Measurements and interpretations of $W^{\pm}Z$ production cross-sections in $pp$ collisions at $\sqrt{s} =$ 13 TeV with the ATLAS detector

TL;DR

This work reports precise measurements of integrated and differential $W^{\pm}Z$ production cross-sections in $pp$ collisions at $\sqrt{s}=13$ TeV using the ATLAS detector with 140 fb$^{-1}$, reconstructed in leptonic final states and unfolded to a fiducial phase space. It benchmarks the results against state-of-the-art SM predictions from fixed-order NNLO QCD with EW corrections (MATRIX) and MC generators, finding overall agreement and validating the SM description of gauge couplings. The analysis extends differential observables, includes CP-sensitive measures, and performs a comprehensive SMEFT interpretation, placing limits on CP-conserving and CP-violating dimension-6 operators through both linear and quadratic EFT contributions, and employing a ML-based CP-odd observable to enhance sensitivity. The results provide competitive constraints and complement existing bounds from other diboson and Higgs-related measurements, strengthening the global picture of electroweak interactions and potential new physics scales.

Abstract

Measurements of integrated and differential cross-sections for $W^{\pm}Z$ production in proton-proton collisions are presented. The data collected by the ATLAS detector at the Large Hadron Collider from 2015 to 2018 at a centre-of-mass energy of $\sqrt{s} =$ 13 TeV are used, corresponding to an integrated luminosity of 140 fb$^{-1}$. The $W^{\pm}Z$ candidate events are reconstructed using leptonic decay modes of the gauge bosons into electrons or muons. The integrated cross-section per lepton flavour for the production of $W^{\pm}Z$ is measured in the detector fiducial region with a relative precision of 4%. The measured value is compared with the Standard Model prediction at a precision of up to next-to-next-to-leading-order in QCD and next-to-leading-order in electroweak. Cross-sections for $W^+Z$ and $W^-Z$ production and their ratio are presented. The $W^{\pm}Z$ production is also measured differentially as functions of various kinematic variables, including new observables sensitive to CP-violation effects. All measurements are compared with state-of-the-art Standard Model predictions from fixed-order calculations or Monte Carlo generators based on next-to-leading-order matrix elements interfaced with parton showers. An effective field theory interpretation of the measurements is performed, considering both CP-conserving and CP-violating dimension-6 operators modifying the $W^{\pm}Z$ production. In the absence of observed deviations from the Standard Model, limits on CP-conserving Wilson coefficients are extracted using the transverse mass of the $W^{\pm}Z$ system. For CP-violating coefficients a machine learning approach is used to construct an observable with enhanced sensitivity to CP-violation effects.

Figures (15)

• Figure 1: Distribution of (a) $m_{Z}$ for events in the $ZZ$ control sample and (b) $m_{\mathrm{T}}^{W}$ for events in the $t\bar{t}+V$ control sample. The points correspond to the data with the error bars representing the statistical uncertainties, and the histograms correspond to the predictions of the various SM processes. The sum of the background processes with misidentified leptons is labelled "Misid. leptons". The red histogram shows the total prediction; the shaded band is the total uncertainty of this prediction. The last bin in (b) contains the overflow. The lower panels in each figure show the ratio of the data points to the open red histogram with their respective uncertainties.
• Figure 2: The distributions of observed and expected events after the $W^{\pm}Z$ inclusive selection described in Section \ref{['sec:selection']}, for the sum of all channels, of the kinematic variables (a) $m_{\mathrm{T}}^{W}$, (b) $m_{Z}$, (c) $p_{\mathrm{T}}^Z$ and (d) $\Delta\phi(\ell^W,Z)$. The points correspond to the data with the error bars representing the statistical uncertainties, and the histograms correspond to the predictions of the various SM processes. The sum of the background processes with misidentified leptons is labelled "Misid. leptons". The Sherpa MC prediction is used for the $W^{\pm}Z$ signal contribution. The red histogram shows the total prediction; the shaded band is the total uncertainty in this prediction. The last bin in (a), (c) and (d) contains the overflow. The lower panels in each figure show the ratio of the data points to the open red histogram with their respective uncertainties.
• Figure 3: The measured $W^{\pm}Z$ integrated cross-sections in the fiducial phase space 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 $\mathrm{NNLO \, QCD}\times \mathrm{EW}_{\mathrm{qq}}$ SM prediction from MATRIX using the [3.1nnlo_as_118_luxqed] PDF set is shown as the red line; the shaded band shows the effect of QCD scale uncertainties on this prediction. The $\mathrm{NNLO \, QCD} + \mathrm{EW}$ predictions from MATRIX is also represented by the dashed-red line, as well as the $\mathrm{NNLO \, QCD}\times \mathrm{EW}_{\mathrm{qq}}$MATRIX prediction using the [nnlo]MSHT20 PDF set represented by the dotted-dashed red line.
• Figure 4: Measured ratio $\sigma^{\mathrm{fid.}}_{W^{+}Z} / \sigma^{\mathrm{fid.}}_{W^{-}Z}$ 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, which are dominated by the statistical uncertainties. The $\mathrm{NNLO \, QCD}\times \mathrm{EW}_{\mathrm{qq}}$ SM predictions from MATRIX using the [18nnlo] PDF set is represented as a single red line. It is equal to the prediction from Sherpa using the [3.0nnlo] PDF set. The dashed band represents the effect of PDF uncertainties estimated by using the Sherpa prediction from the [3.0nnlo] eigenvectors and the envelope of the differences between the [18nnlo], [nnlo]MSHT20, [3.1nnlo] and [15nnlo] PDF sets. The MATRIX prediction displayed by the dashed-blue line is using the [3.1nnlo_as_118_luxqed] PDF set.
• Figure 5: The measured $W^{\pm}Z$ differential cross-section in the fiducial phase space as a function of (a) $p_\textrm{T}^Z$, (b) $p_\textrm{T}^W$, (c) $p_{\mathrm{T}}^\nu$ and (d) $m_\mathrm{T}^{WZ}$. The inner and outer error bars on the data points represent the statistical and total uncertainties, respectively. The measurements are compared with the prediction from MATRIX using either the $\mathrm{NNLO \, QCD}\times \mathrm{EW}_{\mathrm{qq}}$ (red line) or the $\mathrm{NNLO \, QCD} + \mathrm{EW}$ (dashed-red) line schemes. The shaded band shows how the QCD scale uncertainties affect the MATRIX predictions. The predictions from the Sherpa and Powheg+Pythia MC generators are also indicated by dotted-blue and dotted-dashed violet lines, respectively. The right vertical axis refers to the last cross-section point, separated from the others by vertical dashed lines, as this last bin is integrated up to the maximum value reached in the phase space and the cross-section is not divided by the bin width.