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| CMS-PAS-SMP-25-002 | ||
| Constraints on Effective Field Theory operators from multiboson production measurements at $ \sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 2026-07-30 | ||
| Abstract: A search for new physics in electroweak multiboson production is performed through a statistical combination of ten CMS measurements using proton-proton collision data collected at $ \sqrt{s}= $ 13 TeV during 2016--2018, corresponding to an integrated luminosity of 138 fb$ ^{-1} $. The combination encompasses six vector boson scattering channels: same-sign $ \mathrm{WW} $ production in fully leptonic and $ \ell\tau_\mathrm{h} $ final states, opposite-sign $ \mathrm{WW} $, $ \mathrm{WZ} $, and two VBS channels with a hadronically decaying vector boson ($ \mathrm{WV} $ and $ \mathrm{ZV} $); two vector boson fusion channels ($ \mathrm{Wjj} $ and $ \mathrm{Zjj} $), inclusive $ \mathrm{W^+W^-} $ diboson production, and triboson VVV (no $ \gamma $) production. Within the standard model effective field theory framework, potential contributions from physics beyond the standard model are parameterized in terms of six CP-even bosonic dimension-six operators of the Warsaw basis: $ \mathcal{O}_{W} $, $ \mathcal{O}_{HW} $, $ \mathcal{O}_{HWB} $, $ \mathcal{O}_{H\square} $, $ \mathcal{O}_{HB} $, and $ \mathcal{O}_{HD} $. Their effects are introduced through event-by-event reweighting of leading-order Monte Carlo simulations, enabling a consistent propagation of EFT effects to detector level with a consistent treatment of systematic uncertainties. Constraints on the associated Wilson coefficients are extracted using a binned profile likelihood fit, in scenarios ranging from individual coefficients to the fully profiled six-dimensional fit. No significant deviations from the standard model are observed. The combination improves substantially upon any individual analysis and constitutes the first detector-level combination of direct EFT measurements targeting bosonic dimension-six operators at the LHC. | ||
| Links: CDS record (PDF) ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Representative SM diagrams for the EW production processes considered in this combination. Each row corresponds to one of the four production mechanisms entering the combination -- VBS, VBF, diboson $ \mathrm{W^+}\mathrm{W^-} $, and triboson VVV -- with the generic production diagram shown on the left; the shaded blob denotes the EW production amplitude, summing the multiple diagrams contributing to each process. The dimension-six operators of Table 1 can affect both this production amplitude and the subsequent decay vertices of the vector bosons. The columns on the right show the specific decay topologies corresponding to the final states of each analysis listed in Table 2. |
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Figure 2:
Summary of the expected and observed one-dimensional 68% and 95% CL intervals, considering both linear-only and linear + quadratic SMEFT contributions (left panel). Results for the Wilson coefficient under analysis are obtained by fixing to zero the coefficients of the rest of the operators. The central panel shows the fractional contribution $ f_j^{\alpha} $ of each analysis $ \alpha $ to the combined limit on each Wilson coefficient $ c_j $, while the right panel shows the limits on the energy scale $ \Lambda $. |
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Figure 3:
68% (solid line) and 95% (dashed line) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported dim-6 Wilson coefficient pairs, both expected (black) and observed (orange). All results are obtained by considering the combination of all the channels, fixing the operators not under analysis to zero. A full table showing all pairs of operatoprs is reported in appendix 15. |
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Figure 3-a:
68% (solid line) and 95% (dashed line) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported dim-6 Wilson coefficient pairs, both expected (black) and observed (orange). All results are obtained by considering the combination of all the channels, fixing the operators not under analysis to zero. A full table showing all pairs of operatoprs is reported in appendix 15. |
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Figure 3-b:
68% (solid line) and 95% (dashed line) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported dim-6 Wilson coefficient pairs, both expected (black) and observed (orange). All results are obtained by considering the combination of all the channels, fixing the operators not under analysis to zero. A full table showing all pairs of operatoprs is reported in appendix 15. |
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Figure 4:
$ -2\ln\Delta\mathcal{L} $ observed scans for the six bosonic operators, fully profiled. The profiled combination fits (solid black line) were performed leaving all of the operators not under study freely floating, as well as all of the nuisance parameters. They are shown in comparison to the individual fit (red dashed line), in which all of the operators not under study are fixed to zero. Horizontal lines represent the 95% and 68% CL. |
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Figure 4-a:
$ -2\ln\Delta\mathcal{L} $ observed scans for the six bosonic operators, fully profiled. The profiled combination fits (solid black line) were performed leaving all of the operators not under study freely floating, as well as all of the nuisance parameters. They are shown in comparison to the individual fit (red dashed line), in which all of the operators not under study are fixed to zero. Horizontal lines represent the 95% and 68% CL. |
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Figure 4-b:
$ -2\ln\Delta\mathcal{L} $ observed scans for the six bosonic operators, fully profiled. The profiled combination fits (solid black line) were performed leaving all of the operators not under study freely floating, as well as all of the nuisance parameters. They are shown in comparison to the individual fit (red dashed line), in which all of the operators not under study are fixed to zero. Horizontal lines represent the 95% and 68% CL. |
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Figure 4-c:
$ -2\ln\Delta\mathcal{L} $ observed scans for the six bosonic operators, fully profiled. The profiled combination fits (solid black line) were performed leaving all of the operators not under study freely floating, as well as all of the nuisance parameters. They are shown in comparison to the individual fit (red dashed line), in which all of the operators not under study are fixed to zero. Horizontal lines represent the 95% and 68% CL. |
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Figure 4-d:
$ -2\ln\Delta\mathcal{L} $ observed scans for the six bosonic operators, fully profiled. The profiled combination fits (solid black line) were performed leaving all of the operators not under study freely floating, as well as all of the nuisance parameters. They are shown in comparison to the individual fit (red dashed line), in which all of the operators not under study are fixed to zero. Horizontal lines represent the 95% and 68% CL. |
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Figure 4-e:
$ -2\ln\Delta\mathcal{L} $ observed scans for the six bosonic operators, fully profiled. The profiled combination fits (solid black line) were performed leaving all of the operators not under study freely floating, as well as all of the nuisance parameters. They are shown in comparison to the individual fit (red dashed line), in which all of the operators not under study are fixed to zero. Horizontal lines represent the 95% and 68% CL. |
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Figure 4-f:
$ -2\ln\Delta\mathcal{L} $ observed scans for the six bosonic operators, fully profiled. The profiled combination fits (solid black line) were performed leaving all of the operators not under study freely floating, as well as all of the nuisance parameters. They are shown in comparison to the individual fit (red dashed line), in which all of the operators not under study are fixed to zero. Horizontal lines represent the 95% and 68% CL. |
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Figure 5:
Distributions of the dilepton invariant mass $ m_{\ell\ell} $ used to extract the SMEFT signal in the $ \mathrm{W^+}\mathrm{W^-} $ analysis. Left: the $ m_{\ell\ell} $ distribution in the 0-jet signal region after the combined fit. Right: the $ m_{\ell\ell} $ distribution in the 1-jet signal region after the combined fit. The lower panels show the ratio to the best-fit prediction. Different SMEFT scenarios, each corresponding to a distinct value of a Wilson coefficient, are shown as solid coloured lines. |
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Figure 5-a:
Distributions of the dilepton invariant mass $ m_{\ell\ell} $ used to extract the SMEFT signal in the $ \mathrm{W^+}\mathrm{W^-} $ analysis. Left: the $ m_{\ell\ell} $ distribution in the 0-jet signal region after the combined fit. Right: the $ m_{\ell\ell} $ distribution in the 1-jet signal region after the combined fit. The lower panels show the ratio to the best-fit prediction. Different SMEFT scenarios, each corresponding to a distinct value of a Wilson coefficient, are shown as solid coloured lines. |
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Figure 5-b:
Distributions of the dilepton invariant mass $ m_{\ell\ell} $ used to extract the SMEFT signal in the $ \mathrm{W^+}\mathrm{W^-} $ analysis. Left: the $ m_{\ell\ell} $ distribution in the 0-jet signal region after the combined fit. Right: the $ m_{\ell\ell} $ distribution in the 1-jet signal region after the combined fit. The lower panels show the ratio to the best-fit prediction. Different SMEFT scenarios, each corresponding to a distinct value of a Wilson coefficient, are shown as solid coloured lines. |
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Figure 6:
Distributions of the observables used to extract the SMEFT signal in the VBF analyses. Left: the $ \Delta\phi{{\mathrm{j}}{\mathrm{j}}} $ distribution in the VBF-W signal region after the combined fit. Right: the $ \Delta\phi{{\mathrm{j}}{\mathrm{j}}} $ distribution in windows of DNN score used to discriminate the VBF signal from the SM backgrounds in the VBF-Z analysis. The lower panels show the ratio to the best-fit prediction. Different SMEFT scenarios, each corresponding to a distinct value of a Wilson coefficient, are shown as solid coloured lines. |
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Figure 6-a:
Distributions of the observables used to extract the SMEFT signal in the VBF analyses. Left: the $ \Delta\phi{{\mathrm{j}}{\mathrm{j}}} $ distribution in the VBF-W signal region after the combined fit. Right: the $ \Delta\phi{{\mathrm{j}}{\mathrm{j}}} $ distribution in windows of DNN score used to discriminate the VBF signal from the SM backgrounds in the VBF-Z analysis. The lower panels show the ratio to the best-fit prediction. Different SMEFT scenarios, each corresponding to a distinct value of a Wilson coefficient, are shown as solid coloured lines. |
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Figure 6-b:
Distributions of the observables used to extract the SMEFT signal in the VBF analyses. Left: the $ \Delta\phi{{\mathrm{j}}{\mathrm{j}}} $ distribution in the VBF-W signal region after the combined fit. Right: the $ \Delta\phi{{\mathrm{j}}{\mathrm{j}}} $ distribution in windows of DNN score used to discriminate the VBF signal from the SM backgrounds in the VBF-Z analysis. The lower panels show the ratio to the best-fit prediction. Different SMEFT scenarios, each corresponding to a distinct value of a Wilson coefficient, are shown as solid coloured lines. |
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Figure 7:
Distributions of the observables used to extract the SMEFT signal in the SSWW, WZ and OSWW analyses. Top left: the $ m_{jj} $ distribution in windows of $ m_{\ell\ell} $ in the SSWW signal region, after the combined fit. Top right: the $ m_{T}^{WZ} $ distribution in windows of $ m_{jj} $ in the WZ signal region, after the combined fit. Bottom: the $ m_{jj} $ distribution in the OSWW signal region, for the 2016 data taking period (left) and 2017 and 2018 (right). The lower panels of each plot show the ratio to the best-fit prediction. Different SMEFT scenarios, each corresponding to a distinct value of a Wilson coefficient, are shown as solid coloured lines. |
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Figure 7-a:
Distributions of the observables used to extract the SMEFT signal in the SSWW, WZ and OSWW analyses. Top left: the $ m_{jj} $ distribution in windows of $ m_{\ell\ell} $ in the SSWW signal region, after the combined fit. Top right: the $ m_{T}^{WZ} $ distribution in windows of $ m_{jj} $ in the WZ signal region, after the combined fit. Bottom: the $ m_{jj} $ distribution in the OSWW signal region, for the 2016 data taking period (left) and 2017 and 2018 (right). The lower panels of each plot show the ratio to the best-fit prediction. Different SMEFT scenarios, each corresponding to a distinct value of a Wilson coefficient, are shown as solid coloured lines. |
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Figure 7-b:
Distributions of the observables used to extract the SMEFT signal in the SSWW, WZ and OSWW analyses. Top left: the $ m_{jj} $ distribution in windows of $ m_{\ell\ell} $ in the SSWW signal region, after the combined fit. Top right: the $ m_{T}^{WZ} $ distribution in windows of $ m_{jj} $ in the WZ signal region, after the combined fit. Bottom: the $ m_{jj} $ distribution in the OSWW signal region, for the 2016 data taking period (left) and 2017 and 2018 (right). The lower panels of each plot show the ratio to the best-fit prediction. Different SMEFT scenarios, each corresponding to a distinct value of a Wilson coefficient, are shown as solid coloured lines. |
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Figure 7-c:
Distributions of the observables used to extract the SMEFT signal in the SSWW, WZ and OSWW analyses. Top left: the $ m_{jj} $ distribution in windows of $ m_{\ell\ell} $ in the SSWW signal region, after the combined fit. Top right: the $ m_{T}^{WZ} $ distribution in windows of $ m_{jj} $ in the WZ signal region, after the combined fit. Bottom: the $ m_{jj} $ distribution in the OSWW signal region, for the 2016 data taking period (left) and 2017 and 2018 (right). The lower panels of each plot show the ratio to the best-fit prediction. Different SMEFT scenarios, each corresponding to a distinct value of a Wilson coefficient, are shown as solid coloured lines. |
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Figure 7-d:
Distributions of the observables used to extract the SMEFT signal in the SSWW, WZ and OSWW analyses. Top left: the $ m_{jj} $ distribution in windows of $ m_{\ell\ell} $ in the SSWW signal region, after the combined fit. Top right: the $ m_{T}^{WZ} $ distribution in windows of $ m_{jj} $ in the WZ signal region, after the combined fit. Bottom: the $ m_{jj} $ distribution in the OSWW signal region, for the 2016 data taking period (left) and 2017 and 2018 (right). The lower panels of each plot show the ratio to the best-fit prediction. Different SMEFT scenarios, each corresponding to a distinct value of a Wilson coefficient, are shown as solid coloured lines. |
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Figure 8:
$ -2\ln\Delta\mathcal{L} $ profiles for individual bosonic operators. On the left, the combined fits (black solid line) are compared to the individual fits in each channel (colored lines). Only the likelihood scans of the most sensitive channels are shown. On the right, the observed fits (orange lines) are compared to the expected fits (black lines), both considering the linear+quadratic (solid) and linear (dashed) SMEFT contributions. Horizontal lines represent the 95% and 68% CL. Results for the Wilson coefficient under analysis are obtained by fixing to zero the coefficients of the rest of the operators. |
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Figure 8-a:
$ -2\ln\Delta\mathcal{L} $ profiles for individual bosonic operators. On the left, the combined fits (black solid line) are compared to the individual fits in each channel (colored lines). Only the likelihood scans of the most sensitive channels are shown. On the right, the observed fits (orange lines) are compared to the expected fits (black lines), both considering the linear+quadratic (solid) and linear (dashed) SMEFT contributions. Horizontal lines represent the 95% and 68% CL. Results for the Wilson coefficient under analysis are obtained by fixing to zero the coefficients of the rest of the operators. |
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Figure 8-b:
$ -2\ln\Delta\mathcal{L} $ profiles for individual bosonic operators. On the left, the combined fits (black solid line) are compared to the individual fits in each channel (colored lines). Only the likelihood scans of the most sensitive channels are shown. On the right, the observed fits (orange lines) are compared to the expected fits (black lines), both considering the linear+quadratic (solid) and linear (dashed) SMEFT contributions. Horizontal lines represent the 95% and 68% CL. Results for the Wilson coefficient under analysis are obtained by fixing to zero the coefficients of the rest of the operators. |
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Figure 8-c:
$ -2\ln\Delta\mathcal{L} $ profiles for individual bosonic operators. On the left, the combined fits (black solid line) are compared to the individual fits in each channel (colored lines). Only the likelihood scans of the most sensitive channels are shown. On the right, the observed fits (orange lines) are compared to the expected fits (black lines), both considering the linear+quadratic (solid) and linear (dashed) SMEFT contributions. Horizontal lines represent the 95% and 68% CL. Results for the Wilson coefficient under analysis are obtained by fixing to zero the coefficients of the rest of the operators. |
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Figure 8-d:
$ -2\ln\Delta\mathcal{L} $ profiles for individual bosonic operators. On the left, the combined fits (black solid line) are compared to the individual fits in each channel (colored lines). Only the likelihood scans of the most sensitive channels are shown. On the right, the observed fits (orange lines) are compared to the expected fits (black lines), both considering the linear+quadratic (solid) and linear (dashed) SMEFT contributions. Horizontal lines represent the 95% and 68% CL. Results for the Wilson coefficient under analysis are obtained by fixing to zero the coefficients of the rest of the operators. |
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Figure 8-e:
$ -2\ln\Delta\mathcal{L} $ profiles for individual bosonic operators. On the left, the combined fits (black solid line) are compared to the individual fits in each channel (colored lines). Only the likelihood scans of the most sensitive channels are shown. On the right, the observed fits (orange lines) are compared to the expected fits (black lines), both considering the linear+quadratic (solid) and linear (dashed) SMEFT contributions. Horizontal lines represent the 95% and 68% CL. Results for the Wilson coefficient under analysis are obtained by fixing to zero the coefficients of the rest of the operators. |
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Figure 8-f:
$ -2\ln\Delta\mathcal{L} $ profiles for individual bosonic operators. On the left, the combined fits (black solid line) are compared to the individual fits in each channel (colored lines). Only the likelihood scans of the most sensitive channels are shown. On the right, the observed fits (orange lines) are compared to the expected fits (black lines), both considering the linear+quadratic (solid) and linear (dashed) SMEFT contributions. Horizontal lines represent the 95% and 68% CL. Results for the Wilson coefficient under analysis are obtained by fixing to zero the coefficients of the rest of the operators. |
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Figure 9:
$ -2\ln\Delta\mathcal{L} $ profiles for individual bosonic operators. On the left, the combined fits (black solid line) are compared to the individual fits in each channel (colored lines). Only the likelihood scans of the most sensitive channels are shown. On the right, the observed fits (orange lines) are compared to the expected fits (black lines), both considering the linear+quadratic (solid) and linear (dashed) SMEFT contributions. Horizontal lines represent the 95% and 68% CL. Results for the Wilson coefficient under analysis are obtained by fixing to zero the coefficients of the rest of the operators. |
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Figure 9-a:
$ -2\ln\Delta\mathcal{L} $ profiles for individual bosonic operators. On the left, the combined fits (black solid line) are compared to the individual fits in each channel (colored lines). Only the likelihood scans of the most sensitive channels are shown. On the right, the observed fits (orange lines) are compared to the expected fits (black lines), both considering the linear+quadratic (solid) and linear (dashed) SMEFT contributions. Horizontal lines represent the 95% and 68% CL. Results for the Wilson coefficient under analysis are obtained by fixing to zero the coefficients of the rest of the operators. |
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Figure 9-b:
$ -2\ln\Delta\mathcal{L} $ profiles for individual bosonic operators. On the left, the combined fits (black solid line) are compared to the individual fits in each channel (colored lines). Only the likelihood scans of the most sensitive channels are shown. On the right, the observed fits (orange lines) are compared to the expected fits (black lines), both considering the linear+quadratic (solid) and linear (dashed) SMEFT contributions. Horizontal lines represent the 95% and 68% CL. Results for the Wilson coefficient under analysis are obtained by fixing to zero the coefficients of the rest of the operators. |
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Figure 9-c:
$ -2\ln\Delta\mathcal{L} $ profiles for individual bosonic operators. On the left, the combined fits (black solid line) are compared to the individual fits in each channel (colored lines). Only the likelihood scans of the most sensitive channels are shown. On the right, the observed fits (orange lines) are compared to the expected fits (black lines), both considering the linear+quadratic (solid) and linear (dashed) SMEFT contributions. Horizontal lines represent the 95% and 68% CL. Results for the Wilson coefficient under analysis are obtained by fixing to zero the coefficients of the rest of the operators. |
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Figure 9-d:
$ -2\ln\Delta\mathcal{L} $ profiles for individual bosonic operators. On the left, the combined fits (black solid line) are compared to the individual fits in each channel (colored lines). Only the likelihood scans of the most sensitive channels are shown. On the right, the observed fits (orange lines) are compared to the expected fits (black lines), both considering the linear+quadratic (solid) and linear (dashed) SMEFT contributions. Horizontal lines represent the 95% and 68% CL. Results for the Wilson coefficient under analysis are obtained by fixing to zero the coefficients of the rest of the operators. |
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Figure 9-e:
$ -2\ln\Delta\mathcal{L} $ profiles for individual bosonic operators. On the left, the combined fits (black solid line) are compared to the individual fits in each channel (colored lines). Only the likelihood scans of the most sensitive channels are shown. On the right, the observed fits (orange lines) are compared to the expected fits (black lines), both considering the linear+quadratic (solid) and linear (dashed) SMEFT contributions. Horizontal lines represent the 95% and 68% CL. Results for the Wilson coefficient under analysis are obtained by fixing to zero the coefficients of the rest of the operators. |
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Figure 9-f:
$ -2\ln\Delta\mathcal{L} $ profiles for individual bosonic operators. On the left, the combined fits (black solid line) are compared to the individual fits in each channel (colored lines). Only the likelihood scans of the most sensitive channels are shown. On the right, the observed fits (orange lines) are compared to the expected fits (black lines), both considering the linear+quadratic (solid) and linear (dashed) SMEFT contributions. Horizontal lines represent the 95% and 68% CL. Results for the Wilson coefficient under analysis are obtained by fixing to zero the coefficients of the rest of the operators. |
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Figure 10:
68% (solid line) and 95% (dashed line) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported dim-6 Wilson coefficient pairs. Expected results are reported in black, while observed ones are reported in orange. All results are obtained by considering the combination of all the channels, fixing the operators not under analysis to zero. |
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Figure 10-a:
68% (solid line) and 95% (dashed line) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported dim-6 Wilson coefficient pairs. Expected results are reported in black, while observed ones are reported in orange. All results are obtained by considering the combination of all the channels, fixing the operators not under analysis to zero. |
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Figure 10-b:
68% (solid line) and 95% (dashed line) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported dim-6 Wilson coefficient pairs. Expected results are reported in black, while observed ones are reported in orange. All results are obtained by considering the combination of all the channels, fixing the operators not under analysis to zero. |
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Figure 10-c:
68% (solid line) and 95% (dashed line) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported dim-6 Wilson coefficient pairs. Expected results are reported in black, while observed ones are reported in orange. All results are obtained by considering the combination of all the channels, fixing the operators not under analysis to zero. |
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Figure 10-d:
68% (solid line) and 95% (dashed line) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported dim-6 Wilson coefficient pairs. Expected results are reported in black, while observed ones are reported in orange. All results are obtained by considering the combination of all the channels, fixing the operators not under analysis to zero. |
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Figure 10-e:
68% (solid line) and 95% (dashed line) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported dim-6 Wilson coefficient pairs. Expected results are reported in black, while observed ones are reported in orange. All results are obtained by considering the combination of all the channels, fixing the operators not under analysis to zero. |
png pdf |
Figure 10-f:
68% (solid line) and 95% (dashed line) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported dim-6 Wilson coefficient pairs. Expected results are reported in black, while observed ones are reported in orange. All results are obtained by considering the combination of all the channels, fixing the operators not under analysis to zero. |
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Figure 10-g:
68% (solid line) and 95% (dashed line) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported dim-6 Wilson coefficient pairs. Expected results are reported in black, while observed ones are reported in orange. All results are obtained by considering the combination of all the channels, fixing the operators not under analysis to zero. |
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Figure 10-h:
68% (solid line) and 95% (dashed line) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported dim-6 Wilson coefficient pairs. Expected results are reported in black, while observed ones are reported in orange. All results are obtained by considering the combination of all the channels, fixing the operators not under analysis to zero. |
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Figure 10-i:
68% (solid line) and 95% (dashed line) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported dim-6 Wilson coefficient pairs. Expected results are reported in black, while observed ones are reported in orange. All results are obtained by considering the combination of all the channels, fixing the operators not under analysis to zero. |
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Figure 10-j:
68% (solid line) and 95% (dashed line) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported dim-6 Wilson coefficient pairs. Expected results are reported in black, while observed ones are reported in orange. All results are obtained by considering the combination of all the channels, fixing the operators not under analysis to zero. |
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Figure 10-k:
68% (solid line) and 95% (dashed line) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported dim-6 Wilson coefficient pairs. Expected results are reported in black, while observed ones are reported in orange. All results are obtained by considering the combination of all the channels, fixing the operators not under analysis to zero. |
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Figure 10-l:
68% (solid line) and 95% (dashed line) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported dim-6 Wilson coefficient pairs. Expected results are reported in black, while observed ones are reported in orange. All results are obtained by considering the combination of all the channels, fixing the operators not under analysis to zero. |
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Figure 10-m:
68% (solid line) and 95% (dashed line) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported dim-6 Wilson coefficient pairs. Expected results are reported in black, while observed ones are reported in orange. All results are obtained by considering the combination of all the channels, fixing the operators not under analysis to zero. |
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Figure 10-n:
68% (solid line) and 95% (dashed line) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported dim-6 Wilson coefficient pairs. Expected results are reported in black, while observed ones are reported in orange. All results are obtained by considering the combination of all the channels, fixing the operators not under analysis to zero. |
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Figure 10-o:
68% (solid line) and 95% (dashed line) CL contours for $ -2\ln\Delta\mathcal{L} $ as functions of the reported dim-6 Wilson coefficient pairs. Expected results are reported in black, while observed ones are reported in orange. All results are obtained by considering the combination of all the channels, fixing the operators not under analysis to zero. |
| Tables | |
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Table 1:
The subset of Warsaw basis operators considered in this work, following the definitions of [1,none]. Repeated indices are summed over. These purely bosonic operators are independent of the flavour symmetry imposed on the SMEFT Lagrangian. The symbol $ H $ refers to the Higgs doublet; $ D_\mu $ is a covariant derivative and $ \square = D^\mu D_\mu $ the d'Alembert operator; $ W^i_{\mu\nu} $ and $ B_{\mu\nu} $ are the $ \mathrm{SU}(2)_L $ and $ \mathrm{U}(1)_Y $ field strength tensors; $ i,j,k $ are $ \mathrm{SU}(2) $ adjoint indices. |
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Table 2:
Summary of the analyses considered in the combination and the reference to the specific CMS study on that final state. The final state for each analysis is specified, where $ {\ell}^{\pm} $ denotes a light lepton (e, $ \mu $) and $ \tau_\mathrm{h} $ represents a hadronically decaying $ \tau $ lepton. The last two columns indicate the operators contributing as vertex corrections to the diagrams associated with each specific final state and the single CMS publication on that final state. |
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Table 3:
Summary of the signal regions (SRs) entering the combined fit. Some rows merge multiple SRs sharing an identical discriminating variable and binning, with yields summed accordingly. SRs are further split by the Zeppenfeld variable [50] (VBS-OSWW), DNN score or b-tag multiplicity (VBS-WV/ZV), and, for VVV$ /\gamma $, by lepton/$ \tau_\mathrm{h} $/VTJ multiplicity, lepton charge (SS: same-sign, OS: opposite-sign), flavor (OF: opposite-, SF: same-flavor), and $ m_{\ell\ell} $ proximity to the Z pole (Z/noZ); a BDT separates signal in the $ \tau_\mathrm{h} $ channels. Full definitions are given in the original references of Table 2. The second column gives the discriminating variable, with a colon for bidimensional observables; $ m $/$ m_{\mathrm{T}} $ denote invariant/transverse mass of the sub/superscripted system. Remaining columns: number of bins and edges, nuisance parameters (NP), and observed events. |
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Table 4:
Observed 68% and 95% 1D confidence level (CL) intervals on the Wilson coefficients associated with the SMEFT dim-6 operators considered. All CL are reported for the fits including both linear and quadratic SMEFT components. 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. |
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Table 5:
MadGraph-5_aMC@NLO commands for generating SM components of the processes of interest. Where relevant, charge conjugate processes were included. The shortcut l- stands for electron, muon, or tau lepton. |
| Summary |
| A search for physics beyond the standard model is performed in the framework of the standard model effective field theory (SMEFT) through a statistical combination of ten CMS measurements of electroweak (EW) processes. The combination includes vector boson scattering (VBS), vector boson fusion (VBF), diboson, and triboson production, probing final states with one, two, and three EW gauge bosons. The analyses use the full Run 2 proton-proton collision dataset recorded by the CMS experiment at the CERN LHC at $ \sqrt{s}= $ 13 TeV, corresponding to an integrated luminosity of 138 fb$ ^{-1} $. For all measurements, the SMEFT parametrization is propagated directly to detector level through event-by-event reweighting, allowing a consistent treatment of detector effects and systematic uncertainties while avoiding the model assumptions required by unfolding. Six Wilson coefficients associated with bosonic dimension-six operators are constrained: $ c_W $, $ c_{HW} $, $ c_{HWB} $, $ c_{H\square} $, $ c_{HB} $, and $ c_{HD} $. Limits are extracted in single-parameter, two-parameter, and global profiling scenarios. The combination significantly improves the sensitivity to all six operators compared with the individual measurements, with no single analysis dominating any constraint. The strongest limit is obtained for $ c_W $, while the remaining coefficients are constrained through complementary sensitivity of the VBS, VBF, diboson, and triboson channels. No evidence for deviations from the standard model is observed. These results provide competitive constraints on bosonic dimension-six operators and constitute the first statistical combination of direct detector-level SMEFT measurements of bosonic operators. |
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