A search for a new $Z'$ gauge boson predicted by $L_{\mu}-L_{\tau}$ models, based on charged-current Drell-Yan production, $pp \rightarrow W^{\pm(*)} \rightarrow Z' \mu^{\pm} \nu \rightarrow \mu^{\pm}\mu^{\mp}\mu^{\pm}\nu$, is presented. The data sample used corresponds to an integrated luminosity of 140 fb$^{-1}$ of proton-proton collisions at $\sqrt{s} = 13$ TeV recorded by the ATLAS detector at the Large Hadron Collider. The search examines a final state of $3\mu$ plus large missing transverse momentum. Upper limits are set on the $Z'$ production cross-section times branching ratio in the mass range of 5-81 GeV. After combining with the previous $Z'$ search using the neutral-current Drell-Yan production with a $4\mu$ final state, the most stringent exclusion limits to date are achieved in the parameter space of the $Z'$ coupling strength and mass.

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 heavy right-handed Majorana or Dirac neutrinos $N_{\mathrm{R}}$ and heavy right-handed gauge bosons $W_{\mathrm{R}}$ is performed in events with energetic electrons or muons, with the same or opposite electric charge, and energetic jets. The search is carried out separately for topologies of clearly separated final-state products (``resolved'' channel) and topologies with boosted final states with hadronic and/or leptonic products partially overlapping and reconstructed as a large-radius jet (``boosted'' channel). The events are selected from $pp$ collision data at the LHC with an integrated luminosity of 139 fb$^{-1}$ collected by the ATLAS detector at $\sqrt{s}$ = 13 TeV. No significant deviations from the Standard Model predictions are observed. The results are interpreted within the theoretical framework of a left-right symmetric model, and lower limits are set on masses in the heavy right-handed $W_{\mathrm{R}}$ boson and $N_{\mathrm{R}}$ plane. The excluded region extends to about $m(W_{\mathrm{R}}) = 6.4$ TeV for both Majorana and Dirac $N_{\mathrm{R}}$ neutrinos at $m(N_{\mathrm{R}})<1$ TeV. $N_{\mathrm{R}}$ with masses of less than 3.5 (3.6) TeV are excluded in the electron (muon) channel at $m(W_{\mathrm{R}})=4.8$ TeV for the Majorana neutrinos, and limits of $m(N_{\mathrm{R}})$ up to 3.6 TeV for $m(W_{\mathrm{R}}) = 5.2$ (5.0) TeV in the electron (muon) channel are set for the Dirac neutrinos. These constitute the most stringent exclusion limits to date for the model considered.

Searches for the exclusive decays of the Higgs boson into $D^*\gamma$ and of the $Z$ boson into $D^0\gamma$ and $K^0_s\gamma$ can probe flavour-violating Higgs and $Z$ boson couplings to light quarks. Searches for these decays are performed with a $pp$ collision data sample corresponding to an integrated luminosity of $136.3$ fb$^{-1}$ collected at $\sqrt{s}=13$ TeV between 2016-2018 with the ATLAS detector at the CERN Large Hadron Collider. In the $D^*\gamma$ and $D^0\gamma$ channels, the observed (expected) 95$\%$ confidence-level upper limits on the respective branching fractions are ${\cal B}(H\rightarrow D^*\gamma)< 1.0 (1.2)\times 10^{-3}$, ${\cal B}(Z\rightarrow D^0\gamma)< 4.0 (3.4)\times 10^{-6}$, while the corresponding results in the $K^0_s\gamma$ channel are ${\cal B}(Z\rightarrow K^0_s\gamma)< 3.1 (3.0)\times 10^{-6}$.

A search for nonresonant Higgs boson pair production in the $b\bar{b}\gamma\gamma$ final state is performed using 140 fb$^{-1}$ of proton-proton collisions at a centre-of-mass energy of 13 TeV recorded by the ATLAS detector at the CERN Large Hadron Collider. This analysis supersedes and expands upon the previous nonresonant ATLAS results in this final state based on the same data sample. The analysis strategy is optimised to probe anomalous values not only of the Higgs ($H$) boson self-coupling modifier $\kappa_\lambda$ but also of the quartic $HHVV$ ($V=W,Z$) coupling modifier $\kappa_{2V}$. No significant excess above the expected background from Standard Model processes is observed. An observed upper limit $\mu_{HH}<4.0$ is set at 95% confidence level on the Higgs boson pair production cross-section normalised to its Standard Model prediction. The 95% confidence intervals for the coupling modifiers are $-1.4<\kappa_\lambda<6.9$ and $-0.5<\kappa_{2V}<2.7$, assuming all other Higgs boson couplings except the one under study are fixed to the Standard Model predictions. The results are interpreted in the Standard Model effective field theory and Higgs effective field theory frameworks in terms of constraints on the couplings of anomalous Higgs boson (self-)interactions.

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.

A search is presented for a third-generation leptoquark (LQ) coupled exclusively to a $\tau$ lepton and a b quark. The search is based on proton-proton collision data at a center-of-mass energy of 13 TeV recorded with the CMS detector, corresponding to an integrated luminosity of 138 fb$^{-1}$. Events with $\tau$ leptons and a varying number of jets originating from b quarks are considered, targeting the single and pair production of LQs, as well as nonresonant $t$-channel LQ exchange. An excess is observed in the data with respect to the background expectation in the combined analysis of all search regions. For a benchmark LQ mass of 2 TeV and an LQ-b-$\tau$ coupling strength of 2.5, the excess reaches a local significance of up to 2.8 standard deviations. Upper limits at the 95% confidence level are placed on the LQ production cross section in the LQ mass range 0.5-2.3 TeV, and up to 3 TeV for $t$-channel LQ exchange. Leptoquarks are excluded below masses of 1.22-1.88 TeV for different LQ models and varying coupling strengths up to 2.5. The study of nonresonant $\tau\tau$ production through $t$-channel LQ exchange allows lower limits on the LQ mass of up to 2.3 TeV to be obtained.

A search is presented for flavour-changing neutral-current interactions involving the top quark, the Higgs boson and an up-type quark ($q=u,c$) with the ATLAS detector at the Large Hadron Collider. The analysis considers leptonic decays of the top quark along with Higgs boson decays into two $W$ bosons, two $Z$ bosons or a $\tau^{+}\tau^{-}$ pair. It focuses on final states containing either two leptons (electrons or muons) of the same charge or three leptons. The considered processes are $t\bar{t}$ and $Ht$ production. For the $t\bar{t}$ production, one top quark decays via $t\to Hq$. The proton-proton collision data set analysed amounts to 140 fb$^{-1}$ at $\sqrt{s}=13$ TeV. No significant excess beyond Standard Model expectations is observed and upper limits are set on the $t\to Hq$ branching ratios at 95% confidence level, amounting to observed (expected) limits of $\mathcal{B}(t\to Hu)<2.8\,(3.0) \times 10^{-4}$ and $\mathcal{B}(t\to Hc)<3.3\,(3.8) \times 10^{-4}$. Combining this search with other searches for $tHq$ flavour-changing neutral-current interactions previously conducted by ATLAS, considering $H\to b\bar{b}$ and $H\to\gamma\gamma$ decays, as well as $H\to\tau^{+}\tau^{-}$ decays with one or two hadronically decaying $\tau$-leptons, yields observed (expected) upper limits on the branching ratios of $\mathcal{B}(t\to Hu)<2.6\,(1.8) \times 10^{-4}$ and $\mathcal{B}(t\to Hc)<3.4\,(2.3) \times 10^{-4}$.

A search is reported for excited $\tau$-leptons and leptoquarks in events with two hadronically decaying $\tau$-leptons and two or more jets. The search uses proton-proton (pp) collision data at $\sqrt{s} = 13$ TeV recorded by the ATLAS experiment during the Run 2 of the Large Hadron Collider in 2015-2018. The total integrated luminosity is 139 fb$^{-1}$. The excited $\tau$-lepton is assumed to be produced and to decay via a four-fermion contact interaction into an ordinary $\tau$-lepton and a quark-antiquark pair. The leptoquarks are assumed to be produced in pairs via the strong interaction, and each leptoquark is assumed to couple to a charm or lighter quark and a $\tau$-lepton. No excess over the background prediction is observed. Excited $\tau$-leptons with masses below 2.8 TeV are excluded at 95% CL in scenarios with the contact interaction scale $\Lambda$ set to 10 TeV. At the extreme limit of model validity where $\Lambda$ is set equal to the excited $\tau$-lepton mass, excited $\tau$-leptons with masses below 4.6 TeV are excluded. Leptoquarks with masses below 1.3 TeV are excluded at 95% CL if their branching ratio to a charm quark and a $\tau$-lepton equals 1. The analysis does not exploit flavour-tagging in the signal region.

A search is reported for long-lived dark photons with masses between 0.1 GeV and 15 GeV, from exotic decays of Higgs bosons produced via vector-boson-fusion. Events that contain displaced collimated Standard Model fermions reconstructed in the calorimeter or muon spectrometer are probed. This search uses the full LHC Run 2 (2015-2018) data sample collected in proton-proton collisions at $\sqrt{s}=13$ TeV, corresponding to an integrated luminosity of 139 $fb^{-1}$. Dominant backgrounds from Standard Model processes and non-collision sources are estimated by using data-driven techniques. The observed event yields in the signal regions are consistent with the expected background. Upper limits on the Higgs boson to dark photon branching fraction are reported as a function of the dark-photon mean proper decay length or of the dark-photon mass and the coupling between the Standard Model and the potential dark sector. This search is combined with previous ATLAS searches obtained in the gluon-gluon fusion and \textit{WH} production modes. A branching fraction above 10% is excluded at 95% CL for a 125 GeV Higgs boson decaying into two dark photons for dark-photon mean proper decay lengths between 173 and 1296 mm and mass of 10 GeV.