CMSPASHIG22011  
Search for ZZ and ZH production in the $ \rm{b}\bar{\rm{b}}\rm{b}\bar{\rm{b}} $ final state using protonproton collisions at $ \sqrt{s}= $ 13 TeV  
CMS Collaboration  
4 December 2023  
Abstract: A search for ZZ and ZH production in the $ \mathrm{b}\bar{\mathrm{b}}\mathrm{b}\bar{\mathrm{b}} $ final state is presented. The search uses an event sample of protonproton collisions corresponding to an integrated luminosity of 133 fb$ ^{1} $ at a centerofmass energy of 13 TeV with the CMS detector at the LHC. This analysis introduces several novel techniques for deriving and validating the datadriven background model using synthetic data sets, derived from the hemispheremixing technique. A multiclass multivariate classifier customized for the $ \mathrm{b}\bar{\mathrm{b}}\mathrm{b}\bar{\mathrm{b}} $ final state is developed to both extract the signal and derive the background model. The data are found to be consistent, within uncertainties, with the standard model (SM) predictions. The observed (expected) upper limit at 95% confidence level corresponds to 3.8 (3.8) and 5.0 (2.9) times the SM prediction for the ZZ and ZH production cross sections, respectively. The ZZ and ZH $ \rightarrow \mathrm{b}\bar{\mathrm{b}}\mathrm{b}\bar{\mathrm{b}} $ processes share the experimental challenges of the HH $ \rightarrow \mathrm{b}\bar{\mathrm{b}}\mathrm{b}\bar{\mathrm{b}} $ analysis. The novel techniques developed and demonstrated in the ZZ and ZH search are used to analyze the HH $ \rightarrow \mathrm{b}\bar{\mathrm{b}}\mathrm{b}\bar{\mathrm{b}} $ background. The ZZ, ZH, and HH $ \rightarrow \mathrm{b}\bar{\mathrm{b}}\mathrm{b}\bar{\mathrm{b}} $ expected sensitivities are extrapolated to an integrated luminosity of 3000 $ \mathrm{fb}^{1} $.  
Links:
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These preliminary results are superseded in this paper, Submitted to EPJC. The superseded preliminary plots can be found here. 
Figures & Tables  Summary  Additional Figures  References  CMS Publications 

Figures  
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Figure 1:
Signal (left) and fourtag data (right) passing the event selection. The signal region is defined by the union of the red dashed lines. 
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Figure 1a:
Signal (left) and fourtag data (right) passing the event selection. The signal region is defined by the union of the red dashed lines. 
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Figure 1b:
Signal (left) and fourtag data (right) passing the event selection. The signal region is defined by the union of the red dashed lines. 
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Figure 2:
Event selection acceptance times efficiency as a function of the generated four body mass $ m_{4\mathrm{b}} $gen for the ZZ (left) and ZH (right) signal. The plots show the cumulative efficiency with respect to the inclusive sample. The expected $ m_{4\mathrm{b}} $gen distribution of the inclusive ZZ and ZH\ signal is given in gray with arbitrary normalization. 
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Figure 2a:
Event selection acceptance times efficiency as a function of the generated four body mass $ m_{4\mathrm{b}} $gen for the ZZ (left) and ZH (right) signal. The plots show the cumulative efficiency with respect to the inclusive sample. The expected $ m_{4\mathrm{b}} $gen distribution of the inclusive ZZ and ZH\ signal is given in gray with arbitrary normalization. 
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Figure 2b:
Event selection acceptance times efficiency as a function of the generated four body mass $ m_{4\mathrm{b}} $gen for the ZZ (left) and ZH (right) signal. The plots show the cumulative efficiency with respect to the inclusive sample. The expected $ m_{4\mathrm{b}} $gen distribution of the inclusive ZZ and ZH\ signal is given in gray with arbitrary normalization. 
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Figure 3:
A highlevel sketch of the HCR classifier architecture. Bosoncandidate jets are shown on the left with the three possible jet pairings. The HCR architecture is shown in the right. The boxes represent pixels, with the labels indicating which jet, dijet, or quadjet the pixel refers to. The different jet pairings on the left are each represented within the network, as indicated by the color coding. 
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Figure 4:
Jet (left) and btagged jet (right) multiplicity distributions in the sideband region. The black data points show the observed fourtag data, the blue distribution the $ \mathrm{t} \overline{\mathrm{t}} $ simulation, and the yellow the threetag multijet prior to the JCM corrections. The red distribution shows the result of the fitted JCM model. 
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Figure 4a:
Jet (left) and btagged jet (right) multiplicity distributions in the sideband region. The black data points show the observed fourtag data, the blue distribution the $ \mathrm{t} \overline{\mathrm{t}} $ simulation, and the yellow the threetag multijet prior to the JCM corrections. The red distribution shows the result of the fitted JCM model. 
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Figure 4b:
Jet (left) and btagged jet (right) multiplicity distributions in the sideband region. The black data points show the observed fourtag data, the blue distribution the $ \mathrm{t} \overline{\mathrm{t}} $ simulation, and the yellow the threetag multijet prior to the JCM corrections. The red distribution shows the result of the fitted JCM model. 
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Figure 5:
Distributions illustrating one of the key differences between the three and fourtag samples shown with the JCM correction but before kinematic reweighting. The $ \Delta\text{R}(j,j) $ distribution of the two bosoncandidate jets with the smallest angular separation is shown on the left. The $ \Delta\text{R}(j,j) $ distribution of the other two bosonscandidate jets is shown on the right. 
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Figure 5a:
Distributions illustrating one of the key differences between the three and fourtag samples shown with the JCM correction but before kinematic reweighting. The $ \Delta\text{R}(j,j) $ distribution of the two bosoncandidate jets with the smallest angular separation is shown on the left. The $ \Delta\text{R}(j,j) $ distribution of the other two bosonscandidate jets is shown on the right. 
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Figure 5b:
Distributions illustrating one of the key differences between the three and fourtag samples shown with the JCM correction but before kinematic reweighting. The $ \Delta\text{R}(j,j) $ distribution of the two bosoncandidate jets with the smallest angular separation is shown on the left. The $ \Delta\text{R}(j,j) $ distribution of the other two bosonscandidate jets is shown on the right. 
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Figure 6:
Signal probabilities for ZZ (left) and ZH (right) events in the sideband with the JCM correction but before kinematic reweighting. 
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Figure 6a:
Signal probabilities for ZZ (left) and ZH (right) events in the sideband with the JCM correction but before kinematic reweighting. 
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Figure 6b:
Signal probabilities for ZZ (left) and ZH (right) events in the sideband with the JCM correction but before kinematic reweighting. 
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Figure 7:
The $ \Delta\text{R}(j,j) $ distributions shown in Fig. 5 after including the FvT corrections. 
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Figure 7a:
The $ \Delta\text{R}(j,j) $ distributions shown in Fig. 5 after including the FvT corrections. 
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Figure 7b:
The $ \Delta\text{R}(j,j) $ distributions shown in Fig. 5 after including the FvT corrections. 
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Figure 8:
Signal probabilities for ZZ (left) and ZH (right) events in the sideband after including the FvT corrections. 
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Figure 8a:
Signal probabilities for ZZ (left) and ZH (right) events in the sideband after including the FvT corrections. 
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Figure 8b:
Signal probabilities for ZZ (left) and ZH (right) events in the sideband after including the FvT corrections. 
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Figure 9:
Signal probabilities for ZZ (upper row) and ZH (lower row) events in the sideband (left) and signal region (right). The yellow distributions show the multijet model before applying the FvT corrections. The average of the mixed models (red) provides a highstatistics proxy of the 4b background (black) that allows the extrapolation of the background model to be tested with precision. 
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Figure 9a:
Signal probabilities for ZZ (upper row) and ZH (lower row) events in the sideband (left) and signal region (right). The yellow distributions show the multijet model before applying the FvT corrections. The average of the mixed models (red) provides a highstatistics proxy of the 4b background (black) that allows the extrapolation of the background model to be tested with precision. 
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Figure 9b:
Signal probabilities for ZZ (upper row) and ZH (lower row) events in the sideband (left) and signal region (right). The yellow distributions show the multijet model before applying the FvT corrections. The average of the mixed models (red) provides a highstatistics proxy of the 4b background (black) that allows the extrapolation of the background model to be tested with precision. 
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Figure 9c:
Signal probabilities for ZZ (upper row) and ZH (lower row) events in the sideband (left) and signal region (right). The yellow distributions show the multijet model before applying the FvT corrections. The average of the mixed models (red) provides a highstatistics proxy of the 4b background (black) that allows the extrapolation of the background model to be tested with precision. 
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Figure 9d:
Signal probabilities for ZZ (upper row) and ZH (lower row) events in the sideband (left) and signal region (right). The yellow distributions show the multijet model before applying the FvT corrections. The average of the mixed models (red) provides a highstatistics proxy of the 4b background (black) that allows the extrapolation of the background model to be tested with precision. 
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Figure 10:
The ZZ (left) and ZH (right) background models fit to the observed signalregion yield in the mixed models. The black data points show the average of the mixed models, the yellow distributions the average of the multijet models. The red distribution shows the postfit background model. The lower panels show the pre and postfit pulls. The ZZ distribution is fit with all five basis coefficients constrained. The ZH distribution is fit with two of the four basis parameters unconstrained. 
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Figure 10a:
The ZZ (left) and ZH (right) background models fit to the observed signalregion yield in the mixed models. The black data points show the average of the mixed models, the yellow distributions the average of the multijet models. The red distribution shows the postfit background model. The lower panels show the pre and postfit pulls. The ZZ distribution is fit with all five basis coefficients constrained. The ZH distribution is fit with two of the four basis parameters unconstrained. 
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Figure 10b:
The ZZ (left) and ZH (right) background models fit to the observed signalregion yield in the mixed models. The black data points show the average of the mixed models, the yellow distributions the average of the multijet models. The red distribution shows the postfit background model. The lower panels show the pre and postfit pulls. The ZZ distribution is fit with all five basis coefficients constrained. The ZH distribution is fit with two of the four basis parameters unconstrained. 
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Figure 11:
Postfit backgroundonly SvB signal probability distributions in the ZZ region (left) and the ZH region (right). 
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Figure 11a:
Postfit backgroundonly SvB signal probability distributions in the ZZ region (left) and the ZH region (right). 
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Figure 11b:
Postfit backgroundonly SvB signal probability distributions in the ZZ region (left) and the ZH region (right). 
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Figure 12:
Projected ZZ, ZH, and $ \mathrm{H}\mathrm{H} \rightarrow 4\mathrm{b} $ 95% CL exclusion limits up to 3000 fb$ ^{1} $. The HH projections are shown with four different background uncertainty scaling assumptions. 
Tables  
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Table 1:
Summary of relative uncertainties on the measured signal strength, expressed in percentage of total uncertainty. The total uncertainties include the effect of correlations. 
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Table 2:
Expected and observed significance and 95% CL limit for ZZ, and ZH signal strengths. The limits are computed under the hypothesis of no $ \mathrm{Z}\mathrm{Z}\rightarrow 4\mathrm{b} $ or $ \mathrm{Z}\mathrm{H}\rightarrow 4\mathrm{b} $ signal. 
Summary 
Sensitivity to diHiggs boson (HH) production is driven by combining the $ \mathrm{b}\overline{\mathrm{b}}\gamma\gamma $, $ \mathrm{b}\overline{\mathrm{b}}\tau\tau $, and $ \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ (4b) decay modes. Extracting all available information from the 4b decay mode will require the development and validation of a highdimensional datadriven background model. The $ \mathrm{Z}\mathrm{Z}\rightarrow 4\mathrm{b} $ and $ \mathrm{Z}\mathrm{H} \rightarrow4\mathrm{b} $ processes provide standard candles that can be used to validate the 4b background model in situ. A search for ZZ and ZH production in the 4b final state was presented. The search uses the full 20162018 data set of protonproton collisions at a centerofmass energy of 13 TeV recorded with the CMS detector at the LHC, corresponding to an integrated luminosity of 133 fb$ ^{1} $. This analysis benefits from a multiclass multivariate classifier, which uses convolutions to solve the combinatoric jetpairing problem, and has been designed with an architecture customized to the 4b final state. The classifier is used both for signalversusbackground discrimination and for the derivation and validation of the background model. A novel technique for assessing background modeling uncertainties, using a synthetic data set derived from hemisphere mixing, allows both the extrapolation uncertainty and variance of the background model to be measured with a precision better than the statistical uncertainties of the fourtag data. The observed (expected) 95% CL upper limits on the $ \mathrm{Z}\mathrm{Z} \rightarrow 4\mathrm{b} $ and $ \mathrm{Z}\mathrm{H} \rightarrow 4\mathrm{b} $ production cross sections correspond to 3.8 (3.8) and 5.0 (2.9) times the standard model prediction, respectively. The results of this analysis, in addition to the expected HH sensitivity, have been extrapolated to 3000 fb$ ^{1} $. These projections indicate that, using the current analysis strategy, the $ \mathrm{Z}\mathrm{Z} \rightarrow 4\mathrm{b} $ and $ \mathrm{Z}\mathrm{H} \rightarrow 4\mathrm{b} $ signals are within reach of the HLLHC and that the sensitivity to $ \mathrm{H}\mathrm{H} \rightarrow 4\mathrm{b} $ would be close to the cross section predicted in the standard model. These projections are conservative as they do not consider improvements from the upgraded HLLHC detectors or from analysis strategies developed with the much larger data sets. 
Additional Figures  
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Additional Figure 1:
Event selection acceptance times efficiency as a function of the generated four body mass $ m_{4\mathrm{b}} $gen for the ZZ (left) and ZH (right) signal. The plots show the relative efficiency of each selection requirement. 
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Additional Figure 1a:
Event selection acceptance times efficiency as a function of the generated four body mass $ m_{4\mathrm{b}} $gen for the ZZ (left) and ZH (right) signal. The plots show the relative efficiency of each selection requirement. 
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Additional Figure 1b:
Event selection acceptance times efficiency as a function of the generated four body mass $ m_{4\mathrm{b}} $gen for the ZZ (left) and ZH (right) signal. The plots show the relative efficiency of each selection requirement. 
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Additional Figure 2:
Comparison of the performance of the nominal HCR SvB to a simpler likelihoodbased classifier using the two dijet invariant masses. A comparison is also made to a version of the HCR SvB with out multijet attention block including the kinematics from the additional nonbosoncandidate jets. ZZ is shown on the left and ZH on the right. 
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Additional Figure 2a:
Comparison of the performance of the nominal HCR SvB to a simpler likelihoodbased classifier using the two dijet invariant masses. A comparison is also made to a version of the HCR SvB with out multijet attention block including the kinematics from the additional nonbosoncandidate jets. ZZ is shown on the left and ZH on the right. 
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Additional Figure 2b:
Comparison of the performance of the nominal HCR SvB to a simpler likelihoodbased classifier using the two dijet invariant masses. A comparison is also made to a version of the HCR SvB with out multijet attention block including the kinematics from the additional nonbosoncandidate jets. ZZ is shown on the left and ZH on the right. 
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Additional Figure 3:
The FvT classifier reweight distribution before (left) and after (right) applying the FvT corrections. 
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Additional Figure 3a:
The FvT classifier reweight distribution before (left) and after (right) applying the FvT corrections. 
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Additional Figure 3b:
The FvT classifier reweight distribution before (left) and after (right) applying the FvT corrections. 
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Additional Figure 4:
The ZZ SvB distribution in the signal region for one of the mixed data subsamples (left) and after averaging over all fifteen of the mixed subsamples (right). 
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Additional Figure 4a:
The ZZ SvB distribution in the signal region for one of the mixed data subsamples (left) and after averaging over all fifteen of the mixed subsamples (right). 
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Additional Figure 4b:
The ZZ SvB distribution in the signal region for one of the mixed data subsamples (left) and after averaging over all fifteen of the mixed subsamples (right). 
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Additional Figure 5:
The ZH SvB distribution in the signal region for one of the mixed data subsamples (left) and after averaging over all fifteen of the mixed subsamples (right). 
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Additional Figure 5a:
The ZH SvB distribution in the signal region for one of the mixed data subsamples (left) and after averaging over all fifteen of the mixed subsamples (right). 
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Additional Figure 5b:
The ZH SvB distribution in the signal region for one of the mixed data subsamples (left) and after averaging over all fifteen of the mixed subsamples (right). 
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Additional Figure 6:
The predicted multijet ZZ SvB distributions in the mixed data signal regions fit to their average. The plots show the results of fitting with an increasing number of basis functions, from one in the upper left figure, to five in the lower row. The predictions from each mixed model are shown separately in yellow by adding the mixed data set index to offset the signal SvB distribution. The black data points show the average of the predictions. The predictions, including the fitted basis corrections, are shown in blue. The lower panels show the pulls before and after adding the basis corrections. The pull of adjacent bins are tested for statistical correlation. The correlation coefficient (r) is reported in the legend along with the pvalue used to test for lack of correlation. Basis functions are added until the pvalue is above 5%. 
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Additional Figure 6a:
The predicted multijet ZZ SvB distributions in the mixed data signal regions fit to their average. The plots show the results of fitting with an increasing number of basis functions, from one in the upper left figure, to five in the lower row. The predictions from each mixed model are shown separately in yellow by adding the mixed data set index to offset the signal SvB distribution. The black data points show the average of the predictions. The predictions, including the fitted basis corrections, are shown in blue. The lower panels show the pulls before and after adding the basis corrections. The pull of adjacent bins are tested for statistical correlation. The correlation coefficient (r) is reported in the legend along with the pvalue used to test for lack of correlation. Basis functions are added until the pvalue is above 5%. 
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Additional Figure 6b:
The predicted multijet ZZ SvB distributions in the mixed data signal regions fit to their average. The plots show the results of fitting with an increasing number of basis functions, from one in the upper left figure, to five in the lower row. The predictions from each mixed model are shown separately in yellow by adding the mixed data set index to offset the signal SvB distribution. The black data points show the average of the predictions. The predictions, including the fitted basis corrections, are shown in blue. The lower panels show the pulls before and after adding the basis corrections. The pull of adjacent bins are tested for statistical correlation. The correlation coefficient (r) is reported in the legend along with the pvalue used to test for lack of correlation. Basis functions are added until the pvalue is above 5%. 
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Additional Figure 6c:
The predicted multijet ZZ SvB distributions in the mixed data signal regions fit to their average. The plots show the results of fitting with an increasing number of basis functions, from one in the upper left figure, to five in the lower row. The predictions from each mixed model are shown separately in yellow by adding the mixed data set index to offset the signal SvB distribution. The black data points show the average of the predictions. The predictions, including the fitted basis corrections, are shown in blue. The lower panels show the pulls before and after adding the basis corrections. The pull of adjacent bins are tested for statistical correlation. The correlation coefficient (r) is reported in the legend along with the pvalue used to test for lack of correlation. Basis functions are added until the pvalue is above 5%. 
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Additional Figure 6d:
The predicted multijet ZZ SvB distributions in the mixed data signal regions fit to their average. The plots show the results of fitting with an increasing number of basis functions, from one in the upper left figure, to five in the lower row. The predictions from each mixed model are shown separately in yellow by adding the mixed data set index to offset the signal SvB distribution. The black data points show the average of the predictions. The predictions, including the fitted basis corrections, are shown in blue. The lower panels show the pulls before and after adding the basis corrections. The pull of adjacent bins are tested for statistical correlation. The correlation coefficient (r) is reported in the legend along with the pvalue used to test for lack of correlation. Basis functions are added until the pvalue is above 5%. 
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Additional Figure 6e:
The predicted multijet ZZ SvB distributions in the mixed data signal regions fit to their average. The plots show the results of fitting with an increasing number of basis functions, from one in the upper left figure, to five in the lower row. The predictions from each mixed model are shown separately in yellow by adding the mixed data set index to offset the signal SvB distribution. The black data points show the average of the predictions. The predictions, including the fitted basis corrections, are shown in blue. The lower panels show the pulls before and after adding the basis corrections. The pull of adjacent bins are tested for statistical correlation. The correlation coefficient (r) is reported in the legend along with the pvalue used to test for lack of correlation. Basis functions are added until the pvalue is above 5%. 
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Additional Figure 7:
The predicted multijet ZH SvB distributions in the mixed data signal regions fit to their average. The plots show the results of fitting with an increasing number of basis functions, from one in the upper left figure, to four in the lower right. The predictions from each mixed model are shown separately in yellow by adding the mixed data set index to offset the signal SvB distribution. The black data points show the average of the predictions. The predictions, including the fitted basis corrections, are shown in blue. The lower panels show the pulls before and after adding the basis corrections. The pull of adjacent bins are tested for statistical correlation. The correlation coefficient (r) is reported in the legend along with the pvalue used to test for lack of correlation. Basis functions are added until the pvalue is above 5%. 
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Additional Figure 7a:
The predicted multijet ZH SvB distributions in the mixed data signal regions fit to their average. The plots show the results of fitting with an increasing number of basis functions, from one in the upper left figure, to four in the lower right. The predictions from each mixed model are shown separately in yellow by adding the mixed data set index to offset the signal SvB distribution. The black data points show the average of the predictions. The predictions, including the fitted basis corrections, are shown in blue. The lower panels show the pulls before and after adding the basis corrections. The pull of adjacent bins are tested for statistical correlation. The correlation coefficient (r) is reported in the legend along with the pvalue used to test for lack of correlation. Basis functions are added until the pvalue is above 5%. 
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Additional Figure 7b:
The predicted multijet ZH SvB distributions in the mixed data signal regions fit to their average. The plots show the results of fitting with an increasing number of basis functions, from one in the upper left figure, to four in the lower right. The predictions from each mixed model are shown separately in yellow by adding the mixed data set index to offset the signal SvB distribution. The black data points show the average of the predictions. The predictions, including the fitted basis corrections, are shown in blue. The lower panels show the pulls before and after adding the basis corrections. The pull of adjacent bins are tested for statistical correlation. The correlation coefficient (r) is reported in the legend along with the pvalue used to test for lack of correlation. Basis functions are added until the pvalue is above 5%. 
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Additional Figure 7c:
The predicted multijet ZH SvB distributions in the mixed data signal regions fit to their average. The plots show the results of fitting with an increasing number of basis functions, from one in the upper left figure, to four in the lower right. The predictions from each mixed model are shown separately in yellow by adding the mixed data set index to offset the signal SvB distribution. The black data points show the average of the predictions. The predictions, including the fitted basis corrections, are shown in blue. The lower panels show the pulls before and after adding the basis corrections. The pull of adjacent bins are tested for statistical correlation. The correlation coefficient (r) is reported in the legend along with the pvalue used to test for lack of correlation. Basis functions are added until the pvalue is above 5%. 
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Additional Figure 7d:
The predicted multijet ZH SvB distributions in the mixed data signal regions fit to their average. The plots show the results of fitting with an increasing number of basis functions, from one in the upper left figure, to four in the lower right. The predictions from each mixed model are shown separately in yellow by adding the mixed data set index to offset the signal SvB distribution. The black data points show the average of the predictions. The predictions, including the fitted basis corrections, are shown in blue. The lower panels show the pulls before and after adding the basis corrections. The pull of adjacent bins are tested for statistical correlation. The correlation coefficient (r) is reported in the legend along with the pvalue used to test for lack of correlation. Basis functions are added until the pvalue is above 5%. 
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Additional Figure 8:
Fits of the ZH background model to the observed signalregion yield in the mixed models. The black data points show the average of the mixed models, the yellow distributions the average of the multijet models. The lower panels show the pre and postfit pulls. The figure on the left (right) shows the fit with zero (one) unconstrained basis parameter(s). 
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Additional Figure 8a:
Fits of the ZH background model to the observed signalregion yield in the mixed models. The black data points show the average of the mixed models, the yellow distributions the average of the multijet models. The lower panels show the pre and postfit pulls. The figure on the left (right) shows the fit with zero (one) unconstrained basis parameter(s). 
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Additional Figure 8b:
Fits of the ZH background model to the observed signalregion yield in the mixed models. The black data points show the average of the mixed models, the yellow distributions the average of the multijet models. The lower panels show the pre and postfit pulls. The figure on the left (right) shows the fit with zero (one) unconstrained basis parameter(s). 
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Additional Figure 9:
The prefit signal SvB signal probability distributions in the ZZ region (left) and the ZH region (right). 
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Additional Figure 9a:
The prefit signal SvB signal probability distributions in the ZZ region (left) and the ZH region (right). 
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Additional Figure 9b:
The prefit signal SvB signal probability distributions in the ZZ region (left) and the ZH region (right). 
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Additional Figure 10:
The postfit signal plus background SvB signal probability distributions in the ZZ region (left) and the ZH region (right). 
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Additional Figure 10a:
The postfit signal plus background SvB signal probability distributions in the ZZ region (left) and the ZH region (right). 
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Additional Figure 10b:
The postfit signal plus background SvB signal probability distributions in the ZZ region (left) and the ZH region (right). 
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