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| CMS-SMP-22-008 ; CERN-EP-2024-234 | ||
| Study of same-sign W boson scattering and anomalous couplings in events with one tau lepton from pp collisions at $ \sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 5 October 2024 | ||
| JHEP 2510 (2025) 219 | ||
| Abstract: A first study is presented of the cross section for the scattering of same-sign W boson pairs via the detection of a $ \tau $ lepton. The data from proton-proton collisions at the center-of-mass energy of 13 TeV were collected by the CMS detector at the LHC, and correspond to an integrated luminosity of 138 fb$ ^{-1} $. Events were selected that contain two jets with large pseudorapidity and large invariant mass, one $ \tau $ lepton, one light lepton (e or $ \mu $), and significant missing transverse momentum. The measured cross section for electroweak same-sign WW scattering is 1.44 $ ^{+0.63}_{-0.56} $ times the standard model prediction. In addition, a search is presented for the indirect effects of processes beyond the standard model via the effective field theory framework, in terms of dimension-6 and dimension-8 operators. | ||
| Links: e-print arXiv:2410.04210 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Representative tree-level Feynman diagrams contributing to the process $ \mathrm{q}\mathrm{q}^\prime \to \tau^{\pm}\nu_{\!\tau} \ell^{\pm} \nu_{\ell} jj $, $ \ell=$ e, $\mu $, leading to cross sections of order $ \alpha_\text{EW}^6 $ (left) and $ \alpha_\mathrm{S}^{2}\alpha_\text{EW}^4 $ (right). |
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Figure 1-a:
Representative tree-level Feynman diagrams contributing to the process $ \mathrm{q}\mathrm{q}^\prime \to \tau^{\pm}\nu_{\!\tau} \ell^{\pm} \nu_{\ell} jj $, $ \ell=$ e, $\mu $, leading to cross sections of order $ \alpha_\text{EW}^6 $ (left) and $ \alpha_\mathrm{S}^{2}\alpha_\text{EW}^4 $ (right). |
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Figure 1-b:
Representative tree-level Feynman diagrams contributing to the process $ \mathrm{q}\mathrm{q}^\prime \to \tau^{\pm}\nu_{\!\tau} \ell^{\pm} \nu_{\ell} jj $, $ \ell=$ e, $\mu $, leading to cross sections of order $ \alpha_\text{EW}^6 $ (left) and $ \alpha_\mathrm{S}^{2}\alpha_\text{EW}^4 $ (right). |
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Figure 2:
Distributions in the invariant mass of the dijet system for the data and the pre-fit background prediction for the (left) $ \mathrm{e}\tau_\mathrm{h} $ and (right) $ \mu\tau_\mathrm{h} $ nonprompt VRs. The stacked filled histograms show the background components, with the overflow count included in the last bin. The expectation for the EW SSWW signal is shown by the dashed red line. The hatched error band shows the bin-by-bin statistical uncertainty. The lower panels show the ratio of data to the total background prediction, with statistical uncertainties indicated by error bars and shading, respectively. In all the panels, the vertical bars represent the statistical uncertainty assigned to the observed number of events. |
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Figure 2-a:
Distributions in the invariant mass of the dijet system for the data and the pre-fit background prediction for the (left) $ \mathrm{e}\tau_\mathrm{h} $ and (right) $ \mu\tau_\mathrm{h} $ nonprompt VRs. The stacked filled histograms show the background components, with the overflow count included in the last bin. The expectation for the EW SSWW signal is shown by the dashed red line. The hatched error band shows the bin-by-bin statistical uncertainty. The lower panels show the ratio of data to the total background prediction, with statistical uncertainties indicated by error bars and shading, respectively. In all the panels, the vertical bars represent the statistical uncertainty assigned to the observed number of events. |
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Figure 2-b:
Distributions in the invariant mass of the dijet system for the data and the pre-fit background prediction for the (left) $ \mathrm{e}\tau_\mathrm{h} $ and (right) $ \mu\tau_\mathrm{h} $ nonprompt VRs. The stacked filled histograms show the background components, with the overflow count included in the last bin. The expectation for the EW SSWW signal is shown by the dashed red line. The hatched error band shows the bin-by-bin statistical uncertainty. The lower panels show the ratio of data to the total background prediction, with statistical uncertainties indicated by error bars and shading, respectively. In all the panels, the vertical bars represent the statistical uncertainty assigned to the observed number of events. |
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Figure 3:
Distributions in $ m_{\circ 1} $ transverse mass 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 stacked filled histograms show the background components, and the overflow count is included in the last bin. The expectations for the EW SSWW signal, the $ \mathcal{O}_{W} $ dim-6 operator with $ c_{W} = $ 1 TeV$^{-2}$, and the $ \mathcal{Q}_{T1} $ dim-8 operator with $ f_{T1} = $ 1 TeV$^{-4}$ are shown by the dashed red, blue, and green lines, respectively. For the latter two, the interference with SM and pure EFT contributions are summed together with the SM contribution. The hatched error band shows the bin-by-bin statistical uncertainty. The lower panels show the ratio of data to the total background prediction, with statistical uncertainties indicated by error bars and shading, respectively. In all the panels, the vertical bars represent the statistical uncertainty assigned to the observed number of events. |
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Figure 3-a:
Distributions in $ m_{\circ 1} $ transverse mass 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 stacked filled histograms show the background components, and the overflow count is included in the last bin. The expectations for the EW SSWW signal, the $ \mathcal{O}_{W} $ dim-6 operator with $ c_{W} = $ 1 TeV$^{-2}$, and the $ \mathcal{Q}_{T1} $ dim-8 operator with $ f_{T1} = $ 1 TeV$^{-4}$ are shown by the dashed red, blue, and green lines, respectively. For the latter two, the interference with SM and pure EFT contributions are summed together with the SM contribution. The hatched error band shows the bin-by-bin statistical uncertainty. The lower panels show the ratio of data to the total background prediction, with statistical uncertainties indicated by error bars and shading, respectively. In all the panels, the vertical bars represent the statistical uncertainty assigned to the observed number of events. |
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Figure 3-b:
Distributions in $ m_{\circ 1} $ transverse mass 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 stacked filled histograms show the background components, and the overflow count is included in the last bin. The expectations for the EW SSWW signal, the $ \mathcal{O}_{W} $ dim-6 operator with $ c_{W} = $ 1 TeV$^{-2}$, and the $ \mathcal{Q}_{T1} $ dim-8 operator with $ f_{T1} = $ 1 TeV$^{-4}$ are shown by the dashed red, blue, and green lines, respectively. For the latter two, the interference with SM and pure EFT contributions are summed together with the SM contribution. The hatched error band shows the bin-by-bin statistical uncertainty. The lower panels show the ratio of data to the total background prediction, with statistical uncertainties indicated by error bars and shading, respectively. In all the panels, the vertical bars represent the statistical uncertainty assigned to the observed number of events. |
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Figure 4:
Distribution of the DNN output for the (left) $ \mathrm{e}\tau_\mathrm{h} $ and (right) $ \mu\tau_\mathrm{h} $ SR. The data points are overlaid on the post-fit background plus signal (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 corresponding colored bands indicate the systematic component of the uncertainty. The lower panels show the distributions of the pulls, defined in the text. The vertical bars represent the statistical uncertainty assigned to the observed number of events for the upper panel, and its propagation to the quantities shown in the middle panel. |
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Figure 4-a:
Distribution of the DNN output for the (left) $ \mathrm{e}\tau_\mathrm{h} $ and (right) $ \mu\tau_\mathrm{h} $ SR. The data points are overlaid on the post-fit background plus signal (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 corresponding colored bands indicate the systematic component of the uncertainty. The lower panels show the distributions of the pulls, defined in the text. The vertical bars represent the statistical uncertainty assigned to the observed number of events for the upper panel, and its propagation to the quantities shown in the middle panel. |
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Figure 4-b:
Distribution of the DNN output for the (left) $ \mathrm{e}\tau_\mathrm{h} $ and (right) $ \mu\tau_\mathrm{h} $ SR. The data points are overlaid on the post-fit background plus signal (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 corresponding colored bands indicate the systematic component of the uncertainty. The lower panels show the distributions of the pulls, defined in the text. The vertical bars represent the statistical uncertainty assigned to the observed number of events for the upper panel, and its propagation to the quantities shown in the middle panel. |
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Figure 5:
Observed (black) and expected (red) 68 (solid) and 95% (dashed) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported dim-6 bosonic (upper two rows) and mixed (lower row) Wilson coefficient pairs. When there are two contours for the same CL value, the constrained set of Wilson coefficient values is represented by the area between the two of them if they are concentric, otherwise it consists of the internal areas of the contours. |
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Figure 5-a:
Observed (black) and expected (red) 68 (solid) and 95% (dashed) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported dim-6 bosonic (upper two rows) and mixed (lower row) Wilson coefficient pairs. When there are two contours for the same CL value, the constrained set of Wilson coefficient values is represented by the area between the two of them if they are concentric, otherwise it consists of the internal areas of the contours. |
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Figure 5-b:
Observed (black) and expected (red) 68 (solid) and 95% (dashed) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported dim-6 bosonic (upper two rows) and mixed (lower row) Wilson coefficient pairs. When there are two contours for the same CL value, the constrained set of Wilson coefficient values is represented by the area between the two of them if they are concentric, otherwise it consists of the internal areas of the contours. |
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Figure 5-c:
Observed (black) and expected (red) 68 (solid) and 95% (dashed) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported dim-6 bosonic (upper two rows) and mixed (lower row) Wilson coefficient pairs. When there are two contours for the same CL value, the constrained set of Wilson coefficient values is represented by the area between the two of them if they are concentric, otherwise it consists of the internal areas of the contours. |
png pdf |
Figure 5-d:
Observed (black) and expected (red) 68 (solid) and 95% (dashed) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported dim-6 bosonic (upper two rows) and mixed (lower row) Wilson coefficient pairs. When there are two contours for the same CL value, the constrained set of Wilson coefficient values is represented by the area between the two of them if they are concentric, otherwise it consists of the internal areas of the contours. |
png pdf |
Figure 5-e:
Observed (black) and expected (red) 68 (solid) and 95% (dashed) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported dim-6 bosonic (upper two rows) and mixed (lower row) Wilson coefficient pairs. When there are two contours for the same CL value, the constrained set of Wilson coefficient values is represented by the area between the two of them if they are concentric, otherwise it consists of the internal areas of the contours. |
png pdf |
Figure 5-f:
Observed (black) and expected (red) 68 (solid) and 95% (dashed) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported dim-6 bosonic (upper two rows) and mixed (lower row) Wilson coefficient pairs. When there are two contours for the same CL value, the constrained set of Wilson coefficient values is represented by the area between the two of them if they are concentric, otherwise it consists of the internal areas of the contours. |
png pdf |
Figure 5-g:
Observed (black) and expected (red) 68 (solid) and 95% (dashed) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported dim-6 bosonic (upper two rows) and mixed (lower row) Wilson coefficient pairs. When there are two contours for the same CL value, the constrained set of Wilson coefficient values is represented by the area between the two of them if they are concentric, otherwise it consists of the internal areas of the contours. |
png pdf |
Figure 6:
Observed (black) and expected (red) 68 (solid) and 95% (dashed) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported (dim-6, dim-8) Wilson coefficient pairs. |
png pdf |
Figure 6-a:
Observed (black) and expected (red) 68 (solid) and 95% (dashed) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported (dim-6, dim-8) Wilson coefficient pairs. |
png pdf |
Figure 6-b:
Observed (black) and expected (red) 68 (solid) and 95% (dashed) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported (dim-6, dim-8) Wilson coefficient pairs. |
png pdf |
Figure 6-c:
Observed (black) and expected (red) 68 (solid) and 95% (dashed) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported (dim-6, dim-8) Wilson coefficient pairs. |
png pdf |
Figure 6-d:
Observed (black) and expected (red) 68 (solid) and 95% (dashed) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported (dim-6, dim-8) Wilson coefficient pairs. |
png pdf |
Figure 6-e:
Observed (black) and expected (red) 68 (solid) and 95% (dashed) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported (dim-6, dim-8) Wilson coefficient pairs. |
png pdf |
Figure 6-f:
Observed (black) and expected (red) 68 (solid) and 95% (dashed) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported (dim-6, dim-8) Wilson coefficient pairs. |
png pdf |
Figure 6-g:
Observed (black) and expected (red) 68 (solid) and 95% (dashed) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported (dim-6, dim-8) Wilson coefficient pairs. |
png pdf |
Figure 6-h:
Observed (black) and expected (red) 68 (solid) and 95% (dashed) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported (dim-6, dim-8) Wilson coefficient pairs. |
png pdf |
Figure 6-i:
Observed (black) and expected (red) 68 (solid) and 95% (dashed) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported (dim-6, dim-8) Wilson coefficient pairs. |
| Tables | |
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Table 1:
Definitions of the SR, CRs, and VR defined for this analysis. The $ \checkmark $ symbol indicates that the requirement described in the column heading is applied in that region, whereas the $ \times $ symbol means that the opposite selection is applied. The symbols T and L refer to the tight and loose selection rules, respectively. The SR and three CRs (nonprompt, $ \mathrm{t} \overline{\mathrm{t}} $, OS) are selected from an inclusive lepton trigger. |
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Table 2:
List of the input variables for the three DNN models developed in this study. The check mark indicates that the variable is included in the DNN model identified in the column header. |
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Table 3:
The impact of each systematic uncertainty, together with the impact of the data statistical uncertainty, on the signal strength $ \mu $, as extracted from the fit to measure the SM SSWW VBS signal with the DNN output distributions. Upper and lower uncertainties are given for the various sources. |
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Table 4:
Observed and expected 68 and 95% 1D confidence level (CL) intervals on the Wilson coefficients associated with the EFT dim-6 and dim-8 operators considered. The results reported here are obtained by fixing the Wilson coefficients other than the one of interest to their SM values in the fit procedure. These limits are reported in units of TeV$^{-2}$ (TeV$^{-4}$) for the dim-6 (dim-8) Wilson coefficients. |
| Summary |
| Electroweak (EW) production of a same-sign W boson pair in association with two jets, with a hadronically decaying $ \tau $ lepton in the final state, is investigated for the first time, together with an interpretation of possible deviations from the standard model expectations in terms of effective field theory (EFT) operators of dimension 6 and 8. 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 in 2016--2018, corresponding to an integrated luminosity of 138 fb$ ^{-1} $. Events are selected with the requirement of one $ \tau $ lepton together with one light lepton (e or $ \mu $) of the same sign, missing transverse momentum, and two jets with large pseudorapidity separation and large dijet invariant mass. Deep neural network algorithms are employed to discriminate different types of signal events from the main backgrounds, significantly boosting the sensitivity of the search. The amplitude for same-sign WW production includes terms that account for strong interactions between partons with W boson radiation. A small fraction of these QCD-mediated events falls within the acceptance of the search. The measured cross section for EW same-sign WW scattering, extracted with the QCD-mediated amplitudes fixed to the standard model (SM) expectations, is 1.44 $ ^{+0.63}_{-0.56} $ times the SM prediction. The observed (expected) significance of the EW signal is 2.7 (1.9) standard deviations. A measurement of the combined EW and residual QCD-mediated contributions yields an observed (expected) significance of 2.9 (2.0) standard deviations. Also presented are the limits on dimension-6 EFT operator contributions, including both one operator and two operators active at the same time, extracted with a reconstruction-level strategy for the first time in vector boson scattering. This is the first study of the combined effects of EFT operators with different dimensions, showing that focusing on one dimensionality can lead to an overestimate of the sensitivity to the corresponding EFT operator class, and that the contributions of terms combining operators with different dimensions should not be neglected, in accordance with the latest recommendations from the EFT theory community. |
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