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Signal yield from simulation (\cmsLeft) and from four-tag events in data (\cmsRight), as a function of \mlead and \msubl. The color scale to the right of each plot gives the range of values. The signal region is defined by the union of the regions enclosed by the dashed red contours.

Signal yield from simulation (\cmsLeft) and from four-tag events in data (\cmsRight), as a function of \mlead and \msubl. The color scale to the right of each plot gives the range of values. The signal region is defined by the union of the regions enclosed by the dashed red contours.

Event selection acceptance times efficiency as a function of the generated four-body mass $m_{4\PQb}^{\text{gen}}$ for the \ZZ\ (\cmsLeft) and \ZH (\cmsRight) signals. The plots show the cumulative efficiency with respect to the inclusive sample. The expected $m_{4\PQb}^{\text{gen}}$ distributions of the inclusive \ZZ\ and \ZH\ events are shown by the gray-shaded areas with arbitrary normalization.

Event selection acceptance times efficiency as a function of the generated four-body mass $m_{4\PQb}^{\text{gen}}$ for the \ZZ\ (\cmsLeft) and \ZH (\cmsRight) signals. The plots show the cumulative efficiency with respect to the inclusive sample. The expected $m_{4\PQb}^{\text{gen}}$ distributions of the inclusive \ZZ\ and \ZH\ events are shown by the gray-shaded areas with arbitrary normalization.

A high-level sketch of the HCR classifier architecture. Boson-candidate jets are shown on the left with the three possible jet pairings. The HCR architecture is shown on 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. The output P(class) corresponds to the the probability that an event belongs to the corresponding class used in training.

Jet (\cmsLeft) and \btagged jet (\cmsRight) multiplicity distributions in the SB region. The black data points show the observed four-tag data, the blue distribution the \ttbar simulation, and the yellow histogram the three-tag multijet prior to the JCM corrections. The red histogram shows the result of the fit to the JCM model. The quality of the fit is given by the $\chi^2$ per degrees of freedom (dof) and corresponding $p$-value in the legend. The lower panels display the ratio of the data to the fit prediction.

Jet (\cmsLeft) and \btagged jet (\cmsRight) multiplicity distributions in the SB region. The black data points show the observed four-tag data, the blue distribution the \ttbar simulation, and the yellow histogram the three-tag multijet prior to the JCM corrections. The red histogram shows the result of the fit to the JCM model. The quality of the fit is given by the $\chi^2$ per degrees of freedom (dof) and corresponding $p$-value in the legend. The lower panels display the ratio of the data to the fit prediction.

Distributions of $\Delta R(j, j)_{\text{close}}$ (\cmsLeft) and $\Delta R(j, j)_{\text{complement}}$ (\cmsRight). The four-tag SB events are shown by the points. The QCD multijet distribution (yellow region) is from the three-tag SB sample after the JCM correction but before the FvT kinematic reweighting, and the \ttbar\ distribution (blue region) is from simulation. The lower panels display the ratio of the four-tag data to the total background, which is the sum of the QCD multijet and \ttbar\ distributions. The hatched area gives the statistical uncertainty in the background.

Distributions of $\Delta R(j, j)_{\text{close}}$ (\cmsLeft) and $\Delta R(j, j)_{\text{complement}}$ (\cmsRight). The four-tag SB events are shown by the points. The QCD multijet distribution (yellow region) is from the three-tag SB sample after the JCM correction but before the FvT kinematic reweighting, and the \ttbar\ distribution (blue region) is from simulation. The lower panels display the ratio of the four-tag data to the total background, which is the sum of the QCD multijet and \ttbar\ distributions. The hatched area gives the statistical uncertainty in the background.

Distributions of the signal probabilities for \ZZ (\cmsLeft) and \ZH (\cmsRight) in the SB region, respectively. The four-tag SB events are shown by the points. The QCD multijet distribution (yellow region) is from the three-tag SB sample after the JCM correction but before the FvT kinematic reweighting, and the \ttbar\ distribution (blue region) is from simulation. The lower panels display the ratio of the four-tag data to the total background, which is the sum of the QCD multijet and \ttbar\ distributions. The hatched area gives the statistical uncertainty in the background.

Distributions of the signal probabilities for \ZZ (\cmsLeft) and \ZH (\cmsRight) in the SB region, respectively. The four-tag SB events are shown by the points. The QCD multijet distribution (yellow region) is from the three-tag SB sample after the JCM correction but before the FvT kinematic reweighting, and the \ttbar\ distribution (blue region) is from simulation. The lower panels display the ratio of the four-tag data to the total background, which is the sum of the QCD multijet and \ttbar\ distributions. The hatched area gives the statistical uncertainty in the background.

The \dR distributions shown in Figure~\ref{fig:dR} after including the FvT corrections to the QCD multijet prediction.

The \dR distributions shown in Figure~\ref{fig:dR} after including the FvT corrections to the QCD multijet prediction.

Distribution of signal probabilities for \ZZ (\cmsLeft) and \ZH (\cmsRight) events in the SB region after including the FvT corrections to the QCD multijet prediction.

Distribution of signal probabilities for \ZZ (\cmsLeft) and \ZH (\cmsRight) events in the SB region after including the FvT corrections to the QCD multijet prediction.

An illustration of the hemisphere mixing procedure, adapted from Ref.~\cite{CMS:2018sxu}. Three-tag events are divided into two halves by cutting along the axis perpendicular to the transverse thrust axis. In a preliminary step, each event in the four-tag data set is split into two hemispheres that are collected in a library of hemispheres. Once the library is created, each three-tag event is used as a basis for creating a synthetic event. These are constructed by picking the two hemispheres from the library that are most similar to the hemispheres making up the original event.

Distribution of signal probabilities for \ZZ (upper row) and \ZH (lower row) events in the sideband (left) and signal regions (right). The four-tag events are shown by the points. The QCD multijet distribution before the FvT corrections is given by the yellow region, and the simulated \ttbar\ distribution by the blue area. The average of the mixed models (red) provides a high-event-count proxy of the 4\PQb background (black) that allows the extrapolation of the background model to be tested precisely. The lower panels display the ratio of the four-tag data to the average of the mixed models (red) and to the QCD multijet distribution (black).

Distribution of signal probabilities for \ZZ (upper row) and \ZH (lower row) events in the sideband (left) and signal regions (right). The four-tag events are shown by the points. The QCD multijet distribution before the FvT corrections is given by the yellow region, and the simulated \ttbar\ distribution by the blue area. The average of the mixed models (red) provides a high-event-count proxy of the 4\PQb background (black) that allows the extrapolation of the background model to be tested precisely. The lower panels display the ratio of the four-tag data to the average of the mixed models (red) and to the QCD multijet distribution (black).

Distribution of signal probabilities for \ZZ (upper row) and \ZH (lower row) events in the sideband (left) and signal regions (right). The four-tag events are shown by the points. The QCD multijet distribution before the FvT corrections is given by the yellow region, and the simulated \ttbar\ distribution by the blue area. The average of the mixed models (red) provides a high-event-count proxy of the 4\PQb background (black) that allows the extrapolation of the background model to be tested precisely. The lower panels display the ratio of the four-tag data to the average of the mixed models (red) and to the QCD multijet distribution (black).

Distribution of signal probabilities for \ZZ (upper row) and \ZH (lower row) events in the sideband (left) and signal regions (right). The four-tag events are shown by the points. The QCD multijet distribution before the FvT corrections is given by the yellow region, and the simulated \ttbar\ distribution by the blue area. The average of the mixed models (red) provides a high-event-count proxy of the 4\PQb background (black) that allows the extrapolation of the background model to be tested precisely. The lower panels display the ratio of the four-tag data to the average of the mixed models (red) and to the QCD multijet distribution (black).

The distributions of the \ZZ (\cmsLeft) and \ZH (\cmsRight) signal probabilities. The black data points show the average of the mixed models. The yellow and blue distributions show the average of the QCD multijet models and the \ttbar\ simulation, respectively. The red histogram displays the post-fit results of the data fit to the background model. The \ZZ channel data distribution is fit with all five basic coefficients constrained, while the \ZH channel distribution has two of the four coefficients unconstrained. The lower panels give the pre- (blue) and post-fit (red) pulls.

The distributions of the \ZZ (\cmsLeft) and \ZH (\cmsRight) signal probabilities. The black data points show the average of the mixed models. The yellow and blue distributions show the average of the QCD multijet models and the \ttbar\ simulation, respectively. The red histogram displays the post-fit results of the data fit to the background model. The \ZZ channel data distribution is fit with all five basic coefficients constrained, while the \ZH channel distribution has two of the four coefficients unconstrained. The lower panels give the pre- (blue) and post-fit (red) pulls.

Distributions of signal probabilities for \ZZ (\cmsLeft) and \ZH (\cmsRight) channels (points), along with the post-fit QCD multijet (yellow region) plus \ttbar\ (blue region) distributions. The \ZH and \ZZ signal distributions scaled to the fitted signal strengths are shown, stacked on top of the background prediction. The expected \ZH (red histograms) and \ZZ (green histograms) signal channel distributions are also shown separately, multiplied by 100 for visibility. The lower panels display the ratio of the data to the result of the signal plus background fit, with the hatched area showing the uncertainty in the combined fit.

Distributions of signal probabilities for \ZZ (\cmsLeft) and \ZH (\cmsRight) channels (points), along with the post-fit QCD multijet (yellow region) plus \ttbar\ (blue region) distributions. The \ZH and \ZZ signal distributions scaled to the fitted signal strengths are shown, stacked on top of the background prediction. The expected \ZH (red histograms) and \ZZ (green histograms) signal channel distributions are also shown separately, multiplied by 100 for visibility. The lower panels display the ratio of the data to the result of the signal plus background fit, with the hatched area showing the uncertainty in the combined fit.