DOI: 10.17182/hepdata.149992.v1/t9
title: "Table 9" of "Studies of the energy dependence of diboson polarization fractions and the Radiation Amplitude Zero effect in WZ production with the ATLAS detector"

description: $|\Delta Y(l_{W}Z)|$ Migration matrix RAZ Region $p_{T}^{WZ}&lt; 40$ GeV of the TT state.
description: CERN-LHC. This Letter presents the first study of the energy-dependence of diboson polarization fractions in $WZ \rightarrow \ell\nu \ell'\ell'~(\ell, \ell'=e, \mu)$ production. The data set used corresponds to an integrated luminosity of 140 fb$^{-1}$ of proton-proton collisions at a center-of-mass energy of 13 TeV recorded by the ATLAS detector. Two fiducial regions with an enhanced presence of events featuring two longitudinally-polarized bosons are defined. A non-zero fraction of events with two longitudinally-polarized bosons is measured with an observed significance of 5.3 standard deviations in the region with $100200$ GeV, where $p_T^Z$ is the transverse momentum of the $Z$ boson. This Letter also reports the first study of the Radiation Amplitude Zero effect. Events with two transversely-polarized bosons are analyzed for the $\Delta Y(\ell_W Z)$ and $\Delta Y(WZ)$ distributions defined respectively as the rapidity difference between the lepton from the $W$ boson decay and the $Z$ boson and the rapidity difference between the $W$ boson and the $Z$ boson. Significant suppression of events near zero is observed in both distributions. Unfolded $\Delta Y(\ell_W Z)$ and $\Delta Y(WZ)$ distributions are also measured and compared to theoretical predictions.


Fiducial phase space definition for the measurement:
 - $p_{\mathrm{T}}$ of electrons and muons from $Z$ 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 $Z$ boson are separated by $\Delta R(\ell,\ell) &gt; 0.2$ from each other
 - Leptons from the $Z$ and W bosons are separated by $\Delta R(\ell,\ell) &gt; 0.3$ from each other
 - |dilepton mass - $Z$ mass| &lt; 10 GeV
 - $m_{\mathrm{T}}$ of $W^{\pm}$ &gt; 30 GeV.
 - $p_{\mathrm{T}}$ of jets &gt; 30 GeV
 - $|\eta|$ of jets &lt; 4.5.
 
 In the RAZ measurement, three signal regions are defined:
 -$p_{\mathrm{T}}^{WZ}$ &lt; 20, 40, 70 GeV. 
 In the $WZ$ polarization fraction measurement, two signal regions are defined:
 -$p_{\mathrm{T}}^{WZ}$ &lt; 70 GeV && $p_{\mathrm{T}}^{Z}$ &gt; 200 GeV, 
 -$p_{\mathrm{T}}^{WZ}$ &lt; 70 GeV && 100 &lt; $p_{\mathrm{T}}^{Z} \leq$ 200 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.