{"@context":"http://schema.org","@id":"https://doi.org/10.17182/hepdata.135074.v2","@reverse":{"isBasedOn":[{"@type":"ScholarlyArticle","identifier":{"@type":"PropertyValue","propertyID":"URL","value":"https://inspirehep.net/literature/2183192"}},{"@id":"https://doi.org/10.1016/j.physletb.2023.137895","@type":"JournalArticle"}]},"@type":"Dataset","additionalType":"Collection","author":{"@type":"Organization","name":"ATLAS Collaboration"},"creator":{"@type":"Organization","name":"ATLAS Collaboration"},"datePublished":"2023","description":"CERN-LHC. Measurements of joint-polarisation states of $W$ and $Z$ gauge bosons in $W^{\\pm}Z$ production are presented.\nThe data set used corresponds to an integrated luminosity of \\mbox{$139$~fb$^{-1}$} of proton\u2013proton collisions at a centre-of-mass energy of $13$~TeV recorded by the ATLAS detector at the CERN Large Hadron Collider.\nThe $W^{\\pm}Z$ candidate events are reconstructed using leptonic decay modes of the gauge bosons into electrons and muons.\nThe simultaneous pair-production of longitudinally polarised vector bosons is measured for the first time with a significance of $7.1$ standard deviations.\nThe measured joint helicity fractions integrated over the fiducial region are $f_{\\mathrm{00}} = 0.067 \\pm 0.010$, $f_{\\mathrm{0T}} = 0.110 \\pm 0.029$, $f_{\\mathrm{T0}} = 0.179 \\pm 0.023$ and $f_{\\mathrm{TT}} = 0.644 \\pm 0.032$, in agreement with the next-to-leading-order Standard Model predictions.\nIndividual helicity fractions of the $W$ and $Z$ bosons are also measured and found to be consistent with joint helicity fractions within\nthe expected amounts of correlation.\nBoth the joint and individual helicity fractions are also measured separately in $W^+Z$ and $W^-Z$ events.\nInclusive and differential cross sections for several kinematic observables sensitive to polarisation are presented.\n\nMeasured differential cross sections are reported in this HEPdata entry.\n\nIntegrated cross sections over bins of different kinematic observables are reported. \nThe reported cross sections are not divided by the bin width.\n\nThe cross sections are measured in a fiducial phase space reflecting the detector acceptance, defined by:\n- $p_{\\mathrm{T}}$ of electrons and muons from Z0 decays > 15 GeV\n- $p_{\\mathrm{T}}$ of electrons and muons from the $W^{\\pm}$ decays > 20 GeV\n- $|\\eta|$ of muons and electrons < 2.5\n- Leptons from the Z0 boson are separated by $\\Delta R(\\ell,\\ell) > 0.2$ from each other\n- Leptons from the Z0 and W bosons are separated by $\\Delta R(\\ell,\\ell) > 0.3$ from each other\n- |dilepton mass - Z0 mass| < 10 GeV\n- $m_{\\mathrm{T}}$ of $W^{\\pm}$ > 30 GeV.\n\n\nCross sections are reported using kinematics of final-state prompt leptons defined before QED final-state radiation (FSR),\ni.e. Born leptons, or using dressed leptons.\n\nAt particle level, the kinematics of final-state prompt dressed electrons and muons is computed including the contributions from final-state radiated photons within a distance in the ($\\eta,\\phi$) plane of \n$\\Delta R = \\sqrt{(\\Delta\\eta)^2 + (\\Delta\\phi)^2} = 0.1$ around the direction of the charged lepton. \nThese dressed leptons and the final-state neutrinos that do not originate from hadron or $\\tau$ decays  are \nassociated with the $W$ and $Z$ boson decay products with an algorithmic approach, called ``resonant shape''. \nThis algorithm is  based on the value of an estimator expressing the product of the nominal line shapes of \nthe $W$ and $Z$ resonances\n\n   $P = \\left| \\frac{1}{ m^2_{(\\ell^+,\\ell^-)} - \\left(m_Z^{\\textrm{PDG}}\\right)^2 + i \\; \\Gamma_Z^{\\textrm{PDG}} \\; m_Z^{\\textrm{PDG}} } \\right|^2  \\times \\; \\left| \\frac {1} { m^2_{(\\ell',\\nu_{\\ell'})} - \\left(m_W^{\\textrm{PDG}}\\right)^2 + i \\; \\Gamma_W^{\\textrm{PDG}} \\; m_W^{\\textrm{PDG}} } \\right|^2$\n\nwhere $m_Z^{\\textrm{PDG}}$ ($m_W^{\\textrm{PDG}}$) and $\\Gamma_Z^{\\textrm{PDG}}$ ($\\Gamma_W^{\\textrm{PDG}}$) are the \nworld average mass and total width of the $Z$ ($W$) boson, respectively, as reported by the Particle Data Group. \nThe input to the estimator is the invariant mass $m$ of all possible pairs ($\\ell^+,\\ell^-$) and\n($\\ell',\\nu_{\\ell'}$) satisfying the fiducial selection requirements. \nThe final choice of which leptons are assigned to the $W$ or $Z$ bosons corresponds to the configuration \nexhibiting the highest value of the estimator.\n\nFor cross sections using Born leptons, the association of leptons to $W$ or $Z$ bosons is performed using the Powheg Monte Carlo generator.","hasPart":[{"@id":"https://doi.org/10.17182/hepdata.135074.v2/t1","@type":"Dataset","description":"Measured fiducial Born-level cross section for a single leptonic decay channel $\\ell'^\\pm \\nu \\ell^+ \\ell'^-$ of the $W$ and $Z$...","name":"Table 1"},{"@id":"https://doi.org/10.17182/hepdata.135074.v2/t2","@type":"Dataset","description":"Correlation matrix for the unfolded cross section.","name":"Table 2"},{"@id":"https://doi.org/10.17182/hepdata.135074.v2/t3","@type":"Dataset","description":"Measured fiducial Born-level cross section for a single leptonic decay channel $\\ell'^\\pm \\nu \\ell^+ \\ell'^-$ of the $W$ and $Z$...","name":"Table 3"},{"@id":"https://doi.org/10.17182/hepdata.135074.v2/t4","@type":"Dataset","description":"Correlation matrix for the unfolded cross section.","name":"Table 4"},{"@id":"https://doi.org/10.17182/hepdata.135074.v2/t5","@type":"Dataset","description":"Measured fiducial Born-level 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9"},{"@id":"https://doi.org/10.17182/hepdata.135074.v2/t10","@type":"Dataset","description":"Correlation matrix for the unfolded cross section.","name":"Table 10"},{"@id":"https://doi.org/10.17182/hepdata.135074.v2/t11","@type":"Dataset","description":"Measured fiducial dressed-level cross section for a single leptonic decay channel $\\ell'^\\pm \\nu \\ell^+ \\ell'^-$ of the $W$ and $Z$...","name":"Table 11"},{"@id":"https://doi.org/10.17182/hepdata.135074.v2/t12","@type":"Dataset","description":"Correlation matrix for the unfolded cross section.","name":"Table 12"},{"@id":"https://doi.org/10.17182/hepdata.135074.v2/t13","@type":"Dataset","description":"Measured fiducial dressed-level cross section for a single leptonic decay channel $\\ell'^\\pm \\nu \\ell^+ \\ell'^-$ of the $W$ and $Z$...","name":"Table 13"},{"@id":"https://doi.org/10.17182/hepdata.135074.v2/t14","@type":"Dataset","description":"Correlation matrix for the unfolded cross section.","name":"Table 14"},{"@id":"https://doi.org/10.17182/hepdata.135074.v2/t15","@type":"Dataset","description":"Measured fiducial dressed-level cross section for a single leptonic decay channel $\\ell'^\\pm \\nu \\ell^+ \\ell'^-$ of the $W$ and $Z$...","name":"Table 15"},{"@id":"https://doi.org/10.17182/hepdata.135074.v2/t16","@type":"Dataset","description":"Correlation matrix for the unfolded cross section.","name":"Table 16"},{"@id":"https://doi.org/10.17182/hepdata.135074.v2/t17","@type":"Dataset","description":"Measured fiducial dressed-level cross section for a single leptonic decay channel $\\ell'^\\pm \\nu \\ell^+ \\ell'^-$ of the $W$ and $Z$...","name":"Table 17"},{"@id":"https://doi.org/10.17182/hepdata.135074.v2/t18","@type":"Dataset","description":"Correlation matrix for the unfolded cross section.","name":"Table 18"},{"@id":"https://doi.org/10.17182/hepdata.135074.v2/t19","@type":"Dataset","description":"Measured fiducial dressed-level cross section for a single leptonic decay channel $\\ell'^\\pm \\nu \\ell^+ \\ell'^-$ of the $W$ and $Z$...","name":"Table 19"},{"@id":"https://doi.org/10.17182/hepdata.135074.v2/t20","@type":"Dataset","description":"Correlation matrix for the unfolded cross section.","name":"Table 20"}],"identifier":[{"@type":"PropertyValue","propertyID":"HEPDataRecord","value":"https://www.hepdata.net/record/ins2183192?version=2"},{"@type":"PropertyValue","propertyID":"HEPDataRecordAlt","value":"https://www.hepdata.net/record/135074"}],"inLanguage":"en","name":"Observation of gauge boson joint-polarisation states in $W^{\\pm}Z$ production from $pp$ collisions at $\\sqrt{s} = 13$ TeV with the ATLAS detector","provider":{"@type":"Organization","name":"HEPData"},"publisher":{"@type":"Organization","name":"HEPData"},"url":"https://www.hepdata.net/record/ins2183192?version=2","version":2}