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| CMS-SMP-24-017 ; CERN-EP-2026-041 | ||
| Search for new physics in triple boson production in proton-proton collisions at $ \sqrt{s} = $ 13 TeV using the effective field theory approach | ||
| CMS Collaboration | ||
| 14 May 2026 | ||
| Submitted to the Journal of High Energy Physics | ||
| Abstract: A search for new physics in the production of three massive gauge bosons ($ \mathrm{V}\mathrm{V}\mathrm{V} $, where V is a W or Z boson) is presented. The event selection is most effective in the Lorentz-boosted regime in which all three bosons have a transverse momentum ($ p_{\mathrm{T}} $) above 200 GeV. Standard model (SM) processes contribute few events in this regime. When a boosted W or Z boson decays hadronically, the decay products tend to form a large-radius jet with substructure that reflects the presence of two quarks from the decay; such jets are called V-tagged jets. Special techniques to reconstruct and select V-tagged jets are applied. Events are categorized according to the number and kinematic features of charged leptons and V-tagged jets. Event yields are obtained in bins of a suitable kinematic variable such as the scalar $ p_{\mathrm{T}} $ sum of the reconstructed objects in the event. No excess over SM expectations is observed. Bounds are placed on Wilson coefficients for a set of mass dimension-6 and -8 operators in the framework of SM effective field theory. The two most stringent bounds placed by this analysis are $ -0.13 < c_\mathrm{W}/\Lambda^2 < 0.12 \text{TeV}^{-2} $ and $ -0.24 < c_{\text{Hq3}}/\Lambda^2 < 0.21 \text{TeV}^{-2} $ at 95% CL, where $ c_\mathrm{W} $ and $ c_{\text{Hq3}} $ are dimension-6 Wilson coefficients in the Warsaw basis and $ \Lambda $ is the mass scale of new physics. | ||
| Links: e-print arXiv:2605.15023 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Comparison of the $ m_{\text{SD}} $ distribution in data and simulation for events in a control region dominated by $ \mathrm{t} \overline{\mathrm{t}} $ production. $ \mathrm{W}\to\mathrm{q}\overline{\mathrm{q}} $ represents V-tagged jets that match the hadronic decay of a W boson; a prominent peak at the W boson mass is seen. The contribution marked Initial-state radiation corresponds to V-tagged jets matched to gluons emitted in the initial state. Jets containing single b quarks will sometimes be selected as V-tagged jets. Both ISR and b jets peak at small $ m_{\text{SD}} $ but not near the W boson mass. A small contamination from non- $ \mathrm{t} \overline{\mathrm{t}} $ events is marked as Other in the plot. The data are represented by black dots with error bars. The shaded band in the data/MC ratio plot shows the MC statistical uncertainty. This plot shows the MC prediction after fitting, i.e.,, these are post-fit distributions. |
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Figure 2:
Tests of the ABCD method in the SR-0\ell-2VTJ (left) and SR-0\ell-3VTJ (right) channels. The validation regions are dominated by QCD multijet backgrounds. The ABCD method is used to predict the QCD multijet background and the total SM background is compared to the data, showing good agreement. The shaded band in the ratio plot shows the MC statistical uncertainty. The black dots with error bars represent the data with statistical uncertainties. These are pre-fit distributions. |
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Figure 2-a:
Tests of the ABCD method in the SR-0\ell-2VTJ (left) and SR-0\ell-3VTJ (right) channels. The validation regions are dominated by QCD multijet backgrounds. The ABCD method is used to predict the QCD multijet background and the total SM background is compared to the data, showing good agreement. The shaded band in the ratio plot shows the MC statistical uncertainty. The black dots with error bars represent the data with statistical uncertainties. These are pre-fit distributions. |
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Figure 2-b:
Tests of the ABCD method in the SR-0\ell-2VTJ (left) and SR-0\ell-3VTJ (right) channels. The validation regions are dominated by QCD multijet backgrounds. The ABCD method is used to predict the QCD multijet background and the total SM background is compared to the data, showing good agreement. The shaded band in the ratio plot shows the MC statistical uncertainty. The black dots with error bars represent the data with statistical uncertainties. These are pre-fit distributions. |
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Figure 3:
Comparison of the $ S_\text{T} $ distributions for events in the zero-lepton signal regions with two V-tagged jets (left) and three V-tagged jets (right). The shaded band in the ratio plot shows the total uncertainty. The black dots with error bars represent the data with statistical uncertainties. These distributions are made after the fit, i.e.,, they are post-fit distributions. |
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Figure 3-a:
Comparison of the $ S_\text{T} $ distributions for events in the zero-lepton signal regions with two V-tagged jets (left) and three V-tagged jets (right). The shaded band in the ratio plot shows the total uncertainty. The black dots with error bars represent the data with statistical uncertainties. These distributions are made after the fit, i.e.,, they are post-fit distributions. |
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Figure 3-b:
Comparison of the $ S_\text{T} $ distributions for events in the zero-lepton signal regions with two V-tagged jets (left) and three V-tagged jets (right). The shaded band in the ratio plot shows the total uncertainty. The black dots with error bars represent the data with statistical uncertainties. These distributions are made after the fit, i.e.,, they are post-fit distributions. |
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Figure 4:
Comparison of the pre-fit $ m_{\mathrm{JJ}\ell\nu} $ distributions for the one-lepton control regions for $ \mathrm{W}+ $jets (left) and $ \mathrm{t} \overline{\mathrm{t}} $ (right) backgrounds. The shaded band in the ratio plot represents the MC statistical uncertainty. The black dots with error bars represent the data with statistical uncertainties. |
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Figure 4-a:
Comparison of the pre-fit $ m_{\mathrm{JJ}\ell\nu} $ distributions for the one-lepton control regions for $ \mathrm{W}+ $jets (left) and $ \mathrm{t} \overline{\mathrm{t}} $ (right) backgrounds. The shaded band in the ratio plot represents the MC statistical uncertainty. The black dots with error bars represent the data with statistical uncertainties. |
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Figure 4-b:
Comparison of the pre-fit $ m_{\mathrm{JJ}\ell\nu} $ distributions for the one-lepton control regions for $ \mathrm{W}+ $jets (left) and $ \mathrm{t} \overline{\mathrm{t}} $ (right) backgrounds. The shaded band in the ratio plot represents the MC statistical uncertainty. The black dots with error bars represent the data with statistical uncertainties. |
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Figure 5:
Comparison of the post-fit $ m_{\mathrm{JJ}\ell\nu} $ distributions for the one-lepton and two V-tagged jets (SR-1\ell-2VTJ ) signal region. The shaded band in the ratio plot represents the total uncertainty. The black dots with error bars represent the data with statistical uncertainties. |
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Figure 6:
Comparison of the pre-fit $ S_\text{T} $ distributions for the opposite-sign dilepton plus two V-tagged jets (SR-2\ell-OS-2VTJ ) control regions for $ \mathrm{Z}+ $jets (left) and $ \mathrm{t} \overline{\mathrm{t}} $ (right) backgrounds. The shaded band in the ratio plot represents the MC statistical uncertainty. The black dots with error bars represent the data with statistical uncertainties. |
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Figure 6-a:
Comparison of the pre-fit $ S_\text{T} $ distributions for the opposite-sign dilepton plus two V-tagged jets (SR-2\ell-OS-2VTJ ) control regions for $ \mathrm{Z}+ $jets (left) and $ \mathrm{t} \overline{\mathrm{t}} $ (right) backgrounds. The shaded band in the ratio plot represents the MC statistical uncertainty. The black dots with error bars represent the data with statistical uncertainties. |
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Figure 6-b:
Comparison of the pre-fit $ S_\text{T} $ distributions for the opposite-sign dilepton plus two V-tagged jets (SR-2\ell-OS-2VTJ ) control regions for $ \mathrm{Z}+ $jets (left) and $ \mathrm{t} \overline{\mathrm{t}} $ (right) backgrounds. The shaded band in the ratio plot represents the MC statistical uncertainty. The black dots with error bars represent the data with statistical uncertainties. |
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Figure 7:
Comparison of the post-fit $ S_\text{T} $ distributions. The upper plots and the lower left plot correspond to the opposite-sign dilepton and one V-tagged jet (SR-2\ell-OS-1VTJ ) channel, while the lower right plot corresponds to the opposite-sign dilepton and two or more V-tagged jets (SR-2\ell-OS-2VTJ ) channel. The shaded bands in the ratio plots represent the total uncertainties. The black dots with error bars represent the data with statistical uncertainties. |
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Figure 7-a:
Comparison of the post-fit $ S_\text{T} $ distributions. The upper plots and the lower left plot correspond to the opposite-sign dilepton and one V-tagged jet (SR-2\ell-OS-1VTJ ) channel, while the lower right plot corresponds to the opposite-sign dilepton and two or more V-tagged jets (SR-2\ell-OS-2VTJ ) channel. The shaded bands in the ratio plots represent the total uncertainties. The black dots with error bars represent the data with statistical uncertainties. |
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Figure 7-b:
Comparison of the post-fit $ S_\text{T} $ distributions. The upper plots and the lower left plot correspond to the opposite-sign dilepton and one V-tagged jet (SR-2\ell-OS-1VTJ ) channel, while the lower right plot corresponds to the opposite-sign dilepton and two or more V-tagged jets (SR-2\ell-OS-2VTJ ) channel. The shaded bands in the ratio plots represent the total uncertainties. The black dots with error bars represent the data with statistical uncertainties. |
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Figure 7-c:
Comparison of the post-fit $ S_\text{T} $ distributions. The upper plots and the lower left plot correspond to the opposite-sign dilepton and one V-tagged jet (SR-2\ell-OS-1VTJ ) channel, while the lower right plot corresponds to the opposite-sign dilepton and two or more V-tagged jets (SR-2\ell-OS-2VTJ ) channel. The shaded bands in the ratio plots represent the total uncertainties. The black dots with error bars represent the data with statistical uncertainties. |
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Figure 7-d:
Comparison of the post-fit $ S_\text{T} $ distributions. The upper plots and the lower left plot correspond to the opposite-sign dilepton and one V-tagged jet (SR-2\ell-OS-1VTJ ) channel, while the lower right plot corresponds to the opposite-sign dilepton and two or more V-tagged jets (SR-2\ell-OS-2VTJ ) channel. The shaded bands in the ratio plots represent the total uncertainties. The black dots with error bars represent the data with statistical uncertainties. |
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Figure 8:
Comparison of pre-fit $ S_\text{T} $ distributions for the $ \mathrm{t} \overline{\mathrm{t}} $ (left) and WZ (right) control regions in the SR-2\ell-SS-1VTJ channel. The shaded band in the ratio plot represents the MC statistical uncertainty. The black dots with error bars represent the data with statistical uncertainties. |
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Figure 8-a:
Comparison of pre-fit $ S_\text{T} $ distributions for the $ \mathrm{t} \overline{\mathrm{t}} $ (left) and WZ (right) control regions in the SR-2\ell-SS-1VTJ channel. The shaded band in the ratio plot represents the MC statistical uncertainty. The black dots with error bars represent the data with statistical uncertainties. |
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Figure 8-b:
Comparison of pre-fit $ S_\text{T} $ distributions for the $ \mathrm{t} \overline{\mathrm{t}} $ (left) and WZ (right) control regions in the SR-2\ell-SS-1VTJ channel. The shaded band in the ratio plot represents the MC statistical uncertainty. The black dots with error bars represent the data with statistical uncertainties. |
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Figure 9:
Comparison of the post-fit $ S_\text{T} $ distributions for the same-sign dilepton plus one V-tagged jets (SR-2\ell-SS-1VTJ ) signal region. The shaded band in the ratio plot represents the total uncertainty. The black dots with error bars represent the data with statistical uncertainties. |
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Figure 10:
Comparison of the post-fit distributions binned in the BDT score and $ S_\text{T} $ for the SR-1\ell-1$ \tau_\mathrm{h} $-1VTJ (left) and SR-2\ell-1$ \tau_\mathrm{h} $-0VTJ (right) signal regions. The shaded bands in the ratio plots represent the MC total uncertainties. The black dots with error bars represent the data with statistical uncertainties. |
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Figure 10-a:
Comparison of the post-fit distributions binned in the BDT score and $ S_\text{T} $ for the SR-1\ell-1$ \tau_\mathrm{h} $-1VTJ (left) and SR-2\ell-1$ \tau_\mathrm{h} $-0VTJ (right) signal regions. The shaded bands in the ratio plots represent the MC total uncertainties. The black dots with error bars represent the data with statistical uncertainties. |
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Figure 10-b:
Comparison of the post-fit distributions binned in the BDT score and $ S_\text{T} $ for the SR-1\ell-1$ \tau_\mathrm{h} $-1VTJ (left) and SR-2\ell-1$ \tau_\mathrm{h} $-0VTJ (right) signal regions. The shaded bands in the ratio plots represent the MC total uncertainties. The black dots with error bars represent the data with statistical uncertainties. |
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Figure 11:
Summary of the bin-by-bin yields in all signal regions and associated limits on $ c_\mathrm{W}/\Lambda^2 $. The channels are listed from left to right in order of increasing sensitivity to $ c_\mathrm{W}/\Lambda^2 $. In the upper panel, the beige histogram shows the predicted SM yields including SM $ \mathrm{V}\mathrm{V}\mathrm{V} $ production while the red line represents the additional contribution expected when $ c_\mathrm{W}/\Lambda^2 = 0.123 \text{TeV}^{-2} $. The black dots with error bars represent the data with statistical uncertainties. The lower panel shows the expected and observed limits on $ c_\mathrm{W}/\Lambda^2 $ for each bin in each channel. The 95% CL combined limit on $ c_\mathrm{W}/\Lambda^{-2} $ is obtained by performing the fit on all 37 bins; the observed (expected) result is represented by the magenta (cyan) bar. |
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Figure 12:
Bounds on pairs of Wilson coefficients. The dashed black (solid blue) curves show the 68% (95%) CL bounds determined by 2D likelihood quantiles. The red plus sign indicates the minimum of 2 $ \Delta $ NLL which can be compared to the SM expectation (i.e.,, zero for both Wilson coefficients). The three plots on the left are made freezing all Wilson coefficients to zero except for the two indicated on the plot. The three plots on the right are made allowing all dim-6 Wilson coefficients to vary simultaneously. |
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Figure 12-a:
Bounds on pairs of Wilson coefficients. The dashed black (solid blue) curves show the 68% (95%) CL bounds determined by 2D likelihood quantiles. The red plus sign indicates the minimum of 2 $ \Delta $ NLL which can be compared to the SM expectation (i.e.,, zero for both Wilson coefficients). The three plots on the left are made freezing all Wilson coefficients to zero except for the two indicated on the plot. The three plots on the right are made allowing all dim-6 Wilson coefficients to vary simultaneously. |
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Figure 12-b:
Bounds on pairs of Wilson coefficients. The dashed black (solid blue) curves show the 68% (95%) CL bounds determined by 2D likelihood quantiles. The red plus sign indicates the minimum of 2 $ \Delta $ NLL which can be compared to the SM expectation (i.e.,, zero for both Wilson coefficients). The three plots on the left are made freezing all Wilson coefficients to zero except for the two indicated on the plot. The three plots on the right are made allowing all dim-6 Wilson coefficients to vary simultaneously. |
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Figure 12-c:
Bounds on pairs of Wilson coefficients. The dashed black (solid blue) curves show the 68% (95%) CL bounds determined by 2D likelihood quantiles. The red plus sign indicates the minimum of 2 $ \Delta $ NLL which can be compared to the SM expectation (i.e.,, zero for both Wilson coefficients). The three plots on the left are made freezing all Wilson coefficients to zero except for the two indicated on the plot. The three plots on the right are made allowing all dim-6 Wilson coefficients to vary simultaneously. |
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Figure 12-d:
Bounds on pairs of Wilson coefficients. The dashed black (solid blue) curves show the 68% (95%) CL bounds determined by 2D likelihood quantiles. The red plus sign indicates the minimum of 2 $ \Delta $ NLL which can be compared to the SM expectation (i.e.,, zero for both Wilson coefficients). The three plots on the left are made freezing all Wilson coefficients to zero except for the two indicated on the plot. The three plots on the right are made allowing all dim-6 Wilson coefficients to vary simultaneously. |
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Figure 12-e:
Bounds on pairs of Wilson coefficients. The dashed black (solid blue) curves show the 68% (95%) CL bounds determined by 2D likelihood quantiles. The red plus sign indicates the minimum of 2 $ \Delta $ NLL which can be compared to the SM expectation (i.e.,, zero for both Wilson coefficients). The three plots on the left are made freezing all Wilson coefficients to zero except for the two indicated on the plot. The three plots on the right are made allowing all dim-6 Wilson coefficients to vary simultaneously. |
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Figure 12-f:
Bounds on pairs of Wilson coefficients. The dashed black (solid blue) curves show the 68% (95%) CL bounds determined by 2D likelihood quantiles. The red plus sign indicates the minimum of 2 $ \Delta $ NLL which can be compared to the SM expectation (i.e.,, zero for both Wilson coefficients). The three plots on the left are made freezing all Wilson coefficients to zero except for the two indicated on the plot. The three plots on the right are made allowing all dim-6 Wilson coefficients to vary simultaneously. |
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Figure 13:
Illustration of the impact of the clipping procedure. The horizontal axis indicates the threshold values placed in $ m_{\mathrm{V}\mathrm{V}\mathrm{V}} $ (see text). When the threshold is high, there is little impact and the bounds on Wilson coefficients $ c_\mathrm{W}/\Lambda^2 $ (left) and $ f_{T,0}/\Lambda^4 $ (right) are essentially the same as reported in Tables 5 and 6. As the upper bound on $ m_{\mathrm{V}\mathrm{V}\mathrm{V}} $ is reduced, however, the bounds on Wilson coefficients weaken substantially. The solid (dashed) blue lines show the expected bounds computing using Asimov [56] data sets including all (statistical) uncertainties. |
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Figure 13-a:
Illustration of the impact of the clipping procedure. The horizontal axis indicates the threshold values placed in $ m_{\mathrm{V}\mathrm{V}\mathrm{V}} $ (see text). When the threshold is high, there is little impact and the bounds on Wilson coefficients $ c_\mathrm{W}/\Lambda^2 $ (left) and $ f_{T,0}/\Lambda^4 $ (right) are essentially the same as reported in Tables 5 and 6. As the upper bound on $ m_{\mathrm{V}\mathrm{V}\mathrm{V}} $ is reduced, however, the bounds on Wilson coefficients weaken substantially. The solid (dashed) blue lines show the expected bounds computing using Asimov [56] data sets including all (statistical) uncertainties. |
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Figure 13-b:
Illustration of the impact of the clipping procedure. The horizontal axis indicates the threshold values placed in $ m_{\mathrm{V}\mathrm{V}\mathrm{V}} $ (see text). When the threshold is high, there is little impact and the bounds on Wilson coefficients $ c_\mathrm{W}/\Lambda^2 $ (left) and $ f_{T,0}/\Lambda^4 $ (right) are essentially the same as reported in Tables 5 and 6. As the upper bound on $ m_{\mathrm{V}\mathrm{V}\mathrm{V}} $ is reduced, however, the bounds on Wilson coefficients weaken substantially. The solid (dashed) blue lines show the expected bounds computing using Asimov [56] data sets including all (statistical) uncertainties. |
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Figure 14:
Visual summary of fitted multiplicative values obtained from the template fit. In essence, this plot shows the $ m_{\mathrm{V}\mathrm{V}\mathrm{V}} $ distribution inferred from the data (black points) which agrees with the SM prediction (blue points). The red and orange points correspond to new physics scenarios (see text). The shaded regions centered on the red, orange, and blue points show the predicted total uncertainties based on fits to Asimov data sets. The error bars for the black dots show the total uncertainties when fitting the data. The black and blue points are slightly displaced to avoid overlap that would obscure them. The values are listed in Table 8. |
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Figure 15:
Sensitivity to the SM $ \mathrm{V}\mathrm{V}\mathrm{V} $ production process. The curves show the variation of 2 $ \Delta $NNL with the SM signal strength, $ \mu_{\text{SM}} $. The Asimov curves for all the channels are shown, and the solid black curve shows the combined Asimov result. The solid magenta curve shows the combined result based on CMS data. Numerical values for 68% CL Asimov intervals and point values are listed in the box below the plot. |
| Tables | |
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Table 1:
The set of 12 dim-6 operators studied in this analysis |
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Table 2:
The set of 20 dim-8 operators studied in this analysis. H.c. stands for Hermitian conjugate. |
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Table 3:
Definitions of the discriminating kinematic variables. Here, SR-2\ell-OS-1VTJ stands for SR-2\ell-OSoffZ-1VTJ, SR-2\ell-OSonZ-1VTJ, and SR-2\ell-OSDF-1VTJ (OSDF stands for opposite-sign, different-flavor). In the definition of $ m_{\mathrm{JJ}\ell\nu} $, $ p $ stands for a four-vector. |
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Table 4:
Summary of the SM expected and observed numbers of events. The post-fit uncertainties in the expected numbers of events include all statistical and systematic uncertainties relating to the prediction. The row ``Sum highest bins'' is computed by summing the expected and observed numbers of events for the last bin in each channel; the last bin in each channel is usually the most sensitive one. |
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Table 5:
Summary of the 95% CL bounds on the dim-6 Wilson coefficients. We consider the case of a single varying Wilson coefficient (``Freeze other WCs'') as well as the case when the other Wilson coefficients are profiled (``Profile other WCs''). The Wilson coefficients are ordered by increasing confidence interval width. |
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Table 6:
Summary of the 95% CL bounds and measurements on the dim-8 Wilson coefficients, when considering a single varying Wilson coefficient at a time. The Wilson coefficients are ordered by increasing confidence interval width. |
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Table 7:
Summary of the measurements of the dim-6 Wilson coefficients. We consider the case of a single varying Wilson coefficient (``Freeze other WCs'') as well as the case when the other Wilson coefficients are profiled (``Profile other WCs''). |
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Table 8:
Summary of the fitted multiplicative values in the template fit. The case $ c_\mathrm{W}/\Lambda^2 = 1 \text{TeV}^{-2} $ defines the reference model and $ c_{\text{Hq3}}/\Lambda^2 = 1 \text{TeV}^{-2} $ is an alternative scenario resulting in multiplicative values less than unity. The SM expectation is zero and the measured values are consistent with the SM. |
| Summary |
| A search for new physics in the production of three massive gauge bosons in proton-proton collisions ($ \mathrm{p}\mathrm{p}\to\mathrm{V}\mathrm{V}\mathrm{V} $, with $ \mathrm{V} = \mathrm{W} $ or Z) has been reported. The analysis targets the boosted regime in which the bosons have transverse momentum $ p_{\mathrm{T}} > $ 200 GeV. When they decay hadronically, large-radius jets with substructure are formed; we identify such V-tagged jets using the PARTICLENET algorithm. Signal V-tagged jets have a soft-drop mass consistent with the W or Z boson mass. Several analysis channels are defined according to the multiplicities of leptons and V-tagged jets in an event; two channels feature hadronically decaying $ \tau $ leptons. Signal regions are defined by a suitable kinematic variable that correlates well with the triboson invariant mass, $ m_{\mathrm{V}\mathrm{V}\mathrm{V}} $. The observed signal yields are interpreted in a standard model effective field theory framework with twelve dimension-6 and twenty dimension-8 Wilson operators. Agreement with the SM predictions is good, and bounds are placed on Wilson coefficients at 95% CL in two scenarios. In the first, all Wilson coefficients are fixed to zero except the one under consideration, and in the second, all coefficients are allowed to float. Examples of bounds on pairs of Wilson coefficients are given, as well. Potential difficulties with unitarity are handled using a clipping procedure: the bounds on individual Wilson coefficients weaken as the threshold on $ m_{\mathrm{V}\mathrm{V}\mathrm{V}} $ is lowered. A template fit is introduced to infer the $ m_{\mathrm{V}\mathrm{V}\mathrm{V}} $ distribution; the result is consistent with the SM. Finally, the result of a fit for the signal strength for SM $ \mathrm{V}\mathrm{V}\mathrm{V} $ production is, again, consistent with the SM. |
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