The inclusive production rates of isolated, prompt photons in $p$+Pb collisions at $\sqrt{s_\mathrm{NN}} = 8.16$ TeV are studied with the ATLAS detector at the Large Hadron Collider using a dataset with an integrated luminosity of 165 nb$^{-1}$ recorded in 2016. The cross-section and nuclear modification factor $R_{p\mathrm{Pb}}$ are measured as a function of photon transverse energy from 20 GeV to 550 GeV and in three nucleon-nucleon centre-of-mass pseudorapidity regions, (-2.83,-2.02), (-1.84,0.91), and (1.09,1.90). The cross-section and $R_{p\mathrm{Pb}}$ values are compared with the results of a next-to-leading-order perturbative QCD calculation, with and without nuclear parton distribution function modifications, and with expectations based on a model of the energy loss of partons prior to the hard scattering. The data disfavour a large amount of energy loss and provide new constraints on the parton densities in nuclei.

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.

A search for heavy long-lived multi-charged particles is performed using the ATLAS detector at the LHC. Data with an integrated luminosity of 36.1 fb$^{-1}$ collected in 2015 and 2016 from proton-proton collisions at $\sqrt{s}$ = 13 TeV are examined. Particles producing anomalously high ionization, consistent with long-lived massive particles with electric charges from |q|=2e to |q|=7e, are searched for. No events are observed, and 95% confidence level cross-section upper limits are interpreted as lower mass limits for a Drell-Yan production model. Multi-charged particles with masses between 50 GeV and 980-1220 GeV (depending on their electric charge) are excluded.

A search for excited electrons produced in $pp$ collisions at $\sqrt{s} = 13$ TeV via a contact interaction $q\bar{q} \to ee^*$ is presented. The search uses 36.1 fb$^{-1}$ of data collected in 2015 and 2016 by the ATLAS experiment at the Large Hadron Collider. Decays of the excited electron via a contact interaction into an electron and a pair of quarks ($eq\bar{q}$) are targeted in final states with two electrons and two hadronic jets, and decays via a gauge interaction into a neutrino and a $W$ boson ($\nu W$) are probed in final states with an electron, missing transverse momentum, and a large-radius jet consistent with a hadronically decaying $W$ boson. No significant excess is observed over the expected backgrounds. Upper limits are calculated for the $pp \to ee^* \to eeq\bar{q}$ and $pp \to ee^* \to e\nu W$ production cross sections as a function of the excited electron mass $m_{e^*}$ at 95% confidence level. The limits are translated into lower bounds on the compositeness scale parameter $\Lambda$ of the model as a function of $m_{e^*}$. For $m_{e^*} < 0.5$ TeV, the lower bound for $\Lambda$ is 11 TeV. In the special case of $m_{e^*} = \Lambda$, the values of $m_{e^*} < 4.8$ TeV are excluded. The presented limits on $\Lambda$ are more stringent than those obtained in previous searches.

The fragmentation of high-energy gluons at small opening angles is largely unconstrained by present measurements. Gluon splitting to $b$-quark pairs is a unique probe into the properties of gluon fragmentation because identified $b$-tagged jets provide a proxy for the quark daughters of the initial gluon. In this study, key differential distributions related to the $g\rightarrow b\bar{b}$ process are measured using 33 fb$^{-1}$ of $\sqrt{s}=13$ TeV $pp$ collision data recorded by the ATLAS experiment at the LHC in 2016. Jets constructed from charged-particle tracks, clustered with the anti-$k_t$ jet algorithm with radius parameter $R = 0.2$, are used to probe angular scales below the $R=0.4$ jet radius. The observables are unfolded to particle level in order to facilitate direct comparisons with predictions from present and future simulations. Multiple significant differences are observed between the data and parton shower Monte Carlo predictions, providing input to improve these predictions of the main source of background events in analyses involving boosted Higgs bosons decaying into $b$-quarks.

This paper presents a measurement of forward-forward and forward-central dijet azimuthal angular correlations and conditional yields in proton-proton ($pp$) and proton-lead ($p$+Pb) collisions as a probe of the nuclear gluon density in regions where the fraction of the average momentum per nucleon carried by the parton entering the hard scattering is low. In these regions, gluon saturation can modify the rapidly increasing parton distribution function of the gluon. The analysis utilizes 25 pb$^{-1}$ of $pp$ data and 360 $\mu \mathrm{b}^{-1}$ of $p$+Pb data, both at $\sqrt{s_{\rm NN}}$ = 5.02 TeV, collected in 2015 and 2016, respectively, with the ATLAS detector at the LHC. The measurement is performed in the center-of-mass frame of the nucleon-nucleon system in the rapidity range between $-$4.0 and 4.0 using the two highest transverse momentum jets in each event, with the highest transverse momentum jet restricted to the forward rapidity range. No significant broadening of azimuthal angular correlations is observed for forward-forward or forward-central dijets in $p$+Pb compared to $pp$ collisions. For forward-forward jet pairs in the proton-going direction, the ratio of conditional yields in $p$+Pb collisions to those in $pp$ collisions is suppressed by approximately 20%, with no significant dependence on the transverse momentum of the dijet system. No modification of conditional yields is observed for forward-central dijets.

This paper describes a search for pairs of neutral, long-lived particles decaying in the ATLAS calorimeter. Long-lived particles occur in many extensions to the Standard Model and may elude searches for new promptly decaying particles. The analysis considers neutral, long-lived scalars with masses between 5 GeV and 400 GeV, produced from decays of heavy bosons with masses between 125 GeV and 1000 GeV, where the long-lived scalars decay into Standard Model fermions. The analysis uses either 10.8 fb$^{-1}$ or 33.0 fb$^{-1}$ of data (depending on the trigger) recorded in 2016 at the LHC with the ATLAS detector in proton-proton collisions at a centre-of-mass energy of 13 TeV. No significant excess is observed, and limits are reported on the production cross section times branching ratio as a function of the proper decay length of the long-lived particles.

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 ratio of the cross sections for inclusive isolated-photon production in $pp$ collisions at centre-of-mass energies of 13 and 8 TeV is measured using the ATLAS detector at the LHC. The integrated luminosities of the 13 TeV and 8 TeV datasets are 3.2 fb$^{-1}$ and 20.2 fb$^{-1}$, respectively. The ratio is measured as a function of the photon transverse energy in different regions of the photon pseudorapidity. The predictions from next-to-leading-order perturbative QCD calculations are compared with the measured ratio. The experimental systematic uncertainties as well as the uncertainties affecting the predictions are evaluated taking into account the correlations between the two centre-of-mass energies, resulting in a reduction of up to a factor of $2.5$ ($5$) in the experimental (theoretical) systematic uncertainties. The predictions based on several parameterisations of the proton parton distribution functions agree with the data within the reduced experimental and theoretical uncertainties. In addition, this ratio to that of the fiducial cross sections for $Z$ boson production at 13 and 8 TeV using the decay channels $Z \rightarrow e^+e^-$ and $Z \rightarrow \mu^+\mu^-$ is made and compared with the theoretical predictions. In this double ratio, a further reduction of the experimental uncertainty is obtained because the uncertainties arising from the luminosity measurement cancel out. The predictions describe the measurements of the double ratio within the theoretical and experimental uncertainties.

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 measurement of the associated production of a top-quark pair ($t\bar{t}$) with a vector boson ($W$, $Z$) in proton-proton collisions at a center-of-mass energy of 13 TeV is presented, using $36.1$ fb$^{-1}$ of integrated luminosity collected by the ATLAS detector at the Large Hadron Collider. Events are selected in channels with two same- or opposite-sign leptons (electrons or muons), three leptons or four leptons, and each channel is further divided into multiple regions to maximize the sensitivity of the measurement. The $t\bar{t}Z$ and $t\bar{t}W$ production cross sections are simultaneously measured using a combined fit to all regions. The best-fit values of the production cross sections are $\sigma_{t\bar{t}Z} = 0.95 \pm 0.08_{\mathrm{stat.}} \pm 0.10_{\mathrm{syst.}}$ pb and $\sigma_{t\bar{t}W} = 0.87 \pm 0.13_{\mathrm{stat.}} \pm 0.14_{\mathrm{syst.}}$ pb in agreement with the Standard Model predictions. The measurement of the $t\bar{t}Z$ cross section is used to set constraints on effective field theory operators which modify the $t\bar{t}Z$ vertex.

A search for new particles decaying into a pair of top quarks is performed using proton-proton collision data recorded with the ATLAS detector at the Large Hadron Collider at a center-of-mass energy of $\sqrt{s} = $13 TeV corresponding to an integrated luminosity of 36.1 fb$^{-1}$. Events consistent with top-quark pair production and the fully hadronic decay mode of the top quarks are selected by requiring multiple high transverse momentum jets including those containing $b$-hadrons. Two analysis techniques, exploiting dedicated top-quark pair reconstruction in different kinematic regimes, are used to optimize the search sensitivity to new hypothetical particles over a wide mass range. The invariant mass distribution of the two reconstructed top-quark candidates is examined for resonant production of new particles with various spins and decay widths. No significant deviation from the Standard Model prediction is observed and limits are set on the production cross-section times branching fraction for new hypothetical $Z'$ bosons, dark-matter mediators, Kaluza-Klein gravitons and Kaluza-Klein gluons. By comparing with the predicted production cross-sections, the $Z'$ boson in the topcolor-assisted-technicolor model is excluded for masses up to 3.1$-$3.6 TeV, the dark-matter mediators in a simplified framework are excluded in the mass ranges from 0.8 TeV to 0.9 TeV and from 2.0 TeV to 2.2 TeV, and the Kaluza-Klein gluon is excluded for masses up to 3.4 TeV, depending on the decay widths of the particles.

A search is performed for localised excesses in dijet mass distributions of low-dijet-mass events produced in association with a high transverse energy photon. The search uses up to 79.8 fb$^{-1}$ of LHC proton-proton collisions collected by the ATLAS experiment at a centre-of-mass energy of 13 TeV during 2015-2017. Two variants are presented: one which makes no jet flavour requirements and one which requires both jets to be tagged as $b$-jets. The observed mass distributions are consistent with multi-jet processes in the Standard Model. The data are used to set upper limits on the production cross-section for a benchmark $Z^\prime$ model and, separately, on generic Gaussian-shape contributions to the mass distributions, extending the current ATLAS constraints on dijet resonances to the mass range between 225 and 1100 GeV.

A search for a narrow scalar resonance decaying into an opposite-sign muon pair produced in events with and without $b$-tagged jets is presented in this paper. The search uses 36.1 fb$^{-1}$ of $\sqrt{s}= 13$ TeV proton-proton collision data recorded by the ATLAS experiment at the LHC. No significant excess of events above the expected Standard Model background is observed in the investigated mass range of 0.2 to 1.0 TeV. The observed upper limits at 95$\%$ confidence level on the cross section times branching ratio for $b$-quark associated production and gluon-gluon fusion are between 1.9 and 41 fb and 1.6 and 44 fb respectively, which is consistent with expectations.

A search for a right-handed gauge boson $W_{\mathrm{R}}$, decaying into a boosted right-handed heavy neutrino $N_{\mathrm{R}}$, in the framework of Left-Right Symmetric Models is presented. It is based on data from proton-proton collisions with a centre-of-mass energy of 13 TeV collected by the ATLAS detector at the Large Hadron Collider during the years 2015, 2016 and 2017, corresponding to an integrated luminosity of 80 fb$^{-1}$. The search is performed separately for electrons and muons in the final state. A distinguishing feature of the search is the use of large-radius jets containing electrons. Selections based on the signal topology result in smaller background compared with to expected signal. No significant deviation from the Standard Model prediction is observed and lower limits are set in the $W_{\mathrm{R}}$ and $N_{\mathrm{R}}$ mass plane. Mass values of the $W_{\mathrm{R}}$ smaller than 3.8-5 TeV are excluded for $N_{\mathrm{R}}$ in the mass range 0.1-1.8 TeV.

This paper reports on a search for the electroweak diboson ($WW/WZ/ZZ$) production in association with a high-mass dijet system, using data from proton-proton collisions at a center-of-mass energy of $\sqrt{s}=13$ TeV. The data, corresponding to an integrated luminosity of 35.5 fb$^{-1}$, were recorded with the ATLAS detector in 2015 and 2016 at the Large Hadron Collider. The search is performed in final states in which one boson decays leptonically, and the other boson decays hadronically. The hadronically decaying $W/Z$ boson is reconstructed as either two small-radius jets or one large-radius jet using jet substructure techniques. The electroweak production of $WW/WZ/ZZ$ in association with two jets is measured with an observed (expected) significance of 2.7 (2.5) standard deviations, and the fiducial cross section is measured to be $45.1 \pm 8.6(\mathrm{stat.}) ^{+15.9} _{-14.6} (\mathrm{syst.})$ fb.

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.

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 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.

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.

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 $60<|z|\le100$.

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.

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 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

A search for a heavy charged-boson resonance decaying into a charged lepton (electron or muon) and a neutrino is reported. A data sample of 139 fb$^{-1}$ of proton-proton collisions at $\sqrt{s} = 13$ TeV collected with the ATLAS detector at the LHC during 2015-2018 is used in the search. The observed transverse mass distribution computed from the lepton and missing transverse momenta is consistent with the distribution expected from the Standard Model, and upper limits on the cross section for $pp \to W^\prime \to \ell\nu$ are extracted ($\ell = e$ or $\mu$). These vary between 1.3 pb and 0.05 fb depending on the resonance mass in the range between 0.15 and 7.0 TeV at 95% confidence level for the electron and muon channels combined. Gauge bosons with a mass below 6.0 TeV and 5.1 TeV are excluded in the electron and muon channels, respectively, in a model with a resonance that has couplings to fermions identical to those of the Standard Model $W$ boson. Cross-section limits are also provided for resonances with several fixed $\Gamma / m$ values in the range between 1% and 15%. Model-independent limits are derived in single-bin signal regions defined by a varying minimum transverse mass threshold. The resulting visible cross-section upper limits range between 4.6 (15) pb and 22 (22) ab as the threshold increases from 130 (110) GeV to 5.1 (5.1) TeV in the electron (muon) channel.

The inclusive cross-section for jet production in association with a Z boson decaying into an electron-positron pair is measured as a function of the transverse momentum and the absolute rapidity of jets using 19.9 fb$^{-1}$ of $\sqrt s = 8$ TeV proton-proton collision data collected with the ATLAS detector at the Large Hadron Collider. The measured Z + jets cross-section is unfolded to the particle level. The cross-section is compared with state-of-the-art Standard Model calculations, including the next-to-leading-order and next-to-next-to-leading-order perturbative QCD calculations, corrected for non-perturbative and QED radiation effects. The results of the measurements cover final-state jets with transverse momenta up to 1 TeV, and show good agreement with fixed-order calculations.

Single- and double-differential cross-section measurements are presented for the production of top-quark pairs, in the lepton + jets channel at particle and parton level. Two topologies, resolved and boosted, are considered and the results are presented as a function of several kinematic variables characterising the top and $t\bar{t}$ system and jet multiplicities. The study was performed using data from $pp$ collisions at centre-of-mass energy of 13 TeV collected in 2015 and 2016 by the ATLAS detector at the CERN Large Hadron Collider (LHC), corresponding to an integrated luminosity of $36~\mathrm{fb}^{-1}$. Due to the large $t\bar{t}$ cross-section at the LHC, such measurements allow a detailed study of the properties of top-quark production and decay, enabling precision tests of several Monte Carlo generators and fixed-order Standard Model predictions. Overall, there is good agreement between the theoretical predictions and the data.

Several models of physics beyond the Standard Model predict the existence of dark photons, light neutral particles decaying into collimated leptons or light hadrons. This paper presents a search for long-lived dark photons produced from the decay of a Higgs boson or a heavy scalar boson and decaying into displaced collimated Standard Model fermions. The search uses data corresponding to an integrated luminosity of 36.1 fb$^{-1}$ collected in proton-proton collisions at $\sqrt{s} =$ 13 TeV recorded in 2015-2016 with the ATLAS detector at the Large Hadron Collider. The observed number of events is consistent with the expected background, and limits on the production cross section times branching fraction as a function of the proper decay length of the dark photon are reported. A cross section times branching fraction above 4 pb is excluded for a Higgs boson decaying into two dark photons for dark-photon decay lengths between 1.5 mm and 307 mm.

A search for supersymmetry through the pair production of electroweakinos with mass splittings near the electroweak scale and decaying via on-shell $W$ and $Z$ bosons is presented for a three-lepton final state. The analyzed proton-proton collision data taken at a center-of-mass energy of $\sqrt{s}$ = 13 TeV were collected between 2015 and 2018 by the ATLAS experiment at the Large Hadron Collider, corresponding to an integrated luminosity of 139 fb$^{-1}$. A search, emulating the recursive jigsaw reconstruction technique with easily reproducible laboratory-frame variables, is performed. The two excesses observed in the 2015-2016 data recursive jigsaw analysis in the low-mass three-lepton phase space are reproduced. Results with the full dataset are in agreement with the Standard Model expectations. They are interpreted to set exclusion limits at 95% confidence level on simplified models of chargino-neutralino pair production for masses up to 345 GeV.

A search for the electroweak production of charginos and sleptons decaying into final states with two electrons or muons is presented. The analysis is based on 139 fb$^{-1}$ of proton-proton collisions recorded by the ATLAS detector at the Large Hadron Collider at $\sqrt{s}=13$ TeV. Three $R$-parity-conserving scenarios where the lightest neutralino is the lightest supersymmetric particle are considered: the production of chargino pairs with decays via either $W$ bosons or sleptons, and the direct production of slepton pairs. The analysis is optimised for the first of these scenarios, but the results are also interpreted in the others. No significant deviations from the Standard Model expectations are observed and limits at 95 % confidence level are set on the masses of relevant supersymmetric particles in each of the scenarios. For a massless lightest neutralino, masses up to 420 GeV are excluded for the production of the lightest-chargino pairs assuming $W$-boson-mediated decays and up to 1 TeV for slepton-mediated decays, whereas for slepton-pair production masses up to 700 GeV are excluded assuming three generations of mass-degenerate sleptons.

A search for flavour-changing neutral current (FCNC) events via the coupling of a top quark, a photon, and an up or charm quark is presented using 81 fb$^{-1}$ of proton-proton collision data taken at a centre-of-mass energy of 13 TeV with the ATLAS detector at the LHC. Events with a photon, an electron or muon, a $b$-tagged jet, and missing transverse momentum are selected. A neural network based on kinematic variables differentiates between events from signal and background processes. The data are consistent with the background-only hypothesis, and limits are set on the strength of the $tq\gamma$ coupling in an effective field theory. These are also interpreted as 95% CL upper limits on the cross section for FCNC $t\gamma$ production via a left-handed (right-handed) $tu\gamma$ coupling of 36 fb (78 fb) and on the branching ratio for $t\rightarrow \gamma u$ of $2.8\times 10^{-5}$ ($6.1\times 10^{-5}$). In addition, they are interpreted as 95% CL upper limits on the cross section for FCNC $t\gamma$ production via a left-handed (right-handed) $tc\gamma$ coupling of 40 fb (33 fb) and on the branching ratio for $t\rightarrow \gamma c$ of $22\times 10^{-5}$ ($18\times 10^{-5}$).

A search for long-lived particles decaying into hadrons and at least one muon is presented. The analysis selects events that pass a muon or missing-transverse-momentum trigger and contain a displaced muon track and a displaced vertex. The analyzed dataset of proton-proton collisions at $\sqrt{s} = 13$ TeV was collected with the ATLAS detector and corresponds to 136 fb$^{-1}$. The search employs dedicated reconstruction techniques that significantly increase the sensitivity to long-lived particle decays that occur in the ATLAS inner detector. Background estimates for Standard Model processes and instrumental effects are extracted from data. The observed event yields are compatible with those expected from background processes. The results are presented as limits at 95% confidence level on model-independent cross sections for processes beyond the Standard Model, and interpreted as exclusion limits in scenarios with pair-production of long-lived top squarks that decay via a small $R$-parity-violating coupling into a quark and a muon. Top squarks with masses up to 1.7 TeV are excluded for a lifetime of 0.1 ns, and masses below 1.3 TeV are excluded for lifetimes between 0.01 ns and 30 ns.

A search for a chargino$-$neutralino pair decaying via the 125 GeV Higgs boson into photons is presented. The study is based on the data collected between 2015 and 2018 with the ATLAS detector at the LHC, corresponding to an integrated luminosity of 139 fb$^{-1}$ of $pp$ collisions at a centre-of-mass energy of 13 TeV. No significant excess over the expected background is observed. Upper limits at 95% confidence level for a massless $\tilde{\chi}^{0}_{1}$ are set on several electroweakino production cross-sections and the visible cross-section for beyond the Standard Model processes. In the context of simplified supersymmetric models, 95% confidence-level limits of up to 310 GeV in $m(\tilde{\chi}^{\pm}_{1}/\tilde{\chi}^{0}_{2})$, where $m(\tilde{\chi}^{0}_{1})=0.5$ GeV, are set. Limits at 95% confidence level are also set on the $\tilde{\chi}^{\pm}_{1}\tilde{\chi}^{0}_{2}$ cross-section in the mass plane of $m(\tilde{\chi}^{\pm}_{1}/\tilde{\chi}^{0}_{2})$ and $m(\tilde{\chi}^{0}_{1})$, and on scenarios with gravitino as the lightest supersymmetric particle. Upper limits at the 95% confidence-level are set on the higgsino production cross-section. Higgsino masses below 380 GeV are excluded for the case of the higgsino fully decaying into a Higgs boson and a gravitino.

A search for charged leptons with large impact parameters using 139 fb$^{-1}$ of $\sqrt{s} = 13$ TeV $pp$ collision data from the ATLAS detector at the LHC is presented, addressing a long-standing gap in coverage of possible new physics signatures. Results are consistent with the background prediction. This search provides unique sensitivity to long-lived scalar supersymmetric lepton-partners (sleptons). For lifetimes of 0.1 ns, selectron, smuon and stau masses up to 720 GeV, 680 GeV, and 340 GeV are respectively excluded at 95% confidence level, drastically improving on the previous best limits from LEP.

A measurement of prompt photon-pair production in proton-proton collisions at $\sqrt{s}=13$ TeV is presented. The data were recorded by the ATLAS detector at the LHC with an integrated luminosity of 139 fb$^{-1}$. Events with two photons in the well-instrumented region of the detector are selected. The photons are required to be isolated and have a transverse momentum of $p_\mathrm{T,\gamma_{1(2)}} > 40(30)$ GeV for the leading (sub-leading) photon. The differential cross sections as functions of several observables for the diphoton system are measured and compared with theoretical predictions from state-of-the-art Monte Carlo and fixed-order calculations. The QCD predictions from next-to-next-to-leading-order calculations and multi-leg merged calculations are able to describe the measured integrated and differential cross sections within uncertainties, whereas lower-order calculations show significant deviations, demonstrating that higher-order perturbative QCD corrections are crucial for this process. The resummed predictions with parton showers additionally provide an excellent description of the low transverse-momentum regime of the diphoton system.

The azimuthal variation of jet yields in heavy-ion collisions provides information about the path-length dependence of the energy loss experienced by partons passing through the hot, dense nuclear matter known as the quark-gluon plasma. This paper presents the azimuthal anisotropy coefficients $v_2$, $v_3$, and $v_4$ measured for jets in Pb+Pb collisions at $\sqrt{s_{NN}} =$ 5.02 TeV using the ATLAS detector at the LHC. The measurement uses data collected in 2015 and 2018, corresponding to an integrated luminosity of 2.2 nb$^{-1}$. The $v_n$ values are measured as a function of the transverse momentum of the jets between 71 GeV and 398 GeV and the event centrality. A nonzero value of $v_2$ is observed in all but the most central collisions. The value of $v_2$ is largest for jets with lower transverse momentum, with values up to 0.05 in mid-central collisions. A smaller, nonzero value of $v_3$ of approximately 0.01 is measured with no significant dependence on jet $p_T$ or centrality, suggesting that fluctuations in the initial state play a small but distinct role in jet energy loss. No significant deviation of $v_4$ from zero is observed in the measured kinematic region.

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.

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 for new phenomena in final states with hadronically decaying tau leptons, $b$-jets, and missing transverse momentum is presented. The analyzed dataset comprises $pp$~collision data at a center-of-mass energy of $\sqrt s = 13$ TeV with an integrated luminosity of 139/fb, delivered by the Large Hadron Collider and recorded with the ATLAS detector from 2015 to 2018. The observed data are compatible with the expected Standard Model background. The results are interpreted in simplified models for two different scenarios. The first model is based on supersymmetry and considers pair production of top squarks, each of which decays into a $b$-quark, a neutrino and a tau slepton. Each tau slepton in turn decays into a tau lepton and a nearly massless gravitino. Within this model, top-squark masses up to 1.4 TeV can be excluded at the 95% confidence level over a wide range of tau-slepton masses. The second model considers pair production of leptoquarks with decays into third-generation leptons and quarks. Depending on the branching fraction into charged leptons, leptoquarks with masses up to around 1.25 TeV can be excluded at the 95% confidence level for the case of scalar leptoquarks and up to 1.8 TeV (1.5 TeV) for vector leptoquarks in a Yang--Mills (minimal-coupling) scenario. In addition, model-independent upper limits are set on the cross section of processes beyond the Standard Model.

Differential and double-differential distributions of kinematic variables of leptons from decays of top-quark pairs ($t\bar{t}$) are measured using the full LHC Run 2 data sample collected with the ATLAS detector. The data were collected at a $pp$ collision energy of $\sqrt{s}=13$ TeV and correspond to an integrated luminosity of 140 fb$^{-1}$. The measurements use events containing an oppositely charged $e\mu$ pair and $b$-tagged jets. The results are compared with predictions from several Monte Carlo generators. While no prediction is found to be consistent with all distributions, a better agreement with measurements of the lepton $p_{\text{T}}$ distributions is obtained by reweighting the $t\bar{t}$ sample so as to reproduce the top-quark $p_{\text{T}}$ distribution from an NNLO calculation. The inclusive top-quark pair production cross-section is measured as well, both in a fiducial region and in the full phase-space. The total inclusive cross-section is found to be \[ \sigma_{t\bar{t}} = 829 \pm 1\;(\textrm{stat}) \pm 13\;(\textrm{syst}) \pm 8\;(\textrm{lumi}) \pm 2\; (\textrm{beam})\ \textrm{pb}, \] where the uncertainties are due to statistics, systematic effects, the integrated luminosity and the beam energy. This is in excellent agreement with the theoretical expectation.