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| CMS-SMP-25-001 ; CERN-EP-2026-210 | ||
| Search for anomalous couplings in WW and WZ production with single-lepton final states in proton-proton collisions at $ \sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 18 August 2026 | ||
| Submitted to Physics Letters B | ||
| Abstract: A search for deviations from the standard model using an effective field theory approach is carried out using the proton-proton collision data set recorded by the CMS experiment at the LHC at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. In this study Wilson coefficients corresponding to dimension-six effective field theory operators that would lead to anomalous gauge boson self-couplings and modified couplings between vector bosons and quarks are constrained. Diboson (WW and WZ) production processes with one W boson decaying to a lepton plus antineutrino or charge conjugate and the second W or Z boson decaying hadronically are considered. Since the contribution from anomalous couplings is expected to be most visible at high energy scales, the focus is on final states where the hadronic decay products of a W or Z boson are merged into a single large-radius jet. A dedicated classifier based on machine learning is employed to separate hadronic W and Z boson decays from background processes. The most stringent constraints to date on the Wilson coefficients of operators corresponding to anomalous triple gauge boson couplings are reported. The bounds set on the couplings between vector bosons and quarks are competitive with those from previous inclusive jet measurements. | ||
| Links: e-print arXiv:2608.18245 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
The leading order Feynman diagram for the process studied in this analysis, with an anomalous triple gauge coupling vertex, where one W boson decays to a lepton and a neutrino and another W (Z) boson decays to quarks. |
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Figure 2:
Large-$ R $ jet $ m_{\text{SD}}^{\text{jet}} $ in the combined $ \mathrm{W}{+\text{jets}} $ CR and the signal region (left) and in the $ {\mathrm{t}\overline{\mathrm{t}}} $ control region (center) after applying the tagger. The $ \mathrm{W}/\mathrm{Z} $ boson tagging score in the $ \mathrm{W}{+\text{jets}} $ CR without tagger requirement is shown in the right panel. These pre-fit distributions are obtained after combining the electron and muon channels and, the data-taking years. The vertical error bars on the data points represent the statistical uncertainty of the data. The uncertainty band shown in the ratio plot contains both statistical and systematic components on the predictions. |
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Figure 2-a:
Large-$ R $ jet $ m_{\text{SD}}^{\text{jet}} $ in the combined $ \mathrm{W}{+\text{jets}} $ CR and the signal region (left) and in the $ {\mathrm{t}\overline{\mathrm{t}}} $ control region (center) after applying the tagger. The $ \mathrm{W}/\mathrm{Z} $ boson tagging score in the $ \mathrm{W}{+\text{jets}} $ CR without tagger requirement is shown in the right panel. These pre-fit distributions are obtained after combining the electron and muon channels and, the data-taking years. The vertical error bars on the data points represent the statistical uncertainty of the data. The uncertainty band shown in the ratio plot contains both statistical and systematic components on the predictions. |
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Figure 2-b:
Large-$ R $ jet $ m_{\text{SD}}^{\text{jet}} $ in the combined $ \mathrm{W}{+\text{jets}} $ CR and the signal region (left) and in the $ {\mathrm{t}\overline{\mathrm{t}}} $ control region (center) after applying the tagger. The $ \mathrm{W}/\mathrm{Z} $ boson tagging score in the $ \mathrm{W}{+\text{jets}} $ CR without tagger requirement is shown in the right panel. These pre-fit distributions are obtained after combining the electron and muon channels and, the data-taking years. The vertical error bars on the data points represent the statistical uncertainty of the data. The uncertainty band shown in the ratio plot contains both statistical and systematic components on the predictions. |
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Figure 2-c:
Large-$ R $ jet $ m_{\text{SD}}^{\text{jet}} $ in the combined $ \mathrm{W}{+\text{jets}} $ CR and the signal region (left) and in the $ {\mathrm{t}\overline{\mathrm{t}}} $ control region (center) after applying the tagger. The $ \mathrm{W}/\mathrm{Z} $ boson tagging score in the $ \mathrm{W}{+\text{jets}} $ CR without tagger requirement is shown in the right panel. These pre-fit distributions are obtained after combining the electron and muon channels and, the data-taking years. The vertical error bars on the data points represent the statistical uncertainty of the data. The uncertainty band shown in the ratio plot contains both statistical and systematic components on the predictions. |
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Figure 3:
Large-R jet $ m_{\text{SD}}^{\text{jet}} $ in the $ \mathrm{W}{+\text{jets}} $ CR and the signal region for the combined electron and muon channels and the data-taking years after the ML fit. The SM WW and WZ processes are plotted individually as colored lines while rest of the background predictions are shown as filled histograms. The vertical error bars on the data points represent the statistical uncertainty of the data. The uncertainty bands, shown on the shaded histograms and on the ratio plot at the bottom panel, contain both statistical and systematic components on the predictions before the ML fit. |
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Figure 4:
The $ m_{\mathrm{W}\mathrm{V}} $ distribution in the $ \mathrm{W}{+\text{jets}} $ low (left) and high (center) sidebands and $ {\mathrm{t}\overline{\mathrm{t}}} $ (right) control regions in the muon (left) and electron (right) channels after the ML fit considering the SM-only scenario (background-only fit). The vertical error bars on the data points represent the statistical uncertainty of the data. The lower panels show the ratio of the data to the postfit signal plus background prediction. The uncertainty bands, shown on the shaded histograms and on the ratio plot at the bottom panel, contain both statistical and systematic components on the predictions after the ML fit. |
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Figure 4-a:
The $ m_{\mathrm{W}\mathrm{V}} $ distribution in the $ \mathrm{W}{+\text{jets}} $ low (left) and high (center) sidebands and $ {\mathrm{t}\overline{\mathrm{t}}} $ (right) control regions in the muon (left) and electron (right) channels after the ML fit considering the SM-only scenario (background-only fit). The vertical error bars on the data points represent the statistical uncertainty of the data. The lower panels show the ratio of the data to the postfit signal plus background prediction. The uncertainty bands, shown on the shaded histograms and on the ratio plot at the bottom panel, contain both statistical and systematic components on the predictions after the ML fit. |
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Figure 4-b:
The $ m_{\mathrm{W}\mathrm{V}} $ distribution in the $ \mathrm{W}{+\text{jets}} $ low (left) and high (center) sidebands and $ {\mathrm{t}\overline{\mathrm{t}}} $ (right) control regions in the muon (left) and electron (right) channels after the ML fit considering the SM-only scenario (background-only fit). The vertical error bars on the data points represent the statistical uncertainty of the data. The lower panels show the ratio of the data to the postfit signal plus background prediction. The uncertainty bands, shown on the shaded histograms and on the ratio plot at the bottom panel, contain both statistical and systematic components on the predictions after the ML fit. |
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Figure 4-c:
The $ m_{\mathrm{W}\mathrm{V}} $ distribution in the $ \mathrm{W}{+\text{jets}} $ low (left) and high (center) sidebands and $ {\mathrm{t}\overline{\mathrm{t}}} $ (right) control regions in the muon (left) and electron (right) channels after the ML fit considering the SM-only scenario (background-only fit). The vertical error bars on the data points represent the statistical uncertainty of the data. The lower panels show the ratio of the data to the postfit signal plus background prediction. The uncertainty bands, shown on the shaded histograms and on the ratio plot at the bottom panel, contain both statistical and systematic components on the predictions after the ML fit. |
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Figure 4-d:
The $ m_{\mathrm{W}\mathrm{V}} $ distribution in the $ \mathrm{W}{+\text{jets}} $ low (left) and high (center) sidebands and $ {\mathrm{t}\overline{\mathrm{t}}} $ (right) control regions in the muon (left) and electron (right) channels after the ML fit considering the SM-only scenario (background-only fit). The vertical error bars on the data points represent the statistical uncertainty of the data. The lower panels show the ratio of the data to the postfit signal plus background prediction. The uncertainty bands, shown on the shaded histograms and on the ratio plot at the bottom panel, contain both statistical and systematic components on the predictions after the ML fit. |
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Figure 4-e:
The $ m_{\mathrm{W}\mathrm{V}} $ distribution in the $ \mathrm{W}{+\text{jets}} $ low (left) and high (center) sidebands and $ {\mathrm{t}\overline{\mathrm{t}}} $ (right) control regions in the muon (left) and electron (right) channels after the ML fit considering the SM-only scenario (background-only fit). The vertical error bars on the data points represent the statistical uncertainty of the data. The lower panels show the ratio of the data to the postfit signal plus background prediction. The uncertainty bands, shown on the shaded histograms and on the ratio plot at the bottom panel, contain both statistical and systematic components on the predictions after the ML fit. |
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Figure 4-f:
The $ m_{\mathrm{W}\mathrm{V}} $ distribution in the $ \mathrm{W}{+\text{jets}} $ low (left) and high (center) sidebands and $ {\mathrm{t}\overline{\mathrm{t}}} $ (right) control regions in the muon (left) and electron (right) channels after the ML fit considering the SM-only scenario (background-only fit). The vertical error bars on the data points represent the statistical uncertainty of the data. The lower panels show the ratio of the data to the postfit signal plus background prediction. The uncertainty bands, shown on the shaded histograms and on the ratio plot at the bottom panel, contain both statistical and systematic components on the predictions after the ML fit. |
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Figure 5:
The $ m_{\mathrm{W}\mathrm{V}} $ distribution in the signal region low (left) and high (right) in the muon (left) and electron (right) channels after the ML fit assuming no signal. The prefit signal contribution from the summed linear and quadratic terms corresponding to $ c_{\mathrm{W}} = 0.1 \text{TeV}^{-2} $ are also shown. The vertical error bars on the data points represent the statistical uncertainty of the data. The lower panels show the ratio of the data to the postfit signal plus background prediction. The uncertainty bands, shown on the shaded histograms and on the ratio plot at the bottom panel, contain both statistical and systematic components on the predictions after the ML fit. |
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Figure 5-a:
The $ m_{\mathrm{W}\mathrm{V}} $ distribution in the signal region low (left) and high (right) in the muon (left) and electron (right) channels after the ML fit assuming no signal. The prefit signal contribution from the summed linear and quadratic terms corresponding to $ c_{\mathrm{W}} = 0.1 \text{TeV}^{-2} $ are also shown. The vertical error bars on the data points represent the statistical uncertainty of the data. The lower panels show the ratio of the data to the postfit signal plus background prediction. The uncertainty bands, shown on the shaded histograms and on the ratio plot at the bottom panel, contain both statistical and systematic components on the predictions after the ML fit. |
png pdf |
Figure 5-b:
The $ m_{\mathrm{W}\mathrm{V}} $ distribution in the signal region low (left) and high (right) in the muon (left) and electron (right) channels after the ML fit assuming no signal. The prefit signal contribution from the summed linear and quadratic terms corresponding to $ c_{\mathrm{W}} = 0.1 \text{TeV}^{-2} $ are also shown. The vertical error bars on the data points represent the statistical uncertainty of the data. The lower panels show the ratio of the data to the postfit signal plus background prediction. The uncertainty bands, shown on the shaded histograms and on the ratio plot at the bottom panel, contain both statistical and systematic components on the predictions after the ML fit. |
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Figure 5-c:
The $ m_{\mathrm{W}\mathrm{V}} $ distribution in the signal region low (left) and high (right) in the muon (left) and electron (right) channels after the ML fit assuming no signal. The prefit signal contribution from the summed linear and quadratic terms corresponding to $ c_{\mathrm{W}} = 0.1 \text{TeV}^{-2} $ are also shown. The vertical error bars on the data points represent the statistical uncertainty of the data. The lower panels show the ratio of the data to the postfit signal plus background prediction. The uncertainty bands, shown on the shaded histograms and on the ratio plot at the bottom panel, contain both statistical and systematic components on the predictions after the ML fit. |
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Figure 5-d:
The $ m_{\mathrm{W}\mathrm{V}} $ distribution in the signal region low (left) and high (right) in the muon (left) and electron (right) channels after the ML fit assuming no signal. The prefit signal contribution from the summed linear and quadratic terms corresponding to $ c_{\mathrm{W}} = 0.1 \text{TeV}^{-2} $ are also shown. The vertical error bars on the data points represent the statistical uncertainty of the data. The lower panels show the ratio of the data to the postfit signal plus background prediction. The uncertainty bands, shown on the shaded histograms and on the ratio plot at the bottom panel, contain both statistical and systematic components on the predictions after the ML fit. |
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Figure 6:
Profile likelihood scan of the WC $ c_{\mathrm{W}} $ obtained from a simultaneous fit to data in the SRs and background CRs for the case when all other WCs are fixed to zero. Both linear and quadratic contributions in the EFT expansion are included in the fit. The horizontal dashed lines correspond to the 68% and 95% confidence levels. Different profile likelihood curves correspond to cases where: all systematic uncertainty nuisance parameters are included and varied in the fit, theory uncertainty parameters are fixed to their best fit values, and where all nuisance parameters are fixed (statistical only). |
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Figure 7:
Likelihood scans as functions of the pairs of WCs from HISZ model: $ c_{\mathrm{W}} $ and $ c_{{\mathrm{B}}} $ (left), $ c_{\mathrm{W}\mathrm{W}\mathrm{W}} $ and $ c_{\mathrm{W}} $ (center), and $ c_{\mathrm{W}\mathrm{W}\mathrm{W}} $ and $ c_{{\mathrm{B}}} $ (right). All WCs that are not scanned are fixed to zero. The best fit value is shown with a marker and the dotted lines correspond to the crossing points of $ -2\Delta\ln L $ at 2.28 and 5.99, which correspond to the 68% and 95% confidence levels in the asymptotic approximation. |
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Figure 7-a:
Likelihood scans as functions of the pairs of WCs from HISZ model: $ c_{\mathrm{W}} $ and $ c_{{\mathrm{B}}} $ (left), $ c_{\mathrm{W}\mathrm{W}\mathrm{W}} $ and $ c_{\mathrm{W}} $ (center), and $ c_{\mathrm{W}\mathrm{W}\mathrm{W}} $ and $ c_{{\mathrm{B}}} $ (right). All WCs that are not scanned are fixed to zero. The best fit value is shown with a marker and the dotted lines correspond to the crossing points of $ -2\Delta\ln L $ at 2.28 and 5.99, which correspond to the 68% and 95% confidence levels in the asymptotic approximation. |
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Figure 7-b:
Likelihood scans as functions of the pairs of WCs from HISZ model: $ c_{\mathrm{W}} $ and $ c_{{\mathrm{B}}} $ (left), $ c_{\mathrm{W}\mathrm{W}\mathrm{W}} $ and $ c_{\mathrm{W}} $ (center), and $ c_{\mathrm{W}\mathrm{W}\mathrm{W}} $ and $ c_{{\mathrm{B}}} $ (right). All WCs that are not scanned are fixed to zero. The best fit value is shown with a marker and the dotted lines correspond to the crossing points of $ -2\Delta\ln L $ at 2.28 and 5.99, which correspond to the 68% and 95% confidence levels in the asymptotic approximation. |
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Figure 7-c:
Likelihood scans as functions of the pairs of WCs from HISZ model: $ c_{\mathrm{W}} $ and $ c_{{\mathrm{B}}} $ (left), $ c_{\mathrm{W}\mathrm{W}\mathrm{W}} $ and $ c_{\mathrm{W}} $ (center), and $ c_{\mathrm{W}\mathrm{W}\mathrm{W}} $ and $ c_{{\mathrm{B}}} $ (right). All WCs that are not scanned are fixed to zero. The best fit value is shown with a marker and the dotted lines correspond to the crossing points of $ -2\Delta\ln L $ at 2.28 and 5.99, which correspond to the 68% and 95% confidence levels in the asymptotic approximation. |
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Figure 8:
Comparison of observed limits on different WCs at 95% confidence level with existing analyses at different center-of-mass energies and different final states [95,96,97,25,31]. The limits from some of the analyses are scaled down or up so as to fit on the same scale as for the best constraints. The corresponding scale factor is mentioned, next to the limits, which should be multiplied with the plotted limits to extract the actual constraints. |
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Figure 9:
Summary of the lower limits on the energy scales $ \Lambda_{j} $, obtained from the observed limits on the WCs at 95% confidence interval, for the indicated values of the $ c_{j} $. |
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Figure 10:
Likelihood scans as a function of the pairs of WCs from SMEFT model: $c_{qq}^{(3,8)} $ and $c_{qq}^{(3,1)} $ (left left), $c_{Hq}^{(3)} $ and $ c_{\mathrm{W}} $ (left right), $c_{Hq}^{(3)} $ and $c_{Hq}^{(1)} $ (right left), and $c_{Hq}^{(1)} $ and $ c_{\mathrm{W}} $ (right right). All WCs that are not scanned are fixed to zero. The best fit value is shown with a marker and the colored lines correspond to the crossing points of $ -2\Delta\ln L $ at 2.28 and 5.99. |
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Figure 10-a:
Likelihood scans as a function of the pairs of WCs from SMEFT model: $c_{qq}^{(3,8)} $ and $c_{qq}^{(3,1)} $ (left left), $c_{Hq}^{(3)} $ and $ c_{\mathrm{W}} $ (left right), $c_{Hq}^{(3)} $ and $c_{Hq}^{(1)} $ (right left), and $c_{Hq}^{(1)} $ and $ c_{\mathrm{W}} $ (right right). All WCs that are not scanned are fixed to zero. The best fit value is shown with a marker and the colored lines correspond to the crossing points of $ -2\Delta\ln L $ at 2.28 and 5.99. |
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Figure 10-b:
Likelihood scans as a function of the pairs of WCs from SMEFT model: $c_{qq}^{(3,8)} $ and $c_{qq}^{(3,1)} $ (left left), $c_{Hq}^{(3)} $ and $ c_{\mathrm{W}} $ (left right), $c_{Hq}^{(3)} $ and $c_{Hq}^{(1)} $ (right left), and $c_{Hq}^{(1)} $ and $ c_{\mathrm{W}} $ (right right). All WCs that are not scanned are fixed to zero. The best fit value is shown with a marker and the colored lines correspond to the crossing points of $ -2\Delta\ln L $ at 2.28 and 5.99. |
png pdf |
Figure 10-c:
Likelihood scans as a function of the pairs of WCs from SMEFT model: $c_{qq}^{(3,8)} $ and $c_{qq}^{(3,1)} $ (left left), $c_{Hq}^{(3)} $ and $ c_{\mathrm{W}} $ (left right), $c_{Hq}^{(3)} $ and $c_{Hq}^{(1)} $ (right left), and $c_{Hq}^{(1)} $ and $ c_{\mathrm{W}} $ (right right). All WCs that are not scanned are fixed to zero. The best fit value is shown with a marker and the colored lines correspond to the crossing points of $ -2\Delta\ln L $ at 2.28 and 5.99. |
png pdf |
Figure 10-d:
Likelihood scans as a function of the pairs of WCs from SMEFT model: $c_{qq}^{(3,8)} $ and $c_{qq}^{(3,1)} $ (left left), $c_{Hq}^{(3)} $ and $ c_{\mathrm{W}} $ (left right), $c_{Hq}^{(3)} $ and $c_{Hq}^{(1)} $ (right left), and $c_{Hq}^{(1)} $ and $ c_{\mathrm{W}} $ (right right). All WCs that are not scanned are fixed to zero. The best fit value is shown with a marker and the colored lines correspond to the crossing points of $ -2\Delta\ln L $ at 2.28 and 5.99. |
| Tables | |
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Table 1:
The dimension-six SMEFT operators $ (\mathcal{Q}) $ and their corresponding Wilson coefficients ($ c $) studied in this analysis, following the definitions of Refs. [12,6], where $ (q\ \mathrm{or}\ u,d) $ denote quark fields of the first two generations and $ (l\ \mathrm{or}\ e,\nu) $ lepton fields of all three generations. The Higgs doublet field is indicated by $ H $; $ D $ represents a covariant derivative; $ {\overset\leftrightarrow{D_{\mu}}} $ denotes the Hermitian bidirectional covariant derivative; $ X = G, W, B $ denotes a vector boson field strength tensor; $ p $ and $ r $ are flavor indices; and $ \sigma^{i} $ ($ i = 1,2, $ 3) are the Pauli matrices. Fermion fields are represented by $ \psi $, with $ L $ and $ R $ indicating left- and right-handed fermion fields, respectively. |
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Table 2:
Event yields from SM processes and observed data events in the low and high SRs for the electron and muon channels. The combination of the statistical and systematic uncertainties is indicated. The event yields are shown with their best fit (post-fit) normalizations from the simultaneous fit to the data, assuming no signal, i.e.,, for the SM case. The contributions from SM WW and WZ processes are grouped under the SM WV category. |
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Table 3:
Expected and observed individual limits on the WCs, from HISZ basis as 68% and 95% confidence intervals. |
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Table 4:
Expected and observed individual limits on WCs in SMEFT scenarios as 68% and 95% confidence intervals. |
| Summary |
| A search for deviations from the standard model using an effective field theory approach has been presented in the diboson (WW and WZ) production processes with one W boson decaying to lepton plus antineutrino or charge conjugate and the second W or Z boson decaying hadronically. The results are based on data recorded in proton-proton collisions at $ \sqrt{s} = $ 13 TeV with the CMS detector at the CERN LHC, corresponding to an integrated luminosity of 138 fb$^{-1}$. In this study we constrain Wilson coefficients corresponding to dimension-six effective field theory operators that would lead to anomalous gauge boson self- and vector boson to quark couplings. Since the contribution from anomalous couplings is expected to be most visible at high energy scales, we focus on final states where the hadronic decay products from the W and Z bosons merge into a single large-radius jet. A dedicated classifier, based on machine learning, is employed to separate such jets from vector boson decays from those originating in background processes. We report the most stringent constraints to date on the Wilson coefficients of operators corresponding to anomalous triple gauge boson couplings. The bounds set on vector boson to quark couplings are competitive with those from previous inclusive jet measurements. |
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