Measurements of $W^{\pm }Z$ production cross sections in $pp$ collisions at $\sqrt{s}=8\mathrm{TeV}$ with the ATLAS detector and limits on anomalous gauge boson self-couplings

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 $20.3{\mathrm{fb}}^{-1}$. The measured inclusive cross section in the detector fiducial region is ${\sigma }_{W^{\pm }Z\to {\ell }^{\prime }\nu \ell \ell }=35.1\pm 0.9(\mathrm{stat})\pm 0.8(\mathrm{sys})\pm 0.8(\mathrm{lumi})\mathrm{fb}$, for one leptonic decay channel. In comparison, the next-to-leading-order Standard Model expectation is $30.0\pm 2.1\mathrm{fb}$. 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 $0.13\pm 0.01\mathrm{fb}$. Limits on anomalous quartic gauge boson couplings are also extracted.

Figure 1

Distributions, summed over all channels, of the following kinematic variables: (a) the transverse momentum of the reconstructed $Z$ boson $p_{\mathrm{T}}^Z$, (b) the mass of the $Z$ $m_Z$, (c) the transverse mass of the reconstructed $W$ boson $m_{\mathrm{T}}^W$, and (d) the transverse-masslike variable for the $WZ$ system $m_{\mathrm{T}}^{WZ}$. The points correspond to the data and the histograms to the expectations of the different SM processes. All Monte Carlo expectations are scaled to the integrated luminosity of the data using the predicted MC cross sections of each sample. The sum of background events containing misidentified leptons is labeled “Misid. leptons.” The powheg+pythia MC prediction is used for the $W^{\pm }Z$ signal contribution. It is scaled by a global factor of 1.17 to match the measured inclusive $W^{\pm }Z$ cross section. The open red histogram shows the total prediction and the shaded orange band its estimated total uncertainty. The last bin contains the overflow.

Figure 2

Ratio of the measured $W^{\pm }Z$ integrated cross sections in the fiducial phase space to the NLO SM prediction from powheg+pythia using the CT10 PDF set and renormalization and factorization scales ${\mu }_R={\mu }_F=m_{WZ}/2$, in each of the four channels and for their combination. The inner and outer error bars on the data points represent the statistical and total uncertainties, respectively. The shaded orange band represents the uncertainty associated with the SM prediction.

Figure 3

Measured ratios ${\sigma }_{W^{+}Z}^{\mathrm{fid}}/{\sigma }_{W^{-}Z}^{\mathrm{fid}}$ of $W^{+}Z$ and $W^{-}Z$ integrated cross sections in the fiducial phase space in each of the four channels and for their combination. The error bars on the data points represent the total uncertainties, dominated by statistical uncertainties. The NLO SM prediction from powheg+pythia using the CT10 PDF set and renormalization and factorization scales ${\mu }_R={\mu }_F=m_{WZ}/2$ is represented by the red line and the shaded orange band for the associated uncertainty. The powheg+pythia prediction using the ATLAS-epWZ12 PDF set is also displayed as the dashed line.

Figure 4

The measured $W^{\pm }Z$ differential cross section in the fiducial phase space as a function of (a) $p_{\mathrm{T}}^Z$ and (b) $p_{\mathrm{T}}^W$. The inner and outer error bars on the data points represent the statistical and total uncertainties, respectively. The measurements are compared to the prediction from powheg+pythia (red line, see text for details). The orange band represents its total theoretical uncertainty and the hatched red area the part of the theoretical uncertainty arising from the PDF and parton shower uncertainties. The predictions from the mc@nlo and sherpa MC generators are also indicated by dashed and dot-dashed lines, respectively. The sherpa prediction is rescaled to the integrated cross section predicted by powheg+pythia. The right $y$ axis refers to the last cross-section point, separated from the others by a vertical dashed line, as this last bin is integrated up to the maximum value reached in the phase space.

Figure 5

The measured $W^{\pm }Z$ differential cross section in the fiducial phase space as a function of $m_{\mathrm{T}}^{WZ}$. The inner and outer error bars on the data points represent the statistical and total uncertainties, respectively. The measurements are compared to the prediction from powheg+pythia (red line, see text for details). The orange band represents its total theoretical uncertainty and the hatched red area the part of the theoretical uncertainty arising from the PDF and shower uncertainties. The predictions from the mc@nlo and sherpa MC generators are also indicated by dashed and dot-dashed lines, respectively. The sherpa prediction is rescaled to the integrated cross section predicted by powheg+pythia. The right $y$ axis refers to the last cross-section point, separated from the others by a vertical dashed line, as this last bin is integrated up to the maximum value reached in the phase space.

Figure 6

The measured $W^{\pm }Z$ differential cross section in the fiducial phase space as a function of (a) $p_{\mathrm{T}}^{\nu }$ and (b) $|y_Z-y_{\ell ,W}|$. The inner and outer error bars on the data points represent the statistical and total uncertainties, respectively. The measurements are compared to the prediction from powheg+pythia (red line, see text for details). The orange band represents its total theoretical uncertainty and the hatched red area the part of the theoretical uncertainty arising from the PDF and shower uncertainties. The predictions from the mc@nlo and sherpa MC generators are also indicated by dashed and dot-dashed lines, respectively. The Sherpa prediction is rescaled to the integrated cross section predicted by powheg+pythia. The right $y$ axis in (a) refers to the last cross-section point, separated from the others by a vertical dashed line, as this last bin is integrated up to the maximum value reached in the phase space.

Figure 7

The ratio of the $W^{+}Z$ and $W^{-}Z$ differential cross sections in the fiducial phase space as a function of (a) $p_{\mathrm{T}}^Z$ and (b) $p_{\mathrm{T}}^W$. The inner and outer error bars on the data points represent the statistical and total uncertainties, respectively. The measurements are compared to the prediction from powheg+pythia (red line; see text for details). The orange band represents its total theoretical uncertainty, which is dominated by the PDF uncertainty. The predictions from the mc@nlo and sherpa MC generators are also indicated by dashed and dot-dashed lines, respectively.

Figure 8

The ratio of the $W^{+}Z$ and $W^{-}Z$ differential cross sections in the fiducial phase space as a function of $m_{\mathrm{T}}^{WZ}$. The inner and outer error bars on the data points represent the statistical and total uncertainties, respectively. The measurements are compared to the prediction from powheg+pythia (red line, see text for details). The orange band represents its total theoretical uncertainty, which is dominated by the PDF uncertainty. The predictions from the mc@nlo and sherpa MC generators are also indicated by dashed and dot-dashed lines, respectively.

Figure 9

The ratio of the $W^{+}Z$ and $W^{-}Z$ differential cross sections in the fiducial phase space as a function of (a) $p_{\mathrm{T}}^{\nu }$ and (b) $|y_Z-y_{\ell ,W}|$. The inner and outer error bars on the data points represent the statistical and total uncertainties, respectively. The measurements are compared to the prediction from powheg+pythia (red line; see text for details). The orange band represents its total theoretical uncertainty, which is dominated by the PDF uncertainty. The predictions from the mc@nlo and sherpa MC generators are also indicated by dashed and dot-dashed lines, respectively.

Figure 10

The measured $W^{\pm }Z$ differential cross section in the fiducial phase space as a function of the exclusive jet multiplicity of jets with $p_{\mathrm{T}}>25\mathrm{GeV}$. The inner and outer error bars on the data points represent the statistical and total uncertainties, respectively. The measurements are compared to the prediction from sherpa (red line), powheg+pythia (dashed blue line), and mc@nlo (dot-dashed violet line). The sherpa prediction is rescaled to the integrated cross section predicted by powheg+pythia. The right $y$ axis refers to the last cross section point, separated from the others by a vertical dashed line, as this last bin is integrated up to the maximum value reached in the phase space.

Figure 11

The measured $W^{\pm }Z$ differential cross section as a function of the invariant mass of the two leading jets with $p_{\mathrm{T}}>30\mathrm{GeV}$. The inner and outer error bars on the data points represent the statistical and total uncertainties, respectively. The measurements are compared to the prediction from sherpa (red line), which includes both the $WZjj\text{−}\mathrm{QCD}$ and $WZjj\text{−}\mathrm{EW}$ processes, powheg+pythia (dashed blue line) and mc@nlo (dot-dashed violet line). The part of the sherpa prediction corresponding to $WZjj\text{−}\mathrm{EW}$ events is also represented by a dashed red line. In the bottom panel the dashed red line therefore corresponds to the $WZjj\text{−}\mathrm{EW}$ fraction of the total sherpa prediction. The right $y$ axis refers to the last cross section point, separated from the others by a vertical dashed line, as this last bin is integrated up to the maximum value reached in the phase space.

Figure 12

Distribution of $m_{\mathrm{T}}^{WZ}$ in the sum of all channels with the same binning as used for the calculation of limits on aTGC. The points correspond to the data and the histograms to the expectations of the different SM processes. All Monte Carlo expectations are scaled to the integrated luminosity of the data using the predicted MC cross sections of each sample. The powheg+pythia MC prediction is used for the SM $W^{\pm }Z$ signal contribution. The open red histogram shows the total prediction and the shaded orange band its estimated total uncertainty. The last bin contains the overflow. Two predictions with nonzero values of some of the anomalous coupling parameters are also represented by the dashed and dot-dashed lines, respectively.

Figure 13

Expected and observed 95% C.L. limit contours for ${\mathrm{\Lambda }}_{\mathrm{co}}\to \infty$ in the planes ($\mathrm{\Delta }{\kappa }^Z$, $\mathrm{\Delta }{g}_1^Z$), ($\mathrm{\Delta }{g}_1^Z$, ${\lambda }^Z$), and ($\mathrm{\Delta }{\kappa }^Z$, ${\lambda }^Z$). The solid and dashed lines in the figures represent the observed and expected limits, respectively. The regions outside the black contours are excluded. The green and yellow bands correspond to the $1\sigma$ and $2\sigma$ uncertainty on the expected limit, respectively. The vertical and horizontal lines represent the 95% C.L. one-dimensional limits calculated separately.

Figure 14

Comparison of one-dimensional limits at 95% C.L. on the anomalous coupling parameters using a cutoff scale of ${\mathrm{\Lambda }}_{\mathrm{co}}=2\mathrm{TeV}$ and obtained from the analysis of $W^{\pm }Z$ events by the ATLAS [3], D0 [84], and CDF experiments [1].

Figure 15

Distribution of the difference in azimuthal angle between the reconstructed $W$ and $Z$ bosons, (a) $|\mathrm{\Delta }\varphi (W,Z)|$, and of the scalar sum of the transverse momenta of the three charged leptons associated with the $W$ and $Z$ bosons, (b) $\sum |p_{\mathrm{T}}^{\ell }|$, for the sum of all channels, in the VBS phase space. All Monte Carlo expectations are scaled to the integrated luminosity of the data using the predicted MC cross sections of each sample. The sherpa MC prediction is used for the SM $WZjj\text{−}\mathrm{QCD}$ and $WZjj\text{−}\mathrm{EW}$ predictions. The open red histogram shows the total prediction and the shaded orange band its estimated total uncertainty. The prediction with nonzero values of one of the aQGC parameters is also represented by the dashed line.

Figure 16

Expected and observed 95% C.L. limit contours on aQGC parameters ${\alpha }_4$ and ${\alpha }_5$. The solid and dashed lines in the figures represent the observed and expected limits, respectively. The regions outside the black contours are excluded. The green and yellow bands correspond to the $1\sigma$ and $2\sigma$ uncertainty on the expected limit, respectively. The expected exclusion contour from an analysis by the ATLAS Collaboration using $W^{\pm }{W}^{\pm }jj$ events [88] is indicated by the dotted line.