Measurements of $ZZ$ production in the $\ell^{+}\ell^{-}\ell^{\prime +}\ell^{\prime -}$ channel in proton-proton collisions at 13 TeV center-of-mass energy at the Large Hadron Collider are presented. The data correspond to 36.1 $\mathrm{fb}^{-1}$ of collisions collected by the ATLAS experiment in 2015 and 2016. Here $\ell$ and $\ell'$ stand for electrons or muons. Integrated and differential $ZZ \to \ell^{+}\ell^{-}\ell^{\prime +}\ell^{\prime -}$ cross sections with $Z \to \ell^+\ell^-$ candidate masses in the range of 66 GeV to 116 GeV are measured in a fiducial phase space corresponding to the detector acceptance and corrected for detector effects. The differential cross sections are presented in bins of twenty observables, including several that describe the jet activity. The integrated cross section is also extrapolated to a total phase space and to all Standard-Model decays of $Z$ bosons with mass between 66 GeV and 116 GeV, resulting in a value of $17.3 \pm 0.9$ [$\pm 0.6$ (stat.) $\pm 0.5$ (syst.) $\pm 0.6$ (lumi.)] pb. The measurements are found to be in good agreement with the Standard-Model predictions. A search for neutral triple gauge couplings is performed using the transverse momentum distribution of the leading $Z$-boson candidate. No evidence for such couplings is found and exclusion limits are set on their parameters.

Jet substructure quantities are measured using jets groomed with the soft-drop grooming procedure in dijet events from 32.9 fb$^{-1}$ of $pp$ collisions collected with the ATLAS detector at $\sqrt{s} = 13$ TeV. These observables are sensitive to a wide range of QCD phenomena. Some observables, such as the jet mass and opening angle between the two subjets which pass the soft-drop condition, can be described by a high-order (resummed) series in the strong coupling constant $\alpha_S$. Other observables, such as the momentum sharing between the two subjets, are nearly independent of $\alpha_S$. These observables can be constructed using all interacting particles or using only charged particles reconstructed in the inner tracking detectors. Track-based versions of these observables are not collinear safe, but are measured more precisely, and universal non-perturbative functions can absorb the collinear singularities. The unfolded data are directly compared with QCD calculations and hadron-level Monte Carlo simulations. The measurements are performed in different pseudorapidity regions, which are then used to extract quark and gluon jet shapes using the predicted quark and gluon fractions in each region. All of the parton shower and analytical calculations provide an excellent description of the data in most regions of phase space.

Jet substructure observables have significantly extended the search program for physics beyond the Standard Model at the Large Hadron Collider. The state-of-the-art tools have been motivated by theoretical calculations, but there has never been a direct comparison between data and calculations of jet substructure observables that are accurate beyond leading-logarithm approximation. Such observables are significant not only for probing the collinear regime of QCD that is largely unexplored at a hadron collider, but also for improving the understanding of jet substructure properties that are used in many studies at the Large Hadron Collider. This Letter documents a measurement of the first jet substructure quantity at a hadron collider to be calculated at next-to-next-to-leading-logarithm accuracy. The normalized, differential cross-section is measured as a function of log$_{10}\rho^2$, where $\rho$ is the ratio of the soft-drop mass to the ungroomed jet transverse momentum. This quantity is measured in dijet events from 32.9 fb$^{-1}$ of $\sqrt{s} = 13$ TeV proton-proton collisions recorded by the ATLAS detector. The data are unfolded to correct for detector effects and compared to precise QCD calculations and leading-logarithm particle-level Monte Carlo simulations.

Measurements of distributions of charged particles produced in proton-proton collisions with a centre-of-mass energy of 13 TeV are presented. The data were recorded by the ATLAS detector at the LHC and correspond to an integrated luminosity of 151 $\mu$b$^{-1}$. The particles are required to have a transverse momentum greater than 100 MeV and an absolute pseudorapidity less than 2.5. The charged-particle multiplicity, its dependence on transverse momentum and pseudorapidity and the dependence of the mean transverse momentum on multiplicity are measured in events containing at least two charged particles satisfying the above kinematic criteria. The results are corrected for detector effects and compared to the predictions from several Monte Carlo event generators.

Charged-particle distributions are measured in proton-proton collisions at a centre-of-mass energy of 13 TeV, using a data sample of nearly 9 million events, corresponding to an integrated luminosity of 170 $\mu$b$^{-1}$, recorded by the ATLAS detector during a special Large Hadron Collider fill. The charged-particle multiplicity, its dependence on transverse momentum and pseudorapidity and the dependence of the mean transverse momentum on the charged-particle multiplicity are presented. The measurements are performed with charged particles with transverse momentum greater than 500 MeV and absolute pseudorapidity less than 2.5, in events with at least one charged particle satisfying these kinematic requirements. Additional measurements in a reduced phase space with absolute pseudorapidity less than 0.8 are also presented, in order to compare with other experiments. The results are corrected for detector effects, presented as particle-level distributions and are compared to the predictions of various Monte Carlo event generators.

Cross-section measurements for a $Z$ boson produced in association with high-transverse-momentum jets ($p_{\mathrm{T}} \geq 100$ GeV) and decaying into a charged-lepton pair ($e^+e^-,\mu^+\mu^-$) are presented. The measurements are performed using proton-proton collisions at $\sqrt{s}=13$ TeV corresponding to an integrated luminosity of $139$ fb$^{-1}$ collected by the ATLAS experiment at the LHC. Measurements of angular correlations between the $Z$ boson and the closest jet are performed in events with at least one jet with $p_{\mathrm{T}} \geq 500$ GeV. Event topologies of particular interest are the collinear emission of a $Z$ boson in dijet events and a boosted $Z$ boson recoiling against a jet. Fiducial cross sections are compared with state-of-the-art theoretical predictions. The data are found to agree with next-to-next-to-leading-order predictions by NNLOjet and with the next-to-leading-order multi-leg generators MadGraph5_aMC@NLO and Sherpa.

Measurements of transverse energy$-$energy correlations and their associated azimuthal asymmetries in multijet events are presented. The analysis is performed using a data sample corresponding to 139 $\mbox{fb\(^{-1}\)}$ of proton$-$proton collisions at a centre-of-mass energy of $\sqrt{s} = 13$ TeV, collected with the ATLAS detector at the Large Hadron Collider. The measurements are presented in bins of the scalar sum of the transverse momenta of the two leading jets and unfolded to particle level. They are then compared to next-to-next-to-leading-order perturbative QCD calculations for the first time, which feature a significant reduction in the theoretical uncertainties estimated using variations of the renormalisation and factorisation scales. The agreement between data and theory is good, thus providing a precision test of QCD at large momentum transfers $Q$. The strong coupling constant $\alpha_s$ is extracted differentially as a function of $Q$, showing a good agreement with the renormalisation group equation and with previous analyses. A simultaneous fit to all transverse energy$-$energy correlation distributions across different kinematic regions yields a value of $\alpha_\mathrm{s}(m_Z) = 0.1175 \pm 0.0006 \mbox{ (exp.)} ^{+0.0034}_{-0.0017} \mbox{ (theo.)}$, while the global fit to the asymmetry distributions yields $\alpha_{\mathrm{s}}(m_Z) = 0.1185 \pm 0.0009 \mbox{ (exp.)} ^{+0.0025}_{-0.0012} \mbox{ (theo.)}$.

Measurements of single-, double-, and triple-differential cross-sections are presented for boosted top-quark pair-production in 13 $\text{TeV}$ proton-proton collisions recorded by the ATLAS detector at the LHC. The top quarks are observed through their hadronic decay and reconstructed as large-radius jets with the leading jet having transverse momentum ($p_{\text{T}}$) greater than 500 GeV. The observed data are unfolded to remove detector effects. The particle-level cross-section, multiplied by the $t\bar{t} \rightarrow W W b \bar{b}$ branching fraction and measured in a fiducial phase space defined by requiring the leading and second-leading jets to have $p_{\text{T}} > 500$ GeV and $p_{\text{T}} > 350$ GeV, respectively, is $331 \pm 3 \text{(stat.)} \pm 39 \text{(syst.)}$ fb. This is approximately 20$\%$ lower than the prediction of $398^{+48}_{-49}$ fb by Powheg+Pythia 8 with next-to-leading-order (NLO) accuracy but consistent within the theoretical uncertainties. Results are also presented at the parton level, where the effects of top-quark decay, parton showering, and hadronization are removed such that they can be compared with fixed-order next-to-next-to-leading-order (NNLO) calculations. The parton-level cross-section, measured in a fiducial phase space similar to that at particle level, is $1.94 \pm 0.02 \text{(stat.)} \pm 0.25 \text{(syst.)}$ pb. This agrees with the NNLO prediction of $1.96^{+0.02}_{-0.17}$ pb. Reasonable agreement with the differential cross-sections is found for most NLO models, while the NNLO calculations are generally in better agreement with the data. The differential cross-sections are interpreted using a Standard Model effective field-theory formalism and limits are set on Wilson coefficients of several four-fermion operators.

Differential cross-section measurements are presented for the electroweak production of two jets in association with a $Z$ boson. These measurements are sensitive to the vector-boson fusion production mechanism and provide a fundamental test of the gauge structure of the Standard Model. The analysis is performed using proton-proton collision data collected by ATLAS at $\sqrt{s}$=13 TeV and with an integrated luminosity of 139 fb$^{-1}$. The differential cross-sections are measured in the $Z\rightarrow \ell^+\ell^-$ decay channel ($\ell=e,\mu$) as a function of four observables: the dijet invariant mass, the rapidity interval spanned by the two jets, the signed azimuthal angle between the two jets, and the transverse momentum of the dilepton pair. The data are corrected for the effects of detector inefficiency and resolution and are sufficiently precise to distinguish between different state-of-the-art theoretical predictions calculated using Powheg+Pythia8, Herwig7+Vbfnlo and Sherpa 2.2. The differential cross-sections are used to search for anomalous weak-boson self-interactions using a dimension-six effective field theory. The differential cross-section as a function of the signed azimuthal angle between the two jets is found to be particularly sensitive to the interference between the Standard Model and dimension-six scattering amplitudes and provides a direct test of charge-conjugation and parity invariance in the weak-boson self-interactions.

This paper presents measurements of $W^{\pm}Z$ production cross sections in $pp$ collisions at a centre-of-mass energy of 13 TeV. The data were collected in 2015 and 2016 by the ATLAS experiment at the Large Hadron Collider, and correspond to an integrated luminosity of 36.1 fb$^{-1}$. The $W^{\pm}Z$ candidate events are reconstructed using leptonic decay modes of the gauge bosons into electrons and muons. The measured inclusive cross section in the detector fiducial region for a single leptonic decay mode is $\sigma_{W^\pm Z \rightarrow \ell^{'} \nu \ell \ell}^{\textrm{fid.}} = 63.7 \pm 1.0$ (stat.) $\pm 2.3$ (syst.) $\pm 1.4$ (lumi.) fb, reproduced by the next-to-next-to-leading-order Standard Model prediction of $61.5^{+1.4}_{-1.3}$ fb. Cross sections for $W^+Z$ and $W^-Z$ production and their ratio are presented as well as differential cross sections for several kinematic observables. An analysis of angular distributions of leptons from decays of $W$ and $Z$ bosons is performed for the first time in pair-produced events in hadronic collisions, and integrated helicity fractions in the detector fiducial region are measured for the $W$ and $Z$ bosons separately. Of particular interest, the longitudinal helicity fraction of pair-produced vector bosons is also measured.