CMSPASSMP22008  
Measurement of W$^{\pm}$W$^{\pm} $ scattering in protonproton collisions at $ \sqrt{s} =$ 13 TeV in final states with one tau lepton  
CMS Collaboration  
21 August 2023  
Abstract: A measurement of the cross section for the scattering of samesign W bosons is presented. This is the first study of a vector boson scattering process in the decay channel with a tau lepton ($ \tau $). The analysis is performed with protonproton collision data collected by the CMS detector at the LHC at a centerofmass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb$ ^{1} $. Events are selected with the requirement of one $ \tau $, one light lepton ($ e $ or $ \mu $), missing transverse momentum, and two jets with large pseudorapidity separation and large dijet invariant mass. The measured electroweak samesign WW scattering cross section, extracted with the amplitude for the QCDassociated diboson production fixed to the standard model value, is 1.44 $ ^{+0.63}_{0.56} $ times the standard model prediction. The observed (expected) signal significance is 2.7 (1.9) standard deviations. A measurement of the combined electroweak and QCDassociated samesign diboson production yields an observed (expected) significance of 2.9 (2.0) standard deviations.  
Links: CDS record (PDF) ; CADI line (restricted) ; 
Figures & Tables  Summary  Additional Figures & Tables  References  CMS Publications 

Figures  
png pdf 
Figure 1:
Representative Born level Feynman diagrams contributing to the process $ pp \rightarrow \tau^{\pm} \nu_{\tau} \ell^{\pm} \nu_{\ell} jj $, $ \ell=$ e, $ \mu $, with $ \mathcal{O}(\alpha^6) $ (left) and $ \mathcal{O}(\alpha_{s}^{2}\alpha^4) $ (right) couplings. 
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Figure 1a:
Representative Born level Feynman diagrams contributing to the process $ pp \rightarrow \tau^{\pm} \nu_{\tau} \ell^{\pm} \nu_{\ell} jj $, $ \ell=$ e, $ \mu $, with $ \mathcal{O}(\alpha^6) $ (left) and $ \mathcal{O}(\alpha_{s}^{2}\alpha^4) $ (right) couplings. 
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Figure 1b:
Representative Born level Feynman diagrams contributing to the process $ pp \rightarrow \tau^{\pm} \nu_{\tau} \ell^{\pm} \nu_{\ell} jj $, $ \ell=$ e, $ \mu $, with $ \mathcal{O}(\alpha^6) $ (left) and $ \mathcal{O}(\alpha_{s}^{2}\alpha^4) $ (right) couplings. 
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Figure 2:
Distributions in the invariant mass of the dijet system for the data and the prefit background prediction for the (left) e+$\tau_\mathrm{h} $ and (right) $\mu$+$\tau_\mathrm{h} $ nonprompt CRs. The overflow count is included in the last bin. The solid red line shows the expectation for the EW ssWW signal. 
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Figure 2a:
Distributions in the invariant mass of the dijet system for the data and the prefit background prediction for the (left) e+$\tau_\mathrm{h} $ and (right) $\mu$+$\tau_\mathrm{h} $ nonprompt CRs. The overflow count is included in the last bin. The solid red line shows the expectation for the EW ssWW signal. 
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Figure 2b:
Distributions in the invariant mass of the dijet system for the data and the prefit background prediction for the (left) e+$\tau_\mathrm{h} $ and (right) $\mu$+$\tau_\mathrm{h} $ nonprompt CRs. The overflow count is included in the last bin. The solid red line shows the expectation for the EW ssWW signal. 
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Figure 3:
Distribution of DNN output for the e+$\tau_\mathrm{h} $ (left) and $\mu$+$\tau_\mathrm{h} $ (right) channels for the full data sample, in the $ \mathrm{t} \overline{\mathrm{t}} $ CR (upper), OS CR (middle), and SR (lower) rows. Data points are overlaid on the postfit background (stacked histograms). The overflow is included in the last bin. The middle panels show ratios of the data to the prefit background prediction and postfit background yield in yellow and green, respectively. The yellow (green) bands in the middle panels indicate the systematic component of the prefit (postfit) uncertainty. The lower panels show the distributions of the pulls, defined in the text. 
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Figure 3a:
Distribution of DNN output for the e+$\tau_\mathrm{h} $ (left) and $\mu$+$\tau_\mathrm{h} $ (right) channels for the full data sample, in the $ \mathrm{t} \overline{\mathrm{t}} $ CR (upper), OS CR (middle), and SR (lower) rows. Data points are overlaid on the postfit background (stacked histograms). The overflow is included in the last bin. The middle panels show ratios of the data to the prefit background prediction and postfit background yield in yellow and green, respectively. The yellow (green) bands in the middle panels indicate the systematic component of the prefit (postfit) uncertainty. The lower panels show the distributions of the pulls, defined in the text. 
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Figure 3b:
Distribution of DNN output for the e+$\tau_\mathrm{h} $ (left) and $\mu$+$\tau_\mathrm{h} $ (right) channels for the full data sample, in the $ \mathrm{t} \overline{\mathrm{t}} $ CR (upper), OS CR (middle), and SR (lower) rows. Data points are overlaid on the postfit background (stacked histograms). The overflow is included in the last bin. The middle panels show ratios of the data to the prefit background prediction and postfit background yield in yellow and green, respectively. The yellow (green) bands in the middle panels indicate the systematic component of the prefit (postfit) uncertainty. The lower panels show the distributions of the pulls, defined in the text. 
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Figure 3c:
Distribution of DNN output for the e+$\tau_\mathrm{h} $ (left) and $\mu$+$\tau_\mathrm{h} $ (right) channels for the full data sample, in the $ \mathrm{t} \overline{\mathrm{t}} $ CR (upper), OS CR (middle), and SR (lower) rows. Data points are overlaid on the postfit background (stacked histograms). The overflow is included in the last bin. The middle panels show ratios of the data to the prefit background prediction and postfit background yield in yellow and green, respectively. The yellow (green) bands in the middle panels indicate the systematic component of the prefit (postfit) uncertainty. The lower panels show the distributions of the pulls, defined in the text. 
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Figure 3d:
Distribution of DNN output for the e+$\tau_\mathrm{h} $ (left) and $\mu$+$\tau_\mathrm{h} $ (right) channels for the full data sample, in the $ \mathrm{t} \overline{\mathrm{t}} $ CR (upper), OS CR (middle), and SR (lower) rows. Data points are overlaid on the postfit background (stacked histograms). The overflow is included in the last bin. The middle panels show ratios of the data to the prefit background prediction and postfit background yield in yellow and green, respectively. The yellow (green) bands in the middle panels indicate the systematic component of the prefit (postfit) uncertainty. The lower panels show the distributions of the pulls, defined in the text. 
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Figure 3e:
Distribution of DNN output for the e+$\tau_\mathrm{h} $ (left) and $\mu$+$\tau_\mathrm{h} $ (right) channels for the full data sample, in the $ \mathrm{t} \overline{\mathrm{t}} $ CR (upper), OS CR (middle), and SR (lower) rows. Data points are overlaid on the postfit background (stacked histograms). The overflow is included in the last bin. The middle panels show ratios of the data to the prefit background prediction and postfit background yield in yellow and green, respectively. The yellow (green) bands in the middle panels indicate the systematic component of the prefit (postfit) uncertainty. The lower panels show the distributions of the pulls, defined in the text. 
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Figure 3f:
Distribution of DNN output for the e+$\tau_\mathrm{h} $ (left) and $\mu$+$\tau_\mathrm{h} $ (right) channels for the full data sample, in the $ \mathrm{t} \overline{\mathrm{t}} $ CR (upper), OS CR (middle), and SR (lower) rows. Data points are overlaid on the postfit background (stacked histograms). The overflow is included in the last bin. The middle panels show ratios of the data to the prefit background prediction and postfit background yield in yellow and green, respectively. The yellow (green) bands in the middle panels indicate the systematic component of the prefit (postfit) uncertainty. The lower panels show the distributions of the pulls, defined in the text. 
Tables  
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Table 1:
Definition of the SR and four CRs. All regions are disjoint. The SR and three CRs (Nonprompt, $ \mathrm{t} \overline{\mathrm{t}} $, OS) are selected from an inclusive lepton trigger; the QCD enriched CR (last row) is selected from a jetbased trigger. 
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Table 2:
The impact of each systematic uncertainty on the signal strength $ \mu $ as extracted from the fit to measure the SM ssWW VBS signal with the DNN output distributions. Upper and lower uncertainties are given for the various sources. 
Summary 
Electroweak production of samesign W boson pairs (ssWW) with a hadronically decaying $ \tau $ ($ \tau_\mathrm{h} $) in the final state is investigated for the first time. The analysis is performed with a sample of protonproton collisions at $ \sqrt{s} $ = 13 TeV recorded by the CMS experiment at the CERN LHC, corresponding to an integrated luminosity of 138 fb$ ^{1} $. Deep neural network algorithms are employed to discriminate signal events from the main backgrounds. The measured cross section for electroweak samesign WW scattering is 1.44 $ ^{+0.63}_{0.56} $ times the standard model prediction, obtained keeping the QCDassociated diboson production fixed to its standard model prediction. The observed signal significance is 2.7 standard deviations with 1.9 expected. The simultaneous measurement of the electroweak and QCDassociated diboson production is measured with an observed (expected) significance of 2.9 (2.0) standard deviations. 
Additional Figures  
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Additional Figure 1:
Distributions of the transverse mass $ M_{o1} $ for the data and the prefit background prediction for the (left) $ \mathrm{e}+\tau_\mathrm{h} $ and (right) $ \mu+\tau_\mathrm{h} $ SRs. The overflow count is included in the last bin. The solid red line shows the expectation for the EW ssWW signal, the solid blue line the total one for the $ \mathcal{O}_{W} $ dim6 operator with $ c_{W}= $ 1 TeV$ ^{2} $, the solid green line the total one for the $ \mathcal{Q}_{T1} $ dim8 operator with $ f_{T1}= $ 1 TeV$^{4} $. For the latter two, the interference with SM and pure EFT contributions are summed together with the SM contribution. 
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Additional Figure 1a:
Distributions of the transverse mass $ M_{o1} $ for the data and the prefit background prediction for the (left) $ \mathrm{e}+\tau_\mathrm{h} $ and (right) $ \mu+\tau_\mathrm{h} $ SRs. The overflow count is included in the last bin. The solid red line shows the expectation for the EW ssWW signal, the solid blue line the total one for the $ \mathcal{O}_{W} $ dim6 operator with $ c_{W}= $ 1 TeV$ ^{2} $, the solid green line the total one for the $ \mathcal{Q}_{T1} $ dim8 operator with $ f_{T1}= $ 1 TeV$^{4} $. For the latter two, the interference with SM and pure EFT contributions are summed together with the SM contribution. 
png pdf 
Additional Figure 1b:
Distributions of the transverse mass $ M_{o1} $ for the data and the prefit background prediction for the (left) $ \mathrm{e}+\tau_\mathrm{h} $ and (right) $ \mu+\tau_\mathrm{h} $ SRs. The overflow count is included in the last bin. The solid red line shows the expectation for the EW ssWW signal, the solid blue line the total one for the $ \mathcal{O}_{W} $ dim6 operator with $ c_{W}= $ 1 TeV$ ^{2} $, the solid green line the total one for the $ \mathcal{Q}_{T1} $ dim8 operator with $ f_{T1}= $ 1 TeV$^{4} $. For the latter two, the interference with SM and pure EFT contributions are summed together with the SM contribution. 
png pdf 
Additional Figure 2:
Constraints on pairs of Wilson coefficients, derived from likelihood scans in which all other coefficients are fixed to zero. The pair investigated consists of two EFT operators giving linear and quadratic contributions with similar magnitude and similarly modifying the scattering amplitude by acting on the same type of fields. For the relevant dim6 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the twodimensional $ 2\ln\Delta\mathcal{L} $ are reported as functions of the corresponding Wilson coefficient pairs. For these studies, the distributions of the transverse mass $ M_{o1} $ are used in the scans in place of the EFT DNN output distributions. 
png pdf 
Additional Figure 2a:
Constraints on pairs of Wilson coefficients, derived from likelihood scans in which all other coefficients are fixed to zero. The pair investigated consists of two EFT operators giving linear and quadratic contributions with similar magnitude and similarly modifying the scattering amplitude by acting on the same type of fields. For the relevant dim6 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the twodimensional $ 2\ln\Delta\mathcal{L} $ are reported as functions of the corresponding Wilson coefficient pairs. For these studies, the distributions of the transverse mass $ M_{o1} $ are used in the scans in place of the EFT DNN output distributions. 
png pdf 
Additional Figure 2b:
Constraints on pairs of Wilson coefficients, derived from likelihood scans in which all other coefficients are fixed to zero. The pair investigated consists of two EFT operators giving linear and quadratic contributions with similar magnitude and similarly modifying the scattering amplitude by acting on the same type of fields. For the relevant dim6 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the twodimensional $ 2\ln\Delta\mathcal{L} $ are reported as functions of the corresponding Wilson coefficient pairs. For these studies, the distributions of the transverse mass $ M_{o1} $ are used in the scans in place of the EFT DNN output distributions. 
png pdf 
Additional Figure 2c:
Constraints on pairs of Wilson coefficients, derived from likelihood scans in which all other coefficients are fixed to zero. The pair investigated consists of two EFT operators giving linear and quadratic contributions with similar magnitude and similarly modifying the scattering amplitude by acting on the same type of fields. For the relevant dim6 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the twodimensional $ 2\ln\Delta\mathcal{L} $ are reported as functions of the corresponding Wilson coefficient pairs. For these studies, the distributions of the transverse mass $ M_{o1} $ are used in the scans in place of the EFT DNN output distributions. 
png pdf 
Additional Figure 2d:
Constraints on pairs of Wilson coefficients, derived from likelihood scans in which all other coefficients are fixed to zero. The pair investigated consists of two EFT operators giving linear and quadratic contributions with similar magnitude and similarly modifying the scattering amplitude by acting on the same type of fields. For the relevant dim6 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the twodimensional $ 2\ln\Delta\mathcal{L} $ are reported as functions of the corresponding Wilson coefficient pairs. For these studies, the distributions of the transverse mass $ M_{o1} $ are used in the scans in place of the EFT DNN output distributions. 
png pdf 
Additional Figure 2e:
Constraints on pairs of Wilson coefficients, derived from likelihood scans in which all other coefficients are fixed to zero. The pair investigated consists of two EFT operators giving linear and quadratic contributions with similar magnitude and similarly modifying the scattering amplitude by acting on the same type of fields. For the relevant dim6 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the twodimensional $ 2\ln\Delta\mathcal{L} $ are reported as functions of the corresponding Wilson coefficient pairs. For these studies, the distributions of the transverse mass $ M_{o1} $ are used in the scans in place of the EFT DNN output distributions. 
png pdf 
Additional Figure 2f:
Constraints on pairs of Wilson coefficients, derived from likelihood scans in which all other coefficients are fixed to zero. The pair investigated consists of two EFT operators giving linear and quadratic contributions with similar magnitude and similarly modifying the scattering amplitude by acting on the same type of fields. For the relevant dim6 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the twodimensional $ 2\ln\Delta\mathcal{L} $ are reported as functions of the corresponding Wilson coefficient pairs. For these studies, the distributions of the transverse mass $ M_{o1} $ are used in the scans in place of the EFT DNN output distributions. 
png pdf 
Additional Figure 3:
The sensitivity of the measurement to the effects of two EFT operators turned on at the same time is evaluated with a likelihood scan performed by varying the corresponding Wilson coefficients. The pair investigated consists of two EFT operators giving linear and quadratic contributions with similar magnitude and similarly modifying the scattering amplitude by acting on the same type of fields. For the relevant dim6 mixed operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the twodimensional $ 2\ln\Delta\mathcal{L} $ are reported as functions of the corresponding Wilson coefficient pairs. For these studies, the distributions of the transverse mass $ M_{o1} $ are used in the scans in place of the EFT DNN output distributions to facilitate the physics interpretation of the results. 
png pdf 
Additional Figure 3a:
The sensitivity of the measurement to the effects of two EFT operators turned on at the same time is evaluated with a likelihood scan performed by varying the corresponding Wilson coefficients. The pair investigated consists of two EFT operators giving linear and quadratic contributions with similar magnitude and similarly modifying the scattering amplitude by acting on the same type of fields. For the relevant dim6 mixed operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the twodimensional $ 2\ln\Delta\mathcal{L} $ are reported as functions of the corresponding Wilson coefficient pairs. For these studies, the distributions of the transverse mass $ M_{o1} $ are used in the scans in place of the EFT DNN output distributions to facilitate the physics interpretation of the results. 
png pdf 
Additional Figure 3b:
The sensitivity of the measurement to the effects of two EFT operators turned on at the same time is evaluated with a likelihood scan performed by varying the corresponding Wilson coefficients. The pair investigated consists of two EFT operators giving linear and quadratic contributions with similar magnitude and similarly modifying the scattering amplitude by acting on the same type of fields. For the relevant dim6 mixed operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the twodimensional $ 2\ln\Delta\mathcal{L} $ are reported as functions of the corresponding Wilson coefficient pairs. For these studies, the distributions of the transverse mass $ M_{o1} $ are used in the scans in place of the EFT DNN output distributions to facilitate the physics interpretation of the results. 
png pdf 
Additional Figure 3c:
The sensitivity of the measurement to the effects of two EFT operators turned on at the same time is evaluated with a likelihood scan performed by varying the corresponding Wilson coefficients. The pair investigated consists of two EFT operators giving linear and quadratic contributions with similar magnitude and similarly modifying the scattering amplitude by acting on the same type of fields. For the relevant dim6 mixed operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the twodimensional $ 2\ln\Delta\mathcal{L} $ are reported as functions of the corresponding Wilson coefficient pairs. For these studies, the distributions of the transverse mass $ M_{o1} $ are used in the scans in place of the EFT DNN output distributions to facilitate the physics interpretation of the results. 
png pdf 
Additional Figure 4:
The sensitivity of the measurement to the effects of two EFT operators turned on at the same time (with all the other ones turned off) is evaluated with a likelihood scan performed by varying the corresponding Wilson coefficients. The pair investigated consists of two EFT operators giving linear and quadratic contributions with similar magnitude and similarly modifying the scattering amplitude by acting on the same type of fields. For the relevant dim6/dim8 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the twodimensional $ 2\ln\Delta\mathcal{L} $. For these studies, the distributions of the transverse mass $ M_{o1} $ are used in the scans in place of the EFT DNN output distributions to facilitate the physics interpretation of the results. 
png pdf 
Additional Figure 4a:
The sensitivity of the measurement to the effects of two EFT operators turned on at the same time (with all the other ones turned off) is evaluated with a likelihood scan performed by varying the corresponding Wilson coefficients. The pair investigated consists of two EFT operators giving linear and quadratic contributions with similar magnitude and similarly modifying the scattering amplitude by acting on the same type of fields. For the relevant dim6/dim8 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the twodimensional $ 2\ln\Delta\mathcal{L} $. For these studies, the distributions of the transverse mass $ M_{o1} $ are used in the scans in place of the EFT DNN output distributions to facilitate the physics interpretation of the results. 
png pdf 
Additional Figure 4b:
The sensitivity of the measurement to the effects of two EFT operators turned on at the same time (with all the other ones turned off) is evaluated with a likelihood scan performed by varying the corresponding Wilson coefficients. The pair investigated consists of two EFT operators giving linear and quadratic contributions with similar magnitude and similarly modifying the scattering amplitude by acting on the same type of fields. For the relevant dim6/dim8 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the twodimensional $ 2\ln\Delta\mathcal{L} $. For these studies, the distributions of the transverse mass $ M_{o1} $ are used in the scans in place of the EFT DNN output distributions to facilitate the physics interpretation of the results. 
png pdf 
Additional Figure 4c:
The sensitivity of the measurement to the effects of two EFT operators turned on at the same time (with all the other ones turned off) is evaluated with a likelihood scan performed by varying the corresponding Wilson coefficients. The pair investigated consists of two EFT operators giving linear and quadratic contributions with similar magnitude and similarly modifying the scattering amplitude by acting on the same type of fields. For the relevant dim6/dim8 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the twodimensional $ 2\ln\Delta\mathcal{L} $. For these studies, the distributions of the transverse mass $ M_{o1} $ are used in the scans in place of the EFT DNN output distributions to facilitate the physics interpretation of the results. 
png pdf 
Additional Figure 4d:
The sensitivity of the measurement to the effects of two EFT operators turned on at the same time (with all the other ones turned off) is evaluated with a likelihood scan performed by varying the corresponding Wilson coefficients. The pair investigated consists of two EFT operators giving linear and quadratic contributions with similar magnitude and similarly modifying the scattering amplitude by acting on the same type of fields. For the relevant dim6/dim8 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the twodimensional $ 2\ln\Delta\mathcal{L} $. For these studies, the distributions of the transverse mass $ M_{o1} $ are used in the scans in place of the EFT DNN output distributions to facilitate the physics interpretation of the results. 
png pdf 
Additional Figure 4e:
The sensitivity of the measurement to the effects of two EFT operators turned on at the same time (with all the other ones turned off) is evaluated with a likelihood scan performed by varying the corresponding Wilson coefficients. The pair investigated consists of two EFT operators giving linear and quadratic contributions with similar magnitude and similarly modifying the scattering amplitude by acting on the same type of fields. For the relevant dim6/dim8 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the twodimensional $ 2\ln\Delta\mathcal{L} $. For these studies, the distributions of the transverse mass $ M_{o1} $ are used in the scans in place of the EFT DNN output distributions to facilitate the physics interpretation of the results. 
png pdf 
Additional Figure 4f:
The sensitivity of the measurement to the effects of two EFT operators turned on at the same time (with all the other ones turned off) is evaluated with a likelihood scan performed by varying the corresponding Wilson coefficients. The pair investigated consists of two EFT operators giving linear and quadratic contributions with similar magnitude and similarly modifying the scattering amplitude by acting on the same type of fields. For the relevant dim6/dim8 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the twodimensional $ 2\ln\Delta\mathcal{L} $. For these studies, the distributions of the transverse mass $ M_{o1} $ are used in the scans in place of the EFT DNN output distributions to facilitate the physics interpretation of the results. 
png pdf 
Additional Figure 4g:
The sensitivity of the measurement to the effects of two EFT operators turned on at the same time (with all the other ones turned off) is evaluated with a likelihood scan performed by varying the corresponding Wilson coefficients. The pair investigated consists of two EFT operators giving linear and quadratic contributions with similar magnitude and similarly modifying the scattering amplitude by acting on the same type of fields. For the relevant dim6/dim8 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the twodimensional $ 2\ln\Delta\mathcal{L} $. For these studies, the distributions of the transverse mass $ M_{o1} $ are used in the scans in place of the EFT DNN output distributions to facilitate the physics interpretation of the results. 
png pdf 
Additional Figure 4h:
The sensitivity of the measurement to the effects of two EFT operators turned on at the same time (with all the other ones turned off) is evaluated with a likelihood scan performed by varying the corresponding Wilson coefficients. The pair investigated consists of two EFT operators giving linear and quadratic contributions with similar magnitude and similarly modifying the scattering amplitude by acting on the same type of fields. For the relevant dim6/dim8 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the twodimensional $ 2\ln\Delta\mathcal{L} $. For these studies, the distributions of the transverse mass $ M_{o1} $ are used in the scans in place of the EFT DNN output distributions to facilitate the physics interpretation of the results. 
png pdf 
Additional Figure 4i:
The sensitivity of the measurement to the effects of two EFT operators turned on at the same time (with all the other ones turned off) is evaluated with a likelihood scan performed by varying the corresponding Wilson coefficients. The pair investigated consists of two EFT operators giving linear and quadratic contributions with similar magnitude and similarly modifying the scattering amplitude by acting on the same type of fields. For the relevant dim6/dim8 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the twodimensional $ 2\ln\Delta\mathcal{L} $. For these studies, the distributions of the transverse mass $ M_{o1} $ are used in the scans in place of the EFT DNN output distributions to facilitate the physics interpretation of the results. 
Additional Tables  
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Additional Table 1:
Because of the large background and complex signal topology, sets of significant features (reported below) to separate signals and backgrounds are combined in three machinelearning discriminators, depending on which signal is targeted by the model. The discriminators are the outputs of feedforward deep neural networks (DNNs). The three DNN models are devised to separate the SM VBS (SM DNN), EFT dim6 (dim6 DNN), and EFT dim8 (dim8 DNN) against the competitive SM background processes.\\ Among these variables, $ p_{\mathrm{T}}^{\text{rel}}(\ell, \mathrm{j})$ represents the component of the $ \ell $ or $ \tau_\mathrm{h} $ momentum $ \vec{p}_{\mathrm{l}} $ perpendicular to the momentum $ \vec{p}_{j} $ of VBS jet $ j $, while $ M_{\mathrm{T}} $(\ell, $ \tau_\mathrm{h} $, $ {\vec p}_{\mathrm{T}}^{\kern1pt\text{miss}} $) is defined considering the $\ell$ and the $ \tau_\mathrm{h} $ as a unique visible object, obtained by summing up their fourmomenta. 
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Additional Table 2:
Constraints on each EFT Wilson coefficient, derived from likelihood scans in which all other coefficients are fixed to zero. Results are given for both dim6 and dim8 operators, using fits to the output distributions of the EFT dim6 and dim8 discriminators, respectively. 
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