar with an additional light pseudoscalar. Upper limits at 95% confidence level are set on the product of the production cross section and the branching fraction for each of these two simplified models. Heavy pseudoscalar boson masses between 400 and 700 GeV are excluded for a light pseudoscalar mass of 100 GeV. For the baryonic Z$'$ model, a statistical combination is made with an earlier search based on a data set of 36 fb$^{-1}$ collected in 2016. In this model, Z$'$ boson masses up to 1050 GeV are excluded for a dark matter particle mass of 1 GeV.

A search for pairs of light neutral pseudoscalar bosons (A) resulting from the decay of a Higgs boson is performed. The search is conducted using LHC proton-proton collision data at $\sqrt{s}$ = 13 TeV, collected with the CMS detector in 2016$-$2018 and corresponding to an integrated luminosity of 138 fb$^{-1}$. The A boson decays into a highly collimated electron-positron pair. A novel multivariate algorithm using tracks and calorimeter information is developed to identify these distinctive signatures, and events are selected with two such merged electron-positron pairs. No significant excess above the standard model background predictions is observed. Upper limits on the branching fraction for H $\to$ AA $\to$ 4e are set at 95% confidence level, for masses between 10 and 100 MeV and proper decay lengths below 100 $μ$m, reaching branching fraction sensitivities as low as 10$^{-5}$. This is the first search for Higgs boson decays to four electrons via light pseudoscalars at the LHC. It significantly improves the experimental sensitivity to axion-like particles with masses below 100 MeV.

A search for pair-production of vector-like leptons is presented, considering their decays into a third-generation Standard Model (SM) quark and a vector leptoquark ($U_1$) as predicted by an ultraviolet-complete extension of the SM, referred to as the '4321' model. Given the assumed decay of $U_1$ into third-generation SM fermions, the final state can contain multiple $τ$-leptons and $b$-quarks. This search is based on a dataset of $pp$ collisions at $\sqrt{s}=13$ TeV recorded with the ATLAS detector during Run 2 of the Large Hadron Collider, corresponding to an integrated luminosity of up to 140 fb$^{-1}$. No significant excess above the SM background prediction is observed, and 95% confidence level limits on the cross-section times branching ratio are derived as a function of the vector-like lepton mass. A lower observed (expected) limit of 910 GeV (970 GeV) is set on the vector-like lepton mass. Additionally, the results are interpreted for a supersymmetric model with an $R$-parity violating coupling to the third-generation quarks and leptons. Lower observed (expected) limits are obtained on the higgsino mass at 880 GeV (940 GeV) and on the wino mass at 1170 GeV (1170 GeV).

A search for a new massive charged gauge boson, $W'$, is performed with the ATLAS detector at the LHC. The dataset used in this analysis was collected from proton-proton collisions at a centre-of-mass energy of $\sqrt{s} =13$ TeV, and corresponds to an integrated luminosity of 139 fb$^{-1}$. The reconstructed $tb$ invariant mass is used to search for a $W'$ boson decaying into a top quark and a bottom quark. The result is interpreted in terms of a $W'$ boson with purely right-handed or left-handed chirality in a mass range of 0.5-6 TeV. Different values for the coupling of the $W'$ boson to the top and bottom quarks are considered, taking into account interference with single-top-quark production in the $s$-channel. No significant deviation from the background prediction is observed. The results are expressed as upper limits on the $W' \rightarrow tb$ production cross-section times branching ratio as a function of the $W'$-boson mass and in the plane of the coupling vs the $W'$-boson mass.

A search is presented for a heavy scalar ($H$) or pseudo-scalar ($A$) predicted by the two-Higgs-doublet models, where the $H/A$ is produced in association with a top-quark pair ($t\bar{t}H/A$), and with the $H/A$ decaying into a $t\bar{t}$ pair. Events are selected requiring exactly one or two opposite-charge electrons or muons. Data-driven corrections are applied to improve the modelling of the $t\bar{t}$+jets background in the regime with high jet and $b$-jet multiplicities. These include a novel multi-dimensional kinematic reweighting based on a neural network trained using data and simulations. An $H/A$-mass parameterised graph neural network is trained to optimise the signal-to-background discrimination. In combination with the previous search performed by the ATLAS Collaboration in the multilepton final state, the observed upper limits on the $t\bar{t}H/A \rightarrow t\bar{t}t\bar{t}$ production cross-section at 95% confidence level range between 14 fb and 5.0 fb for an $H/A$ with mass between 400 GeV and 1000 GeV, respectively. Assuming that both the $H$ and $A$ contribute to the $t\bar{t}t\bar{t}$ cross-section, $\tanβ$ values below 1.7 or 0.7 are excluded for a mass of 400 GeV or 1000 GeV, respectively. The results are also used to constrain a model predicting the pair production of a colour-octet scalar, with the scalar decaying into a $t\bar{t}$ pair.