A search for the production of three massive vector bosons in proton--proton collisions is performed using data at $\sqrt{s}=13\,TeV$ recorded with the ATLAS detector at the Large Hadron Collider in the years 2015--2017, corresponding to an integrated luminosity of $79.8\,\text{fb}^{-1}$. Events with two same-sign leptons $\ell$ (electrons or muons) and at least two reconstructed jets are selected to search for $WWW\to\ell\nu\ell\nu qq$. Events with three leptons without any same-flavour opposite-sign lepton pairs are used to search for $WWW\to\ell\nu\ell\nu\ell\nu$, while events with three leptons and at least one same-flavour opposite-sign lepton pair and one or more reconstructed jets are used to search for $WWZ\to\ell\nu qq \ell\ell$. Finally, events with four leptons are analysed to search for $WWZ\to\ell\nu\ell\nu\ell\ell$ and $WZZ\to qq \ell\ell\ell\ell$. Evidence for the joint production of three massive vector bosons is observed with a significance of 4.0 standard deviations, where the expectation is 3.1 standard deviations.

This letter describes the observation of the light-by-light scattering process, $\gamma\gamma\rightarrow\gamma\gamma$, in Pb+Pb collisions at $\sqrt{s_\mathrm{NN}}$ = 5.02 TeV. The analysis is conducted using a data sample corresponding to an integrated luminosity of 1.73 nb$^{-1}$, collected in November 2018 by the ATLAS experiment at the LHC. Light-by-light scattering candidates are selected in events with two photons produced exclusively, each with transverse energy $E_{\textrm{T}}^{\gamma} > 3$ GeV and pseudorapidity $|\eta_{\gamma}| < 2.37$, diphoton invariant mass above 6 GeV, and small diphoton transverse momentum and acoplanarity. After applying all selection criteria, 59 candidate events are observed for a background expectation of 12 $\pm$ 3 events. The observed excess of events over the expected background has a significance of 8.2 standard deviations. The measured fiducial cross section is 78 $\pm$ 13 (stat.) $\pm$ 7 (syst.) $\pm$ 3 (lumi.) nb.

Two-particle long-range azimuthal correlations are measured in photonuclear collisions using 1.7 nb$^{-1}$ of 5.02 TeV Pb+Pb collision data collected by the ATLAS experiment at the LHC. Candidate events are selected using a dedicated high-multiplicity photonuclear event trigger, a combination of information from the zero-degree calorimeters and forward calorimeters, and from pseudorapidity gaps constructed using calorimeter energy clusters and charged-particle tracks. Distributions of event properties are compared between data and Monte Carlo simulations of photonuclear processes. Two-particle correlation functions are formed using charged-particle tracks in the selected events, and a template-fitting method is employed to subtract the non-flow contribution to the correlation. Significant nonzero values of the second- and third-order flow coefficients are observed and presented as a function of charged-particle multiplicity and transverse momentum. The results are compared with flow coefficients obtained in proton-proton and proton-lead collisions in similar multiplicity ranges, and with theoretical expectations. The unique initial conditions present in this measurement provide a new way to probe the origin of the collective signatures previously observed only in hadronic collisions.

Exclusive dimuon production in ultraperipheral collisions (UPC), resulting from photon-photon interactions in the strong electromagnetic fields of colliding high-energy lead nuclei, $\mathrm{PbPb}(\gamma\gamma) \rightarrow \mu^+\mu^- (\mathrm{Pb}^{(\star)}\mathrm{Pb}^{(\star)} )$, is studied using $\mathcal{L}_{\mathrm{int}} = 0.48$ nb$^{-1}$ of $\sqrt{s_\mathrm{NN}}=5.02$ TeV lead-lead collision data at the LHC with the ATLAS detector. Dimuon pairs are measured in the fiducial region $p_{\mathrm{T}\mu} > 4$ GeV, $|\eta_{\mu}| < 2.4$, invariant mass $m_{\mu\mu} > 10$ GeV, and $p_{\mathrm{T,\mu\mu}} < 2$ GeV. The primary background from single-dissociative processes is extracted from the data using a template fitting technique. Differential cross sections are presented as a function of $m_{\mu\mu}$, absolute pair rapidity ($|y_{\mu\mu}|$), scattering angle in the dimuon rest frame ($|\cos \vartheta^{\star}_{\mu\mu}|$) and the colliding photon energies. The total cross section of the UPC $\gamma \gamma \rightarrow \mu^{+}\mu^{-}$ process in the fiducial volume is measured to be $\sigma_{\mathrm{fid}}^{\mu\mu} = 34.1 \! \pm \! 0.3 \mathrm{(stat.)} \! \pm \! 0.7 \mathrm{(syst.)}$ $\mu\mathrm{b}$. Generally good agreement is found with calculations from STARlight, which incorporate the leading-order Breit-Wheeler process with no final-state effects, albeit differences between the measurements and theoretical expectations are observed. In particular, the measured cross sections at larger $|y_{\mu\mu}|$ are found to be about 10-20% larger in data than in the calculations, suggesting the presence of larger fluxes of photons in the initial state. Modification of the dimuon cross sections in the presence of forward and/or backward neutron production is also studied and is found to be associated with a harder incoming photon spectrum, consistent with expectations.

Measurements of four-lepton differential and integrated fiducial cross-sections in events with two same-flavour, opposite-charge electron or muon pairs are presented. The data correspond to 139 fb$^{-1}$ of $\sqrt{s}=13$ TeV proton-proton collisions, collected by the ATLAS detector during Run 2 of the Large Hadron Collider (2015-2018). The final state has contributions from a number of interesting Standard Model processes that dominate in different four-lepton invariant mass regions, including single $Z$ boson production, Higgs boson production and on-shell $ZZ$ production, with a complex mix of interference terms, and possible contributions from physics beyond the Standard Model. The differential cross-sections include the four-lepton invariant mass inclusively, in slices of other kinematic variables, and in different lepton flavour categories. Also measured are dilepton invariant masses, transverse momenta, and angular correlation variables, in four regions of four-lepton invariant mass, each dominated by different processes. The measurements are corrected for detector effects and are compared with state-of-the-art Standard Model calculations, which are found to be consistent with the data. The $Z\rightarrow 4\ell$ branching fraction is extracted, giving a value of $\left(4.41 \pm 0.30\right) \times 10^{-6}$. Constraints on effective field theory parameters and a model based on a spontaneously broken $B-L$ gauge symmetry are also evaluated. Further reinterpretations can be performed with the provided information.

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.

The prevalence of hadronic jets at the LHC requires that a deep understanding of jet formation and structure is achieved in order to reach the highest levels of experimental and theoretical precision. There have been many measurements of jet substructure at the LHC and previous colliders, but the targeted observables mix physical effects from various origins. Based on a recent proposal to factorize physical effects, this Letter presents a double-differential cross-section measurement of the Lund jet plane using 139 fb$^{-1}$ of $\sqrt{s}=13$ TeV proton-proton collision data collected with the ATLAS detector using jets with transverse momentum above 675 GeV. The measurement uses charged particles to achieve a fine angular resolution and is corrected for acceptance and detector effects. Several parton shower Monte Carlo models are compared with the data. No single model is found to be in agreement with the measured data across the entire plane.

This letter presents a combination of searches for Higgs boson pair production using up to 36.1 fb$^{-1}$ of proton-proton collision data at a centre-of-mass energy $\sqrt{s} = 13$ TeV recorded with the ATLAS detector at the LHC. The combination is performed using six analyses searching for Higgs boson pairs decaying into the bbbb, bbWW, bb$\tau\tau$, WWWW, bb$\gamma \gamma$ and WW$\gamma\gamma$ final states. Results are presented for non-resonant and resonant Higgs boson pair production modes. No statistically significant excess in data above the Standard Model predictions is found. The combined observed (expected) limit at 95% confidence level on the non-resonant Higgs boson pair production cross-section is 6.9 (10) times the predicted Standard Model cross-section. Limits are also set on the ratio ($ \kappa_{\lambda} $) of the Higgs boson self-coupling to its Standard Model value. This ratio is constrained at 95% confidence level in observation (expectation) to $ -5.0 < \kappa_{\lambda} <12.0 $ ($ -5.8 < \kappa_{\lambda} <12.0 $). In addition, limits are set on the production of narrow scalar resonances and spin-2 Kaluza-Klein Randall-Sundrum gravitons. Exclusion regions are also provided in the parameter space of the habemus Minimal Supersymmetric Standard Model and the Electroweak Singlet Model.

This paper presents a measurement of quantities related to the formation of jets from high-energy quarks and gluons (fragmentation). Jets with transverse momentum 100 GeV $<p_T<$ 2.5 TeV and pseudorapidity $|\eta| < 2.1$ from an integrated luminosity of 33 fb$^{-1}$ of $\sqrt{s}=13$ TeV proton-proton collisions are reconstructed with the ATLAS detector at the Large Hadron Collider. Charged-particle tracks with $p_T > 500$ MeV and $|\eta| < 2.5$ are used to probe the detailed structure of the jet. The fragmentation properties of the more forward and the more central of the two leading jets from each event are studied. The data are unfolded to correct for detector resolution and acceptance effects. Comparisons with parton shower Monte Carlo generators indicate that existing models provide a reasonable description of the data across a wide range of phase space, but there are also significant differences. Furthermore, the data are interpreted in the context of quark- and gluon-initiated jets by exploiting the rapidity dependence of the jet flavor fraction. A first measurement of the charged-particle multiplicity using model-independent jet labels (topic modeling) provides a promising alternative to traditional quark and gluon extractions using input from simulation. The simulations provide a reasonable description of the quark-like data across the jet $p_T$ range presented in this measurement, but the gluon-like data have systematically fewer charged particles than the simulations.

The dynamics of isolated-photon plus two-jet production in $pp$ collisions at a centre-of-mass energy of 13 TeV are studied with the ATLAS detector at the LHC using a dataset corresponding to an integrated luminosity of 36.1 fb$^{-1}$. Cross sections are measured as functions of a variety of observables, including angular correlations and invariant masses of the objects in the final state, $\gamma+jet+jet$. Measurements are also performed in phase-space regions enriched in each of the two underlying physical mechanisms, namely direct and fragmentation processes. The measurements cover the range of photon (jet) transverse momenta from 150 GeV (100 GeV) to 2 TeV. The tree-level plus parton-shower predictions from SHERPA and PYTHIA as well as the next-to-leading-order QCD predictions from SHERPA are compared with the measurements. The next-to-leading-order QCD predictions describe the data adequately in shape and normalisation except for regions of phase space such as those with high values of the invariant mass or rapidity separation of the two jets, where the predictions overestimate the data.

A search for magnetic monopoles and high-electric-charge objects is presented using 34.4 fb$^{-1}$ of 13 TeV $pp$ collision data collected by the ATLAS detector at the LHC during 2015 and 2016. The considered signature is based upon high ionization in the transition radiation tracker of the inner detector associated with a pencil-shape energy deposit in the electromagnetic calorimeter. The data were collected by a dedicated trigger based on the tracker high-threshold hit capability. The results are interpreted in models of Drell-Yan pair production of stable particles with two spin hypotheses (0 and 1/2) and masses ranging from 200 GeV to 4000 GeV. The search improves by approximately a factor of five the constraints on the direct production of magnetic monopoles carrying one or two Dirac magnetic charges and stable objects with electric charge in the range $20\le|z|\le60$ and extends the charge range to $60<|z|\le100$.

Multi-particle azimuthal cumulants are measured as a function of centrality and transverse momentum using 470 $\mu$b$^{-1}$ of Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV with the ATLAS detector at the LHC. These cumulants provide information on the event-by-event fluctuations of harmonic flow coefficients $v_n$ and correlated fluctuations between two harmonics $v_n$ and $v_m$. For the first time, a non-zero four-particle cumulant is observed for dipolar flow, $v_1$. The four-particle cumulants for elliptic flow, $v_2$, and triangular flow, $v_3$, exhibit a strong centrality dependence and change sign in ultra-central collisions. This sign change is consistent with significant non-Gaussian fluctuations in $v_2$ and $v_3$. The four-particle cumulant for quadrangular flow, $v_4$, is found to change sign in mid-central collisions. Correlations between two harmonics are studied with three- and four-particle mixed-harmonic cumulants, which indicate an anti-correlation between $v_2$ and $v_3$, and a positive correlation between $v_2$ and $v_4$. These correlations decrease in strength towards central collisions and either approach zero or change sign in ultra-central collisions. To investigate the possible flow fluctuations arising from intrinsic centrality or volume fluctuations, the results are compared between two different event classes used for centrality definitions. In peripheral and mid-central collisions where the cumulant signals are large, only small differences are observed. In ultra-central collisions, the differences are much larger and transverse momentum dependent. These results provide new information to disentangle flow fluctuations from the initial and final states, as well as new insights on the influence of centrality fluctuations.

The azimuthal anisotropy of charged particles produced in $\sqrt{s_{\mathrm{NN}}}=8.16$ TeV $p$+Pb collisions is measured with the ATLAS detector at the LHC. The data correspond to an integrated luminosity of $165$ $\mathrm{nb}^{-1}$ that was collected in 2016. Azimuthal anisotropy coefficients, elliptic $v_2$ and triangular $v_3$, extracted using two-particle correlations with a non-flow template fit procedure, are presented as a function of particle transverse momentum ($p_\mathrm{T}$) between $0.5$ and $50$ GeV. The $v_2$ results are also reported as a function of centrality in three different particle $p_\mathrm{T}$ intervals. The results are reported from minimum-bias events and jet-triggered events, where two jet $p_\mathrm{T}$ thresholds are used. The anisotropies for particles with $p_\mathrm{T}$ less than about $2$ GeV are consistent with hydrodynamic flow expectations, while the significant non-zero anisotropies for $p_\mathrm{T}$ in the range $9$-$50$ GeV are not explained within current theoretical frameworks. In the $p_\mathrm{T}$ range $2$-$9$ GeV, the anisotropies are larger in minimum-bias than in jet-triggered events. Possible origins of these effects, such as the changing admixture of particles from hard scattering and the underlying event, are discussed.

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.

This paper presents studies of Bose-Einstein correlations (BEC) in proton-proton collisions at a centre-of-mass energy of 13 TeV, using data from the ATLAS detector at the CERN Large Hadron Collider. Data were collected in a special low-luminosity configuration with a minimum-bias trigger and a high-multiplicity track trigger, accumulating integrated luminosities of 151 $\mu$b$^{-1}$ and 8.4 nb$^{-1}$ respectively. The BEC are measured for pairs of like-sign charged particles, each with $|\eta|$ < 2.5, for two kinematic ranges: the first with particle $p_T$ > 100 MeV and the second with particle $p_T$ > 500 MeV. The BEC parameters, characterizing the source radius and particle correlation strength, are investigated as functions of charged-particle multiplicity (up to 300) and average transverse momentum of the pair (up to 1.5 GeV). The double-differential dependence on charged-particle multiplicity and average transverse momentum of the pair is also studied. The BEC radius is found to be independent of the charged-particle multiplicity for high charged-particle multiplicity (above 100), confirming a previous observation at lower energy. This saturation occurs independent of the transverse momentum of the pair.

A search is performed for the electroweak pair production of charginos and associated production of a chargino and neutralino, each of which decays through an $R$-parity-violating coupling into a lepton and a $W$, $Z$, or Higgs boson. The trilepton invariant-mass spectrum is constructed from events with three or more leptons, targeting chargino decays that include an electron or muon and a leptonically decaying $Z$ boson. The analyzed dataset corresponds to an integrated luminosity of 139 fb$^{-1}$ of proton-proton collision data produced by the Large Hadron Collider at a center-of-mass energy of $\sqrt{s}$ = 13 TeV and collected by the ATLAS experiment between 2015 and 2018. The data are found to be consistent with predictions from the Standard Model. The results are interpreted as limits at 95% confidence level on model-independent cross sections for processes beyond the Standard Model. Limits are also set on the production of charginos and neutralinos for a Minimal Supersymmetric Standard Model with an approximate $B$-$L$ symmetry. Charginos and neutralinos with masses between 100 GeV and 1100 GeV are excluded depending on the assumed decay branching fractions into a lepton (electron, muon, or $\tau$-lepton) plus a boson ($W$, $Z$, or Higgs).

This paper reports on a search for heavy resonances decaying into $WW$, $ZZ$ or $WZ$ using proton-proton collision data at a centre-of-mass energy of $\sqrt{s}=13$ TeV. The data, corresponding to an integrated luminosity of 139 $\mathrm{fb^{-1}}$, were recorded with the ATLAS detector from 2015 to 2018 at the Large Hadron Collider. The search is performed for final states in which one $W$ or $Z$ boson decays leptonically, and the other $W$ boson or $Z$ boson decays hadronically. The data are found to be described well by expected backgrounds. Upper bounds on the production cross sections of heavy scalar, vector or tensor resonances are derived in the mass range 300-5000 GeV within the context of Standard Model extensions with warped extra dimensions or including a heavy vector triplet. Production through gluon-gluon fusion, Drell-Yan or vector-boson fusion are considered, depending on the assumed model.

A measurement of $W^\pm$ boson production in lead-lead collisions at $\sqrt{s_\mathrm{NN}} = 5.02$ TeV is reported using data recorded by the ATLAS experiment at the LHC in 2015, corresponding to a total integrated luminosity of $0.49\;\mathrm{nb^{-1}}$. The $W^\pm$ bosons are reconstructed in the electron or muon leptonic decay channels. Production yields of leptonically decaying $W^\pm$ bosons, normalised by the total number of minimum-bias events and the nuclear thickness function, are measured within a fiducial region defined by the detector acceptance and the main kinematic requirements. These normalised yields are measured separately for $W^+$ and $W^-$ bosons, and are presented as a function of the absolute value of pseudorapidity of the charged lepton and of the collision centrality. The lepton charge asymmetry is also measured as a function of the absolute value of lepton pseudorapidity. In addition, nuclear modification factors are calculated using the $W^\pm$ boson production cross-sections measured in $pp$ collisions. The results are compared with predictions based on next-to-leading-order calculations with CT14 parton distribution functions as well as with predictions obtained with the EPPS16 and nCTEQ15 nuclear parton distribution functions. No dependence of normalised production yields on centrality and a good agreement with predictions are observed for mid-central and central collisions. For peripheral collisions, the data agree with predictions within 1.7 (0.9) standard deviations for $W^-$ ($W^+$) bosons.

A dedicated sample of Large Hadron Collider proton-proton collision data at centre-of-mass energy $\sqrt{s}=8$ TeV is used to study inclusive single diffractive dissociation, $pp \rightarrow Xp$. The intact final-state proton is reconstructed in the ATLAS ALFA forward spectrometer, while charged particles from the dissociated system $X$ are measured in the central detector components. The fiducial range of the measurement is $-4.0 < \log_{10} \xi < -1.6$ and $0.016 < |t| < 0.43 \ {\rm GeV^2}$, where $\xi$ is the proton fractional energy loss and $t$ is the squared four-momentum transfer. The total cross section integrated across the fiducial range is $1.59 \pm 0.13 \ {\rm mb}$. Cross sections are also measured differentially as functions of $\xi$, $t$, and $\Delta \eta$, a variable that characterises the rapidity gap separating the proton and the system $X$. The data are consistent with an exponential $t$ dependence, ${\rm d} \sigma / {\rm d} t \propto \text{e}^{Bt}$ with slope parameter $B = 7.65 \pm 0.34 \ {\rm GeV^{-2}}$. Interpreted in the framework of triple Regge phenomenology, the $\xi$ dependence leads to a pomeron intercept of $\alpha(0) = 1.07 \pm 0.09$.

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.

This paper presents results of searches for electroweak production of supersymmetric particles in models with compressed mass spectra. The searches use 139 fb$^{-1}$ of $\sqrt{s}=13$ TeV proton-proton collision data collected by the ATLAS experiment at the Large Hadron Collider. Events with missing transverse momentum and two same-flavor, oppositely charged, low transverse momentum leptons are selected, and are further categorized by the presence of hadronic activity from initial-state radiation or a topology compatible with vector-boson fusion processes. The data are found to be consistent with predictions from the Standard Model. The results are interpreted using simplified models of $R$-parity-conserving supersymmetry in which the lightest supersymmetric partner is a neutralino with a mass similar to the lightest chargino, the second-to-lightest neutralino or the slepton. Lower limits on the masses of charginos in different simplified models range from 193 GeV to 240 GeV for moderate mass splittings, and extend down to mass splittings of 1.5 GeV to 2.4 GeV at the LEP chargino bounds (92.4 GeV). Similar lower limits on degenerate light-flavor sleptons extend up to masses of 251 GeV and down to mass splittings of 550 MeV. Constraints on vector-boson fusion production of electroweak SUSY states are also presented.

A search for dark matter is conducted in final states containing a photon and missing transverse momentum in proton$-$proton collisions at $\sqrt{s}$ = 13 TeV. The data, collected during 2015$-$2018 by the ATLAS experiment at the CERN LHC, correspond to an integrated luminosity of 139 fb$^{-1}$. No deviations from the predictions of the Standard Model are observed and 95% confidence-level upper limits between 2.45 fb and 0.5 fb are set on the visible cross section for contributions from physics beyond the Standard Model, in different ranges of the missing transverse momentum. The results are interpreted as 95% confidence-level limits in models where weakly interacting dark-matter candidates are pair-produced via an s-channel axial-vector or vector mediator. Dark-matter candidates with masses up to 415 (580) GeV are excluded for axial-vector (vector) mediators, while the maximum excluded mass of the mediator is 1460 (1470) GeV. In addition, the results are expressed in terms of 95% confidence-level limits on the parameters of a model with an axion-like particle produced in association with a photon, and are used to constrain the coupling $g_{aZ\gamma}$ of an axion-like particle to the electroweak gauge bosons.

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.

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 direct production of the supersymmetric partners of $\tau$-leptons (staus) in final states with two hadronically decaying $\tau$-leptons is presented. The analysis uses a dataset of $pp$ collisions corresponding to an integrated luminosity of $139$ fb$^{-1}$, recorded with the ATLAS detector at the Large Hadron Collider at a center-of-mass energy of 13 TeV. No significant deviation from the expected Standard Model background is observed. Limits are derived in scenarios of direct production of stau pairs with each stau decaying into the stable lightest neutralino and one $\tau$-lepton in simplified models where the two stau mass eigenstates are degenerate. Stau masses from 120 GeV to 390 GeV are excluded at 95% confidence level for a massless lightest neutralino.

The elliptic flow of muons from the decay of charm and bottom hadrons is measured in $pp$ collisions at $\sqrt{s}=13$ TeV using a data sample with an integrated luminosity of 150 pb$^{-1}$ recorded by the ATLAS detector at the LHC. The muons from heavy-flavor decay are separated from light-hadron decay muons using momentum imbalance between the tracking and muon spectrometers. The heavy-flavor decay muons are further separated into those from charm decay and those from bottom decay using the distance-of-closest-approach to the collision vertex. The measurement is performed for muons in the transverse momentum range 4-7 GeV and pseudorapidity range $|\eta|<2.4$. A significant non-zero elliptic anisotropy coefficient $v_{2}$ is observed for muons from charm decays, while the $v_{2}$ value for muons from bottom decays is consistent with zero within uncertainties.

This paper presents a search for dark matter in the context of a two-Higgs-doublet model together with an additional pseudoscalar mediator, $a$, which decays into the dark-matter particles. Processes where the pseudoscalar mediator is produced in association with a single top quark in the 2HDM+$a$ model are explored for the first time at the LHC. Several final states which include either one or two charged leptons (electrons or muons) and a significant amount of missing transverse momentum are considered. The analysis is based on proton-proton collision data collected with the ATLAS experiment at $\sqrt{s} = 13$ TeV during LHC Run2 (2015-2018), corresponding to an integrated luminosity of 139 fb$^{-1}$. No significant excess above the Standard Model predictions is found. The results are expressed as 95% confidence-level limits on the parameters of the signal models considered.

This paper presents a search for new heavy particles decaying into a pair of top quarks using 139 fb$^{-1}$ of proton--proton collision data recorded at a centre-of-mass energy of $\sqrt{s}=13$ TeV with the ATLAS detector at the Large Hadron Collider. The search is performed using events consistent with pair production of high-transverse-momentum top quarks and their subsequent decays into the fully hadronic final states. The analysis is optimized for resonances decaying into a $t\bar{t}$ pair with mass above 1.4 TeV, exploiting a dedicated multivariate technique with jet substructure to identify hadronically decaying top quarks using large-radius jets and evaluating the background expectation from data. No significant deviation from the background prediction is observed. Limits are set on the production cross-section times branching fraction for the new $Z'$ boson in a topcolor-assisted-technicolor model. The $Z'$ boson masses below 3.9 and 4.7 TeV are excluded at 95% confidence level for the decay widths of 1% and 3%, respectively.

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 the final state with two light leptons (electrons or muons) of different flavour and charge combinations, with at least two jets and large missing transverse momentum. No significant excess over the Standard Model expectation is observed. The results are translated into exclusion limits on heavy-lepton masses, and the observed lower limit on the mass of the type-III seesaw heavy leptons is 790 GeV at 95% confidence level.

The production cross-sections for $W^{\pm}$ and $Z$ bosons are measured using ATLAS data corresponding to an integrated luminosity of 4.0 pb$^{-1}$ collected at a centre-of-mass energy $\sqrt{s}=2.76$ TeV. The decay channels $W \rightarrow \ell \nu$ and $Z \rightarrow \ell \ell $ are used, where $\ell$ can be an electron or a muon. The cross-sections are presented for a fiducial region defined by the detector acceptance and are also extrapolated to the full phase space for the total inclusive production cross-section. The combined (average) total inclusive cross-sections for the electron and muon channels are: \begin{eqnarray} \sigma^{\text{tot}}_{W^{+}\rightarrow \ell \nu}& = & 2312 \pm 26\ (\text{stat.})\ \pm 27\ (\text{syst.}) \pm 72\ (\text{lumi.}) \pm 30\ (\text{extr.})\text{pb} \nonumber, \\ \sigma^{\text{tot}}_{W^{-}\rightarrow \ell \nu}& = & 1399 \pm 21\ (\text{stat.})\ \pm 17\ (\text{syst.}) \pm 43\ (\text{lumi.}) \pm 21\ (\text{extr.})\text{pb} \nonumber, \\ \sigma^{\text{tot}}_{Z \rightarrow \ell \ell}& = & 323.4 \pm 9.8\ (\text{stat.}) \pm 5.0\ (\text{syst.}) \pm 10.0\ (\text{lumi.}) \pm 5.5 (\text{extr.}) \text{pb} \nonumber. \end{eqnarray} Measured ratios and asymmetries constructed using these cross-sections are also presented. These observables benefit from full or partial cancellation of many systematic uncertainties that are correlated between the different measurements.

The production of a prompt photon in association with a $Z$ boson is studied in proton-proton collisions at a centre-of-mass energy $\sqrt{s} =$ 13 TeV. The analysis uses a data sample with an integrated luminosity of 139 fb$^{-1}$ collected by the ATLAS detector at the LHC from 2015 to 2018. The production cross-section for the process $pp \rightarrow \ell^+\ell^-\gamma+X$ ($\ell = e, \mu$) is measured within a fiducial phase-space region defined by kinematic requirements on the photon and the leptons, and by isolation requirements on the photon. An experimental precision of 2.9% is achieved for the fiducial cross-section. Differential cross-sections are measured as a function of each of six kinematic variables characterising the $\ell^+\ell^-\gamma$ system. The data are compared with theoretical predictions based on next-to-leading-order and next-to-next-to-leading-order perturbative QCD calculations. The impact of next-to-leading-order electroweak corrections is also considered.

The differential cross section for isolated-photon production in $pp$ collisions is measured at a centre-of-mass energy of 13 TeV with the ATLAS detector at the LHC using an integrated luminosity of 36.1 fb$^{-1}$. The differential cross section is presented as a function of the photon transverse energy in different regions of photon pseudorapidity. The differential cross section as a function of the absolute value of the photon pseudorapidity is also presented in different regions of photon transverse energy. Next-to-leading-order QCD calculations from JETPHOX and SHERPA as well as next-to-next-to-leading-order QCD calculations from NNLOJET are compared with the measurement, using several parameterisations of the proton parton distribution functions. The predictions provide a good description of the data within the experimental and theoretical uncertainties.

This paper describes precision measurements of the transverse momentum $p_\mathrm{T}^{\ell\ell}$ ($\ell=e,\mu$) and of the angular variable $\phi^{*}_{\eta}$ distributions of Drell-Yan lepton pairs in a mass range of 66-116 GeV. The analysis uses data from 36.1 fb$^{-1}$ of proton-proton collisions at a centre-of-mass energy of $\sqrt{s}=13$ TeV collected by the ATLAS experiment at the LHC in 2015 and 2016. Measurements in electron-pair and muon-pair final states are performed in the same fiducial volumes, corrected for detector effects, and combined. Compared to previous measurements in proton-proton collisions at $\sqrt{s}=$7 and 8 TeV, these new measurements probe perturbative QCD at a higher centre-of-mass energy with a different composition of initial states. They reach a precision of 0.2% for the normalized spectra at low values of $p_\mathrm{T}^{\ell\ell}$. The data are compared with different QCD predictions, where it is found that predictions based on resummation approaches can describe the full spectrum within uncertainties.

A search for new-physics resonances decaying into a lepton and a jet performed by the ATLAS experiment is presented. Scalar leptoquarks pair-produced in $pp$ collisions at $\sqrt{s}=13$ TeV at the Large Hadron Collider are considered using an integrated luminosity of 139 fb$^{-1}$, corresponding to the full Run 2 dataset. They are searched for in events with two electrons or two muons and two or more jets, including jets identified as arising from the fragmentation of $c$- or $b$-quarks. The observed yield in each channel is consistent with the Standard Model background expectation. Leptoquarks with masses below 1.8 TeV and 1.7 TeV are excluded in the electron and muon channels, respectively, assuming a branching ratio into a charged lepton and a quark of 100%, with minimal dependence on the quark flavour. Upper limits on the aforementioned branching ratio are also given as a function of the leptoquark mass.

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.

Narrow resonances decaying into $WW$, $WZ$ or $ZZ$ boson pairs are searched for in 139 fb$^{-1}$ of proton-proton collision data at a centre-of-mass energy of $\sqrt{s}=13$ TeV recorded with the ATLAS detector at the Large Hadron Collider from 2015 to 2018. The diboson system is reconstructed using pairs of high transverse momentum, large-radius jets. These jets are built from a combination of calorimeter- and tracker-inputs compatible with the hadronic decay of a boosted $W$ or $Z$ boson, using jet mass and substructure properties. The search is performed for diboson resonances with masses greater than 1.3 TeV. No significant deviations from the background expectations are observed. Exclusion limits at the 95% confidence level are set on the production cross-section times branching ratio into dibosons for resonances in a range of theories beyond the Standard Model, with the highest excluded mass of a new gauge boson at 3.8 TeV in the context of mass-degenerate resonances that couple predominantly to gauge bosons.

A search for quantum black holes in electron+jet and muon+jet invariant mass spectra is performed with 140 fb$^{-1}$ of data collected by the ATLAS detector in proton-proton collisions at $\sqrt{s}$ = 13 TeV at the Large Hadron Collider. The observed invariant mass spectrum of lepton+jet pairs is consistent with Standard Model expectations. Upper limits are set at 95% confidence level on the production cross-sections times branching fractions for quantum black holes decaying into a lepton and a quark in a search region with invariant mass above 2.0 TeV. The resulting quantum black hole lower mass threshold limit is 9.2 TeV in the Arkani-Hamed-Dimopoulos-Dvali model, and 6.8 TeV in the Randall-Sundrum model.

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 $b\bar{b}$.

This paper presents measurements of charged-particle distributions sensitive to the properties of the underlying event in events containing a $Z$ boson decaying into a muon pair. The data were obtained using the ATLAS detector at the LHC in proton-proton collisions at a centre-of-mass energy of 13 TeV with an integrated luminosity of 3.2 fb$^{-1}$. Distributions of the charged-particle multiplicity and of the charged-particle transverse momentum are measured in regions of the azimuth defined relative to the $Z$ boson direction. The measured distributions are compared with the predictions of various Monte Carlo generators which implement different underlying-event models. The Monte Carlo model predictions qualitatively describe the data well, but with some significant discrepancies.

This paper presents measurements of the $W^+ \rightarrow \mu^+\nu$ and $W^- \rightarrow \mu^-\nu$ cross-sections and the associated charge asymmetry as a function of the absolute pseudorapidity of the decay muon. The data were collected in proton--proton collisions at a centre-of-mass energy of 8 TeV with the ATLAS experiment at the LHC and correspond to a total integrated luminosity of $20.2~\mbox{fb$^{-1}$}$. The precision of the cross-section measurements varies between 0.8% to 1.5% as a function of the pseudorapidity, excluding the 1.9% uncertainty on the integrated luminosity. The charge asymmetry is measured with an uncertainty between 0.002 and 0.003. The results are compared with predictions based on next-to-next-to-leading-order calculations with various parton distribution functions and have the sensitivity to discriminate between them.

The problems of neutrino masses, matter-antimatter asymmetry, and dark matter could be successfully addressed by postulating right-handed neutrinos with Majorana masses below the electroweak scale. In this work, leptonic decays of $W$ bosons extracted from 32.9 fb$^{-1}$ to 36.1 fb$^{-1}$ of 13 TeV proton-proton collisions at the LHC are used to search for heavy neutral leptons (HNLs) that are produced through mixing with muon or electron neutrinos. The search is conducted using the ATLAS detector in both prompt and displaced leptonic decay signatures. The prompt signature requires three leptons produced at the interaction point (either $\mu\mu e$ or $e e\mu$) with a veto on same-flavour opposite-charge topologies. The displaced signature comprises a prompt muon from the $W$ boson decay and the requirement of a dilepton vertex (either $\mu\mu$ or $\mu e$) displaced in the transverse plane by 4-300 mm from the interaction point. The search sets constraints on the HNL mixing to muon and electron neutrinos for HNL masses in the range 4.5-50 GeV.

This Letter presents a search for the production of new heavy resonances decaying into a Higgs boson and a photon using proton-proton collision data at $\sqrt{s}=13$ TeV collected by the ATLAS detector at the LHC. The data correspond to an integrated luminosity of 139 fb$^{-1}$. The analysis is performed by reconstructing hadronically decaying Higgs boson $(H\to b\bar{b})$ candidates as single large-radius jets. A novel algorithm using information about the jet constituents in the center-of-mass frame of the jet is implemented to identify the two $b$-quarks in the single jet. No significant excess of events is observed above the expected background. Upper limits are set on the production cross-section times branching fraction for narrow spin-1 resonances decaying into a Higgs boson and a photon in the resonance mass range from 0.7 to 4 TeV, cross-sections times branching fraction are excluded between 11.6 fb and 0.11 fb at a 95% confidence level.

To assess the properties of the quark-gluon plasma formed in heavy-ion collisions, the ATLAS experiment at the LHC measures a correlation between the mean transverse momentum and the magnitudes of the flow harmonics. The analysis uses data samples of lead-lead and proton-lead collisions obtained at the centre-of-mass energy per nucleon pair of 5.02 TeV, corresponding to total integrated luminosities of $22 ~\mu b^{-1}$ and $28~nb^{-1}$, respectively. The measurement is performed using a modified Pearson correlation coefficient with the charged-particle tracks on an event-by-event basis. The modified Pearson correlation coefficients for the $2^{nd}$-, 3$^{rd}$-, and 4$^{th}$-order harmonics are measured as a function of event centrality quantified as the number of charged particles or the number of nucleons participating in the collision. The measurements are performed for several intervals of the charged-particle transverse momentum. The correlation coefficients for all studied harmonics exhibit a strong centrality evolution in the lead-lead collisions, which only weakly depends on the charged-particle momentum range. In the proton-lead collisions, the modified Pearson correlation coefficient measured for the second harmonics shows only weak centrality dependence. The data is qualitatively described by the predictions based on the hydrodynamical model.

Azimuthal anisotropies of muons from charm and bottom hadron decays are measured in Pb+Pb collisions at $\sqrt{s_\mathrm{NN}}= 5.02$ TeV. The data were collected with the ATLAS detector at the Large Hadron Collider in 2015 and 2018 with integrated luminosities of $0.5~\mathrm{nb}^{-1}$ and $1.4~\mathrm{nb^{-1}}$, respectively. The kinematic selection for heavy-flavor muons requires transverse momentum $4 < p_\mathrm{T} < 30$ GeV and pseudorapidity $|\eta|<2.0$. The dominant sources of muons in this $p_\mathrm{T}$ range are semi-leptonic decays of charm and bottom hadrons. These heavy-flavor muons are separated from light-hadron decay muons and punch-through hadrons using the momentum imbalance between the measurements in the tracking detector and in the muon spectrometers. Azimuthal anisotropies, quantified by flow coefficients, are measured via the event-plane method for inclusive heavy-flavor muons as a function of the muon $p_\mathrm{T}$ and in intervals of Pb+Pb collision centrality. Heavy-flavor muons are separated into contributions from charm and bottom hadron decays using the muon transverse impact parameter with respect to the event primary vertex. Non-zero elliptic ($v_{2}$) and triangular ($v_{3}$) flow coefficients are extracted for charm and bottom muons, with the charm muon coefficients larger than those for bottom muons for all Pb+Pb collision centralities. The results indicate substantial modification to the charm and bottom quark angular distributions through interactions in the quark-gluon plasma produced in these Pb+Pb collisions, with smaller modifications for the bottom quarks as expected theoretically due to their larger mass.

Results of a search for new physics in final states with an energetic jet and large missing transverse momentum are reported. The search uses proton-proton collision data corresponding to an integrated luminosity of 139 fb$^{-1}$ at a center-of-mass energy of 13 TeV collected in the period 2015-2018 with the ATLAS detector at the Large Hadron Collider. Compared to previous publications, in addition to an increase of almost a factor of four in the data size, the analysis implements a number of improvements in the signal selection and the background determination leading to enhanced sensitivity. Events are required to have at least one jet with transverse momentum above 150 GeV and no reconstructed leptons ($e$, $\mu$ or $\tau$) or photons. Several signal regions are considered with increasing requirements on the missing transverse momentum starting at 200 GeV. Overall agreement is observed between the number of events in data and the Standard Model predictions. Model-independent 95 % confidence-level limits on visible cross sections for new processes are obtained in the range between 736 fb and 0.3 fb with increasing missing transverse momentum. Results are also translated into improved exclusion limits in models with pair-produced weakly interacting dark-matter candidates, large extra spatial dimensions, supersymmetric particles in several compressed scenarios, axion-like particles, and new scalar particles in dark-energy-inspired models. In addition, the data are translated into bounds on the invisible branching ratio of the Higgs boson.

Measurements of $K_S^0$ and $\Lambda^0$ production in $t\bar{t}$ final states have been performed. They are based on a data sample with integrated luminosity of 4.6 $\mathrm{fb}^{-1}$ from proton-proton collisions at a centre-of-mass energy of 7 TeV, collected in 2011 with the ATLAS detector at the Large Hadron Collider. Neutral strange particles are separated into three classes, depending on whether they are contained in a jet, with or without a $b$-tag, or not associated with a selected jet. The aim is to look for differences in their main kinematic distributions. A comparison of data with several Monte Carlo simulations using different hadronisation and fragmentation schemes, colour reconnection models and different tunes for the underlying event has been made. The production of neutral strange particles in $t\bar{t}$ dileptonic events is found to be well described by current Monte Carlo models for $K_S^0$ and $\Lambda^0$ production within jets, but not for those produced outside jets.

A search for new resonances decaying into a pair of jets is reported using the dataset of proton-proton collisions recorded at $\sqrt{s}=13$ TeV with the ATLAS detector at the Large Hadron Collider between 2015 and 2018, corresponding to an integrated luminosity of 139 fb$^{-1}$. The distribution of the invariant mass of the two leading jets is examined for local excesses above a data-derived estimate of the Standard Model background. In addition to an inclusive dijet search, events with jets identified as containing $b$-hadrons are examined specifically. No significant excess of events above the smoothly falling background spectra is observed. The results are used to set cross-section upper limits at 95% confidence level on a range of new physics scenarios. Model-independent limits on Gaussian-shaped signals are also reported. The analysis looking at jets containing $b$-hadrons benefits from improvements in the jet flavour identification at high transverse momentum, which increases its sensitivity relative to the previous analysis beyond that expected from the higher integrated luminosity.

A search for long-lived particles decaying into an oppositely charged lepton pair, $\mu\mu$, $ee$, or $e\mu$, is presented using 32.8 fb$^{-1}$ of $pp$ collision data collected at $\sqrt{s}=13$ TeV by the ATLAS detector at the LHC. Candidate leptons are required to form a vertex, within the inner tracking volume of ATLAS, displaced from the primary $pp$ interaction region. No lepton pairs with an invariant mass greater than 12 GeV are observed, consistent with the background expectations derived from data. The detection efficiencies for generic resonances with lifetimes ($c\tau$) of 100-1000 mm decaying into a dilepton pair with masses between 0.1-1.0 TeV are presented as a function of $p_T$ and decay radius of the resonances to allow the extraction of upper limits on the cross sections for theoretical models. The result is also interpreted in a supersymmetric model in which the lightest neutralino, produced via squark-antisquark production, decays into $\ell^{+}\ell^{'-}\nu$ ($\ell, \ell^{'} = e$, $\mu$) with a finite lifetime due to the presence of R-parity violating couplings. Cross-section limits are presented for specific squark and neutralino masses. For a 700 GeV squark, neutralinos with masses of 50-500 GeV and mean proper lifetimes corresponding to $c\tau$ values between 1 mm to 6 m are excluded. For a 1.6 TeV squark, $c\tau$ values between 3 mm to 1 m are excluded for 1.3 TeV neutralinos.

A measurement of jet substructure variables is presented using data collected in 2016 by the ATLAS experiment at the LHC with proton-proton collisions at $\sqrt{s}=13$ TeV. Large-radius jets groomed with the trimming and soft-drop algorithms are studied. Dedicated event selections are used to study jets produced by light quarks or gluons, and hadronically decaying top quarks and $W$ bosons. The variables measured are sensitive to pronged substructure, and therefore are typically used for tagging jets from boosted massive particles. These include the energy correlation functions and the $N$-subjettiness variables. The number of subjets and the Les Houches angularity are also considered. The distributions of the substructure variables, corrected for detector effects, are compared to the predictions of various Monte Carlo event generators. They are also compared between the large-radius jets originating from light quarks or gluons, and hadronically decaying top quarks and $W$ bosons.

A search is presented for four-top-quark production using an integrated luminosity of 139 fb$^{-1}$ of proton-proton collision data at a centre-of-mass energy of 13 TeV collected by the ATLAS detector at the LHC. Events are selected if they contain a same-sign lepton pair or at least three leptons (electrons or muons). Jet multiplicity, jet flavour and event kinematics are used to separate signal from the background through a multivariate discriminant, and dedicated control regions are used to constrain the dominant backgrounds. The four-top-quark production cross section is measured to be 24$^{+7}_{-6}$ fb. This corresponds to an observed (expected) significance with respect to the background-only hypothesis of 4.3 (2.4) standard deviations and provides evidence for this process.