Abstract (data abstract)

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 $100<p_T^Z\leq200$ GeV and 1.6 standard deviations in the region with $p_T^Z>200$ 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 > 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 $Z$ boson are separated by $\Delta R(\ell,\ell) > 0.2$ from each other - Leptons from the $Z$ and W bosons are separated by $\Delta R(\ell,\ell) > 0.3$ from each other - |dilepton mass - $Z$ mass| < 10 GeV - $m_{\mathrm{T}}$ of $W^{\pm}$ > 30 GeV. - $p_{\mathrm{T}}$ of jets > 30 GeV - $|\eta|$ of jets < 4.5. In the RAZ measurement, three signal regions are defined: -$p_{\mathrm{T}}^{WZ}$ < 20, 40, 70 GeV. In the $WZ$ polarization fraction measurement, two signal regions are defined: -$p_{\mathrm{T}}^{WZ}$ < 70 GeV && $p_{\mathrm{T}}^{Z}$ > 200 GeV, -$p_{\mathrm{T}}^{WZ}$ < 70 GeV && 100 < $p_{\mathrm{T}}^{Z} \leq$ 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.

Table 1

Data from Table 2 of the paper

10.17182/hepdata.149992.v1/t1

Polarization fractions in the region with $100<p_T^Z\leq200$ GeV using three unconstrained parameters.
Table 2

Data from Table 2 of the paper

10.17182/hepdata.149992.v1/t2

Polarization fractions in the region with $p_T^Z>200$ GeV using three unconstrained parameters.
Table 3

Data from Page 7 of the paper

10.17182/hepdata.149992.v1/t3

Fraction of events where both bosons are longitudinally polarized in the region with $100<p_T^Z\leq200$ GeV using two unconstrained parameters.
Table 4

Data from Page 7 of the paper

10.17182/hepdata.149992.v1/t4

Fraction of events where both bosons are longitudinally polarized in the region with $p_T^Z>200$ GeV using two unconstrained parameters.
Table 5

Data from Table 1 of the paper

10.17182/hepdata.149992.v1/t5

Numbers of observed and expected events in the 00-enhanced signal regions, before the fit. The total uncertainties are quoted.
Table 6

Data from Tables 7 and 8 of the paper

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Summary of the relative uncertainties in the measured longitudinal-longitudinal fractions $f_{00}$. The uncertainties are reported as percentages.
Table 7

Data from Auxiliary Table 5

10.17182/hepdata.149992.v1/t7

Numbers of observed and expected events in the 00-enhanced signal regions, after the fit. The total uncertainties are quoted.
Table 8

Data from Auxiliary Figure 8

10.17182/hepdata.149992.v1/t8

$|\Delta Y(l_{W}Z)|$ Migration matrix RAZ Region $p_{T}^{WZ}< 20$ GeV of the TT state.
Table 9

Data from Auxiliary Figure 8

10.17182/hepdata.149992.v1/t9

$|\Delta Y(l_{W}Z)|$ Migration matrix RAZ Region $p_{T}^{WZ}< 40$ GeV of the TT state.
Table 10

Data from Auxiliary Figure 8

10.17182/hepdata.149992.v1/t10

$|\Delta Y(l_{W}Z)|$ Migration matrix RAZ Region $p_{T}^{WZ}< 70$ GeV of the TT state.
Table 11

Data from Auxiliary Figure 9

10.17182/hepdata.149992.v1/t11

$|\Delta Y(l_{W}Z)|$ Migration matrix RAZ Region $p_{T}^{WZ}< 20$ GeV of of the sum of all polarization.
Table 12

Data from Auxiliary Figure 9

10.17182/hepdata.149992.v1/t12

$|\Delta Y(l_{W}Z)|$ Migration matrix RAZ Region $p_{T}^{WZ}< 40$ GeV of of the sum of all polarization.
Table 13

Data from Auxiliary Figure 9

10.17182/hepdata.149992.v1/t13

$|\Delta Y(l_{W}Z)|$ Migration matrix RAZ Region $p_{T}^{WZ}< 70$ GeV of of the sum of all polarization.
Table 14

Data from Auxiliary Figure 8

10.17182/hepdata.149992.v1/t14

$|\Delta Y(WZ)|$ Migration matrix RAZ Region $p_{T}^{WZ}< 20$ GeV of the TT state.
Table 15

Data from Auxiliary Figure 8

10.17182/hepdata.149992.v1/t15

$|\Delta Y(WZ)|$ Migration matrix RAZ Region $p_{T}^{WZ}< 40$ GeV of the TT state.
Table 16

Data from Auxiliary Figure 8

10.17182/hepdata.149992.v1/t16

$|\Delta Y(WZ)|$ Migration matrix RAZ Region $p_{T}^{WZ}< 70$ GeV of the TT state.
Table 17

Data from Auxiliary Figure 9

10.17182/hepdata.149992.v1/t17

$|\Delta Y(WZ)|$ Migration matrix RAZ Region $p_{T}^{WZ}< 20$ GeV of of the sum of all polarization.
Table 18

Data from Auxiliary Figure 9

10.17182/hepdata.149992.v1/t18

$|\Delta Y(WZ)|$ Migration matrix RAZ Region $p_{T}^{WZ}< 40$ GeV of of the sum of all polarization.
Table 19

Data from Auxiliary Figure 9

10.17182/hepdata.149992.v1/t19

$|\Delta Y(WZ)|$ Migration matrix RAZ Region $p_{T}^{WZ}< 70$ GeV of of the sum of all polarization.
Table 20

Data from Auxiliary Figure 11

10.17182/hepdata.149992.v1/t20

The $\mathcal{D}$ value for the unfolded $|\Delta Y(l_{W}Z)|$ distributions of the TT polarization state as a function of the $p_T^{WZ}$...
Table 21

Data from Auxiliary Figure 11

10.17182/hepdata.149992.v1/t21

The $\mathcal{D}$ value for the unfolded $|\Delta Y(WZ)|$ distributions of the TT polarization state as a function of the $p_T^{WZ}$...
Table 22

Data from Auxiliary Figure 12

10.17182/hepdata.149992.v1/t22

Measured normalized differential $|\Delta Y(l_{W}Z)|$ cross-section of the TT state in the RAZ Region $p_{T}^{WZ}< 20$ GeV. The total uncertainties...
Table 23

Data from Auxiliary Figure 12

10.17182/hepdata.149992.v1/t23

Measured normalized differential $|\Delta Y(l_{W}Z)|$ cross-section of the TT state in the RAZ Region $p_{T}^{WZ}< 40$ GeV. The total uncertainties...
Table 24

Data from Auxiliary Figure 12

10.17182/hepdata.149992.v1/t24

Measured normalized differential $|\Delta Y(l_{W}Z)|$ cross-section of the TT state in the RAZ Region $p_{T}^{WZ}< 70$ GeV. The total uncertainties...
Table 25

Data from Auxiliary Figure 13

10.17182/hepdata.149992.v1/t25

Measured normalized differential $|\Delta Y(WZ)|$ cross-section of the TT state in the RAZ Region $p_{T}^{WZ}< 20$ GeV. The total uncertainties...
Table 26

Data from Auxiliary Figure 13

10.17182/hepdata.149992.v1/t26

Measured normalized differential $|\Delta Y(WZ)|$ cross-section of the TT state in the RAZ Region $p_{T}^{WZ}< 40$ GeV. The total uncertainties...
Table 27

Data from Auxiliary Figure 13

10.17182/hepdata.149992.v1/t27

Measured normalized differential $|\Delta Y(WZ)|$ cross-section of the TT state in the RAZ Region $p_{T}^{WZ}< 70$ GeV. The total uncertainties...
Table 28

Data from Auxiliary Figure 12

10.17182/hepdata.149992.v1/t28

Measured normalized differential $|\Delta Y(l_{W}Z)|$ cross-section of the sum of polarization states in the RAZ Region $p_{T}^{WZ}< 20$ GeV. The...
Table 29

Data from Auxiliary Figure 12

10.17182/hepdata.149992.v1/t29

Measured normalized differential $|\Delta Y(l_{W}Z)|$ cross-section of the sum of polarization states in the RAZ Region $p_{T}^{WZ}< 40$ GeV. The...
Table 30

Data from Auxiliary Figure 12

10.17182/hepdata.149992.v1/t30

Measured normalized differential $|\Delta Y(l_{W}Z)|$ cross-section of the sum of polarization states in the RAZ Region $p_{T}^{WZ}< 70$ GeV. The...
Table 31

Data from Auxiliary Figure 13

10.17182/hepdata.149992.v1/t31

Measured normalized differential $|\Delta Y(WZ)|$ cross-section of the sum of polarization states in the RAZ Region $p_{T}^{WZ}< 20$ GeV. The...
Table 32

Data from Auxiliary Figure 13

10.17182/hepdata.149992.v1/t32

Measured normalized differential $|\Delta Y(WZ)|$ cross-section of the sum of polarization states in the RAZ Region $p_{T}^{WZ}< 40$ GeV. The...
Table 33

Data from Auxiliary Figure 13

10.17182/hepdata.149992.v1/t33

Measured normalized differential $|\Delta Y(WZ)|$ cross-section of the sum of polarization states in the RAZ Region $p_{T}^{WZ}< 70$ GeV. The...
Table 34

Data from Auxiliary Table 9

10.17182/hepdata.149992.v1/t34

Summary of the relative uncertainties in the measured depth of the TT state in the RAZ Region $p_{T}^{WZ}<20$ GeV using...
Table 35

Data from Auxiliary Table 10

10.17182/hepdata.149992.v1/t35

Summary of the relative uncertainties in the measured depth of the TT state in the RAZ Region $p_{T}^{WZ}<40$ GeV using...
Table 36

Data from Auxiliary Table 11

10.17182/hepdata.149992.v1/t36

Summary of the relative uncertainties in the measured depth of the TT state in the RAZ Region $p_{T}^{WZ}<70$ GeV using...
Table 37

Data from Auxiliary Table 9

10.17182/hepdata.149992.v1/t37

Summary of the relative uncertainties in the measured depth of the TT state in the RAZ Region $p_{T}^{WZ}<20$ GeV using...
Table 38

Data from Auxiliary Table 10

10.17182/hepdata.149992.v1/t38

Summary of the relative uncertainties in the measured depth of the TT state in the RAZ Region $p_{T}^{WZ}<40$ GeV using...
Table 39

Data from Auxiliary Table 11

10.17182/hepdata.149992.v1/t39

Summary of the relative uncertainties in the measured depth of the TT state in the RAZ Region $p_{T}^{WZ}<70$ GeV using...
Table 40

Data from Auxiliary Table 9

10.17182/hepdata.149992.v1/t40

Summary of the relative uncertainties in the measured depth of the sum of polarization states in the RAZ Region $p_{T}^{WZ}<20$...
Table 41

Data from Auxiliary Table 10

10.17182/hepdata.149992.v1/t41

Summary of the relative uncertainties in the measured depth of the sum of polarization states in the RAZ Region $p_{T}^{WZ}<40$...
Table 42

Data from Auxiliary Table 11

10.17182/hepdata.149992.v1/t42

Summary of the relative uncertainties in the measured depth of the sum of polarization states in the RAZ Region $p_{T}^{WZ}<70$...
Table 43

Data from Auxiliary Table 9

10.17182/hepdata.149992.v1/t43

Summary of the relative uncertainties in the measured depth of the sum of polarization states in the RAZ Region $p_{T}^{WZ}<20$...
Table 44

Data from Auxiliary Table 10

10.17182/hepdata.149992.v1/t44

Summary of the relative uncertainties in the measured depth of the sum of polarization states in the RAZ Region $p_{T}^{WZ}<40$...
Table 45

Data from Auxiliary Table 11

10.17182/hepdata.149992.v1/t45

Summary of the relative uncertainties in the measured depth of the sum of polarization states in the RAZ Region $p_{T}^{WZ}<70$...

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