CMS-PAS-SMP-24-013

CMS-PAS-SMP-24-013
Combination of vector boson scattering measurements with fully- and semi-leptonic final states in proton-proton collisionsat $\sqrt{s} =$ 13 TeV
CMS Collaboration
2 April 2025

Abstract: A statistical combination of vector boson scattering measurements is presented, incorporating fully leptonic and semileptonic decay channels from proton-proton collisions at $\sqrt{s} =$ 13 TeV. The analysis is based on a dataset corresponding to an integrated luminosity of 138 fb $^{-1}$ , collected with the CMS detector between 2016 and 2018. All selected events feature at least two jets with a high invariant mass, large pseudorapidity separation, and at least one heavy vector boson decaying leptonically. A combined measurement of the signal strengths is performed for the production of two same-sign W bosons, two opposite-sign W bosons, two Z bosons, and a WZ final state, comparing the results to Standard Model predictions. Additionally, the measurement is reported separately for different W boson charge states.
Links: CDS record (PDF) ; Physics Briefing ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: The left side shows a representative Feynman diagram for the EW-induced production of VBS involving massive vector bosons. The dashed circle encapsulates different contributions leading to the same final state, including triple and quartic gauge couplings as well as Higgs-boson exchange. On the right, the considered decay channels are categorized into same-sign WW (SSWW), opposite-sign WW (OSWW), WZ, and ZZ pairs, covering both leptonic and semileptonic modes. In all cases, at least one vector boson is required to decay leptonically.
png pdf	Figure 2: The signal fractions for each analysis contributing to the combination are presented. Rows correspond to the names of the analyses, while the x-axis indicates the signal fraction. Different colors, as shown in the legend, represent the distinct signal parameters targeted for measurement. The left half of the figure displays the signal fractions for the six components, separated by the electric charge of the W bosons. The right half of the figure provides the equivalent information for the four components. All signal yields are computed before the combined fit to the signal strengths and including all analyses regions.
png pdf	Figure 3: Measurement of the vector boson scattering (VBS) signal strength modifiers ( $\mu_{i}$ ) and comparison with Standard Model (SM) predictions. The top (bottom) panel presents results considering four (six) independent signal strengths. In each panel, the left side shows the measured signal strengths, with thick (thin) black lines representing the 1 (2) standard deviation confidence intervals. The red and blue bands within the 1 standard deviation interval illustrate the systematic and statistical uncertainties, respectively. The right side displays the observed (black crosses) and expected (filled grey bars) statistical significance of the electroweak VBS signal relative to the SM background.
png pdf	Figure 4: Observed $\log[S(\mu_i=1)/B]$ distributions for the VBS SM combination and four parameters model. From left to right, the filled white histograms represent the overall background contributions while the blue histograms represent the signal yields for $\mu_{OSWW}$ , $\mu_{SSWW}$ , $\mu_{WZ}$ and $\mu_{ZZ}$ . The post-fit 68% uncertainty band on the overall background template is shown in pink. The distribution is binned as a function of the prefit value of $\log[S(\mu_i=1)/B]$ and is filled with the post-fit yields of signal and backgrounds. The latter are assigned to the dominant signal contribution in a specific bin of the input templates.
png pdf	Figure 5: Distributions of the DNN scores for the OSWW analysis in the signal $e\mu$ region after the combined fit. The signal region is divided into two sub-regions based on the Zeppenfeld variable ( $Z_{\ell\ell}$ ), with values either greater or smaller than one. The top and bottom rows show the distributions for $Z_{\ell\ell} <$ 1 and $Z_{\ell\ell} >$ 1, respectively. From left to right, the plots correspond to the 2016, 2017, and 2018 data-taking periods.
png pdf	Figure 5-a: Distributions of the DNN scores for the OSWW analysis in the signal $e\mu$ region after the combined fit. The signal region is divided into two sub-regions based on the Zeppenfeld variable ( $Z_{\ell\ell}$ ), with values either greater or smaller than one. The top and bottom rows show the distributions for $Z_{\ell\ell} <$ 1 and $Z_{\ell\ell} >$ 1, respectively. From left to right, the plots correspond to the 2016, 2017, and 2018 data-taking periods.
png pdf	Figure 5-b: Distributions of the DNN scores for the OSWW analysis in the signal $e\mu$ region after the combined fit. The signal region is divided into two sub-regions based on the Zeppenfeld variable ( $Z_{\ell\ell}$ ), with values either greater or smaller than one. The top and bottom rows show the distributions for $Z_{\ell\ell} <$ 1 and $Z_{\ell\ell} >$ 1, respectively. From left to right, the plots correspond to the 2016, 2017, and 2018 data-taking periods.
png pdf	Figure 5-c: Distributions of the DNN scores for the OSWW analysis in the signal $e\mu$ region after the combined fit. The signal region is divided into two sub-regions based on the Zeppenfeld variable ( $Z_{\ell\ell}$ ), with values either greater or smaller than one. The top and bottom rows show the distributions for $Z_{\ell\ell} <$ 1 and $Z_{\ell\ell} >$ 1, respectively. From left to right, the plots correspond to the 2016, 2017, and 2018 data-taking periods.
png pdf	Figure 5-d: Distributions of the DNN scores for the OSWW analysis in the signal $e\mu$ region after the combined fit. The signal region is divided into two sub-regions based on the Zeppenfeld variable ( $Z_{\ell\ell}$ ), with values either greater or smaller than one. The top and bottom rows show the distributions for $Z_{\ell\ell} <$ 1 and $Z_{\ell\ell} >$ 1, respectively. From left to right, the plots correspond to the 2016, 2017, and 2018 data-taking periods.
png pdf	Figure 5-e: Distributions of the DNN scores for the OSWW analysis in the signal $e\mu$ region after the combined fit. The signal region is divided into two sub-regions based on the Zeppenfeld variable ( $Z_{\ell\ell}$ ), with values either greater or smaller than one. The top and bottom rows show the distributions for $Z_{\ell\ell} <$ 1 and $Z_{\ell\ell} >$ 1, respectively. From left to right, the plots correspond to the 2016, 2017, and 2018 data-taking periods.
png pdf	Figure 5-f: Distributions of the DNN scores for the OSWW analysis in the signal $e\mu$ region after the combined fit. The signal region is divided into two sub-regions based on the Zeppenfeld variable ( $Z_{\ell\ell}$ ), with values either greater or smaller than one. The top and bottom rows show the distributions for $Z_{\ell\ell} <$ 1 and $Z_{\ell\ell} >$ 1, respectively. From left to right, the plots correspond to the 2016, 2017, and 2018 data-taking periods.
png pdf	Figure 6: Distributions for the signal regions of the semileptonic VBS analyses after the combined fit. The top row shows the DNN spectra of the WV analysis merged for the electron and muon cateogries in the boosted signal region (left) and in the resolved signal region (right). The bottom row shows the DNN spectra of the ZV analysis in the boosted signal region (left) and in the resolved signal region (right).
png pdf	Figure 6-a: Distributions for the signal regions of the semileptonic VBS analyses after the combined fit. The top row shows the DNN spectra of the WV analysis merged for the electron and muon cateogries in the boosted signal region (left) and in the resolved signal region (right). The bottom row shows the DNN spectra of the ZV analysis in the boosted signal region (left) and in the resolved signal region (right).
png pdf	Figure 6-b: Distributions for the signal regions of the semileptonic VBS analyses after the combined fit. The top row shows the DNN spectra of the WV analysis merged for the electron and muon cateogries in the boosted signal region (left) and in the resolved signal region (right). The bottom row shows the DNN spectra of the ZV analysis in the boosted signal region (left) and in the resolved signal region (right).
png pdf	Figure 6-c: Distributions for the signal regions of the semileptonic VBS analyses after the combined fit. The top row shows the DNN spectra of the WV analysis merged for the electron and muon cateogries in the boosted signal region (left) and in the resolved signal region (right). The bottom row shows the DNN spectra of the ZV analysis in the boosted signal region (left) and in the resolved signal region (right).
png pdf	Figure 6-d: Distributions for the signal regions of the semileptonic VBS analyses after the combined fit. The top row shows the DNN spectra of the WV analysis merged for the electron and muon cateogries in the boosted signal region (left) and in the resolved signal region (right). The bottom row shows the DNN spectra of the ZV analysis in the boosted signal region (left) and in the resolved signal region (right).
png pdf	Figure 7: The left figure shows the distribution of the $K_{D}$ discriminant used to separate the VBS EW ZZ production from the QCD-induced one in the VBS-ZZ(4 $\ell$ ) signal region. The central figure presents the distribution of the SSWW and WZ analyses in all signal and control regions entering in the combined fit. The right figure shows the distribution fo the DNN score used to separate the SSWW signal from the backgrounds in the SSWW( $\tau_h$ ) signal region. All distributions are shown after the combined fit.
png pdf	Figure 7-a: The left figure shows the distribution of the $K_{D}$ discriminant used to separate the VBS EW ZZ production from the QCD-induced one in the VBS-ZZ(4 $\ell$ ) signal region. The central figure presents the distribution of the SSWW and WZ analyses in all signal and control regions entering in the combined fit. The right figure shows the distribution fo the DNN score used to separate the SSWW signal from the backgrounds in the SSWW( $\tau_h$ ) signal region. All distributions are shown after the combined fit.
png pdf	Figure 7-b: The left figure shows the distribution of the $K_{D}$ discriminant used to separate the VBS EW ZZ production from the QCD-induced one in the VBS-ZZ(4 $\ell$ ) signal region. The central figure presents the distribution of the SSWW and WZ analyses in all signal and control regions entering in the combined fit. The right figure shows the distribution fo the DNN score used to separate the SSWW signal from the backgrounds in the SSWW( $\tau_h$ ) signal region. All distributions are shown after the combined fit.
png pdf	Figure 7-c: The left figure shows the distribution of the $K_{D}$ discriminant used to separate the VBS EW ZZ production from the QCD-induced one in the VBS-ZZ(4 $\ell$ ) signal region. The central figure presents the distribution of the SSWW and WZ analyses in all signal and control regions entering in the combined fit. The right figure shows the distribution fo the DNN score used to separate the SSWW signal from the backgrounds in the SSWW( $\tau_h$ ) signal region. All distributions are shown after the combined fit.
png pdf	Figure 8: The two figures show the likelihood profiles from the combined fit for the various POIs. The left figure shows the $-2\Delta \log L$ profiles for the 4-POIs model while the right one shows the same profiles in the 6-POIs fit.
png pdf	Figure 8-a: The two figures show the likelihood profiles from the combined fit for the various POIs. The left figure shows the $-2\Delta \log L$ profiles for the 4-POIs model while the right one shows the same profiles in the 6-POIs fit.
png pdf	Figure 8-b: The two figures show the likelihood profiles from the combined fit for the various POIs. The left figure shows the $-2\Delta \log L$ profiles for the 4-POIs model while the right one shows the same profiles in the 6-POIs fit.
png pdf	Figure 9: Summary plots of the two-dimensional fits are presented. The left plot displays the 68% confidence level intervals for all pairs of parameters of interest in the 4-POIs model, with the legend listing the POI on the x-axis first, followed by the POI on the y-axis. The right plot provides the corresponding intervals for the 6-POIs model. In all cases, all parameters of interest except the two under study are profiled in the maximum likelihood fit along with the nuisance parameters.
png pdf	Figure 9-a: Summary plots of the two-dimensional fits are presented. The left plot displays the 68% confidence level intervals for all pairs of parameters of interest in the 4-POIs model, with the legend listing the POI on the x-axis first, followed by the POI on the y-axis. The right plot provides the corresponding intervals for the 6-POIs model. In all cases, all parameters of interest except the two under study are profiled in the maximum likelihood fit along with the nuisance parameters.
png pdf	Figure 9-b: Summary plots of the two-dimensional fits are presented. The left plot displays the 68% confidence level intervals for all pairs of parameters of interest in the 4-POIs model, with the legend listing the POI on the x-axis first, followed by the POI on the y-axis. The right plot provides the corresponding intervals for the 6-POIs model. In all cases, all parameters of interest except the two under study are profiled in the maximum likelihood fit along with the nuisance parameters.

Tables
png pdf	Table 1: Summary of the analyses considered in the combination. $\ell$ denotes either an electron or muon, $\tau_h$ an hadronicaly decaying $\tau$ lepton and $j$ is the shorthand notation for a parton.
png pdf	Table 2: Summary of the signal and control regions defined in the analyses entering the combination, including the requirements ensuring their orthogonality. The second column is the number of light leptons ( $\ell = e, \mu$ ), and the third column is the number of hadronically decaying tau leptons. The same-flavor requirement for charged leptons is denoted as SF. A check mark indicates that the SF condition is applied, a cross means it is inverted (different-flavour), and no symbol signifies no restriction on lepton flavors. $\|\sum$ ch. $\|$ is the sum of the electrical charges for leptons in the final state. The b-veto column uses check mark to indicate regions that veto b-jets, a cross for regions requiring at least one b-jet, and no symbol for no restriction on b-jets. $m_{\ell\ell}$ denotes the invariant mass of a charged dilepton pair and is defined in GeV. In WZ and ZZ cases, $m_{\ell\ell}$ and SF refer respectively to the invariant mass and same flavour requirements of the Z boson decay candidates. The next two columns are the invariant mass, in units of GeV, of the two VBS jets and the $\eta$ separation between them. The table finally presents the number of small-radius (AK4) and large-radius (AK8) jets, along with the invariant mass, in GeV, of the hadronically decaying vector boson candidate (W or Z).
png pdf	Table 3: Phase space regions included in the combined fit, along with the corresponding observables and the number of bins. Bidimensional observables are represented with a colon separating the two components. For each subregion, a template is defined based on the specified observable and the number of bins. If the data-taking year is not explicitly specified in the subregion column, an independent template is included for each individual year of data-taking.
png pdf	Table 4: Observed values of the signal strengths $\mu^i = \sigma^i/\sigma^i_{\text{SM}}$ and statistical significance ( $\sigma^i$ ) from the VBS combination. The top row reports the results for the model with four signal strengths while the bottom row reports the same results but splitting the signal strengths for the W boson electrical charge. The expected results are reported within brackets. For the expected signal strengths, only the $\pm$ 1 standard deviation uncertainty is reported as the central value is assumed to be 1.

Summary

This study presents the most comprehensive statistical combination of vector boson scattering (VBS) processes to date, integrating results from seven analyses. The fully leptonic final states are SSWW(

$e,\mu$ ),

$pp \rightarrow W^\pm W^\pm jj \rightarrow 2\ell^\pm 2\nu jj$ ; SSWW(

$\tau_h$ ),

$pp \rightarrow W^\pm W^\pm jj \rightarrow \ell^\pm \tau_h^{\pm} 2\nu jj$ ; OSWW,

$pp \rightarrow W^+ W^{-} jj \rightarrow \ell^+ \ell^{-} 2\nu jj$ ; WZ,

$pp \rightarrow W^\pm Z jj \rightarrow 3\ell \nu jj$ ; and ZZ(4

$\ell$ ),

$pp \rightarrow ZZ jj \rightarrow 4\ell jj$ , where

$\ell = e, \mu$ . The semileptonic final states are WV (

$pp \rightarrow W^\pm V jj \rightarrow \ell \nu jjjj$ ) and ZV (

$pp \rightarrow Z V jj \rightarrow 2\ell jjjj$ ) where

$V$ (W,Z) denotes an hadronically decaying vector boson

$V\rightarrow jj$ . Electroweak (EW) VBS production signal strengths are measured in two configurations: one merging W boson electric charges with four free parameters (

$\mu_{\text{SSWW}}$ ,

$\mu_{\text{OSWW}}$ ,

$\mu_{\text{WZ}}$ ,

$\mu_{\text{ZZ}}$ ) and another splitting W boson charges with six parameters (

$\mu_{W^+W^+}$ ,

$\mu_{W^{-}W^{-}}$ ,

$\mu_{W^+W^{-}}$ ,

$\mu_{W^+Z}$ ,

$\mu_{W^{-}Z}$ ,

$\mu_{ZZ}$ ). The EW signal strengths are measured based on a simultaneous fit of the seven channels. Interference effects between QCD and EW diboson production are negligible in all channels except SSWW(

$e,\mu$ ) and ZZ, where they are treated as part of the EW signal. The results for the four-parameter model are

$\mu_{\text{SSWW}} =$ 1.04

$^{+0.14}_{-0.14}$ ,

$\mu_{\text{OSWW}} =$ 1.09

$^{+0.21}_{-0.18}$ ,

$\mu_{\text{WZ}} =$ 1.19

$^{+0.28}_{-0.23}$ , and

$\mu_{\text{ZZ}} =$ 1.15

$^{+0.44}_{-0.37}$ . For the six-parameter model the results are

$\mu_{W^+W^+} =$ 1.11

$^{+0.17}_{-0.15}$ ,

$\mu_{W^{-}W^{-}} =$ 0.84

$^{+0.27}_{-0.24}$ ,

$\mu_{W^+W^{-}} =$ 1.08

$^{+0.20}_{-0.19}$ ,

$\mu_{W^+Z} =$ 1.15

$^{+0.32}_{-0.27}$ ,

$\mu_{W^{-}Z} =$ 1.30

$^{+0.47}_{-0.40}$ , and

$\mu_{ZZ} =$ 1.16

$^{+0.44}_{-0.38}$ . Simultaneous two-dimensional fits were performed for all VBS EW production components. The compatibility between the observed data and the Standard Model (SM) predictions was evaluated differentially using the

$\log(S/B)$ observable. Overall, all one-dimensional and two-dimensional measurements are found to be consistent with SM predictions at the 68% confidence level.

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