A prescription is presented for a new and practical correlation coefficient, $\phi_K$, based on several refinements to Pearson's hypothesis test of independence of two variables. The combined features of $\phi_K$ form an advantage over existing coefficients. First, it works consistently between categorical, ordinal and interval variables. Second, it captures non-linear dependency. Third, it reverts to the Pearson correlation coefficient in case of a bi-variate normal input distribution. These are useful features when studying the correlation between variables with mixed types. Particular emphasis is paid to the proper evaluation of statistical significance of correlations and to the interpretation of variable relationships in a contingency table, in particular in case of low statistics samples and significant dependencies. Three practical applications are discussed. The presented algorithms are easy to use and available through a public Python library.

This change does not have any impact on the measured helicity fractions, but it changes the obtained limits on the anomalous couplings.

The top-quark mass is measured in the all-hadronic top-antitop quark decay channel using proton-proton collisions at a centre-of-mass energy of √(s)=8 TeV with the ATLAS detector at the CERN Large Hadron Collider. The data set used in the analysis corresponds to an integrated luminosity of 20 . 2 fb −1 . The large multi-jet background is modelled using a data-driven method. The top-quark mass is obtained from template fits to the ratio of the three-jet to the dijet mass. The three-jet mass is obtained from the three jets assigned to the top quark decay. From these three jets the dijet mass is obtained using the two jets assigned to the W boson decay. The top-quark mass is measured to be 173 . 72 ± 0 . 55 (stat . ) ± 1 . 01 (syst . ) GeV.

bstract To probe the W tb vertex structure, top-quark and W -boson polarisation observables are measured from t -channel single-top-quark events produced in proton-proton collisions at a centre-of-mass energy of 8 TeV. The dataset corresponds to an integrated luminosity of 20.2 fb −1 , recorded with the ATLAS detector at the LHC. Selected events contain one isolated electron or muon, large missing transverse momentum and exactly two jets, with one of them identified as likely to contain a b -hadron. Stringent selection requirements are applied to discriminate t -channel single-top-quark events from background. The polarisation observables are extracted from asymmetries in angular distributions measured with respect to spin quantisation axes appropriately chosen for the top quark and the W boson. The asymmetry measurements are performed at parton level by correcting the observed angular distributions for detector effects and hadronisation after subtracting the background contributions. The measured top-quark and W -boson polarisation values are in agreement with the Standard Model predictions. Limits on the imaginary part of the anomalous coupling g R are also set from model-independent measurements.

The reconstruction and calibration algorithms used to calculate missing transverse momentum ([Formula: see text] ) with the ATLAS detector exploit energy deposits in the calorimeter and tracks reconstructed in the inner detector as well as the muon spectrometer. Various strategies are used to suppress effects arising from additional proton-proton interactions, called pileup, concurrent with the hard-scatter processes. Tracking information is used to distinguish contributions from the pileup interactions using their vertex separation along the beam axis. The performance of the [Formula: see text] reconstruction algorithms, especially with respect to the amount of pileup, is evaluated using data collected in proton-proton collisions at a centre-of-mass energy of 8 [Formula: see text] during 2012, and results are shown for a data sample corresponding to an integrated luminosity of [Formula: see text]. The simulation and modelling of [Formula: see text]  in events containing a Z boson decaying to two charged leptons (electrons or muons) or a W boson decaying to a charged lepton and a neutrino are compared to data. The acceptance for different event topologies, with and without high transverse momentum neutrinos, is shown for a range of threshold criteria for [Formula: see text] , and estimates of the systematic uncertainties in the [Formula: see text]  measurements are presented.

A search for dark matter pair production in association with a Higgs boson decaying to a pair of bottom quarks is presented, using 3.2 fb − 1 of pp collisions at a centre-of-mass energy of 13 TeV collected by the ATLAS detector at the LHC. The decay of the Higgs boson is reconstructed as a high-momentum b ¯ b system with either a pair of small-radius jets, or a single large-radius jet with substructure. The observed data are found to be consistent with the expected backgrounds. Results are interpreted using a simplified model with a Z (cid:3) gauge boson mediating the interaction between dark matter and the Standard Model as well as a two-Higgs-doublet model containing an additional Z (cid:3) boson which decays to a Standard Model Higgs boson and a new pseudoscalar Higgs boson, the latter decaying into a pair of dark matter particles.

The W boson angular distribution in events with high transverse momentum jets is measured using data collected by the ATLAS experiment from proton–proton collisions at a centre-of-mass energy √ s = 8 TeV at the Large Hadron Collider, corresponding to an integrated luminosity of 20 . 3 fb − 1 . The focus is on the contributions to W + jets processes from real W emission, which is achieved by studying events where a muon is observed close to a high transverse momentum jet. At small angular separations, these contributions are expected to be large. Various theoretical models of this process are compared to the data in terms of the absolute cross-section and the angular distributions of the muon from the leptonic W decay.

The dynamics of isolated-photon plus one-, two- and three-jet production in pp collisions at a centre-of-mass energy of 8 TeV are studied with the ATLAS detector at the LHC using a data set with an integrated luminosity of 20.2 fb$^{-1}$. Measurements of isolated-photon plus jets cross sections are presented as functions of the photon and jet transverse momenta. The cross sections as functions of the azimuthal angle between the photon and the jets, the azimuthal angle between the jets, the photon--jet invariant mass and the scattering angle in the photon--jet centre-of-mass system are presented. The pattern of QCD radiation around the photon and the leading jet is investigated by measuring jet production in an annular region centred on each object; enhancements are observed around the leading jet with respect to the photon in the directions towards the beams. The experimental measurements are compared to several different theoretical calculations, and overall a good description of the data is found

The centrality dependence of the mean charged-particle multiplicity as a function of pseudorapidity is measured in approximately 1 mu b(-1) of proton-lead collisions at a nucleon-nucleon centre-of-mass energy of root s(NN) = 5.02 TeV using the ATLAS detector at the Large Hadron Collider. Charged particles with absolute pseudorapidity less than 2.7 are reconstructed using the ATLAS pixel detector. The p + Pb collision centrality is characterised by the total transverse energy measured in the Pb-going direction of the forward calorimeter. The charged-particle pseudorapidity distributions are found to vary strongly with centrality, with an increasing asymmetry between the proton-going and Pb-going directions as the collisions become more central. Three different estimations of the number of nucleons participating in the p + Pb collision have been carried out using the Glauber model as well as two Glauber-Gribov inspired extensions to the Glauber model. Charged-particle multiplicities per participant pair are found to vary differently for these three models, highlighting the importance of including colour fluctuations in nucleon-nucleon collisions in the modelling of the initial state of p + Pb collisions.

The production rates of prompt and non-prompt [Formula: see text] and [Formula: see text] mesons in their dimuon decay modes are measured using 2.1 and 11.4 fb[Formula: see text] of data collected with the ATLAS experiment at the Large Hadron Collider, in proton-proton collisions at [Formula: see text] and 8 respectively. Production cross-sections for prompt as well as non-prompt sources, ratios of [Formula: see text] to [Formula: see text] production, and the fractions of non-prompt production for [Formula: see text] and [Formula: see text] are measured as a function of meson transverse momentum and rapidity. The measurements are compared to theoretical predictions.

A search for the decays of the Higgs and Z bosons to a ϕ meson and a photon is performed with a pp collision data sample corresponding to an integrated luminosity of 2.7  fb^{-1} collected at sqrt[s]=13  TeV with the ATLAS detector at the LHC. No significant excess of events is observed above the background, and 95% confidence level upper limits on the branching fractions of the Higgs and Z boson decays to ϕγ of 1.4×10^{-3} and 8.3×10^{-6}, respectively, are obtained.

Searches for new heavy resonances decaying to $WW$, $WZ$, and $ZZ$ bosons are presented, using a data sample corresponding to 3.2 fb$^{-1}$ of $pp$ collisions at $\sqrt{s}=13$ TeV collected with the ATLAS detector at the CERN Large Hadron Collider. Analyses selecting $\nu\nu qq$, $\ell\nu qq$, $\ell\ell qq$ and $qqqq$ final states are combined, searching for a narrow-width resonance with mass between 500 and 3000 GeV. The discriminating variable is either an invariant mass or a transverse mass. No significant deviations from the Standard Model predictions are observed. Three benchmark models are tested: a model predicting the existence of a new heavy scalar singlet, a simplified model predicting a heavy vector-boson triplet, and a bulk Randall-Sundrum model with a heavy spin-2 graviton. Cross-section limits are set at the 95% confidence level and are compared to theoretical cross-section predictions for a variety of models. The data exclude a scalar singlet with mass below 2650 GeV, a heavy vector-boson triplet with mass below 2600 GeV, and a graviton with mass below 1100 GeV. These results significantly extend the previous limits set using $pp$ collisions at $\sqrt{s}=8$ TeV.

The ATLAS experiment has performed extensive searches for the electroweak production of charginos, neutralinos and staus. This article summarizes and extends the search for electroweak supersymmetry with new analyses targeting scenarios not covered by previously published searches. New searches use vector-boson fusion production, initial-state radiation jets, and low-momentum lepton final states, as well as multivariate analysis techniques to improve the sensitivity to scenarios with small mass splittings and low-production cross-sections. Results are based on 20 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}$=8 TeV recorded with the ATLAS experiment at the Large Hadron Collider. No significant excess beyond Standard Model expectations is observed. The new and existing searches are combined and interpreted in terms of 95% confidence-level exclusion limits in simplified models, where a single production process and decay mode is assumed, as well as within phenomenological supersymmetric models.

Event-shape observables measured using charged particles in inclusive Z-boson events are presented, using the electron and muon decay modes of the Z bosons. The measurements are based on an integrated luminosity of [Formula: see text] of proton-proton collisions recorded by the ATLAS detector at the LHC at a centre-of-mass energy [Formula: see text] [Formula: see text]. Charged-particle distributions, excluding the lepton-antilepton pair from the Z-boson decay, are measured in different ranges of transverse momentum of the Z boson. Distributions include multiplicity, scalar sum of transverse momenta, beam thrust, transverse thrust, spherocity, and [Formula: see text]-parameter, which are in particular sensitive to properties of the underlying event at small values of the Z-boson transverse momentum. The measured observables are compared with predictions from Pythia 8, Sherpa, and Herwig 7. Typically, all three Monte Carlo generators provide predictions that are in better agreement with the data at high Z-boson transverse momenta than at low Z-boson transverse momenta, and for the observables that are less sensitive to the number of charged particles in the event.

The last decades have seen tremendous progress in the experimental techniques for measuring key observables of the Standard Theory (ST) as well as in theoretical calculations that has led to highly precise predictions of these observables. Global electroweak fits of the ST compare the precision measurements of electroweak observables from lepton and hadron colliders at CERN and elsewhere with accurate theoretical predictions of the ST calculated at multi-loop level. For a long time, global fits have been used to assess the validity of the ST and to constrain indirectly (by exploiting contributions from quantum loops) the remaining free ST parameters, like the masses of the top quark and Higgs boson before their direct discovery. With the discovery of the Higgs boson at the Large Hadron Collider (LHC), the electroweak sector of the ST is now complete and all fundamental ST parameters are known. Hence the global fits are a powerful tool to probe the internal consistency of the ST, to predict ST parameters with high precision, and to constrain theories describing physics beyond the ST. In this chapter we review the global fits of the electroweak sector of the ST from an experimentalist's perspective. We briefly recall the most important achievements from the past (mainly driven by the precise measurements of Z pole observables), discuss the present situation after the accurate measurements of the top quark and Higgs boson masses, and present prospects of the fits as expected from new measurements at the LHC and future lepton colliders.

A search for the flavour-changing neutral-current decay [Formula: see text] is presented. Data collected by the ATLAS detector during 2012 from proton-proton collisions at the Large Hadron Collider at a centre-of-mass energy of [Formula: see text] TeV, corresponding to an integrated luminosity of 20.3 fb[Formula: see text], are analysed. Top-quark pair-production events with one top quark decaying through the [Formula: see text] ([Formula: see text]) channel and the other through the dominant Standard Model mode [Formula: see text] are considered as signal. Only the decays of the Z boson to charged leptons and leptonic W boson decays are used. No evidence for a signal is found and an observed (expected) upper limit on the [Formula: see text] branching ratio of [Formula: see text] ([Formula: see text]) is set at the 95 % confidence level.

The dijet production cross section for jets containing a b-hadron (b-jets) has been measured in proton-proton collisions with a centre-of-mass energy of [Formula: see text] TeV, using the ATLAS detector at the LHC. The data used correspond to an integrated luminosity of [Formula: see text]. The cross section is measured for events with two identified b-jets with a transverse momentum [Formula: see text] GeV and a minimum separation in the [Formula: see text]-[Formula: see text] plane of [Formula: see text]. At least one of the jets in the event is required to have [Formula: see text] GeV. The cross section is measured differentially as a function of dijet invariant mass, dijet transverse momentum, boost of the dijet system, and the rapidity difference, azimuthal angle and angular distance between the b-jets. The results are compared to different predictions of leading order and next-to-leading order perturbative quantum chromodynamics matrix elements supplemented with models for parton-showers and hadronization.