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CMS-SMP-24-001 ; CERN-EP-2024-129

Measurement of inclusive and differential cross sections for W$^{+}$W$^{-}$ production in proton-proton collisions at $\sqrt{s} =$ 13.6 TeV

CMS Collaboration

7 June 2024

Phys. Lett. B 861 (2025) 139231

Abstract: Measurements at $\sqrt{s}=$ 13.6 TeV of the opposite-sign W boson pair production cross section in proton-proton collisions are presented. The data used in this study were collected with the CMS detector at the CERN LHC in 2022, and correspond to an integrated luminosity of 34.8 fb$^{-1}$. Events are selected by requiring one electron and one muon of opposite charge. A maximum likelihood fit is performed on signal- and background-enriched data categories defined by the flavour and charge of the leptons, the number of jets, and number of jets originating from b quarks. An inclusive W$^{+}$W$^{-}$ production cross section of 125.7 $\pm$ 5.6 pb is measured, in agreement with standard model predictions. Cross sections are also reported in a fiducial region close to that of the detector acceptance, both inclusively and differentially, as a function of the jet multiplicity in the event. For first time in proton-proton collisions, WW events with at least two reconstructed jets are studied and compared with recent theoretical predictions.

Links: e-print arXiv:2406.05101 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; Physics Briefing ; CADI line (restricted) ;

Figures
png pdf	Figure 1: Distributions of the number of reconstructed jets after the fit to the data in the WW SR (upper left), same-sign CR (upper right), $\mathrm{Z}\to\tau\tau$ CR (center left), one b tag CR (center right), and two b tags CR (lower left), and the number of events in the $\mathrm{W}\mathrm{Z}\to3\ell\nu$ and $\mathrm{Z}\mathrm{Z}\to4\ell$ CRs (lower right). The histograms for $\mathrm{t}\mathrm{V}\mathrm{x}$ backgrounds include the contributions from ${\mathrm{t}\overline{\mathrm{t}}} \mathrm{V}(\mathrm{V})$ processes. The histograms for V$\gamma$ backgrounds include the contributions from W$\gamma$ and Z$\gamma$ processes. The overflow is included in the last bin. The bottom panel in each figure shows the ratio of the number of events observed in data to that of the total SM prediction. The grey bands represent the uncertainties in the predicted yields. The vertical bars represent the statistical uncertainties in the data.
png pdf	Figure 1-a: Distributions of the number of reconstructed jets after the fit to the data in the WW SR (upper left), same-sign CR (upper right), $\mathrm{Z}\to\tau\tau$ CR (center left), one b tag CR (center right), and two b tags CR (lower left), and the number of events in the $\mathrm{W}\mathrm{Z}\to3\ell\nu$ and $\mathrm{Z}\mathrm{Z}\to4\ell$ CRs (lower right). The histograms for $\mathrm{t}\mathrm{V}\mathrm{x}$ backgrounds include the contributions from ${\mathrm{t}\overline{\mathrm{t}}} \mathrm{V}(\mathrm{V})$ processes. The histograms for V$\gamma$ backgrounds include the contributions from W$\gamma$ and Z$\gamma$ processes. The overflow is included in the last bin. The bottom panel in each figure shows the ratio of the number of events observed in data to that of the total SM prediction. The grey bands represent the uncertainties in the predicted yields. The vertical bars represent the statistical uncertainties in the data.
png pdf	Figure 1-b: Distributions of the number of reconstructed jets after the fit to the data in the WW SR (upper left), same-sign CR (upper right), $\mathrm{Z}\to\tau\tau$ CR (center left), one b tag CR (center right), and two b tags CR (lower left), and the number of events in the $\mathrm{W}\mathrm{Z}\to3\ell\nu$ and $\mathrm{Z}\mathrm{Z}\to4\ell$ CRs (lower right). The histograms for $\mathrm{t}\mathrm{V}\mathrm{x}$ backgrounds include the contributions from ${\mathrm{t}\overline{\mathrm{t}}} \mathrm{V}(\mathrm{V})$ processes. The histograms for V$\gamma$ backgrounds include the contributions from W$\gamma$ and Z$\gamma$ processes. The overflow is included in the last bin. The bottom panel in each figure shows the ratio of the number of events observed in data to that of the total SM prediction. The grey bands represent the uncertainties in the predicted yields. The vertical bars represent the statistical uncertainties in the data.
png pdf	Figure 1-c: Distributions of the number of reconstructed jets after the fit to the data in the WW SR (upper left), same-sign CR (upper right), $\mathrm{Z}\to\tau\tau$ CR (center left), one b tag CR (center right), and two b tags CR (lower left), and the number of events in the $\mathrm{W}\mathrm{Z}\to3\ell\nu$ and $\mathrm{Z}\mathrm{Z}\to4\ell$ CRs (lower right). The histograms for $\mathrm{t}\mathrm{V}\mathrm{x}$ backgrounds include the contributions from ${\mathrm{t}\overline{\mathrm{t}}} \mathrm{V}(\mathrm{V})$ processes. The histograms for V$\gamma$ backgrounds include the contributions from W$\gamma$ and Z$\gamma$ processes. The overflow is included in the last bin. The bottom panel in each figure shows the ratio of the number of events observed in data to that of the total SM prediction. The grey bands represent the uncertainties in the predicted yields. The vertical bars represent the statistical uncertainties in the data.
png pdf	Figure 1-d: Distributions of the number of reconstructed jets after the fit to the data in the WW SR (upper left), same-sign CR (upper right), $\mathrm{Z}\to\tau\tau$ CR (center left), one b tag CR (center right), and two b tags CR (lower left), and the number of events in the $\mathrm{W}\mathrm{Z}\to3\ell\nu$ and $\mathrm{Z}\mathrm{Z}\to4\ell$ CRs (lower right). The histograms for $\mathrm{t}\mathrm{V}\mathrm{x}$ backgrounds include the contributions from ${\mathrm{t}\overline{\mathrm{t}}} \mathrm{V}(\mathrm{V})$ processes. The histograms for V$\gamma$ backgrounds include the contributions from W$\gamma$ and Z$\gamma$ processes. The overflow is included in the last bin. The bottom panel in each figure shows the ratio of the number of events observed in data to that of the total SM prediction. The grey bands represent the uncertainties in the predicted yields. The vertical bars represent the statistical uncertainties in the data.
png pdf	Figure 1-e: Distributions of the number of reconstructed jets after the fit to the data in the WW SR (upper left), same-sign CR (upper right), $\mathrm{Z}\to\tau\tau$ CR (center left), one b tag CR (center right), and two b tags CR (lower left), and the number of events in the $\mathrm{W}\mathrm{Z}\to3\ell\nu$ and $\mathrm{Z}\mathrm{Z}\to4\ell$ CRs (lower right). The histograms for $\mathrm{t}\mathrm{V}\mathrm{x}$ backgrounds include the contributions from ${\mathrm{t}\overline{\mathrm{t}}} \mathrm{V}(\mathrm{V})$ processes. The histograms for V$\gamma$ backgrounds include the contributions from W$\gamma$ and Z$\gamma$ processes. The overflow is included in the last bin. The bottom panel in each figure shows the ratio of the number of events observed in data to that of the total SM prediction. The grey bands represent the uncertainties in the predicted yields. The vertical bars represent the statistical uncertainties in the data.
png pdf	Figure 1-f: Distributions of the number of reconstructed jets after the fit to the data in the WW SR (upper left), same-sign CR (upper right), $\mathrm{Z}\to\tau\tau$ CR (center left), one b tag CR (center right), and two b tags CR (lower left), and the number of events in the $\mathrm{W}\mathrm{Z}\to3\ell\nu$ and $\mathrm{Z}\mathrm{Z}\to4\ell$ CRs (lower right). The histograms for $\mathrm{t}\mathrm{V}\mathrm{x}$ backgrounds include the contributions from ${\mathrm{t}\overline{\mathrm{t}}} \mathrm{V}(\mathrm{V})$ processes. The histograms for V$\gamma$ backgrounds include the contributions from W$\gamma$ and Z$\gamma$ processes. The overflow is included in the last bin. The bottom panel in each figure shows the ratio of the number of events observed in data to that of the total SM prediction. The grey bands represent the uncertainties in the predicted yields. The vertical bars represent the statistical uncertainties in the data.
png pdf	Figure 2: Results obtained in this analysis and other WW production cross section measurements at different center-of-mass energies for the CMS [6,7,11], ATLAS [5,8,71], CDF [4], and D0 [3] Collaborations are presented, and compared with the NNLO QCD $\times$ NLO EW and NLO predictions from MATRIX. The vertical error bars represent the uncertainty in the measured cross section.
png pdf	Figure 3: The upper panel shows the normalized cross section measurement for events with $N_{\mathrm{j}}=$ 0, 1, ${\ge}$2 jets. The filled circles represent the unfolded data results. The black, blue, and red lines represent the predictions from POWHEG +PYTHIA, MATRIX, and POWHEG MINNLO+PYTHIA, respectively. The lower panels show the ratio of the theoretical predictions to the measurement. In all panels, the error bars on the data points represent the total uncertainty in the measurement, and the shaded band depicts the uncertainty in the prediction.

Tables
png pdf	Table 1: Summary of the requirements defining the WW SR and dilepton CRs.
png pdf	Table 2: Summary of the requirements defining the WZ and ZZ CRs.
png pdf	Table 3: Systematic uncertainties on $\mu$, the measured inclusive cross section divided by the predicted cross section. Lepton experimental uncertainties encompass the effects of calibration of lepton momentum scale and resolution, as well as lepton trigger, reconstruction, identification, and isolation efficiencies. Jet experimental uncertainties encompass the effects of the jet energy scale and resolution. The limited sample size category is related to the finite number of MC events and data events used for data-driven background estimates.
png pdf	Table 4: Definition of the fiducial region.
png pdf	Table 5: Data, signal, and background yields combining all reconstructed jet multiplicity bins. The combination of the statistical and systematic uncertainties is shown. The expected yields are shown with their best fit normalizations from the simultaneous fit to data.
png pdf	Table 6: Data, signal and background yields in events in the WZ and ZZ CRs. The combination of the statistical and systematic uncertainties is shown. The expected yields are shown with their best fit normalizations from the simultaneous fit to data.
png pdf	Table 7: Inclusive fiducial cross section and normalized cross sections for events with $N_{\mathrm{j}}=$ 0, 1, ${\ge}$2 jets. The uncertainty listed is the total uncertainty obtained from the fit to the yields. The expected predictions are obtained from POWHEG +PYTHIA. In parentheses, the split of systematic and statistical uncertainties are reported.

Summary

First measurements at $\sqrt{s}=$ 13.6 TeV of the WW production cross section in proton-proton collisions have been presented. The data used in this study were collected with the CMS detector at the CERN LHC in 2022, and correspond to an integrated luminosity of 34.8 fb$^{-1}$. Events were selected by requiring one electron and one muon of opposite charge. A maximum likelihood fit has been performed in event signal- and background-enriched categories defined by the flavour and charge of the leptons, the number of jets, and number of jets identified as originating from b quarks. An inclusive WW production cross section of 125.7 $\pm$ 2.3 (stat) $\pm$ 4.8 (syst) $\pm$ 1.8 (lumi) pb $=$ 125.7 $\pm$ 5.6 pb is measured, in agreement with the standard model prediction. The overall sensitivity is about 25% better than previous CMS measurements at $\sqrt{s}=$ 13 TeV with a similar integrated luminosity, because of several reduced experimental uncertainties and the improved fit strategy. Cross sections have also been reported in a fiducial region close to that of the detector acceptance, both inclusively and differentially, as a function of the jet multiplicity in the event. For first time in proton-proton collisions, WW events with at least two reconstructed jets are studied and compared with the most precise theoretical predictions.

Additional Figures
png pdf	Additional Figure 1: Distributions of the $m_{\ell\ell}$ (upper left), $p_{\mathrm{T}}^{\ell\ell}$ (upper right), $p_{\mathrm{T}}^{\ell\text{ max}}$ (lower left), and $p_{\mathrm{T}}^{\ell\text{ min}}$ (lower right) variables in the WW SR. The error bars represent the uncertainties associated with statistical and systematic uncertainties before the fit to data.
png pdf	Additional Figure 1-a: Distributions of the $m_{\ell\ell}$ (upper left), $p_{\mathrm{T}}^{\ell\ell}$ (upper right), $p_{\mathrm{T}}^{\ell\text{ max}}$ (lower left), and $p_{\mathrm{T}}^{\ell\text{ min}}$ (lower right) variables in the WW SR. The error bars represent the uncertainties associated with statistical and systematic uncertainties before the fit to data.
png pdf	Additional Figure 1-b: Distributions of the $m_{\ell\ell}$ (upper left), $p_{\mathrm{T}}^{\ell\ell}$ (upper right), $p_{\mathrm{T}}^{\ell\text{ max}}$ (lower left), and $p_{\mathrm{T}}^{\ell\text{ min}}$ (lower right) variables in the WW SR. The error bars represent the uncertainties associated with statistical and systematic uncertainties before the fit to data.
png pdf	Additional Figure 1-c: Distributions of the $m_{\ell\ell}$ (upper left), $p_{\mathrm{T}}^{\ell\ell}$ (upper right), $p_{\mathrm{T}}^{\ell\text{ max}}$ (lower left), and $p_{\mathrm{T}}^{\ell\text{ min}}$ (lower right) variables in the WW SR. The error bars represent the uncertainties associated with statistical and systematic uncertainties before the fit to data.
png pdf	Additional Figure 1-d: Distributions of the $m_{\ell\ell}$ (upper left), $p_{\mathrm{T}}^{\ell\ell}$ (upper right), $p_{\mathrm{T}}^{\ell\text{ max}}$ (lower left), and $p_{\mathrm{T}}^{\ell\text{ min}}$ (lower right) variables in the WW SR. The error bars represent the uncertainties associated with statistical and systematic uncertainties before the fit to data.
png pdf	Additional Figure 2: Distributions of the $m_{\ell\ell}$ (upper left), $p_{\mathrm{T}}^{\ell\ell}$ (upper right), $p_{\mathrm{T}}^{\ell\text{ max}}$ (lower left), and $p_{\mathrm{T}}^{\ell\text{ min}}$ (lower right) variables in the 0-jet WW SR. The error bars represent the uncertainties associated with statistical and systematic uncertainties before the fit to data.
png pdf	Additional Figure 2-a: Distributions of the $m_{\ell\ell}$ (upper left), $p_{\mathrm{T}}^{\ell\ell}$ (upper right), $p_{\mathrm{T}}^{\ell\text{ max}}$ (lower left), and $p_{\mathrm{T}}^{\ell\text{ min}}$ (lower right) variables in the 0-jet WW SR. The error bars represent the uncertainties associated with statistical and systematic uncertainties before the fit to data.
png pdf	Additional Figure 2-b: Distributions of the $m_{\ell\ell}$ (upper left), $p_{\mathrm{T}}^{\ell\ell}$ (upper right), $p_{\mathrm{T}}^{\ell\text{ max}}$ (lower left), and $p_{\mathrm{T}}^{\ell\text{ min}}$ (lower right) variables in the 0-jet WW SR. The error bars represent the uncertainties associated with statistical and systematic uncertainties before the fit to data.
png pdf	Additional Figure 2-c: Distributions of the $m_{\ell\ell}$ (upper left), $p_{\mathrm{T}}^{\ell\ell}$ (upper right), $p_{\mathrm{T}}^{\ell\text{ max}}$ (lower left), and $p_{\mathrm{T}}^{\ell\text{ min}}$ (lower right) variables in the 0-jet WW SR. The error bars represent the uncertainties associated with statistical and systematic uncertainties before the fit to data.
png pdf	Additional Figure 2-d: Distributions of the $m_{\ell\ell}$ (upper left), $p_{\mathrm{T}}^{\ell\ell}$ (upper right), $p_{\mathrm{T}}^{\ell\text{ max}}$ (lower left), and $p_{\mathrm{T}}^{\ell\text{ min}}$ (lower right) variables in the 0-jet WW SR. The error bars represent the uncertainties associated with statistical and systematic uncertainties before the fit to data.
png pdf	Additional Figure 3: Distributions of the $m_{\ell\ell}$ (upper left), $p_{\mathrm{T}}^{\ell\ell}$ (upper right), $p_{\mathrm{T}}^{\ell\text{ max}}$ (lower left), and $p_{\mathrm{T}}^{\ell\text{ min}}$ (lower right) variables in the 1-jet WW SR. The error bars represent the uncertainties associated with statistical and systematic uncertainties before the fit to data.
png pdf	Additional Figure 3-a: Distributions of the $m_{\ell\ell}$ (upper left), $p_{\mathrm{T}}^{\ell\ell}$ (upper right), $p_{\mathrm{T}}^{\ell\text{ max}}$ (lower left), and $p_{\mathrm{T}}^{\ell\text{ min}}$ (lower right) variables in the 1-jet WW SR. The error bars represent the uncertainties associated with statistical and systematic uncertainties before the fit to data.
png pdf	Additional Figure 3-b: Distributions of the $m_{\ell\ell}$ (upper left), $p_{\mathrm{T}}^{\ell\ell}$ (upper right), $p_{\mathrm{T}}^{\ell\text{ max}}$ (lower left), and $p_{\mathrm{T}}^{\ell\text{ min}}$ (lower right) variables in the 1-jet WW SR. The error bars represent the uncertainties associated with statistical and systematic uncertainties before the fit to data.
png pdf	Additional Figure 3-c: Distributions of the $m_{\ell\ell}$ (upper left), $p_{\mathrm{T}}^{\ell\ell}$ (upper right), $p_{\mathrm{T}}^{\ell\text{ max}}$ (lower left), and $p_{\mathrm{T}}^{\ell\text{ min}}$ (lower right) variables in the 1-jet WW SR. The error bars represent the uncertainties associated with statistical and systematic uncertainties before the fit to data.
png pdf	Additional Figure 3-d: Distributions of the $m_{\ell\ell}$ (upper left), $p_{\mathrm{T}}^{\ell\ell}$ (upper right), $p_{\mathrm{T}}^{\ell\text{ max}}$ (lower left), and $p_{\mathrm{T}}^{\ell\text{ min}}$ (lower right) variables in the 1-jet WW SR. The error bars represent the uncertainties associated with statistical and systematic uncertainties before the fit to data.
png pdf	Additional Figure 4: Distributions of the $m_{\ell\ell}$ (upper left), $p_{\mathrm{T}}^{\ell\ell}$ (upper right), $p_{\mathrm{T}}^{\ell\text{ max}}$ (lower left), and $p_{\mathrm{T}}^{\ell\text{ min}}$ (lower right) variables in the 2-jet WW SR. The error bars represent the uncertainties associated with statistical and systematic uncertainties before the fit to data.
png pdf	Additional Figure 4-a: Distributions of the $m_{\ell\ell}$ (upper left), $p_{\mathrm{T}}^{\ell\ell}$ (upper right), $p_{\mathrm{T}}^{\ell\text{ max}}$ (lower left), and $p_{\mathrm{T}}^{\ell\text{ min}}$ (lower right) variables in the 2-jet WW SR. The error bars represent the uncertainties associated with statistical and systematic uncertainties before the fit to data.
png pdf	Additional Figure 4-b: Distributions of the $m_{\ell\ell}$ (upper left), $p_{\mathrm{T}}^{\ell\ell}$ (upper right), $p_{\mathrm{T}}^{\ell\text{ max}}$ (lower left), and $p_{\mathrm{T}}^{\ell\text{ min}}$ (lower right) variables in the 2-jet WW SR. The error bars represent the uncertainties associated with statistical and systematic uncertainties before the fit to data.
png pdf	Additional Figure 4-c: Distributions of the $m_{\ell\ell}$ (upper left), $p_{\mathrm{T}}^{\ell\ell}$ (upper right), $p_{\mathrm{T}}^{\ell\text{ max}}$ (lower left), and $p_{\mathrm{T}}^{\ell\text{ min}}$ (lower right) variables in the 2-jet WW SR. The error bars represent the uncertainties associated with statistical and systematic uncertainties before the fit to data.
png pdf	Additional Figure 4-d: Distributions of the $m_{\ell\ell}$ (upper left), $p_{\mathrm{T}}^{\ell\ell}$ (upper right), $p_{\mathrm{T}}^{\ell\text{ max}}$ (lower left), and $p_{\mathrm{T}}^{\ell\text{ min}}$ (lower right) variables in the 2-jet WW SR. The error bars represent the uncertainties associated with statistical and systematic uncertainties before the fit to data.

Additional Tables
png pdf	Additional Table 1: Correlation matrix among the inclusive fiducial cross sections and the jet bin fractions measured in the analysis.
png pdf	Additional Table 2: Relative fractions at the reconstruction level for each generator-level jet bin.
png pdf	Additional Table 3: Fiducial cross sections as a function of the jet bin obtained in the analysis. The uncertainty listed is the total uncertainty obtained from the fit to the yields.

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64	R. D. Cousins	Lectures on statistics in theory: Prelude to statistics in practice		1807.05996
65	ATLAS Collaboration	Measurement of the $\mathrm{t\bar{t}}$ cross section and its ratio to the Z production cross section using pp collisions at $\sqrt{s}=$ 13.6 TeV with the ATLAS detector	PLB 848 (2024) 138376	2308.09529
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69	CMS Collaboration	HEPData record for this analysis	2024 link
70	CMS Collaboration	Statistical model for this analysis	link
71	ATLAS Collaboration	Measurement of the W$^{+}$W$^{-}$ production cross section in pp collisions at a centre-of-mass energy of $\sqrt{s} =$ 13 TeV with the ATLAS experiment	PLB 773 (2017) 354	1702.04519

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