CMS-PAS-SMP-18-004 | ||

Studies of $\mathrm{W^+W^-}$ production at $\sqrt{s}= $ 13 TeV | ||

CMS Collaboration | ||

April 2020 | ||

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Abstract:
A measurement of the $\mathrm{W}^+\mathrm{W}^-$ boson pair production cross section in proton-proton collisions at $\sqrt{s}= $ 13 TeV is presented. The data used in this study were collected with the CMS detector at the LHC and correspond to an integrated luminosity of 35.9 fb$^{-1}$. The $\mathrm{W}^+\mathrm{W}^-$ candidate events are selected by first requiring two oppositely-charged leptons (electrons or muons). Two methods for reducing background contributions are employed. In the first one, a sequence of requirements on kinematic quantities is applied allowing a measurement of the total cross section: 117.6 $\pm$ 6.8 pb which agrees well with the theoretical cross section. Fiducial cross sections are also reported for events with zero jets or one jet, and the change in the zero-jet fiducial cross section with the jet $p_{\mathrm{T}}$ threshold is measured. Normalized differential cross sections are reported within the fiducial region; these are compared to theoretical predictions based on quantum chromodynamics at next-to-next-to-leading-order accuracy. A second method for suppressing background contributions employs two random forest classifiers. The analysis based on this method includes a measurement of the total cross section and also a measurement of the normalized jet multiplicity distribution in $\mathrm{W}^+\mathrm{W}^-$ events. Finally, a dilepton invariant mass distribution is used to probe for physics beyond the standard model in the context of an effective field theory and limits on the presence of dimension-6 operators are derived.
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Links:
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These preliminary results are superseded in this paper, PRD 102 (2020) 092001.The superseded preliminary plots can be found here. |

Figures | |

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Figure 1:
Kinematic distributions for events with zero jets and DF leptons in the sequential cut analysis. The distributions show the leading and trailing lepton $ {p_{\mathrm {T}}} $ ($ {p_{\text {T}}^{\ell \text {\,max}}} $ and $ {p_{\text {T}}^{\ell \text {\,min}}} $), the dilepton transverse momentum $p_{\text {T}}^{\ell \ell}$, the azimuthal angle between the two leptons $ {\Delta \phi _{\ell \ell}} $, the missing transverse momentum $ {{p_{\mathrm {T}}} ^{\mathrm {miss}}}$, and the dilepton invariant mass $ {m_{\ell \ell}}$. The hatched areas represent the combined systematic and statistical uncertainty in each bin. The last bin includes the overflow. |

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Figure 1-a:
Kinematic distributions for events with zero jets and DF leptons in the sequential cut analysis. The distributions show the leading and trailing lepton $ {p_{\mathrm {T}}} $ ($ {p_{\text {T}}^{\ell \text {\,max}}} $ and $ {p_{\text {T}}^{\ell \text {\,min}}} $), the dilepton transverse momentum $p_{\text {T}}^{\ell \ell}$, the azimuthal angle between the two leptons $ {\Delta \phi _{\ell \ell}} $, the missing transverse momentum $ {{p_{\mathrm {T}}} ^{\mathrm {miss}}}$, and the dilepton invariant mass $ {m_{\ell \ell}}$. The hatched areas represent the combined systematic and statistical uncertainty in each bin. The last bin includes the overflow. |

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Figure 1-b:
Kinematic distributions for events with zero jets and DF leptons in the sequential cut analysis. The distributions show the leading and trailing lepton $ {p_{\mathrm {T}}} $ ($ {p_{\text {T}}^{\ell \text {\,max}}} $ and $ {p_{\text {T}}^{\ell \text {\,min}}} $), the dilepton transverse momentum $p_{\text {T}}^{\ell \ell}$, the azimuthal angle between the two leptons $ {\Delta \phi _{\ell \ell}} $, the missing transverse momentum $ {{p_{\mathrm {T}}} ^{\mathrm {miss}}}$, and the dilepton invariant mass $ {m_{\ell \ell}}$. The hatched areas represent the combined systematic and statistical uncertainty in each bin. The last bin includes the overflow. |

png pdf |
Figure 1-c:
Kinematic distributions for events with zero jets and DF leptons in the sequential cut analysis. The distributions show the leading and trailing lepton $ {p_{\mathrm {T}}} $ ($ {p_{\text {T}}^{\ell \text {\,max}}} $ and $ {p_{\text {T}}^{\ell \text {\,min}}} $), the dilepton transverse momentum $p_{\text {T}}^{\ell \ell}$, the azimuthal angle between the two leptons $ {\Delta \phi _{\ell \ell}} $, the missing transverse momentum $ {{p_{\mathrm {T}}} ^{\mathrm {miss}}}$, and the dilepton invariant mass $ {m_{\ell \ell}}$. The hatched areas represent the combined systematic and statistical uncertainty in each bin. The last bin includes the overflow. |

png pdf |
Figure 1-d:
Kinematic distributions for events with zero jets and DF leptons in the sequential cut analysis. The distributions show the leading and trailing lepton $ {p_{\mathrm {T}}} $ ($ {p_{\text {T}}^{\ell \text {\,max}}} $ and $ {p_{\text {T}}^{\ell \text {\,min}}} $), the dilepton transverse momentum $p_{\text {T}}^{\ell \ell}$, the azimuthal angle between the two leptons $ {\Delta \phi _{\ell \ell}} $, the missing transverse momentum $ {{p_{\mathrm {T}}} ^{\mathrm {miss}}}$, and the dilepton invariant mass $ {m_{\ell \ell}}$. The hatched areas represent the combined systematic and statistical uncertainty in each bin. The last bin includes the overflow. |

png pdf |
Figure 1-e:
Kinematic distributions for events with zero jets and DF leptons in the sequential cut analysis. The distributions show the leading and trailing lepton $ {p_{\mathrm {T}}} $ ($ {p_{\text {T}}^{\ell \text {\,max}}} $ and $ {p_{\text {T}}^{\ell \text {\,min}}} $), the dilepton transverse momentum $p_{\text {T}}^{\ell \ell}$, the azimuthal angle between the two leptons $ {\Delta \phi _{\ell \ell}} $, the missing transverse momentum $ {{p_{\mathrm {T}}} ^{\mathrm {miss}}}$, and the dilepton invariant mass $ {m_{\ell \ell}}$. The hatched areas represent the combined systematic and statistical uncertainty in each bin. The last bin includes the overflow. |

png pdf |
Figure 1-f:
Kinematic distributions for events with zero jets and DF leptons in the sequential cut analysis. The distributions show the leading and trailing lepton $ {p_{\mathrm {T}}} $ ($ {p_{\text {T}}^{\ell \text {\,max}}} $ and $ {p_{\text {T}}^{\ell \text {\,min}}} $), the dilepton transverse momentum $p_{\text {T}}^{\ell \ell}$, the azimuthal angle between the two leptons $ {\Delta \phi _{\ell \ell}} $, the missing transverse momentum $ {{p_{\mathrm {T}}} ^{\mathrm {miss}}}$, and the dilepton invariant mass $ {m_{\ell \ell}}$. The hatched areas represent the combined systematic and statistical uncertainty in each bin. The last bin includes the overflow. |

png pdf |
Figure 2:
Kinematic distributions for events with one jet and DF leptons in the sequential cut analysis. The quantities and the hatched areas are the same as in Fig. xxxxx. |

png pdf |
Figure 2-a:
Kinematic distributions for events with one jet and DF leptons in the sequential cut analysis. The quantities and the hatched areas are the same as in Fig. xxxxx. |

png pdf |
Figure 2-b:
Kinematic distributions for events with one jet and DF leptons in the sequential cut analysis. The quantities and the hatched areas are the same as in Fig. xxxxx. |

png pdf |
Figure 2-c:
Kinematic distributions for events with one jet and DF leptons in the sequential cut analysis. The quantities and the hatched areas are the same as in Fig. xxxxx. |

png pdf |
Figure 2-d:
Kinematic distributions for events with one jet and DF leptons in the sequential cut analysis. The quantities and the hatched areas are the same as in Fig. xxxxx. |

png pdf |
Figure 2-e:
Kinematic distributions for events with one jet and DF leptons in the sequential cut analysis. The quantities and the hatched areas are the same as in Fig. xxxxx. |

png pdf |
Figure 2-f:
Kinematic distributions for events with one jet and DF leptons in the sequential cut analysis. The quantities and the hatched areas are the same as in Fig. xxxxx. |

png pdf |
Figure 3:
Top left: score $S_{\text {DY}}$ distribution for the Drell-Yan discriminating random forest discriminant. The Drell-Yan distribution peaks toward zero and the $ {\mathrm{W} \mathrm{W}} $ distribution peaks toward one. Top right: score $S_{{\mathrm{t} {}\mathrm{\bar{t}}}}$ distribution for the top quark random forest discriminant. The ${\mathrm{t} {}\mathrm{\bar{t}}}$ distribution peaks toward zero and the $ {\mathrm{W} \mathrm{W}} $ peaks toward one. Bottom left: the $S_{\text {DY}}$ distribution after suppressing top quark events with $S_{{\mathrm{t} {}\mathrm{\bar{t}}}} > S_{{\mathrm{t} {}\mathrm{\bar{t}}}}^{\text {min}}= $ 0.6. Bottom right: the $S_{{\mathrm{t} {}\mathrm{\bar{t}}}}$ distribution after suppressing Drell-Yan events with $S_{\text {DY}} > S_{\text {DY}}^{\text {min}}= $ 0.96. |

png pdf |
Figure 3-a:
Top left: score $S_{\text {DY}}$ distribution for the Drell-Yan discriminating random forest discriminant. The Drell-Yan distribution peaks toward zero and the $ {\mathrm{W} \mathrm{W}} $ distribution peaks toward one. Top right: score $S_{{\mathrm{t} {}\mathrm{\bar{t}}}}$ distribution for the top quark random forest discriminant. The ${\mathrm{t} {}\mathrm{\bar{t}}}$ distribution peaks toward zero and the $ {\mathrm{W} \mathrm{W}} $ peaks toward one. Bottom left: the $S_{\text {DY}}$ distribution after suppressing top quark events with $S_{{\mathrm{t} {}\mathrm{\bar{t}}}} > S_{{\mathrm{t} {}\mathrm{\bar{t}}}}^{\text {min}}= $ 0.6. Bottom right: the $S_{{\mathrm{t} {}\mathrm{\bar{t}}}}$ distribution after suppressing Drell-Yan events with $S_{\text {DY}} > S_{\text {DY}}^{\text {min}}= $ 0.96. |

png pdf |
Figure 3-b:
Top left: score $S_{\text {DY}}$ distribution for the Drell-Yan discriminating random forest discriminant. The Drell-Yan distribution peaks toward zero and the $ {\mathrm{W} \mathrm{W}} $ distribution peaks toward one. Top right: score $S_{{\mathrm{t} {}\mathrm{\bar{t}}}}$ distribution for the top quark random forest discriminant. The ${\mathrm{t} {}\mathrm{\bar{t}}}$ distribution peaks toward zero and the $ {\mathrm{W} \mathrm{W}} $ peaks toward one. Bottom left: the $S_{\text {DY}}$ distribution after suppressing top quark events with $S_{{\mathrm{t} {}\mathrm{\bar{t}}}} > S_{{\mathrm{t} {}\mathrm{\bar{t}}}}^{\text {min}}= $ 0.6. Bottom right: the $S_{{\mathrm{t} {}\mathrm{\bar{t}}}}$ distribution after suppressing Drell-Yan events with $S_{\text {DY}} > S_{\text {DY}}^{\text {min}}= $ 0.96. |

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Figure 3-c:
Top left: score $S_{\text {DY}}$ distribution for the Drell-Yan discriminating random forest discriminant. The Drell-Yan distribution peaks toward zero and the $ {\mathrm{W} \mathrm{W}} $ distribution peaks toward one. Top right: score $S_{{\mathrm{t} {}\mathrm{\bar{t}}}}$ distribution for the top quark random forest discriminant. The ${\mathrm{t} {}\mathrm{\bar{t}}}$ distribution peaks toward zero and the $ {\mathrm{W} \mathrm{W}} $ peaks toward one. Bottom left: the $S_{\text {DY}}$ distribution after suppressing top quark events with $S_{{\mathrm{t} {}\mathrm{\bar{t}}}} > S_{{\mathrm{t} {}\mathrm{\bar{t}}}}^{\text {min}}= $ 0.6. Bottom right: the $S_{{\mathrm{t} {}\mathrm{\bar{t}}}}$ distribution after suppressing Drell-Yan events with $S_{\text {DY}} > S_{\text {DY}}^{\text {min}}= $ 0.96. |

png pdf |
Figure 3-d:
Top left: score $S_{\text {DY}}$ distribution for the Drell-Yan discriminating random forest discriminant. The Drell-Yan distribution peaks toward zero and the $ {\mathrm{W} \mathrm{W}} $ distribution peaks toward one. Top right: score $S_{{\mathrm{t} {}\mathrm{\bar{t}}}}$ distribution for the top quark random forest discriminant. The ${\mathrm{t} {}\mathrm{\bar{t}}}$ distribution peaks toward zero and the $ {\mathrm{W} \mathrm{W}} $ peaks toward one. Bottom left: the $S_{\text {DY}}$ distribution after suppressing top quark events with $S_{{\mathrm{t} {}\mathrm{\bar{t}}}} > S_{{\mathrm{t} {}\mathrm{\bar{t}}}}^{\text {min}}= $ 0.6. Bottom right: the $S_{{\mathrm{t} {}\mathrm{\bar{t}}}}$ distribution after suppressing Drell-Yan events with $S_{\text {DY}} > S_{\text {DY}}^{\text {min}}= $ 0.96. |

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Figure 4:
Comparison of efficiencies for the sequential cut and random forest analyses as a function of $p_{\text {T}}^{\mathrm{W} \mathrm{W}} $. The sequential cut analysis includes 0-jet and 1-jet events from both DF and SF lepton combinations, for which the contribution from 0-jet and 1-jet are shown separately. The efficiency curve for $S_{{\mathrm{t} {}\mathrm{\bar{t}}}}^{\text {min}}= $ 0.2 is also shown; this value is used in measuring the jet multiplicity distribution. |

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Figure 5:
The upper panel shows the fiducial cross sections for the production of $ {\mathrm{W^{+}} \mathrm{W^{-}}} $+0-jets as the ${p_{\mathrm {T}}}$ threshold for jets is varied. The fiducial region is defined by two opposite-sign leptons with $ {p_{\mathrm {T}}} > $ 20 GeV and $ {| \eta |} < $ 2.5 excluding the products of $\tau $ lepton decay, and $ {m_{\ell \ell}} > $ 20 GeV, $p_{\text {T}}^{\ell \ell} > $ 30 GeV, and $ {{p_{\mathrm {T}}} ^\text {miss}} > $ 30 GeV. Jets must have $ {p_{\mathrm {T}}} > $ 30 GeV, $ {| \eta |} < $ 4.5, and be separated from each of the two leptons by $\Delta R > $ 0.3. The lower panel shows the ratio of the theoretical prediction to the measurement. The shaded band depicts the uncertainty on the prediction. |

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Figure 6:
The upper panels show the normalized differential cross sections with respect to the dilepton invariant mass, leading lepton ${p_{\mathrm {T}}}$, trailing lepton ${p_{\mathrm {T}}}$, and dilepton azimuthal angular separation, compared to POWHEG predictions. The lower panels show the ratio of the theoretical predictions to the measured values. The gray bands around unity in the ratio plots represent the systematic uncertainties, while the error bars on the markers represent the statistical uncertainties. |

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Figure 6-a:
The upper panels show the normalized differential cross sections with respect to the dilepton invariant mass, leading lepton ${p_{\mathrm {T}}}$, trailing lepton ${p_{\mathrm {T}}}$, and dilepton azimuthal angular separation, compared to POWHEG predictions. The lower panels show the ratio of the theoretical predictions to the measured values. The gray bands around unity in the ratio plots represent the systematic uncertainties, while the error bars on the markers represent the statistical uncertainties. |

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Figure 6-b:
The upper panels show the normalized differential cross sections with respect to the dilepton invariant mass, leading lepton ${p_{\mathrm {T}}}$, trailing lepton ${p_{\mathrm {T}}}$, and dilepton azimuthal angular separation, compared to POWHEG predictions. The lower panels show the ratio of the theoretical predictions to the measured values. The gray bands around unity in the ratio plots represent the systematic uncertainties, while the error bars on the markers represent the statistical uncertainties. |

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Figure 6-c:
The upper panels show the normalized differential cross sections with respect to the dilepton invariant mass, leading lepton ${p_{\mathrm {T}}}$, trailing lepton ${p_{\mathrm {T}}}$, and dilepton azimuthal angular separation, compared to POWHEG predictions. The lower panels show the ratio of the theoretical predictions to the measured values. The gray bands around unity in the ratio plots represent the systematic uncertainties, while the error bars on the markers represent the statistical uncertainties. |

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Figure 6-d:
The upper panels show the normalized differential cross sections with respect to the dilepton invariant mass, leading lepton ${p_{\mathrm {T}}}$, trailing lepton ${p_{\mathrm {T}}}$, and dilepton azimuthal angular separation, compared to POWHEG predictions. The lower panels show the ratio of the theoretical predictions to the measured values. The gray bands around unity in the ratio plots represent the systematic uncertainties, while the error bars on the markers represent the statistical uncertainties. |

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Figure 7:
The upper panel shows the fractions of events with $ {N_{J}} = $ 0, 1, $\ge $2 jets. The circles represent the data after backgrounds are subtracted and pileup and energy resolution are taken into account. The solid lines represent represent the POWHEG+PYTHIA 8 prediction and an uncertainty represented by the grey band. The lower panel shows the ratio of the theoretical prediction to the measurement. The grey band shows the theoretical uncertainty and the error bars on the markers show the total uncertainty on the measurement. |

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Figure 8:
One of the Feynman diagrams through which dimension-6 operators modify the ${\mathrm{p}} {\mathrm{p}} \to {\mathrm{W^{+}} \mathrm{W^{-}}} $ cross section. |

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Figure 9:
Comparison of the template fits to the observed $ {m_{\mathrm{e}\mu}} $ distributions in the zero-jet (left) and one-jet (right) categories. The non-SM contributions for $c_{\mathrm{W} \mathrm{W} \mathrm{W}}/\Lambda ^2 = $ 3.2 TeV$ ^{-2}$, $c_{\mathrm{W}}/\Lambda ^2 = $ 4.9 TeV$ ^{-2}$, and $c_{B}/\Lambda ^2 = $ 15.0 TeV$ ^{-2}$ are shown, not stacked on top of the other contributions. The last bin contains all events with reconstructed $ {m_{\mathrm{e}\mu}} > $ 1 TeV. The hatched areas represents the total uncertainty in the bin yield. |

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Figure 9-a:
Comparison of the template fits to the observed $ {m_{\mathrm{e}\mu}} $ distributions in the zero-jet (left) and one-jet (right) categories. The non-SM contributions for $c_{\mathrm{W} \mathrm{W} \mathrm{W}}/\Lambda ^2 = $ 3.2 TeV$ ^{-2}$, $c_{\mathrm{W}}/\Lambda ^2 = $ 4.9 TeV$ ^{-2}$, and $c_{B}/\Lambda ^2 = $ 15.0 TeV$ ^{-2}$ are shown, not stacked on top of the other contributions. The last bin contains all events with reconstructed $ {m_{\mathrm{e}\mu}} > $ 1 TeV. The hatched areas represents the total uncertainty in the bin yield. |

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Figure 9-b:
Comparison of the template fits to the observed $ {m_{\mathrm{e}\mu}} $ distributions in the zero-jet (left) and one-jet (right) categories. The non-SM contributions for $c_{\mathrm{W} \mathrm{W} \mathrm{W}}/\Lambda ^2 = $ 3.2 TeV$ ^{-2}$, $c_{\mathrm{W}}/\Lambda ^2 = $ 4.9 TeV$ ^{-2}$, and $c_{B}/\Lambda ^2 = $ 15.0 TeV$ ^{-2}$ are shown, not stacked on top of the other contributions. The last bin contains all events with reconstructed $ {m_{\mathrm{e}\mu}} > $ 1 TeV. The hatched areas represents the total uncertainty in the bin yield. |

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Figure 10:
The expected and observed $-2\Delta \ln L$ curves for the $c_{\mathrm{W} \mathrm{W} \mathrm{W}}/\Lambda ^2$, $ c_{\mathrm{W}}/\Lambda ^2$, and $c_{\mathrm{W}}/\Lambda ^2$ 1D scans combining the 0-jet and 1-jet categories. |

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Figure 10-a:
The expected and observed $-2\Delta \ln L$ curves for the $c_{\mathrm{W} \mathrm{W} \mathrm{W}}/\Lambda ^2$, $ c_{\mathrm{W}}/\Lambda ^2$, and $c_{\mathrm{W}}/\Lambda ^2$ 1D scans combining the 0-jet and 1-jet categories. |

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Figure 10-b:
The expected and observed $-2\Delta \ln L$ curves for the $c_{\mathrm{W} \mathrm{W} \mathrm{W}}/\Lambda ^2$, $ c_{\mathrm{W}}/\Lambda ^2$, and $c_{\mathrm{W}}/\Lambda ^2$ 1D scans combining the 0-jet and 1-jet categories. |

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Figure 10-c:
The expected and observed $-2\Delta \ln L$ curves for the $c_{\mathrm{W} \mathrm{W} \mathrm{W}}/\Lambda ^2$, $ c_{\mathrm{W}}/\Lambda ^2$, and $c_{\mathrm{W}}/\Lambda ^2$ 1D scans combining the 0-jet and 1-jet categories. |

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Figure 11-a:
The expected and observed $-2\Delta \ln L$ contours in the $(c_{\mathrm{W} \mathrm{W} \mathrm{W}}/\Lambda ^2, c_{\mathrm{W}}/\Lambda ^2)$, $(c_{\mathrm{W} \mathrm{W} \mathrm{W}}/\Lambda ^2, c_{B}/\Lambda ^2)$, and $(c_{\mathrm{W}}/\Lambda ^2, c_{B}/\Lambda ^2)$ planes combining the 0-jet and 1-jet categories. |

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Figure 11-b:
The expected and observed $-2\Delta \ln L$ contours in the $(c_{\mathrm{W} \mathrm{W} \mathrm{W}}/\Lambda ^2, c_{\mathrm{W}}/\Lambda ^2)$, $(c_{\mathrm{W} \mathrm{W} \mathrm{W}}/\Lambda ^2, c_{B}/\Lambda ^2)$, and $(c_{\mathrm{W}}/\Lambda ^2, c_{B}/\Lambda ^2)$ planes combining the 0-jet and 1-jet categories. |

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Figure 11-c:
The expected and observed $-2\Delta \ln L$ contours in the $(c_{\mathrm{W} \mathrm{W} \mathrm{W}}/\Lambda ^2, c_{\mathrm{W}}/\Lambda ^2)$, $(c_{\mathrm{W} \mathrm{W} \mathrm{W}}/\Lambda ^2, c_{B}/\Lambda ^2)$, and $(c_{\mathrm{W}}/\Lambda ^2, c_{B}/\Lambda ^2)$ planes combining the 0-jet and 1-jet categories. |

Tables | |

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Table 1:
Summary of event selection criteria for the sequential cut analysis and the random forest analyses. DYMVA refers to an event classifier used in the sequential cut analysis to suppress Drell-Yan background events. RF refers to random forest classifiers. Kinematic quantities are measured in GeV. A dash (--) means no requirement applied. |

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Table 2:
Sample composition for the sequential cut and random forest selections after the fits described in Section yyyyy have been executed; the uncertainties shown are based on the total uncertainty obtained from the fit. The purity is the fraction of selected events that are $ {\mathrm{W^{+}} \mathrm{W^{-}}} $ signal events. |

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Table 3:
Features used for the random forest classifiers. The first classifier distinguishes Drell-Yan and $ {\mathrm{W^{+}} \mathrm{W^{-}}} $ signal events, and the second one distinguishes top quark events and signal events. |

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Table 4:
Relative systematic uncertainties of the cross section measurement based on the sequential cut analysis. |

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Table 5:
Summary of signal strengths and total cross sections obtained in the sequential cut analysis. The uncertainty listed is the total uncertainty obtained from the fit to the yields. |

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Table 6:
Fiducial cross sections for the production of $ {\mathrm{W^{+}} \mathrm{W^{-}}} $+0-jets as the ${p_{\mathrm {T}}}$ threshold for jets is varied. The fiducial region is defined by two opposite-sign leptons with $ {p_{\mathrm {T}}} > $ 20 GeV and $ {| \eta |} < $ 2.5 excluding the products of $\tau $ lepton decay, and $ {m_{\ell \ell}} > $ 20 GeV, $p_{\text {T}}^{\ell \ell} > $ 30 GeV, and $ {{p_{\mathrm {T}}} ^\text {miss}} > $ 30 GeV. Jets must have $ {p_{\mathrm {T}}} > $ 30 GeV, $ {| \eta |} < $ 4.5, and be separated from each of the two leptons by $\Delta R > $ 0.3. |

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Table 7:
Efficiency for the random forest selection with respect to preselected events as a function of jet multiplicity. The stated uncertainties are statistical only. |

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Table 8:
Fractions of events with $ {N_{J}} = $ 0, 1, $\ge $2 jets. The first uncertainty is statistical and the second combines systematic uncertainties from the response matrix and from the background subtraction. |

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Table 9:
Expected and observed 68% and 95% confidence intervals on the measurement of the Wilson coefficients associated with the three CP-conserving, dimension-6 operators. |

Summary |

A study of ${\mathrm{W^{+}}\mathrm{W^{-}}} $ boson pair production in proton-proton collisions at $\sqrt{s} = $ 13 TeV was presented. The measurement is based on data collected with the CMS detector at the LHC correspond to an integrated luminosity of $35.9$ fb$^{-1}$. Candidate events were selected which have two electrons or muons with oppositely-signed charges. Two analysis methods were described. The first method relies on a sequence of requirements on kinematic quantities to suppress backgrounds, while the second uses a pair of random forest classifiers. The total cross section measured in the sequential cut analysis is $\sigma_{\text{SC}}^{\text{tot}} = $ 117.6 $\pm$ 1.4 (stat) $\pm$ 5.5 (syst) $\pm$ 1.9 (theo) $\pm$ 3.2 (lumi) pb $=$ 117.6 $\pm$ 6.8 pb, where the individual uncertainties are statistical, experimental systematic, theoretical, and luminosity; this measured value is consistent with the next-to-next-to-leading order theoretical prediction 118.8 $\pm$ 3.6 pb. The sequential cut analysis was also used to measure fiducial cross sections including the change in the zero-jet fiducial cross section with jet ${p_{\mathrm{T}}}$ threshold. Normalized differential cross sections were reported and compared with next-to-leading order Monte Carlo simulations. Good agreement is observed. The random forest analysis was used to measure the total cross section and to measure the normalized jet multiplicity distribution in ${\mathrm{W^{+}}\mathrm{W^{-}}} $ events. Finally, bounds on coefficients of dimension-6 operators in the context of an effective field theory were set using the electron-muon invariant mass distribution. |

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Compact Muon Solenoid LHC, CERN |