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| CMS-PAS-SMP-22-008 | ||
| Measurement of W$^{\pm}$W$^{\pm} $ scattering in proton-proton 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 same-sign W bosons is presented. This is the first study of a vector boson scattering process in the decay channel with a tau lepton ($ \tau $). The analysis is performed with proton-proton collision data collected by the CMS detector at the LHC at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb$ ^{-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 same-sign WW scattering cross section, extracted with the amplitude for the QCD-associated 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 QCD-associated same-sign diboson production yields an observed (expected) significance of 2.9 (2.0) standard deviations. | ||
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Links:
CDS record (PDF) ;
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These preliminary results are superseded in this paper, Submitted to JHEP. The superseded preliminary plots can be found here. |
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| Figures & Tables | Summary | Additional Figures & Tables | References | CMS Publications |
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| Figures | |
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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. |
png pdf |
Figure 1-a:
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. |
png pdf |
Figure 1-b:
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. |
png pdf |
Figure 2:
Distributions in the invariant mass of the di-jet system for the data and the pre-fit 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. |
png pdf |
Figure 2-a:
Distributions in the invariant mass of the di-jet system for the data and the pre-fit 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. |
png pdf |
Figure 2-b:
Distributions in the invariant mass of the di-jet system for the data and the pre-fit 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 post-fit background (stacked histograms). The overflow is included in the last bin. The middle panels show ratios of the data to the pre-fit background prediction and post-fit background yield in yellow and green, respectively. The yellow (green) bands in the middle panels indicate the systematic component of the pre-fit (post-fit) uncertainty. The lower panels show the distributions of the pulls, defined in the text. |
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Figure 3-a:
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 post-fit background (stacked histograms). The overflow is included in the last bin. The middle panels show ratios of the data to the pre-fit background prediction and post-fit background yield in yellow and green, respectively. The yellow (green) bands in the middle panels indicate the systematic component of the pre-fit (post-fit) uncertainty. The lower panels show the distributions of the pulls, defined in the text. |
png pdf |
Figure 3-b:
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 post-fit background (stacked histograms). The overflow is included in the last bin. The middle panels show ratios of the data to the pre-fit background prediction and post-fit background yield in yellow and green, respectively. The yellow (green) bands in the middle panels indicate the systematic component of the pre-fit (post-fit) uncertainty. The lower panels show the distributions of the pulls, defined in the text. |
png pdf |
Figure 3-c:
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 post-fit background (stacked histograms). The overflow is included in the last bin. The middle panels show ratios of the data to the pre-fit background prediction and post-fit background yield in yellow and green, respectively. The yellow (green) bands in the middle panels indicate the systematic component of the pre-fit (post-fit) uncertainty. The lower panels show the distributions of the pulls, defined in the text. |
png pdf |
Figure 3-d:
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 post-fit background (stacked histograms). The overflow is included in the last bin. The middle panels show ratios of the data to the pre-fit background prediction and post-fit background yield in yellow and green, respectively. The yellow (green) bands in the middle panels indicate the systematic component of the pre-fit (post-fit) uncertainty. The lower panels show the distributions of the pulls, defined in the text. |
png pdf |
Figure 3-e:
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 post-fit background (stacked histograms). The overflow is included in the last bin. The middle panels show ratios of the data to the pre-fit background prediction and post-fit background yield in yellow and green, respectively. The yellow (green) bands in the middle panels indicate the systematic component of the pre-fit (post-fit) uncertainty. The lower panels show the distributions of the pulls, defined in the text. |
png pdf |
Figure 3-f:
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 post-fit background (stacked histograms). The overflow is included in the last bin. The middle panels show ratios of the data to the pre-fit background prediction and post-fit background yield in yellow and green, respectively. The yellow (green) bands in the middle panels indicate the systematic component of the pre-fit (post-fit) 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 jet-based 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 same-sign 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 proton-proton 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 same-sign WW scattering is 1.44 $ ^{+0.63}_{-0.56} $ times the standard model prediction, obtained keeping the QCD-associated 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 QCD-associated diboson production is measured with an observed (expected) significance of 2.9 (2.0) standard deviations. |
| Additional Figures | |
png pdf |
Additional Figure 1:
Distributions of the transverse mass $ M_{o1} $ for the data and the pre-fit 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} $ dim-6 operator with $ c_{W}= $ 1 TeV$ ^{-2} $, the solid green line the total one for the $ \mathcal{Q}_{T1} $ dim-8 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 1-a:
Distributions of the transverse mass $ M_{o1} $ for the data and the pre-fit 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} $ dim-6 operator with $ c_{W}= $ 1 TeV$ ^{-2} $, the solid green line the total one for the $ \mathcal{Q}_{T1} $ dim-8 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 1-b:
Distributions of the transverse mass $ M_{o1} $ for the data and the pre-fit 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} $ dim-6 operator with $ c_{W}= $ 1 TeV$ ^{-2} $, the solid green line the total one for the $ \mathcal{Q}_{T1} $ dim-8 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 dim-6 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the two-dimensional $ -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 2-a:
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 dim-6 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the two-dimensional $ -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 2-b:
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 dim-6 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the two-dimensional $ -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 2-c:
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 dim-6 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the two-dimensional $ -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 2-d:
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 dim-6 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the two-dimensional $ -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 2-e:
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 dim-6 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the two-dimensional $ -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 2-f:
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 dim-6 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the two-dimensional $ -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 dim-6 mixed operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the two-dimensional $ -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 3-a:
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 dim-6 mixed operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the two-dimensional $ -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 3-b:
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 dim-6 mixed operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the two-dimensional $ -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 3-c:
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 dim-6 mixed operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the two-dimensional $ -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 dim-6/dim-8 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the two-dimensional $ -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 4-a:
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 dim-6/dim-8 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the two-dimensional $ -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 4-b:
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 dim-6/dim-8 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the two-dimensional $ -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 4-c:
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 dim-6/dim-8 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the two-dimensional $ -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 4-d:
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 dim-6/dim-8 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the two-dimensional $ -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 4-e:
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 dim-6/dim-8 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the two-dimensional $ -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 4-f:
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 dim-6/dim-8 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the two-dimensional $ -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 4-g:
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 dim-6/dim-8 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the two-dimensional $ -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 4-h:
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 dim-6/dim-8 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the two-dimensional $ -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 4-i:
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 dim-6/dim-8 bosonic operator pairs, the observed (black) and expected (red) 68% (solid) and 95% (dashed) CL contours for the two-dimensional $ -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 machine-learning discriminators, depending on which signal is targeted by the model. The discriminators are the outputs of feed-forward deep neural networks (DNNs). The three DNN models are devised to separate the SM VBS (SM DNN), EFT dim-6 (dim-6 DNN), and EFT dim-8 (dim-8 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 four-momenta. |
png pdf |
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 dim-6 and dim-8 operators, using fits to the output distributions of the EFT dim-6 and dim-8 discriminators, respectively. |
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