This paper reports searches for heavy resonances decaying into $ZZ$ or $ZW$ using data from proton--proton collisions at a centre-of-mass energy of $\sqrt{s}=13$ TeV. The data, corresponding to an integrated luminosity of 36.1 fb$^{-1}$, were recorded with the ATLAS detector in 2015 and 2016 at the Large Hadron Collider. The searches are performed in final states in which one $Z$ boson decays into either a pair of light charged leptons (electrons and muons) or a pair of neutrinos, and the associated $W$ boson or the other $Z$ boson decays hadronically. No evidence of the production of heavy resonances is observed. Upper bounds on the production cross sections of heavy resonances times their decay branching ratios to $ZZ$ or $ZW$ are derived in the mass range 300--5000 GeV within the context of Standard Model extensions with additional Higgs bosons, a heavy vector triplet or warped extra dimensions. Production through gluon--gluon fusion, Drell--Yan or vector-boson fusion are considered, depending on the assumed model.

A search is presented for the pair production of heavy vector-like $B$ quarks, primarily targeting $B$ quark decays into a $W$ boson and a top quark. The search is based on $36.1$ $fb^{-1}$ of $pp$ collisions at $\sqrt{s}$ = 13 TeV recorded in 2015 and 2016 with the ATLAS detector at the CERN Large Hadron Collider. Data are analysed in the lepton-plus-jets final state, characterised by a high-transverse-momentum isolated electron or muon, large missing transverse momentum, and multiple jets, of which at least one is $b$-tagged. No significant deviation from the Standard Model expectation is observed. The 95% confidence level lower limit on the $B$ mass is 1350 GeV assuming a 100% branching ratio to $Wt$. In the SU(2) singlet scenario, the lower mass limit is 1170 GeV. This search is also sensitive to a heavy vector-like $B$ quark decaying into other final states ($Zb$ and $Hb$) and thus mass limits on $B$ production are set as a function of the decay branching ratios. The 100% branching ratio limits are found to be also applicable to heavy vector-like $X$ production, with charge $+$5/3, that decay into $Wt$.

A measurement of the total $pp$ cross section at the LHC at $\sqrt{s}=8$ TeV is presented. An integrated luminosity of $500$ $\mu$b$^{-1}$ was accumulated in a special run with high-$\beta^{\star}$ beam optics to measure the differential elastic cross section as a function of the Mandelstam momentum transfer variable $t$. The measurement is performed with the ALFA sub-detector of ATLAS. Using a fit to the differential elastic cross section in the $-t$ range from $0.014$ GeV$^2$ to $0.1$ GeV$^2$ to extrapolate $t\rightarrow 0$, the total cross section, $\sigma_{\mathrm{tot}}(pp\rightarrow X)$, is measured via the optical theorem to be: $\sigma_{\mathrm{tot}}(pp\rightarrow X) = {96.07} \; \pm 0.18 \; ({{stat.}}) \pm 0.85 \; ({{exp.}}) \pm 0.31 \; ({extr.}) \; {mb} \;,$ where the first error is statistical, the second accounts for all experimental systematic uncertainties and the last is related to uncertainties in the extrapolation $t\rightarrow 0$. In addition, the slope of the exponential function describing the elastic cross section at small $t$ is determined to be $B = 19.74 \pm 0.05 \; ({{stat.}}) \pm 0.23 \; ({{syst.}}) \; {GeV}^{-2}$.

Ratios of top-quark pair to $Z$-boson cross sections measured from proton--proton collisions at the LHC centre-of-mass energies of $\sqrt s=13$TeV, 8TeV, and 7TeV are presented by the ATLAS Collaboration. Single ratios, at a given $\sqrt s$ for the two processes and at different $\sqrt s$ for each process, as well as double ratios of the two processes at different $\sqrt s$, are evaluated. The ratios are constructed using previously published ATLAS measurements of the $t\overline{t}$ and $Z$-boson production cross sections, corrected to a common phase space where required, and a new analysis of $Z \rightarrow \ell^+ \ell^-$ where $\ell=e,\mu$ at $\sqrt s=13$TeV performed with data collected in 2015 with an integrated luminosity of $3.2$fb$^{-1}$. Correlations of systematic uncertainties are taken into account when evaluating the uncertainties in the ratios. The correlation model is also used to evaluate the combined cross section of the $Z\rightarrow e^+e^-$ and the $Z\rightarrow \mu^+ \mu^-$ channels for each $\sqrt s$ value. The results are compared to calculations performed at next-to-next-to-leading-order accuracy using recent sets of parton distribution functions. The data demonstrate significant power to constrain the gluon distribution function for the Bjorken-$x$ values near 0.1 and the light-quark sea for $x<0.02$.

A search for physics beyond the Standard Model, in final states with at least one high transverse momentum charged lepton (electron or muon) and two additional high transverse momentum leptons or jets, is performed using 3.2 fb$^{-1}$ of proton--proton collision data recorded by the ATLAS detector at the Large Hadron Collider in 2015 at $\sqrt{s}=13$ TeV. The upper end of the distribution of the scalar sum of the transverse momenta of leptons and jets is sensitive to the production of high-mass objects. No excess of events beyond Standard Model predictions is observed. Exclusion limits are set for models of microscopic black holes with two to six extra dimensions.

The results of a search for vector-like top quarks using events with exactly one lepton, at least four jets, and large missing transverse momentum are reported. The search is optimised for pair production of vector-like top quarks in the $Z(\rightarrow \! \! \nu \nu) \, t + X$ decay channel. LHC pp collision data at a centre-of-mass energy of $\sqrt{s}=13$ TeV recorded by the ATLAS detector in 2015 and 2016 are used, corresponding to an integrated luminosity of 36.1 $\mathrm{fb}^{-1}$. No significant excess over the Standard Model expectation is seen and upper limits on the production cross-section of a vector-like $T$ quark pair as a function of the $T$ quark mass are derived. The observed (expected) 95% CL lower limits on the $T$ mass are 870 GeV (890 GeV) for the weak-isospin singlet model, 1.05 TeV (1.06 TeV) for the weak-isospin doublet model and 1.16 TeV (1.17 TeV) for the pure $Zt$ decay mode. Limits are also set on the mass as a function of the decay branching ratios, excluding large parts of the parameter space for masses below 1 TeV.

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.

The production of a $Z$ boson and a photon in association with a high-mass dijet system is studied using 20.2fb$^{-1}$ of proton-proton collision data at a centre-of-mass energy of $\sqrt{s}$ = 8 TeV recorded with the ATLAS detector in 2012 at the Large Hadron Collider. Final states with a photon and a Z boson decaying into a pair of either electrons, muons, or neutrinos are analysed. Electroweak and total $pp \to Z\gamma j j$ cross-sections are extracted in two fiducial regions with different sensitivities to electroweak production processes. Quartic couplings of vector bosons are studied in regions of phase space with an enhanced contribution from pure electroweak production, sensitive to vector-boson scattering processes $VV \to Z\gamma$. No deviations from Standard Model predictions are observed and constraints are placed on anomalous couplings parameterized by higher-dimensional operators using effective field theory.

A search for heavy neutral Higgs bosons and $Z^{\prime}$ bosons is performed using a data sample corresponding to an integrated luminosity of 36.1 fb$^{-1}$ from proton-proton collisions at $\sqrt{s}$ = 13 TeV recorded by the ATLAS detector at the LHC during 2015 and 2016. The heavy resonance is assumed to decay to $\tau^+\tau^-$ with at least one tau lepton decaying to final states with hadrons and a neutrino. The search is performed in the mass range of 0.2-2.25 TeV for Higgs bosons and 0.2-4.0 TeV for $Z^{\prime}$ bosons. The data are in good agreement with the background predicted by the Standard Model. The results are interpreted in benchmark scenarios. In the context of the hMSSM scenario, the data exclude $\tan\beta > 1.0$ for $m_A$ = 0.25 TeV and $\tan\beta > 42$ for $m_A$ = 1.5 TeV at the 95% confidence level. For the Sequential Standard Model, $Z^{\prime}_\mathrm{SSM}$ with $m_{Z^{\prime}} < 2.42$ TeV is excluded at 95% confidence level, while $Z^{\prime}_\mathrm{NU}$ with $m_{Z^{\prime}} < 2.25$ TeV is excluded for the non-universal $G(221)$ model that exhibits enhanced couplings to third-generation fermions.

A search is performed for new phenomena in events having a photon with high transverse momentum and a jet collected in 36.7 fb$^{-1}$ of proton-proton collisions at a centre-of-mass energy of $\sqrt{s}$ = 13 TeV recorded with the ATLAS detector at the Large Hadron Collider. The invariant mass distribution of the leading photon and jet is examined to look for the resonant production of new particles or the presence of new high-mass states beyond the Standard Model. No significant deviation from the background-only hypothesis is observed and cross-section limits for generic Gaussian-shaped resonances are extracted. Excited quarks hypothesized in quark compositeness models and high-mass states predicted in quantum black hole models with extra dimensions are also examined in the analysis. The observed data exclude, at 95% confidence level, the mass range below 5.3 TeV for excited quarks and 7.1 TeV (4.4 TeV) for quantum black holes in the Arkani-Hamed-Dimopoulos-Dvali (Randall-Sundrum) model with six (one) extra dimensions.