DOI: 10.17182/hepdata.76493.v1/t10
title: "Table 10" of "Measurement of the $W^{\pm}Z$ boson pair-production cross section in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS Detector"

description: Correlation matrix for the total uncertainties, including all sources of systematic and statistical uncertainties, for the differential cross section as a function of the exclusive jet multiplicity.
description: CERN-LHC. The production of $W^{\pm}Z$ events in proton--proton collisions at a centre-of-mass energy of 13 TeV is measured with the ATLAS detector at the LHC. The collected data correspond to an integrated luminosity of 3.2 fb$^{-1}$. The $W^{\pm}Z$ candidates are reconstructed using leptonic decays of the gauge bosons into electrons or muons. The measured inclusive cross section in the detector fiducial region for leptonic decay modes is $\sigma_{W^\pm Z \rightarrow \ell^{'} \nu \ell \ell}^{\textrm{fid.}} = 63.2 \pm 3.2$ (stat.) $\pm 2.6$ (sys.) $\pm 1.5$ (lumi.) fb. In comparison, the next-to-leading-order Standard Model prediction is $53.4^{+3.6}_{-2.8}$ fb. The extrapolation of the measurement from the fiducial to the total phase space yields $\sigma_{W^{\pm}Z}^{\textrm{tot.}} = 50.6 \pm 2.6$ (stat.) $\pm 2.0$ (sys.) $\pm 0.9$ (th.) $\pm 1.2$ (lumi.) pb, in agreement with a recent next-to-next-to-leading-order calculation of $48.2^{+1.1}_{-1.0}$ pb. The cross section as a function of jet multiplicity is also measured, together with the charge-dependent $W^+Z$ and $W^-Z$ cross sections and their ratio. 

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 &gt; 15 GeV
- $p_{\mathrm{T}}$ of electrons and muons from the $W^{\pm}$ decays &gt; 20 GeV
- $|\eta|$ of muons and electrons &lt; 2.5
- Leptons from the Z0 boson are separated by $\Delta R(\ell,\ell) &gt; 0.2$ from each other
- Leptons from the Z0 and W bosons are separated by $\Delta R(\ell,\ell) &gt; 0.3$ from each other
- |dilepton mass - Z0 mass| &lt; 10 GeV
- $m_{\mathrm{T}}$ of $W^{\pm}$ &gt; 30 GeV. 


At particle level, the kinematics of final-state prompt 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.


The inclusive cross section is also extrapolated to the total phase space and all W and Z boson decay modes. The total phase space is defined by requiring the invariant mass of the lepton pair associated with the Z boson decay to be in the range $66