Abstract (data abstract)

CERN-LHC. Measurements of joint-polarisation states of $W$ and $Z$ gauge bosons in $W^{\pm}Z$ production are presented. The data set used corresponds to an integrated luminosity of \mbox{$139$~fb$^{-1}$} of proton–proton collisions at a centre-of-mass energy of $13$~TeV recorded by the ATLAS detector at the CERN Large Hadron Collider. The $W^{\pm}Z$ candidate events are reconstructed using leptonic decay modes of the gauge bosons into electrons and muons. The simultaneous pair-production of longitudinally polarised vector bosons is measured for the first time with a significance of $7.1$ standard deviations. The 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. Individual helicity fractions of the $W$ and $Z$ bosons are also measured and found to be consistent with joint helicity fractions within the expected amounts of correlation. Both the joint and individual helicity fractions are also measured separately in $W^+Z$ and $W^-Z$ events. Inclusive and differential cross sections for several kinematic observables sensitive to polarisation are presented. Measured differential cross sections are reported in this HEPdata entry. Integrated cross sections over bins of different kinematic observables are reported. The reported cross sections are not divided by the bin width. The cross sections are measured in a fiducial phase space reflecting the detector acceptance, defined by: - $p_{\mathrm{T}}$ of electrons and muons from Z0 decays > 15 GeV - $p_{\mathrm{T}}$ of electrons and muons from the $W^{\pm}$ decays > 20 GeV - $|\eta|$ of muons and electrons < 2.5 - Leptons from the Z0 boson are separated by $\Delta R(\ell,\ell) > 0.2$ from each other - Leptons from the Z0 and W bosons are separated by $\Delta R(\ell,\ell) > 0.3$ from each other - |dilepton mass - Z0 mass| < 10 GeV - $m_{\mathrm{T}}$ of $W^{\pm}$ > 30 GeV. Cross sections are reported using kinematics of final-state prompt leptons defined before QED final-state radiation (FSR), i.e. Born leptons, or using dressed leptons. At 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 $\Delta R = \sqrt{(\Delta\eta)^2 + (\Delta\phi)^2} = 0.1$ around the direction of the charged lepton. These dressed leptons and the final-state neutrinos that do not originate from hadron or $\tau$ decays are associated with the $W$ and $Z$ boson decay products with an algorithmic approach, called ``resonant shape''. This algorithm is based on the value of an estimator expressing the product of the nominal line shapes of the $W$ and $Z$ resonances $P = \left| \frac{1}{ m^2_{(\ell^+,\ell^-)} - \left(m_Z^{\textrm{PDG}}\right)^2 + i \; \Gamma_Z^{\textrm{PDG}} \; m_Z^{\textrm{PDG}} } \right|^2 \times \; \left| \frac {1} { m^2_{(\ell',\nu_{\ell'})} - \left(m_W^{\textrm{PDG}}\right)^2 + i \; \Gamma_W^{\textrm{PDG}} \; m_W^{\textrm{PDG}} } \right|^2$ where $m_Z^{\textrm{PDG}}$ ($m_W^{\textrm{PDG}}$) and $\Gamma_Z^{\textrm{PDG}}$ ($\Gamma_W^{\textrm{PDG}}$) are the world average mass and total width of the $Z$ ($W$) boson, respectively, as reported by the Particle Data Group. The input to the estimator is the invariant mass $m$ of all possible pairs ($\ell^+,\ell^-$) and ($\ell',\nu_{\ell'}$) satisfying the fiducial selection requirements. The final choice of which leptons are assigned to the $W$ or $Z$ bosons corresponds to the configuration exhibiting the highest value of the estimator. For cross sections using Born leptons, the association of leptons to $W$ or $Z$ bosons is performed using the Powheg Monte Carlo generator.

Table 1

Data from Figure 5(a) of the paper, but not divided by bin width

10.17182/hepdata.135074.v2/t1

Measured fiducial Born-level cross section for a single leptonic decay channel $\ell'^\pm \nu \ell^+ \ell'^-$ of the $W$ and $Z$...
Table 2

Data from Paper auxiliary material, Table 8

10.17182/hepdata.135074.v2/t2

Correlation matrix for the unfolded cross section.
Table 3

Data from Figure 5(b) of the paper, but not divided by bin width

10.17182/hepdata.135074.v2/t3

Measured fiducial Born-level cross section for a single leptonic decay channel $\ell'^\pm \nu \ell^+ \ell'^-$ of the $W$ and $Z$...
Table 4

Data from Paper auxiliary material, Table 10

10.17182/hepdata.135074.v2/t4

Correlation matrix for the unfolded cross section.
Table 5

Data from Figure 5(c) of the paper, but not divided by bin width

10.17182/hepdata.135074.v2/t5

Measured fiducial Born-level cross section for a single leptonic decay channel $\ell'^\pm \nu \ell^+ \ell'^-$ of the $W$ and $Z$...
Table 6

Data from Paper auxiliary material, Table 12

10.17182/hepdata.135074.v2/t6

Correlation matrix for the unfolded cross section.
Table 7

Data from Figure 5(d) of the paper, but not divided by bin width

10.17182/hepdata.135074.v2/t7

Measured fiducial Born-level cross section for a single leptonic decay channel $\ell'^\pm \nu \ell^+ \ell'^-$ of the $W$ and $Z$...
Table 8

Data from Paper auxiliary material, Table 14

10.17182/hepdata.135074.v2/t8

Correlation matrix for the unfolded cross section.
Table 9

Data from Paper auxiliary material, Table 15

10.17182/hepdata.135074.v2/t9

Measured fiducial Born-level cross section for a single leptonic decay channel $\ell'^\pm \nu \ell^+ \ell'^-$ of the $W$ and $Z$...
Table 10

Data from Paper auxiliary material, Table 16

10.17182/hepdata.135074.v2/t10

Correlation matrix for the unfolded cross section.
Table 11

Data from Paper auxiliary material, Table 17

10.17182/hepdata.135074.v2/t11

Measured fiducial dressed-level cross section for a single leptonic decay channel $\ell'^\pm \nu \ell^+ \ell'^-$ of the $W$ and $Z$...
Table 12

Data from Paper auxiliary material, Table 18

10.17182/hepdata.135074.v2/t12

Correlation matrix for the unfolded cross section.
Table 13

Data from Paper auxiliary material, Table 19

10.17182/hepdata.135074.v2/t13

Measured fiducial dressed-level cross section for a single leptonic decay channel $\ell'^\pm \nu \ell^+ \ell'^-$ of the $W$ and $Z$...
Table 14

Data from Paper auxiliary material, Table 20

10.17182/hepdata.135074.v2/t14

Correlation matrix for the unfolded cross section.
Table 15

Data from Paper auxiliary material, Table 21

10.17182/hepdata.135074.v2/t15

Measured fiducial dressed-level cross section for a single leptonic decay channel $\ell'^\pm \nu \ell^+ \ell'^-$ of the $W$ and $Z$...
Table 16

Data from Paper auxiliary material, Table 22

10.17182/hepdata.135074.v2/t16

Correlation matrix for the unfolded cross section.
Table 17

Data from Paper auxiliary material, Table 23

10.17182/hepdata.135074.v2/t17

Measured fiducial dressed-level cross section for a single leptonic decay channel $\ell'^\pm \nu \ell^+ \ell'^-$ of the $W$ and $Z$...
Table 18

Data from Paper auxiliary material, Table 24

10.17182/hepdata.135074.v2/t18

Correlation matrix for the unfolded cross section.
Table 19

Data from Paper auxiliary material, Table 25

10.17182/hepdata.135074.v2/t19

Measured fiducial dressed-level cross section for a single leptonic decay channel $\ell'^\pm \nu \ell^+ \ell'^-$ of the $W$ and $Z$...
Table 20

Data from Paper auxiliary material, Table 26

10.17182/hepdata.135074.v2/t20

Correlation matrix for the unfolded cross section.

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