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 Higgs boson decaying into a photon and a pair of electrons or muons with an invariant mass $m_{\ell\ell} < 30$ GeV is presented. The analysis is performed using 139 fb$^{-1}$ of proton-proton collision data, produced by the LHC at a centre-of-mass energy of 13 TeV and collected by the ATLAS experiment. Evidence for the $H \rightarrow \ell \ell \gamma$ process is found with a significance of 3.2$\sigma$ over the background-only hypothesis, compared to an expected significance of 2.1$\sigma$. The best-fit value of the signal strength parameter, defined as the ratio of the observed signal yield to the one expected in the Standard Model, is $\mu = 1.5 \pm 0.5$. The Higgs boson production cross-section times the $H \rightarrow\ell\ell\gamma$ branching ratio for $m_{\ell\ell} <$ 30 GeV is determined to be 8.7 $^{+2.8}_{-2.7}$ fb.

This Letter presents direct searches for lepton flavour violation in Higgs boson decays, $H\rightarrow e\tau$ and $H\rightarrow\mu\tau$, performed 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 $36.1\,\mathrm{fb}^{-1}$. No significant excess is observed above the expected background from Standard Model processes. The observed (median expected) 95 % confidence-level upper limits on the lepton-flavour-violating branching ratios are $0.47\%$ ($0.34^{+0.13}_{-0.10}\,\%$) and $0.28\%$ ($0.37^{+0.14}_{-0.10}\,\%$) for $H\to e\tau$ and $H\to\mu\tau$, respectively.

A search for heavy neutral Higgs bosons is performed using the LHC Run 2 data, corresponding to an integrated luminosity of 139 fb$^{-1}$ of proton-proton collisions at $\sqrt{s}=13$ TeV recorded with the ATLAS detector. The search for heavy resonances is performed over the mass range 0.2-2.5 TeV for the $\tau^+\tau^-$ decay with at least one $\tau$-lepton decaying into final states with hadrons. The data are in good agreement with the background prediction of the Standard Model. In the $M_{h}^{125}$ scenario of the Minimal Supersymmetric Standard Model, values of $\tan\beta>8$ and $\tan\beta>21$ are excluded at the 95% confidence level for neutral Higgs boson masses of 1.0 TeV and 1.5 TeV, respectively, where $\tan\beta$ is the ratio of the vacuum expectation values of the two Higgs doublets.

Measurements of the production cross-sections of the Standard Model (SM) Higgs boson ($H$) decaying into a pair of $\tau$-leptons are presented. The measurements use data collected with the ATLAS detector from $pp$ collisions produced at the Large Hadron Collider at a centre-of-mass energy of $\sqrt{s}=13\,\text{TeV}$, corresponding to an integrated luminosity of $139\,\text{fb}^{-1}$. Leptonic ($\tau\to\ell\nu_{\ell}\nu_{\tau}$) and hadronic ($\tau\to\text{hadrons}~\nu_{\tau}$) decays of the $\tau$-lepton are considered. All measurements account for the branching ratio of $H\to\tau\tau$ and are performed with a requirement $|y_H|<2.5$, where $y_H$ is the true Higgs boson rapidity. The cross-section of the $pp\to H\to\tau\tau$ process is measured to be $2.94 \pm 0.21 \text{(stat)} ^{+\,0.37}_{-\,0.32} \text{(syst)}$ pb, in agreement with the SM prediction of $3.17\pm0.09~ \mbox{pb}$. Inclusive cross-sections are determined separately for the four dominant production modes: $2.65 \pm 0.41 \text{(stat)} ^{+\,0.91}_{-\,0.67} \text{(syst)}$ pb for gluon$-$gluon fusion, $0.197 \pm 0.028 \text{(stat)} ^{+\,0.032}_{-\,0.026} \text{(syst)}$ pb for vector-boson fusion, $0.115 \pm 0.058 \text{(stat)} ^{+\,0.042}_{-\,0.040} \text{(syst)}$ pb for vector-boson associated production, and $0.033 \pm 0.031 \text{(stat)} ^{+\,0.022}_{-\,0.017} \text{(syst)}$ pb for top-quark pair associated production. Measurements in exclusive regions of the phase space, using the simplified template cross-section framework, are also performed. All results are in agreement with the SM predictions.

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 search for the $Z\gamma$ decay of the Higgs boson, with $Z$ boson decays into pairs of electrons or muons is presented. The analysis uses proton$-$proton collision data at $\sqrt{s}$ = 13 TeV corresponding to an integrated luminosity of 139 fb$^{-1}$ recorded by the ATLAS detector at the Large Hadron Collider. The observed data are consistent with the expected background with a $p$-value of 1.3%. An upper limit at 95% confidence level on the production cross-section times the branching ratio for $pp\to H\to Z\gamma$ is set at 3.6 times the Standard Model prediction while 2.6 times is expected in the presence of the Standard Model Higgs boson. The best-fit value for the signal yield normalised to the Standard Model prediction is $2.0^{+1.0}_{-0.9}$ where the statistical component of the uncertainty is dominant.

Measurements of the Standard Model Higgs boson decaying into a $b\bar{b}$ pair and produced in association with a $W$ or $Z$ boson decaying into leptons, using proton-proton collision data collected between 2015 and 2018 by the ATLAS detector, are presented. The measurements use collisions produced by the Large Hadron Collider at a centre-of-mass energy of $\sqrt{s} = $13 TeV, corresponding to an integrated luminosity of 139 fb$^{-1}$. The production of a Higgs boson in association with a $W$ or $Z$ boson is established with observed (expected) significances of 4.0 (4.1) and 5.3 (5.1) standard deviations, respectively. Cross-sections of associated production of a Higgs boson decaying into bottom quark pairs with an electroweak gauge boson, $W$ or $Z$, decaying into leptons are measured as a function of the gauge boson transverse momentum in kinematic fiducial volumes. The cross-section measurements are all consistent with the Standard Model expectations, and the total uncertainties vary from 30% in the high gauge boson transverse momentum regions to 85% in the low regions. Limits are subsequently set on the parameters of an effective Lagrangian sensitive to modifications of the $WH$ and $ZH$ processes as well as the Higgs boson decay into $b\bar{b}$.

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 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 $C_{u\phi} <1.16$ $(0.82)$.