DOI: 10.17182/hepdata.75197.v1/t13
title: "Table 13" of "Measurements of $W^\pm Z$ production cross sections in $pp$ collisions at $\sqrt{s} = 8$ TeV with the ATLAS detector and limits on anomalous gauge boson self-couplings"

description: Measured fiducial cross section in all $\ell'^\pm \nu \ell^+ \ell'^-$ channels combined, where $\ell, \ell' = e, \mu$. 
The first systematic uncertainty is the combined systematic uncertainty excluding theory and luminosity uncertainties, 
the second is the luminosity uncertainty. 
The last bin is a cross section for all events above the lower end of the bin.
description: CERN-LHC. This paper presents measurements of $W^\pm Z$ production in $pp$ collisions at a center-of-mass energy of 8 TeV. The gauge bosons are reconstructed using their leptonic decay modes into electrons and muons. The data were collected in 2012 by the ATLAS experiment at the Large Hadron Collider, and correspond to an integrated luminosity of 20.3 fb$^{-1}$. The measured inclusive cross section in the detector fiducial region is $\sigma_{W^\pm Z \rightarrow \ell^{'} \nu\ \ell \ell} = 35.1 \pm$ 0.9 (stat.) $\pm 0.8$ (sys.) $\pm 0.8$ (lumi.) fb, for one leptonic decay channel. In comparison, the next-to-leading-order Standard Model expectation is 30.0 $\pm$ 2.1 fb. Cross sections for $W^+Z$ and $W^-Z$ production and their ratio are presented as well as differential cross sections for several kinematic observables. Limits on anomalous triple gauge boson couplings are derived from the transverse mass spectrum of the $W^\pm Z$ system. From the analysis of events with a $W$ and a $Z$ boson associated with two or more forward jets an upper limit at 95% confidence level on the $W^\pm Z$ scattering cross section of 0.63 fb, for each leptonic decay channel, is established, while the Standard Model prediction at next-to-leading order is 0.13 fb. Limits on anomalous quartic gauge boson couplings are also extracted
The cross sections are measured in a fiducial phase space reflecting the detector acceptance, defined below.

Fiducial phase space definition:
- $p_{\mathrm{T}}$ 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~\cite{Agashe:2014kda}.
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 defined in the next paragraph.
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. 
This result is model-dependent and includes phase space that was not experimentally accessible, so it should be used with caution. 
Whenever possible, the fiducial cross sections should be used instead, since they are only minimally model-dependent.


Fiducial phase space for VBS measurement: additional criteria to the above Fiducial phase space definition
- at least 2 jets
- $p_{\mathrm{T}}$ of jets &gt; 30 GeV
- $|\eta|$ of jets &lt; 4.5
- invariant mass of the 2 leading jets &gt; 500 GeV
- leptons and jets separated by $\Delta R(\ell,jet) &gt; 0.3$

where jets are particle level jets with anti-kt R=0.4.


Fiducial phase space for aQGC measurement: additional criteria to the above VBS phase space definition
- difference in azimuthal angle between W and Z bosons directions $|\Delta \phi(W,Z)| &gt; 2$
- scalar sum of the transverse momenta of the three charged leptons associated with W and Z bosons $\sum |p_{\mathrm{T}}^{\ell}| &gt; 250$ GeV.