The production of dark matter in association with Higgs bosons is predicted in several extensions of the Standard Model. An exploration of such scenarios is presented, considering final states with missing transverse momentum and $b$-tagged jets consistent with a Higgs boson. The analysis uses proton-proton collision data at a centre-of-mass energy of 13 TeV recorded by the ATLAS experiment at the LHC during Run 2, amounting to an integrated luminosity of 139 fb$^{-1}$. The analysis, when compared with previous searches, benefits from a larger dataset, but also has further improvements providing sensitivity to a wider spectrum of signal scenarios. These improvements include both an optimised event selection and advances in the object identification, such as the use of the likelihood-based significance of the missing transverse momentum and variable-radius track-jets. No significant deviation from Standard Model expectations is observed. Limits are set, at 95% confidence level, in two benchmark models with two Higgs doublets extended by either a heavy vector boson $Z'$ or a pseudoscalar singlet $a$ and which both provide a dark matter candidate $\chi$. In the case of the two-Higgs-doublet model with an additional vector boson $Z'$, the observed limits extend up to a $Z'$ mass of 3 TeV for a mass of 100 GeV for the dark matter candidate. The two-Higgs-doublet model with a dark matter particle mass of 10 GeV and an additional pseudoscalar $a$ is excluded for masses of the $a$ up to 520 GeV and 240 GeV for $\tan \beta = 1$ and $\tan \beta = 10$ respectively. Limits on the visible cross-sections are set and range from 0.05 fb to 3.26 fb, depending on the missing transverse momentum and $b$-quark jet multiplicity requirements.

A search for lepton-flavor-violating $Z\to e\tau$ and $Z\to\mu\tau$ decays with $pp$ collision data recorded by the ATLAS detector at the LHC is presented. This analysis uses 139 fb$^{-1}$ of Run 2 $pp$ collisions at $\sqrt{s}=13$ TeV and is combined with the results of a similar ATLAS search in the final state in which the $\tau$-lepton decays hadronically, using the same data set as well as Run 1 data. The addition of leptonically decaying $\tau$-leptons significantly improves the sensitivity reach for $Z\to\ell\tau$ decays. The $Z\to\ell\tau$ branching fractions are constrained in this analysis to $\mathcal{B}(Z\to e\tau)<7.0\times10^{-6}$ and $\mathcal{B}(Z\to \mu\tau)<7.2\times10^{-6}$ at 95% confidence level. The combination with the previously published analyses sets the strongest constraints to date: $\mathcal{B}(Z\to e\tau)<5.0\times10^{-6}$ and $\mathcal{B}(Z\to \mu\tau)<6.5\times10^{-6}$ at 95% confidence level.

A novel search for exotic decays of the Higgs boson into pairs of long-lived neutral particles, each decaying into a bottom quark pair, is performed using 139 fb$^{-1}$ of $\sqrt{s} = 13$ TeV proton-proton collision data collected with the ATLAS detector at the LHC. Events consistent with the production of a Higgs boson in association with a leptonically decaying $Z$ boson are analysed. Long-lived particle (LLP) decays are reconstructed from inner-detector tracks as displaced vertices with high mass and track multiplicity relative to Standard Model processes. The analysis selection requires the presence of at least two displaced vertices, effectively suppressing Standard Model backgrounds. The residual background contribution is estimated using a data-driven technique. No excess over Standard Model predictions is observed, and upper limits are set on the branching ratio of the Higgs boson to LLPs. Branching ratios above 10% are excluded at 95% confidence level for LLP mean proper lifetimes $c\tau$ as small as 4 mm and as large as 100 mm. For LLP masses below 40 GeV, these results represent the most stringent constraint in this lifetime regime.

Searches for new resonances in the diphoton final state, with spin 0 as predicted by theories with an extended Higgs sector and with spin 2 using a warped extra-dimension benchmark model, are presented using 139 fb$^{-1}$ of $\sqrt{s} = $ 13 TeV $pp$ collision data collected by the ATLAS experiment at the LHC. No significant deviation from the Standard Model is observed and upper limits are placed on the production cross-section times branching ratio to two photons as a function of the resonance mass.

A search for the pair production of heavy leptons as predicted by the type-III seesaw mechanism is presented. The search uses proton-proton collision data at a centre-of-mass energy of 13 TeV, corresponding to 139 fb$^{-1}$ of integrated luminosity recorded by the ATLAS detector during Run 2 of the Large Hadron Collider. The analysis focuses on final states with three or four electrons or muons from the possible decays of new heavy leptons via intermediate electroweak bosons. No significant deviations above the Standard Model expectation are observed; upper and lower limits on the heavy lepton production cross-section and masses are derived respectively. These results are then combined for the first time with the ones already published by ATLAS using the channel with two leptons in the final state. The observed lower limit on the mass of the type-III seesaw heavy leptons combining two, three and four lepton channels together is 910 GeV at the 95% confidence level.

A search optimized for new heavy particles decaying to two $b$-quarks and produced in association with additional $b$-quarks is reported. The sensitivity is improved by $b$-tagging at least one lower-$p_{\rm{T}}$ jet in addition to the two highest-$p_{\rm{T}}$ jets. The data used in this search correspond to an integrated luminosity of 103 $\text{fb}^{-1}$ collected with a dedicated trijet trigger during the 2017 and 2018 $\sqrt{s} = 13$ TeV proton-proton collision runs with the ATLAS detector at the LHC. The search looks for resonant peaks in the $b$-tagged dijet invariant mass spectrum over a smoothly falling background. The background is estimated with an innovative data-driven method based on orthonormal functions. The observed $b$-tagged dijet invariant mass spectrum is compatible with the background-only hypothesis. Upper limits at 95% confidence level on a heavy vector-boson production cross section times branching ratio to a pair of $b$-quarks are derived.

This paper reports constraints on Higgs boson production with transverse momentum above 1 TeV. The analyzed data from proton-proton collisions at a center-of-mass energy of 13 TeV were recorded with the ATLAS detector at the Large Hadron Collider from 2015 to 2018 and correspond to an integrated luminosity of 136 fb$^{-1}$. Higgs bosons decaying into $b\bar{b}$ are reconstructed as single large-radius jets recoiling against a hadronic system and identified by the experimental signature of two $b$-hadron decays. The experimental techniques are validated in the same kinematic regime using the $Z\rightarrow b\bar{b}$ process.The 95$\% $ confidence-level upper limit on the cross section for Higgs boson production with transverse momentum above 450 GeV is 115 fb, and above 1 TeV it is 9.6 fb. The Standard Model cross section predictions for a Higgs boson with a mass of 125 GeV in the same kinematic regions are 18.4 fb and 0.13 fb, respectively.

A search for heavy resonances decaying into a pair of $Z$ bosons leading to $\ell^+\ell^-\ell'^+\ell'^-$ and $\ell^+\ell^-\nu\bar\nu$ final states, where $\ell$ stands for either an electron or a muon, is presented. The search uses proton-proton collision data at a centre-of-mass energy of 13 TeV collected from 2015 to 2018 that corresponds to the full integrated luminosity of 139 fb$^{-1}$ recorded by the ATLAS detector during Run 2 of the Large Hadron Collider. Different mass ranges spanning 200 GeV to 2000 GeV for the hypothetical resonances are considered, depending on the final state and model. In the absence of a significant observed excess, the results are interpreted as upper limits on the production cross section of a spin-0 or spin-2 resonance. The upper limits for the spin-0 resonance are translated to exclusion contours in the context of Type-I and Type-II two-Higgs-doublet models, and the limits for the spin-2 resonance are used to constrain the Randall--Sundrum model with an extra dimension giving rise to spin-2 graviton excitations.

A search is presented for the production of the Standard Model Higgs boson in association with a high-energy photon. With a focus on the vector-boson fusion process and the dominant Higgs boson decay into $b$-quark pairs, the search benefits from a large reduction of multijet background compared to more inclusive searches. Results are reported from the analysis of 132 fb$^{-1}$ of $pp$ collision data at $\sqrt{s}$=13 TeV collected with the ATLAS detector at the LHC. The measured Higgs boson signal yield in this final-state signature is $1.3 \pm 1.0$ times the Standard Model prediction. The observed significance of the Higgs boson signal above the background is 1.3 standard deviations, compared to an expected significance of 1.0 standard deviations.

A study of $B_c^+\to J/\psi D_s^+$ and $B_c^+\to J/\psi D_s^{*+}$ decays using 139 fb$^{-1}$ of integrated luminosity collected with the ATLAS detector from $\sqrt{s} = 13$ TeV $pp$ collisions at the LHC is presented. The ratios of the branching fractions of the two decays to the branching fraction of the $B_c^+\to J/\psi \pi^+$ decay are measured: $\mathcal B(B_c^+\to J/\psi D_s^+)/\mathcal B(B_c^+\to J/\psi \pi^+) = 2.76\pm 0.47$ and $\mathcal B(B_c^+\to J/\psi D_s^{*+})/\mathcal B(B_c^+\to J/\psi \pi^+) = 5.33\pm 0.96$. The ratio of the branching fractions of the two decays is found to be $\mathcal B(B_c^+\to J/\psi D_s^{*+})/\mathcal B(B_c^+\to J/\psi D_s^+) = 1.93\pm0.26$. For the $B_c^+\to J/\psi D_s^{*+}$ decay, the transverse polarization fraction, $\Gamma_{\pm\pm}/\Gamma$, is measured to be $0.70\pm0.11$. The reported uncertainties include both the statistical and systematic components added in quadrature. The precision of the measurements exceeds that in all previous studies of these decays. These results supersede those obtained in the earlier ATLAS study of the same decays with $\sqrt{s} = 7$ and 8 TeV $pp$ collision data. A comparison with available theoretical predictions for the measured quantities is presented.