This paper presents direct searches for lepton flavour violation in Higgs boson decays, $H\rightarrow e\tau$ and $H\rightarrow\mu\tau$, performed using data collected with the ATLAS detector at the LHC. The searches are based on a data sample of proton-proton collisions at a centre-of-mass energy $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. Leptonic ($\tau \rightarrow \ell \nu_\ell \nu_\tau$) and hadronic ($\tau \rightarrow $ hadrons $ \nu_\tau$) decays of the $\tau$-lepton are considered. Two background estimation techniques are employed: the MC-template method, based on data-corrected simulation samples, and the Symmetry method, based on exploiting the symmetry between electrons and muons in the Standard Model backgrounds. No significant excess of events is observed and the results are interpreted as upper limits on lepton-flavour-violating branching ratios of the Higgs boson. The observed (expected) upper limits set on the branching ratios at 95% confidence level, $\mathcal{B}(H\rightarrow e\tau)<0.20\%$ (0.12%) and $\mathcal{B}(H\rightarrow \mu\tau)<0.18\%$ (0.09%), are obtained with the MC-template method from a simultaneous measurement of potential $H \rightarrow e\tau$ and $H \rightarrow\mu\tau$ signals. The best-fit branching ratio difference, $\mathcal{B}(H\rightarrow \mu\tau)- \mathcal{B}(H\rightarrow e\tau)$, measured with the Symmetry method in the channel where the $\tau$-lepton decays to leptons, is (0.25 $\pm$ 0.10)%, compatible with a value of zero within 2.5$\sigma$.

A search for flavour-changing neutral current (FCNC) $tqH$ interactions involving a top quark, another up-type quark ($q=u$, $c$), and a Standard Model (SM) Higgs boson decaying into a $\tau$-lepton pair ($H\rightarrow \tau^+\tau^-$) is presented. The search is based on a dataset of $pp$ collisions at $\sqrt{s}=13$ TeV that corresponds to an integrated luminosity of 139 fb$^{-1}$ recorded with the ATLAS detector at the Large Hadron Collider. Two processes are considered: single top quark FCNC production in association with a Higgs boson ($pp\rightarrow tH$), and top quark pair production in which one of the top quarks decays into $Wb$ and the other decays into $qH$ through the FCNC interactions. The search selects events with two hadronically decaying $\tau$-lepton candidates ($\tau_{\text{had}}$) or at least one $\tau_{\text{had}}$ with an additional lepton ($e$, $\mu$), as well as multiple jets. Event kinematics is used to separate signal from the background through a multivariate discriminant. A slight excess of data is observed with a significance of 2.3$\sigma$ above the expected SM background, and 95% CL upper limits on the $t\to qH$ branching ratios are derived. The observed (expected) 95% CL upper limits set on the $t\to cH$ and $t\to uH$ branching ratios are $9.4 \times 10^{-4}$ $(4.8^{+2.2}_{-1.4}\times 10^{-4})$ and $6.9\times 10^{-4}$ $(3.5^{+1.5}_{-1.0}\times 10^{-4})$, respectively. The corresponding combined observed (expected) upper limits on the dimension-6 operator Wilson coefficients in the effective $tqH$ couplings are $C_{c\phi} <1.35$ $(0.97)$ and $C_{u\phi} <1.16$ $(0.82)$.

A measurement of the four-lepton invariant mass spectrum is made with the ATLAS detector, using an integrated luminosity of 36.1 fb$^{-1}$ of proton-proton collisions at $\sqrt{s}$ = 13 TeV delivered by the Large Hadron Collider. The differential cross-section is measured for events containing two same-flavour opposite-sign lepton pairs. It exhibits a rich structure, with different mass regions dominated in the Standard Model by single $Z$ boson production, Higgs boson production, and $Z$ boson pair production, and non-negligible interference effects at high invariant masses. The measurement is compared with state-of-the-art Standard Model calculations, which are found to be consistent with the data. These calculations are used to interpret the data in terms of $gg\rightarrow ZZ \rightarrow 4\ell$ and $Z \rightarrow 4\ell$ subprocesses, and to place constraints on a possible contribution from physics beyond the Standard Model.

A search for the dimuon decay of the Higgs boson was performed using data corresponding to an integrated luminosity of 36.1 fb$^{-1}$ collected with the ATLAS detector in $pp$ collisions at $\sqrt{s}=13$ TeV at the Large Hadron Collider. No significant excess is observed above the expected background. The observed (expected) upper limit on the cross section times branching ratio is 3.0 (3.1) times the Standard Model prediction at the 95% confidence level for a Higgs boson mass of 125 GeV. When combined with the $pp$ collision data at $\sqrt{s}=7$ TeV and $\sqrt{s}=8$ TeV, the observed (expected) upper limit is 2.8 (2.9) times the Standard Model prediction.

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.

A search for pair production of the supersymmetric partners of the Higgs boson (higgsinos $\tilde{H}$) in gauge-mediated scenarios is reported. Each higgsino is assumed to decay to a Higgs boson and a gravitino. Two complementary analyses, targeting high- and low-mass signals, are performed to maximize sensitivity. The two analyses utilize LHC $pp$ collision data at a center-of-mass energy $\sqrt{s} = 13$ TeV, the former with an integrated luminosity of 36.1 fb$^{-1}$ and the latter with 24.3 fb$^{-1}$, collected with the ATLAS detector in 2015 and 2016. The search is performed in events containing missing transverse momentum and several energetic jets, at least three of which must be identified as $b$-quark jets. No significant excess is found above the predicted background. Limits on the cross-section are set as a function of the mass of the $\tilde{H}$ in simplified models assuming production via mass-degenerate higgsinos decaying to a Higgs boson and a gravitino. Higgsinos with masses between 130 and 230 GeV and between 290 and 880 GeV are excluded at the 95% confidence level. Interpretations of the limits in terms of the branching ratio of the higgsino to a $Z$ boson or a Higgs boson are also presented, and a 45% branching ratio to a Higgs boson is excluded for $m_{\tilde{H}} \approx 400$ GeV.

A measurement of the production processes of the recently discovered Higgs boson is performed in the two-photon final state using 5.4 fb$^{-1}$ of proton-proton collisions data at $\sqrt{s}=7$ TeV and 20.3 fb$^{-1}$ at $\sqrt{s}=8$ TeV collected by the ATLAS detector at the Large Hadron Collider. The number of observed Higgs boson decays to diphotons divided by the corresponding Standard Model prediction, called the signal strength, is found to be $\mu = 1.17 \pm 0.27$ at the value of the Higgs boson mass measured by ATLAS, $m_{H}$ = 125.4 GeV. The analysis is optimized to measure the signal strengths for individual Higgs boson production processes at this value of $m_{H}$. They are found to be $\mu_{\mathrm{ggF}} = 1.32 \pm 0.38$, $\mu_{\mathrm{VBF}} = 0.8 \pm 0.7$, $\mu_{{WH}} = 1.0 \pm 1.6 $, $\mu_{{ZH}} = 0.1 ^{+3.7}_{-0.1} $, $\mu_{{t\bar{t}H}} = 1.6 ^{+2.7}_{-1.8} $, for Higgs boson production through gluon fusion, vector-boson fusion, and in association with a $W$ or $Z$ boson or a top-quark pair, respectively. Compared with the previously published ATLAS analysis, the results reported here also benefit from a new energy calibration procedure for photons and the subsequent reduction of the systematic uncertainty on the diphoton mass resolution. No significant deviations from the predictions of the Standard Model are found.

A low-background inclusive search for new physics in events with same-sign dileptons is presented. The search uses proton-proton collisions corresponding to 20.3 fb$^{-1}$ of integrated luminosity taken in 2012 at a centre-of-mass energy of 8 TeV with the ATLAS detector at the LHC. Pairs of isolated leptons with the same electric charge and large transverse momenta of the type $e^{\pm}e^{\pm}, e^{\pm}\mu^{\pm}$, and $\mu^{\pm}\mu^{\pm}$ are selected and their invariant mass distribution is examined. No excess of events above the expected level of Standard Model background is found. The results are used to set upper limits on the cross-sections for processes beyond the Standard Model. Limits are placed as a function of the dilepton invariant mass within a fiducial region corresponding to the signal event selection criteria. Exclusion limits are also derived for a specific model of doubly charged Higgs boson production.

A search for Higgs boson pair production $pp \to hh$ is performed with 19.5 fb$^{-1}$ of proton--proton collision data at $\sqrt{s}=$ 8 TeV, which were recorded by the ATLAS detector at the Large Hadron Collider in 2012. The decay products of each Higgs boson are reconstructed as a high-momentum $b\bar{b}$ system with either a pair of small-radius jets or a single large-radius jet, the latter exploiting jet substructure techniques and associated $b$-tagged track-jets. No evidence for resonant or non-resonant Higgs boson pair production is observed. The data are interpreted in the context of the Randall--Sundrum model with a warped extra dimension as well as the two-Higgs-doublet model. An upper limit on the cross-section for $pp \to G^{*}_{\mathrm{KK}} \to hh \to b\bar{b} b\bar{b}$ of 3.2 (2.3) fb is set for a Kaluza--Klein graviton $G^{*}_{\mathrm{KK}}$ mass of 1.0 (1.5) TeV, at the 95\% confidence level. The search for non-resonant Standard Model $hh$ production sets an observed 95\% confidence level upper limit on the production cross-section $\sigma(pp \to hh \to b\bar{b}b\bar{b})$ of 202 fb, compared to a SM prediction of $\sigma(pp \to hh \to b\bar{b}b\bar{b}) = 3.6 \pm 0.5$ fb.

A search is presented for the direct pair production of a chargino and a neutralino $pp\to\tilde{\chi}^\pm_1\tilde{\chi}^0_2$, where the chargino decays to the lightest neutralino and the $W$ boson, $\tilde{\chi}^\pm_1 \to \tilde{\chi}^0_1 (W^{\pm}\to\ell^{\pm}\nu)$, while the neutralino decays to the lightest neutralino and the 125 GeV Higgs boson, $\tilde{\chi}^0_2 \to \tilde{\chi}^0_1 (h\to bb/\gamma\gamma/\ell^{\pm}\nu qq)$. The final states considered for the search have large missing transverse momentum, an isolated electron or muon, and one of the following: either two jets identified as originating from bottom quarks, or two photons, or a second electron or muon with the same electric charge. The analysis is based on 20.3 fb$^{-1}$ of $\sqrt{s}=8$ TeV proton-proton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with the Standard Model expectations, and limits are set in the context of a simplified supersymmetric model.