CMSHIG22011 ; CERNEP2024026  
Search for ZZ and ZH production in the $ \mathrm{b} \bar{\mathrm{b}}\mathrm{b} \bar{\mathrm{b}} $ final state using protonproton collisions at $ \sqrt{s}= $ 13 TeV  
CMS Collaboration  
29 March 2024  
EPJC 84 (2024) 712  
Abstract: A search for ZZ and ZH production in the $ \mathrm{b} \bar{\mathrm{b}}\mathrm{b} \bar{\mathrm{b}} $ final state is presented, where H is the standard model (SM) Higgs boson. The search uses an event sample of protonproton collisions corresponding to an integrated luminosity of 133 fb$ ^{1} $ collected at a centerofmass energy of 13 TeV with the CMS detector at the CERN LHC. The analysis introduces several novel techniques for deriving and validating a multidimensional background model based on control samples in data. A multiclass multivariate classifier customized for the $ \mathrm{b} \bar{\mathrm{b}}\mathrm{b} \bar{\mathrm{b}} $ final state is developed to derive the background model and extract the signal. The data are found to be consistent, within uncertainties, with the SM predictions. The observed (expected) upper limits at 95% confidence level are found to be 3.8 (3.8) and 5.0 (2.9) times the SM prediction for the ZZ and ZH production cross sections, respectively.  
Links: eprint arXiv:2403.20241 [hepex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; 
Figures & Tables  Summary  Additional Figures  References  CMS Publications 

Figures  
png pdf 
Figure 1:
Signal yield from simulation (left) and from fourtag events in data (right), as a function of $ m_{\mathrm{jj}}^{\text{lead}} $ and $ m_{\mathrm{jj}}^{\text{subl}} $. 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. 
png pdf 
Figure 1a:
Signal yield from simulation (left) and from fourtag events in data (right), as a function of $ m_{\mathrm{jj}}^{\text{lead}} $ and $ m_{\mathrm{jj}}^{\text{subl}} $. 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. 
png pdf 
Figure 1b:
Signal yield from simulation (left) and from fourtag events in data (right), as a function of $ m_{\mathrm{jj}}^{\text{lead}} $ and $ m_{\mathrm{jj}}^{\text{subl}} $. 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. 
png pdf 
Figure 2:
Event selection acceptance times efficiency as a function of the generated fourbody mass $ m_{4\mathrm{b}}^{\text{gen}} $ for the ZZ (left) and ZH (right) signals. The plots show the cumulative efficiency with respect to the inclusive sample. The expected $ m_{4\mathrm{b}}^{\text{gen}} $ distributions of the inclusive ZZ and ZH events are shown by the grayshaded areas with arbitrary normalization. 
png pdf 
Figure 2a:
Event selection acceptance times efficiency as a function of the generated fourbody mass $ m_{4\mathrm{b}}^{\text{gen}} $ for the ZZ (left) and ZH (right) signals. The plots show the cumulative efficiency with respect to the inclusive sample. The expected $ m_{4\mathrm{b}}^{\text{gen}} $ distributions of the inclusive ZZ and ZH events are shown by the grayshaded areas with arbitrary normalization. 
png pdf 
Figure 2b:
Event selection acceptance times efficiency as a function of the generated fourbody mass $ m_{4\mathrm{b}}^{\text{gen}} $ for the ZZ (left) and ZH (right) signals. The plots show the cumulative efficiency with respect to the inclusive sample. The expected $ m_{4\mathrm{b}}^{\text{gen}} $ distributions of the inclusive ZZ and ZH events are shown by the grayshaded areas with arbitrary normalization. 
png pdf 
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 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. 
png pdf 
Figure 4:
Jet (left) and btagged jet (right) multiplicity distributions in the SB region. The black data points show the observed fourtag data, the blue distribution the $ \mathrm{t} \bar{\mathrm{t}} $ simulation, and the yellow histogram the threetag 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. 
png pdf 
Figure 4a:
Jet (left) and btagged jet (right) multiplicity distributions in the SB region. The black data points show the observed fourtag data, the blue distribution the $ \mathrm{t} \bar{\mathrm{t}} $ simulation, and the yellow histogram the threetag 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. 
png pdf 
Figure 4b:
Jet (left) and btagged jet (right) multiplicity distributions in the SB region. The black data points show the observed fourtag data, the blue distribution the $ \mathrm{t} \bar{\mathrm{t}} $ simulation, and the yellow histogram the threetag 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. 
png pdf 
Figure 5:
Distributions of $ \Delta \text{R}(j, j)_{\text{close}} $ (left) and $ \Delta \text{R}(j, j)_{\text{complement}} $ (right). The fourtag SB events are shown by the points. The QCD multijet distribution (yellow region) is from the threetag SB sample after the JCM correction but before the FvT kinematic reweighting, and the $ \mathrm{t} \bar{\mathrm{t}} $ distribution (blue region) is from simulation. The lower panels display the ratio of the fourtag data to the total background, which is the sum of the QCD multijet and $ \mathrm{t} \bar{\mathrm{t}} $ distributions. The hatched area gives the statistical uncertainty in the background. 
png pdf 
Figure 5a:
Distributions of $ \Delta \text{R}(j, j)_{\text{close}} $ (left) and $ \Delta \text{R}(j, j)_{\text{complement}} $ (right). The fourtag SB events are shown by the points. The QCD multijet distribution (yellow region) is from the threetag SB sample after the JCM correction but before the FvT kinematic reweighting, and the $ \mathrm{t} \bar{\mathrm{t}} $ distribution (blue region) is from simulation. The lower panels display the ratio of the fourtag data to the total background, which is the sum of the QCD multijet and $ \mathrm{t} \bar{\mathrm{t}} $ distributions. The hatched area gives the statistical uncertainty in the background. 
png pdf 
Figure 5b:
Distributions of $ \Delta \text{R}(j, j)_{\text{close}} $ (left) and $ \Delta \text{R}(j, j)_{\text{complement}} $ (right). The fourtag SB events are shown by the points. The QCD multijet distribution (yellow region) is from the threetag SB sample after the JCM correction but before the FvT kinematic reweighting, and the $ \mathrm{t} \bar{\mathrm{t}} $ distribution (blue region) is from simulation. The lower panels display the ratio of the fourtag data to the total background, which is the sum of the QCD multijet and $ \mathrm{t} \bar{\mathrm{t}} $ distributions. The hatched area gives the statistical uncertainty in the background. 
png pdf 
Figure 6:
Distributions of the signal probabilities for ZZ (left) and ZH (right) in the SB region, respectively. The fourtag SB events are shown by the points. The QCD multijet distribution (yellow region) is from the threetag SB sample after the JCM correction but before the FvT kinematic reweighting, and the $ \mathrm{t} \bar{\mathrm{t}} $ distribution (blue region) is from simulation. The lower panels display the ratio of the fourtag data to the total background, which is the sum of the QCD multijet and $ \mathrm{t} \bar{\mathrm{t}} $ distributions. The hatched area gives the statistical uncertainty in the background. 
png pdf 
Figure 6a:
Distributions of the signal probabilities for ZZ (left) and ZH (right) in the SB region, respectively. The fourtag SB events are shown by the points. The QCD multijet distribution (yellow region) is from the threetag SB sample after the JCM correction but before the FvT kinematic reweighting, and the $ \mathrm{t} \bar{\mathrm{t}} $ distribution (blue region) is from simulation. The lower panels display the ratio of the fourtag data to the total background, which is the sum of the QCD multijet and $ \mathrm{t} \bar{\mathrm{t}} $ distributions. The hatched area gives the statistical uncertainty in the background. 
png pdf 
Figure 6b:
Distributions of the signal probabilities for ZZ (left) and ZH (right) in the SB region, respectively. The fourtag SB events are shown by the points. The QCD multijet distribution (yellow region) is from the threetag SB sample after the JCM correction but before the FvT kinematic reweighting, and the $ \mathrm{t} \bar{\mathrm{t}} $ distribution (blue region) is from simulation. The lower panels display the ratio of the fourtag data to the total background, which is the sum of the QCD multijet and $ \mathrm{t} \bar{\mathrm{t}} $ distributions. The hatched area gives the statistical uncertainty in the background. 
png pdf 
Figure 7:
The $ \Delta\text{R}(j,j) $ distributions shown in Figure 5 after including the FvT corrections to the QCD multijet prediction. 
png pdf 
Figure 7a:
The $ \Delta\text{R}(j,j) $ distributions shown in Figure 5 after including the FvT corrections to the QCD multijet prediction. 
png pdf 
Figure 7b:
The $ \Delta\text{R}(j,j) $ distributions shown in Figure 5 after including the FvT corrections to the QCD multijet prediction. 
png pdf 
Figure 8:
Distribution of signal probabilities for ZZ (left) and ZH (right) events in the SB region after including the FvT corrections to the QCD multijet prediction. 
png pdf 
Figure 8a:
Distribution of signal probabilities for ZZ (left) and ZH (right) events in the SB region after including the FvT corrections to the QCD multijet prediction. 
png pdf 
Figure 8b:
Distribution of signal probabilities for ZZ (left) and ZH (right) events in the SB region after including the FvT corrections to the QCD multijet prediction. 
png pdf 
Figure 9:
An illustration of the hemisphere mixing procedure, adapted from Ref. [20]. Threetag 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 fourtag data set is split into two hemispheres that are collected in a library of hemispheres. Once the library is created, each threetag 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. 
png pdf 
Figure 10:
Distribution of signal probabilities for ZZ (upper row) and ZH (lower row) events in the sideband (left) and signal regions (right). The fourtag events are shown by the points. The QCD multijet distribution before the FvT corrections is given by the yellow region, and the simulated $ \mathrm{t} \bar{\mathrm{t}} $ distribution by the blue area. The average of the mixed models (red) provides a higheventcount proxy of the 4b background (black) that allows the extrapolation of the background model to be tested precisely. The lower panels display the ratio of the fourtag data to the average of the mixed models (red) and to the QCD multijet distribution (black). 
png pdf 
Figure 10a:
Distribution of signal probabilities for ZZ (upper row) and ZH (lower row) events in the sideband (left) and signal regions (right). The fourtag events are shown by the points. The QCD multijet distribution before the FvT corrections is given by the yellow region, and the simulated $ \mathrm{t} \bar{\mathrm{t}} $ distribution by the blue area. The average of the mixed models (red) provides a higheventcount proxy of the 4b background (black) that allows the extrapolation of the background model to be tested precisely. The lower panels display the ratio of the fourtag data to the average of the mixed models (red) and to the QCD multijet distribution (black). 
png pdf 
Figure 10b:
Distribution of signal probabilities for ZZ (upper row) and ZH (lower row) events in the sideband (left) and signal regions (right). The fourtag events are shown by the points. The QCD multijet distribution before the FvT corrections is given by the yellow region, and the simulated $ \mathrm{t} \bar{\mathrm{t}} $ distribution by the blue area. The average of the mixed models (red) provides a higheventcount proxy of the 4b background (black) that allows the extrapolation of the background model to be tested precisely. The lower panels display the ratio of the fourtag data to the average of the mixed models (red) and to the QCD multijet distribution (black). 
png pdf 
Figure 10c:
Distribution of signal probabilities for ZZ (upper row) and ZH (lower row) events in the sideband (left) and signal regions (right). The fourtag events are shown by the points. The QCD multijet distribution before the FvT corrections is given by the yellow region, and the simulated $ \mathrm{t} \bar{\mathrm{t}} $ distribution by the blue area. The average of the mixed models (red) provides a higheventcount proxy of the 4b background (black) that allows the extrapolation of the background model to be tested precisely. The lower panels display the ratio of the fourtag data to the average of the mixed models (red) and to the QCD multijet distribution (black). 
png pdf 
Figure 10d:
Distribution of signal probabilities for ZZ (upper row) and ZH (lower row) events in the sideband (left) and signal regions (right). The fourtag events are shown by the points. The QCD multijet distribution before the FvT corrections is given by the yellow region, and the simulated $ \mathrm{t} \bar{\mathrm{t}} $ distribution by the blue area. The average of the mixed models (red) provides a higheventcount proxy of the 4b background (black) that allows the extrapolation of the background model to be tested precisely. The lower panels display the ratio of the fourtag data to the average of the mixed models (red) and to the QCD multijet distribution (black). 
png pdf 
Figure 11:
The distributions of the ZZ (left) and ZH (right) 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 $ \mathrm{t} \bar{\mathrm{t}} $ simulation, respectively. The red histogram displays the postfit 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 postfit (red) pulls. 
png pdf 
Figure 11a:
The distributions of the ZZ (left) and ZH (right) 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 $ \mathrm{t} \bar{\mathrm{t}} $ simulation, respectively. The red histogram displays the postfit 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 postfit (red) pulls. 
png pdf 
Figure 11b:
The distributions of the ZZ (left) and ZH (right) 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 $ \mathrm{t} \bar{\mathrm{t}} $ simulation, respectively. The red histogram displays the postfit 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 postfit (red) pulls. 
png pdf 
Figure 12:
Distributions of signal probabilities for ZZ (left) and ZH (right) channels (points), along with the postfit QCD multijet (yellow region) plus $ \mathrm{t} \bar{\mathrm{t}} $ (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. 
png pdf 
Figure 12a:
Distributions of signal probabilities for ZZ (left) and ZH (right) channels (points), along with the postfit QCD multijet (yellow region) plus $ \mathrm{t} \bar{\mathrm{t}} $ (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. 
png pdf 
Figure 12b:
Distributions of signal probabilities for ZZ (left) and ZH (right) channels (points), along with the postfit QCD multijet (yellow region) plus $ \mathrm{t} \bar{\mathrm{t}} $ (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. 
Tables  
png pdf 
Table 1:
Summary of the relative uncertainties form the various sources in the measured signal strength, expressed as a percentage of the total uncertainty for the ZZ and ZH channels. The two uncertainties coming from the background modeling are given separately in parentheses, as well as their sum. The total systematic uncertainties shown include the effects of correlations. 
png pdf 
Table 2:
Expected and observed ZZ and ZH signal strengths and their corresponding 95% CL upper limits. The expected signal strengths and the corresponding expected upper limits shown in parentheses include only the statistical uncertainties. The upper limits are obtained from a fit to the SvB signal probabilities under the hypothesis of no $ \mathrm{Z}\mathrm{Z}\to 4\mathrm{b} $ or $ \mathrm{Z}\mathrm{H}\to 4\mathrm{b} $ signal. 
Summary 
A search for ZZ and ZH production in the 4b final state is 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} $. The analysis benefits from a multiclass multivariate classifier, which uses convolutions to solve the combinatoric jet pairing 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 the background modeling uncertainties, using a synthetic data sample, produced using a hemisphere mixing procedure, allows both the uncertainty in the background model and its variance to be measured with a precision better than the statistical uncertainties in the selected signalregion events. While these techniques are developed and demonstrated in the ZZ and $ \mathrm{Z}\mathrm{H} \to $ 4b searches, they are directly applicable to the $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analysis. The observed (expected) 95% CL upper limits on the $ \mathrm{Z}\mathrm{Z} \to 4\mathrm{b} $ and $ \mathrm{Z}\mathrm{H} \to 4\mathrm{b} $ production cross sections correspond to 3.8 (3.8) and 5.0 (2.9) times the standard model prediction, respectively. 
Additional Figures  
png pdf 
Additional Figure 1:
Acceptance times efficiency as a function of the generated fourbody $ m_{4\mathrm{b}}^{\textrm{gen}} $ for the five different event selection requirements for simulated ZZ (left) and ZH (right). 
png pdf 
Additional Figure 1a:
Acceptance times efficiency as a function of the generated fourbody $ m_{4\mathrm{b}}^{\textrm{gen}} $ for the five different event selection requirements for simulated ZZ (left) and ZH (right). 
png pdf 
Additional Figure 1b:
Acceptance times efficiency as a function of the generated fourbody $ m_{4\mathrm{b}}^{\textrm{gen}} $ for the five different event selection requirements for simulated ZZ (left) and ZH (right). 
png pdf 
Additional Figure 2:
The ZZ (left) and ZH (right) signal efficiences from simulation versus the background efficiency for the nominal HCR SvB classier including additional jets, and for a simpler twodimensional likelihood classifier using the two dijet invariant masses. A version of the HCR SvB classifier that does not include additional jets is also shown. 
png pdf 
Additional Figure 2a:
The ZZ (left) and ZH (right) signal efficiences from simulation versus the background efficiency for the nominal HCR SvB classier including additional jets, and for a simpler twodimensional likelihood classifier using the two dijet invariant masses. A version of the HCR SvB classifier that does not include additional jets is also shown. 
png pdf 
Additional Figure 2b:
The ZZ (left) and ZH (right) signal efficiences from simulation versus the background efficiency for the nominal HCR SvB classier including additional jets, and for a simpler twodimensional likelihood classifier using the two dijet invariant masses. A version of the HCR SvB classifier that does not include additional jets is also shown. 
png pdf 
Additional Figure 3:
Distributions of the FvT classifier weights before (left) and after (right) applying the FvT corrections for the fourtag data (points), and the QCD multijet and $ \mathrm{t} \bar{\mathrm{t}} $ backgrounds (yellow and blue distributions, respectively). The lower panels display the ratio of the data to the sum of the QCD multijet and $ \mathrm{t} \bar{\mathrm{t}} $ distributions. The hatched region represents the uncertainties in the background. 
png pdf 
Additional Figure 3a:
Distributions of the FvT classifier weights before (left) and after (right) applying the FvT corrections for the fourtag data (points), and the QCD multijet and $ \mathrm{t} \bar{\mathrm{t}} $ backgrounds (yellow and blue distributions, respectively). The lower panels display the ratio of the data to the sum of the QCD multijet and $ \mathrm{t} \bar{\mathrm{t}} $ distributions. The hatched region represents the uncertainties in the background. 
png pdf 
Additional Figure 3b:
Distributions of the FvT classifier weights before (left) and after (right) applying the FvT corrections for the fourtag data (points), and the QCD multijet and $ \mathrm{t} \bar{\mathrm{t}} $ backgrounds (yellow and blue distributions, respectively). The lower panels display the ratio of the data to the sum of the QCD multijet and $ \mathrm{t} \bar{\mathrm{t}} $ distributions. The hatched region represents the uncertainties in the background. 
png pdf 
Additional Figure 4:
The SvB signal probability distributions in the ZZ SR for one of the mixed data samples (left) and the average of the fifteen mixed samples (right). The points show the mixed model results, the QCD multijet and $ \mathrm{t} \bar{\mathrm{t}} $ background distributions are shown by the yellow and blue regions, respectively. The expected signal distributions for ZZ and ZH are shown by the green and red histograms, multiplied by 100. The lower panels display the ratio of the mixed sample distribution to the sum of the QCD multijet and $ \mathrm{t} \bar{\mathrm{t}} $ distributions. The hatched area gives the statistical uncertainty in the ratio. 
png pdf 
Additional Figure 4a:
The SvB signal probability distributions in the ZZ SR for one of the mixed data samples (left) and the average of the fifteen mixed samples (right). The points show the mixed model results, the QCD multijet and $ \mathrm{t} \bar{\mathrm{t}} $ background distributions are shown by the yellow and blue regions, respectively. The expected signal distributions for ZZ and ZH are shown by the green and red histograms, multiplied by 100. The lower panels display the ratio of the mixed sample distribution to the sum of the QCD multijet and $ \mathrm{t} \bar{\mathrm{t}} $ distributions. The hatched area gives the statistical uncertainty in the ratio. 
png pdf 
Additional Figure 4b:
The SvB signal probability distributions in the ZZ SR for one of the mixed data samples (left) and the average of the fifteen mixed samples (right). The points show the mixed model results, the QCD multijet and $ \mathrm{t} \bar{\mathrm{t}} $ background distributions are shown by the yellow and blue regions, respectively. The expected signal distributions for ZZ and ZH are shown by the green and red histograms, multiplied by 100. The lower panels display the ratio of the mixed sample distribution to the sum of the QCD multijet and $ \mathrm{t} \bar{\mathrm{t}} $ distributions. The hatched area gives the statistical uncertainty in the ratio. 
png pdf 
Additional Figure 5:
The SvB signal probability distributions in the ZH SR for one of the mixed data samples (left) and the average of the fifteen mixed samples (right). The points show the mixed model results, the QCD multijet and $ \mathrm{t} \bar{\mathrm{t}} $ background distributions are shown by the yellow and blue regions, respectively. The expected signal distributions for ZZ and ZH are shown by the green and red histograms, multiplied by 100. The lower panels display the ratio of the mixed sample distribution to the sum of the QCD multijet and $ \mathrm{t} \bar{\mathrm{t}} $ distributions. The hatched area gives the statistical uncertainty in the ratio. 
png pdf 
Additional Figure 5a:
The SvB signal probability distributions in the ZH SR for one of the mixed data samples (left) and the average of the fifteen mixed samples (right). The points show the mixed model results, the QCD multijet and $ \mathrm{t} \bar{\mathrm{t}} $ background distributions are shown by the yellow and blue regions, respectively. The expected signal distributions for ZZ and ZH are shown by the green and red histograms, multiplied by 100. The lower panels display the ratio of the mixed sample distribution to the sum of the QCD multijet and $ \mathrm{t} \bar{\mathrm{t}} $ distributions. The hatched area gives the statistical uncertainty in the ratio. 
png pdf 
Additional Figure 5b:
The SvB signal probability distributions in the ZH SR for one of the mixed data samples (left) and the average of the fifteen mixed samples (right). The points show the mixed model results, the QCD multijet and $ \mathrm{t} \bar{\mathrm{t}} $ background distributions are shown by the yellow and blue regions, respectively. The expected signal distributions for ZZ and ZH are shown by the green and red histograms, multiplied by 100. The lower panels display the ratio of the mixed sample distribution to the sum of the QCD multijet and $ \mathrm{t} \bar{\mathrm{t}} $ distributions. The hatched area gives the statistical uncertainty in the ratio. 
png pdf 
Additional Figure 6:
The predicted QCD multijet ZZ SvB probability distributions for each of the 15 mixed data sample SRs (yellow regions). The distribution from each mixed data sample is offset by the data sample index number. The black points give the average of the 15 data samples. The solid blue curves show a fit to the individual distributions using an increasing number of basis functions from one in the upper left plot to five in the lowest plot. The lower panels show the pulls before (yellow histogram) and after (blue histogram) adding the basis corrections. The correlation coefficient (r) for a fit testing for correlations is given in the legend, along with the pvalue used to test for lack of correlation. Basis functions are added until the pvalue is greater than 5%. 
png pdf 
Additional Figure 6a:
The predicted QCD multijet ZZ SvB probability distributions for each of the 15 mixed data sample SRs (yellow regions). The distribution from each mixed data sample is offset by the data sample index number. The black points give the average of the 15 data samples. The solid blue curves show a fit to the individual distributions using an increasing number of basis functions from one in the upper left plot to five in the lowest plot. The lower panels show the pulls before (yellow histogram) and after (blue histogram) adding the basis corrections. The correlation coefficient (r) for a fit testing for correlations is given in the legend, along with the pvalue used to test for lack of correlation. Basis functions are added until the pvalue is greater than 5%. 
png pdf 
Additional Figure 6b:
The predicted QCD multijet ZZ SvB probability distributions for each of the 15 mixed data sample SRs (yellow regions). The distribution from each mixed data sample is offset by the data sample index number. The black points give the average of the 15 data samples. The solid blue curves show a fit to the individual distributions using an increasing number of basis functions from one in the upper left plot to five in the lowest plot. The lower panels show the pulls before (yellow histogram) and after (blue histogram) adding the basis corrections. The correlation coefficient (r) for a fit testing for correlations is given in the legend, along with the pvalue used to test for lack of correlation. Basis functions are added until the pvalue is greater than 5%. 
png pdf 
Additional Figure 6c:
The predicted QCD multijet ZZ SvB probability distributions for each of the 15 mixed data sample SRs (yellow regions). The distribution from each mixed data sample is offset by the data sample index number. The black points give the average of the 15 data samples. The solid blue curves show a fit to the individual distributions using an increasing number of basis functions from one in the upper left plot to five in the lowest plot. The lower panels show the pulls before (yellow histogram) and after (blue histogram) adding the basis corrections. The correlation coefficient (r) for a fit testing for correlations is given in the legend, along with the pvalue used to test for lack of correlation. Basis functions are added until the pvalue is greater than 5%. 
png pdf 
Additional Figure 6d:
The predicted QCD multijet ZZ SvB probability distributions for each of the 15 mixed data sample SRs (yellow regions). The distribution from each mixed data sample is offset by the data sample index number. The black points give the average of the 15 data samples. The solid blue curves show a fit to the individual distributions using an increasing number of basis functions from one in the upper left plot to five in the lowest plot. The lower panels show the pulls before (yellow histogram) and after (blue histogram) adding the basis corrections. The correlation coefficient (r) for a fit testing for correlations is given in the legend, along with the pvalue used to test for lack of correlation. Basis functions are added until the pvalue is greater than 5%. 
png pdf 
Additional Figure 6e:
The predicted QCD multijet ZZ SvB probability distributions for each of the 15 mixed data sample SRs (yellow regions). The distribution from each mixed data sample is offset by the data sample index number. The black points give the average of the 15 data samples. The solid blue curves show a fit to the individual distributions using an increasing number of basis functions from one in the upper left plot to five in the lowest plot. The lower panels show the pulls before (yellow histogram) and after (blue histogram) adding the basis corrections. The correlation coefficient (r) for a fit testing for correlations is given in the legend, along with the pvalue used to test for lack of correlation. Basis functions are added until the pvalue is greater than 5%. 
png pdf 
Additional Figure 7:
The predicted QCD multijet ZH SvB probability distributions for each of the 15 mixed data sample SRs (yellow regions). The distribution from each mixed data sample is offset by the data sample index number. The black points give the average of the 15 data samples. The solid blue curves show a fit to the individual distributions using an increasing number of basis functions from one in the upper left plot to five in the lowest plot. The lower panels show the pulls before (yellow histogram) and after (blue histogram) adding the basis corrections. The correlation coefficient (r) for a fit testing for correlations is given in the legend, along with the pvalue used to test for lack of correlation. Basis functions are added until the pvalue is greater than 5%. 
png pdf 
Additional Figure 7a:
The predicted QCD multijet ZH SvB probability distributions for each of the 15 mixed data sample SRs (yellow regions). The distribution from each mixed data sample is offset by the data sample index number. The black points give the average of the 15 data samples. The solid blue curves show a fit to the individual distributions using an increasing number of basis functions from one in the upper left plot to five in the lowest plot. The lower panels show the pulls before (yellow histogram) and after (blue histogram) adding the basis corrections. The correlation coefficient (r) for a fit testing for correlations is given in the legend, along with the pvalue used to test for lack of correlation. Basis functions are added until the pvalue is greater than 5%. 
png pdf 
Additional Figure 7b:
The predicted QCD multijet ZH SvB probability distributions for each of the 15 mixed data sample SRs (yellow regions). The distribution from each mixed data sample is offset by the data sample index number. The black points give the average of the 15 data samples. The solid blue curves show a fit to the individual distributions using an increasing number of basis functions from one in the upper left plot to five in the lowest plot. The lower panels show the pulls before (yellow histogram) and after (blue histogram) adding the basis corrections. The correlation coefficient (r) for a fit testing for correlations is given in the legend, along with the pvalue used to test for lack of correlation. Basis functions are added until the pvalue is greater than 5%. 
png pdf 
Additional Figure 7c:
The predicted QCD multijet ZH SvB probability distributions for each of the 15 mixed data sample SRs (yellow regions). The distribution from each mixed data sample is offset by the data sample index number. The black points give the average of the 15 data samples. The solid blue curves show a fit to the individual distributions using an increasing number of basis functions from one in the upper left plot to five in the lowest plot. The lower panels show the pulls before (yellow histogram) and after (blue histogram) adding the basis corrections. The correlation coefficient (r) for a fit testing for correlations is given in the legend, along with the pvalue used to test for lack of correlation. Basis functions are added until the pvalue is greater than 5%. 
png pdf 
Additional Figure 7d:
The predicted QCD multijet ZH SvB probability distributions for each of the 15 mixed data sample SRs (yellow regions). The distribution from each mixed data sample is offset by the data sample index number. The black points give the average of the 15 data samples. The solid blue curves show a fit to the individual distributions using an increasing number of basis functions from one in the upper left plot to five in the lowest plot. The lower panels show the pulls before (yellow histogram) and after (blue histogram) adding the basis corrections. The correlation coefficient (r) for a fit testing for correlations is given in the legend, along with the pvalue used to test for lack of correlation. Basis functions are added until the pvalue is greater than 5%. 
png pdf 
Additional Figure 8:
Distributions of the ZH signal probability for the average observed SR yields from the mixed models. The yellow and blue regions give the distributions of the average of the QCD multijet models and the $ \mathrm{t} \bar{\mathrm{t}} $ simulation, respectively. The red histogram displays the postfit results of the data fit to the background model with 0 (left) and 1 unconstrained parameter (right) in the fit. The $ \chi^2 $ / dof and the pvalue from the fit are shown in the legend. The lower panels give the pre (blue histograms) and postfit (red histograms) pulls. 
png pdf 
Additional Figure 8a:
Distributions of the ZH signal probability for the average observed SR yields from the mixed models. The yellow and blue regions give the distributions of the average of the QCD multijet models and the $ \mathrm{t} \bar{\mathrm{t}} $ simulation, respectively. The red histogram displays the postfit results of the data fit to the background model with 0 (left) and 1 unconstrained parameter (right) in the fit. The $ \chi^2 $ / dof and the pvalue from the fit are shown in the legend. The lower panels give the pre (blue histograms) and postfit (red histograms) pulls. 
png pdf 
Additional Figure 8b:
Distributions of the ZH signal probability for the average observed SR yields from the mixed models. The yellow and blue regions give the distributions of the average of the QCD multijet models and the $ \mathrm{t} \bar{\mathrm{t}} $ simulation, respectively. The red histogram displays the postfit results of the data fit to the background model with 0 (left) and 1 unconstrained parameter (right) in the fit. The $ \chi^2 $ / dof and the pvalue from the fit are shown in the legend. The lower panels give the pre (blue histograms) and postfit (red histograms) pulls. 
png pdf 
Additional Figure 9:
The prefit signal SvB signal probability distributions for the ZZ (left) and ZH (right). The black points show the fourtag events from data. The yellow and blue regions show the predictions from the QCD multijet model and the $ \mathrm{t} \bar{\mathrm{t}} $ simulation, respectively. The predictions for the ZH and ZZ signal distributions are given by the red and and blue histograms, respectively, multiplied by 100. The lower panels show the ratio of the data to the background, with the hatched area representing the uncertainty in the background. 
png pdf 
Additional Figure 9a:
The prefit signal SvB signal probability distributions for the ZZ (left) and ZH (right). The black points show the fourtag events from data. The yellow and blue regions show the predictions from the QCD multijet model and the $ \mathrm{t} \bar{\mathrm{t}} $ simulation, respectively. The predictions for the ZH and ZZ signal distributions are given by the red and and blue histograms, respectively, multiplied by 100. The lower panels show the ratio of the data to the background, with the hatched area representing the uncertainty in the background. 
png pdf 
Additional Figure 9b:
The prefit signal SvB signal probability distributions for the ZZ (left) and ZH (right). The black points show the fourtag events from data. The yellow and blue regions show the predictions from the QCD multijet model and the $ \mathrm{t} \bar{\mathrm{t}} $ simulation, respectively. The predictions for the ZH and ZZ signal distributions are given by the red and and blue histograms, respectively, multiplied by 100. The lower panels show the ratio of the data to the background, with the hatched area representing the uncertainty in the background. 
png pdf 
Additional Figure 10:
Distributions of signal probabilities for ZZ (left) and ZH (right) channels (points), along with the post backgroundonly fit QCD multijet (yellow region) plus $ \mathrm{t} \bar{\mathrm{t}} $ (blue region) distributions. The expected ZH (red lines) and ZZ (blue lines) signal channel distributions are shown, multiplied by 100 for visibility. The lower panels display the ratio of the data to the total background, with the hatched area showing the uncertainty in the background. 
png pdf 
Additional Figure 10a:
Distributions of signal probabilities for ZZ (left) and ZH (right) channels (points), along with the post backgroundonly fit QCD multijet (yellow region) plus $ \mathrm{t} \bar{\mathrm{t}} $ (blue region) distributions. The expected ZH (red lines) and ZZ (blue lines) signal channel distributions are shown, multiplied by 100 for visibility. The lower panels display the ratio of the data to the total background, with the hatched area showing the uncertainty in the background. 
png pdf 
Additional Figure 10b:
Distributions of signal probabilities for ZZ (left) and ZH (right) channels (points), along with the post backgroundonly fit QCD multijet (yellow region) plus $ \mathrm{t} \bar{\mathrm{t}} $ (blue region) distributions. The expected ZH (red lines) and ZZ (blue lines) signal channel distributions are shown, multiplied by 100 for visibility. The lower panels display the ratio of the data to the total background, with the hatched area showing the uncertainty in the background. 
png pdf 
Additional Figure 11:
Distributions of $\Delta \text{R}_{\mathrm{jj}}^{\text{lead}}$ (left) and $\Delta \text{R}_{\mathrm{jj}}^{\text{subl}}$ (right) as a function of the fourjet mass for signal (top) and fourtag data (bottom). Events falling between the red lines satisfy the selection defined in Eq. 2. 
png pdf 
Additional Figure 11a:
Distributions of $\Delta \text{R}_{\mathrm{jj}}^{\text{lead}}$ (left) and $\Delta \text{R}_{\mathrm{jj}}^{\text{subl}}$ (right) as a function of the fourjet mass for signal (top) and fourtag data (bottom). Events falling between the red lines satisfy the selection defined in Eq. 2. 
png pdf 
Additional Figure 11b:
Distributions of $\Delta \text{R}_{\mathrm{jj}}^{\text{lead}}$ (left) and $\Delta \text{R}_{\mathrm{jj}}^{\text{subl}}$ (right) as a function of the fourjet mass for signal (top) and fourtag data (bottom). Events falling between the red lines satisfy the selection defined in Eq. 2. 
png pdf 
Additional Figure 11c:
Distributions of $\Delta \text{R}_{\mathrm{jj}}^{\text{lead}}$ (left) and $\Delta \text{R}_{\mathrm{jj}}^{\text{subl}}$ (right) as a function of the fourjet mass for signal (top) and fourtag data (bottom). Events falling between the red lines satisfy the selection defined in Eq. 2. 
png pdf 
Additional Figure 11d:
Distributions of $\Delta \text{R}_{\mathrm{jj}}^{\text{lead}}$ (left) and $\Delta \text{R}_{\mathrm{jj}}^{\text{subl}}$ (right) as a function of the fourjet mass for signal (top) and fourtag data (bottom). Events falling between the red lines satisfy the selection defined in Eq. 2. 
png pdf 
Additional Figure 12:
Distribution of background probabilities, QCDmultijet (left) and $ \mathrm{t} \overline{\mathrm{t}} $ (right), for events in the SR region after including the FvT corrections to the QCD multijet prediction. 
png pdf 
Additional Figure 12a:
Distribution of background probabilities, QCDmultijet (left) and $ \mathrm{t} \overline{\mathrm{t}} $ (right), for events in the SR region after including the FvT corrections to the QCD multijet prediction. 
png pdf 
Additional Figure 12b:
Distribution of background probabilities, QCDmultijet (left) and $ \mathrm{t} \overline{\mathrm{t}} $ (right), for events in the SR region after including the FvT corrections to the QCD multijet prediction. 
References  
1  M. Cepeda et al.  Report from working group 2: Higgs physics at the HLLHC and HELHC  CERN Yellow Rep. Monogr. 7 (2019) 221  1902.00134 
2  B. D. Micco, M. Gouzevitch, J. Mazzitelli, and C. Vernieri  Higgs boson potential at colliders: status and perspectives  Rev. Phys. 5 (2020) 100045  1910.00012 
3  CMS Collaboration  A portrait of the Higgs boson by the CMS experiment ten years after the discovery  Nature 607 (2022) 60  CMSHIG22001 2207.00043 
4  CMS Collaboration  Search for Higgs boson pair production in the four b quark final state in protonproton collisions at $ \sqrt{s}= $ 13 TeV  PRL 129 (2022) 081802  CMSHIG20005 2202.09617 
5  ATLAS Collaboration  Search for Higgs boson pair production in the two bottom quarks plus two photons final state in pp collisions at $ \sqrt{s}= $ 13 TeV with the ATLAS detector  PRD 106 (2022) 052001  2112.11876 
6  CMS Collaboration  Search for nonresonant Higgs boson pair production in final state with two bottom quarks and two tau leptons in protonproton collisions at $ \sqrt{s} = $ 13 TeV  PLB 842 (2023) 137531  CMSHIG20010 2206.09401 
7  ATLAS Collaboration  Search for resonant and nonresonant Higgs boson pair production in the $ \mathrm{b}\overline{\mathrm{b}}{\tau}^{+}{\tau}^{} $ decay channel using 13 TeV pp collision data from the ATLAS detector  JHEP 07 (2023) 040  2209.10910 
8  CMS Collaboration  Search for nonresonant Higgs boson pair production in final states with two bottom quarks and two photons in protonproton collisions at $ \sqrt{s} = $ 13 TeV  JHEP 03 (2021) 257  CMSHIG19018 2011.12373 
9  ATLAS Collaboration  Search for nonresonant pair production of Higgs bosons in the $ \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ final state in pp collisions at $ \sqrt{s}= $ 13 TeV with the ATLAS detector  PRD 108 (2023) 052003  2301.03212 
10  CMS Collaboration  Search for nonresonant pair production of highly energetic Higgs bosons decaying to bottom quarks  PRL 131 (2023) 041803  2205.06667 
11  ATLAS Collaboration  Search for pair production of Higgs bosons in the $ \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ final state using protonproton collisions at $ \sqrt{s} = $ 13 TeV with the ATLAS detector  JHEP 01 (2019) 030  1804.06174 
12  CMS Collaboration  Search for resonant pair production of Higgs bosons decaying to bottom quarkantiquark pairs in protonproton collisions at 13 TeV  JHEP 08 (2018) 152  CMSHIG17009 1806.03548 
13  ATLAS Collaboration  Search for pair production of Higgs bosons in the $ \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ final state using protonproton collisions at $ \sqrt{s} = $ 13 TeV with the ATLAS detector  PRD 94 (2016) 052002  1606.04782 
14  ATLAS Collaboration  Search for Higgs boson pair production in the $ \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ final state from pp collisions at $ \sqrt{s} = $ 8 TeV with the ATLAS detector  EPJC 75 (2015) 412  1506.00285 
15  CMS Collaboration  Search for resonant pair production of Higgs bosons decaying to two bottom quarkantiquark pairs in protonproton collisions at 8 TeV  PLB 749 (2015) 560  CMSHIG14013 1503.04114 
16  E. D. L. Cren  A note on the history of markrecapture population estimates  Journal of Animal Ecology 34 (1965) 453  
17  CDF Collaboration  Measurement of $ \sigma B(\textrm{W}\rightarrow\textrm{e}\nu) $ and $ \sigma B({\textrm{Z}}^{0}\rightarrow{\textrm{e}}^{+}{\textrm{e}}^{}) $ in $ \overline{\rm{p}}\rm{p} $ collisions at $ \sqrt{s}= $ 1800 GeV  PRD 44 (1991) 29  
18  O. Behnke, K. Kröninger, G. Schott, and T. SchörnerSadenius  Data analysis in high energy physics: a practical guide to statistical methods  WileyVCH, Weinheim, 2013 link 

19  P. De Castro Manzano et al.  Hemisphere mixing: a fully datadriven model of QCD multijet backgrounds for LHC searches  PoS EPSHEP 370, 2017 link 
1712.02538 
20  CMS Collaboration  Search for nonresonant Higgs boson pair production in the $ \mathrm{b}\mathrm{b}\mathrm{b}\mathrm{b} $ final state at $ \sqrt{s} = $ 13 TeV  JHEP 04 (2019) 112  CMSHIG17017 1810.11854 
21  CMS Collaboration  Measurement of the ZZ production cross section and Z $ \to \ell^+\ell^\ell'^+\ell'^ $ branching fraction in pp collisions at $ \sqrt{s} = $ 13 TeV  PLB 763 (2016) 280  CMSSMP16001 1607.08834 
22  LHC Higgs Cross Section Working Group  Handbook of LHC Higgs cross sections: 4. Deciphering the nature of the Higgs sector  CERN Report CERN2017002M, 2016 link 
1610.07922 
23  CMS Collaboration  Measurements of $ {\mathrm{p}} {\mathrm{p}} \rightarrow {\mathrm{Z}} {\mathrm{Z}} $ production cross sections and constraints on anomalous triple gauge couplings at $ \sqrt{s} = 13\,\text {TeV} $  EPJC 81 (2021) 200  CMSSMP19001 2009.01186 
24  ATLAS Collaboration  $ \rm{ZZ} \to \ell^{+}\ell^{}\ell^{\prime +}\ell^{\prime } $ crosssection measurements and search for anomalous triple gauge couplings in 13 TeV pp collisions with the ATLAS detector  PRD 97 (2018) 032005  1709.07703 
25  CMS Collaboration  Observation of Higgs boson decay to bottom quarks  PRL 121 (2018) 121801  CMSHIG18016 1808.08242 
26  ATLAS Collaboration  Observation of $ \rm{H} \rightarrow \mathrm{b}\overline{\mathrm{b}} $ decays and VH production with the ATLAS detector  PLB 786 (2018) 59  1808.08238 
27  CMS Collaboration  Measurement of simplified template cross sections of the Higgs boson produced in association with W or Z bosons in the H $ \to \mathrm{b}\overline{\mathrm{b}} $ decay channel in protonproton collisions at $ \sqrt{s} $ = 13 TeV  Submitted to Physical Review D, 2023  CMSHIG20001 2312.07562 
28  CMS Collaboration  HEPData record for this analysis  link  
29  CMS Collaboration  The CMS experiment at the CERN LHC  JINST 3 (2008) S08004  
30  CMS Collaboration  Development of the CMS detector for the CERN LHC Run 3  CMSPRF21001 2309.05466 

31  CMS Collaboration  Performance of the CMS Level1 trigger in protonproton collisions at $ \sqrt{s} = $ 13 TeV  JINST 15 (2020) P10017  CMSTRG17001 2006.10165 
32  CMS Collaboration  The CMS trigger system  JINST 12 (2017) P01020  CMSTRG12001 1609.02366 
33  CMS Collaboration  Electron and photon reconstruction and identification with the CMS experiment at the CERN LHC  JINST 16 (2021) P05014  CMSEGM17001 2012.06888 
34  CMS Collaboration  Performance of the CMS muon detector and muon reconstruction with protonproton collisions at $ \sqrt{s}= $ 13 TeV  JINST 13 (2018) P06015  CMSMUO16001 1804.04528 
35  CMS Collaboration  Description and performance of track and primaryvertex reconstruction with the CMS tracker  JINST 9 (2014) P10009  CMSTRK11001 1405.6569 
36  CMS Collaboration  Particleflow reconstruction and global event description with the CMS detector  JINST 12 (2017) P10003  CMSPRF14001 1706.04965 
37  CMS Collaboration  Technical proposal for the PhaseII upgrade of the Compact Muon Solenoid  CMS Technical Proposal CERNLHCC2015010, CMSTDR1502, CERN, 2015 CDS 

38  M. Cacciari, G. P. Salam, and G. Soyez  The anti$ k_{\mathrm{T}} $ jet clustering algorithm  JHEP 04 (2008) 063  0802.1189 
39  M. Cacciari, G. P. Salam, and G. Soyez  FastJet user manual  EPJC 72 (2012) 1896  1111.6097 
40  CMS Collaboration  Pileup mitigation at CMS in $ \sqrt{s}= $ 13 TeV data  JINST 15 (2020) P09018  CMSJME18001 2003.00503 
41  CMS Collaboration  Jet energy scale and resolution in the CMS experiment in protonproton collisions at $ \sqrt{s}= $ 8 TeV  JINST 12 (2017) P02014  CMSJME13004 1607.03663 
42  CMS Collaboration  Jet energy scale and resolution measurement with Run2 legacy data collected by CMS at $ \sqrt{s}= $ 13 TeV  CMS Detector Performance Summary CMSDP2021033, CERN, 2021 CDS 

43  E. Bols et al.  Jet flavour classification using DeepJet  JINST 15 (2020) P12012  2008.10519 
44  CMS Collaboration  Precision luminosity measurement in protonproton collisions at $ \sqrt{s} = $ 13 TeV in 2015 and 2016 at CMS  EPJC 81 (2021) 800  CMSLUM17003 2104.01927 
45  CMS Collaboration  CMS luminosity measurement for the 2017 datataking period at $ \sqrt{s} = $ 13 TeV  CMS Physics Analysis Summary , CERN, 2017 CMSPASLUM17004 
CMSPASLUM17004 
46  CMS Collaboration  CMS luminosity measurement for the 2018 datataking period at $ \sqrt{s} = $ 13 TeV  CMS Physics Analysis Summary , CERN, 2019 CMSPASLUM18002 
CMSPASLUM18002 
47  CMS Collaboration  Identification of heavyflavour jets with the CMS detector in pp collisions at 13 TeV  JINST 13 (2018) P05011  CMSBTV16002 1712.07158 
48  S. Frixione, P. Nason, and G. Ridolfi  A positiveweight nexttoleadingorder Monte Carlo for heavy flavour hadroproduction  JHEP 09 (2007) 126  0707.3088 
49  S. Frixione, P. Nason, and C. Oleari  Matching NLO QCD computations with parton shower simulations: the POWHEG method  JHEP 11 (2007) 070  0709.2092 
50  J. M. Campbell, R. K. Ellis, P. Nason, and E. Re  Toppair production and decay at NLO matched with parton showers  JHEP 04 (2015) 114  1412.1828 
51  J. Alwall et al.  The automated computation of treelevel and nexttoleading order differential cross sections, and their matching to parton shower simulations  JHEP 07 (2014) 79  1405.0301 
52  R. Frederix and S. Frixione  Merging meets matching in MC@NLO  JHEP 12 (2012) 061  1209.6215 
53  K. Mimasu, V. Sanz, and C. Williams  Higher order QCD predictions for associated Higgs production with anomalous couplings to gauge bosons  JHEP 08 (2016) 039  1512.02572 
54  K. Hamilton, P. Nason, and G. Zanderighi  MINLO: Multiscale improved NLO  JHEP 10 (2012) 155  1206.3572 
55  G. Luisoni, P. Nason, C. Oleari, and F. Tramontano  HW/HZ + 0 and 1 jet at NLO with the POWHEG BOX interfaced to GoSam and their merging within MiNLO  JHEP 10 (2013) 083  1306.2542 
56  A. Djouadi, J. Kalinowski, M. Mühlleitner, and M. Spira  Hdecay: Twenty++ years after  Computer Physics Communications 238 (2019)  
57  Particle Data Group , R. L. Workman et al.  Review of particle physics  Prog. Theor. Exp. Phys. 2022 (2022) 083C01  
58  G. Heinrich et al.  NLO predictions for Higgs boson pair production with full top quark mass dependence matched to parton showers  JHEP 08 (2017) 088  1703.09252 
59  S. Dawson, S. Dittmaier, and M. Spira  Neutral Higgs boson pair production at hadron colliders: QCD corrections  PRD 58 (1998) 115012  hepph/9805244 
60  S. Borowka et al.  Higgs boson pair production in gluon fusion at nexttoleading order with full topquark mass dependence  PRL 117 (2016) 012001  1604.06447 
61  J. Baglio et al.  Gluon fusion into Higgs pairs at NLO QCD and the top mass scheme  EPJC 79 (2019) 459  1811.05692 
62  D. de Florian and J. Mazzitelli  Higgs boson pair production at nexttonexttoleading order in QCD  PRL 111 (2013) 201801  1309.6594 
63  D. Y. Shao, C. S. Li, H. T. Li, and J. Wang  Threshold resummation effects in Higgs boson pair production at the LHC  JHEP 07 (2013) 169  1301.1245 
64  D. de Florian and J. Mazzitelli  Higgs pair production at nexttonexttoleading logarithmic accuracy at the LHC  JHEP 09 (2015) 053  1505.07122 
65  M. Grazzini et al.  Higgs boson pair production at NNLO with top quark mass effects  JHEP 05 (2018) 059  1803.02463 
66  J. Baglio et al.  $ \mathrm{g}\mathrm{g}\to \mathrm{H}\mathrm{H} $: Combined uncertainties  PRD 103 (2021) 056002  2008.11626 
67  T. Sjöstrand et al.  An introduction to PYTHIA 8.2  Comp. Phys. Commun. 191 (2015) 159  1410.3012 
68  CMS Collaboration  Extraction and validation of a new set of CMS PYTHIA8 tunes from underlyingevent measurements  EPJC 80 (2020) 4  CMSGEN17001 1903.12179 
69  CMS Collaboration  Event generator tunes obtained from underlying event and multiparton scattering measurements  EPJC 76 (2016) 155  CMSGEN14001 1512.00815 
70  NNPDF Collaboration  Parton distributions for the LHC Run II  JHEP 04 (2015) 040  1410.8849 
71  R. D. Ball et al.  Parton distributions from highprecision collider data  EPJC 77 (2017) 663  1706.00428 
72  GEANT4 Collaboration  GEANT4a simulation toolkit  NIM A 506 (2003) 250  
73  CMS Collaboration  Evidence for the Higgs boson decay to a bottom quarkantiquark pair  PLB 780 (2018) 501  CMSHIG16044 1709.07497 
74  W. Shang, K. Sohn, D. Almeida, and H. Lee  Understanding and improving convolutional neural networks via concatenated rectified linear units  in Proc. 33rd Int. Conf. on Machine Learning, volume 48, PMLR, 2016 link 
1603.05201 
75  K. He, X. Zhang, S. Ren, and J. Sun  Deep residual learning for image recognition  in IEEE Conf, in Computer Vision and Pattern Recognition (CVPR), 2016 link 
1512.03385 
76  A. Vaswani et al.  Attention is all you need  in Advances in Neural Information Processing Systems, volume 30. Curran Associates, Inc, 2017 link 
1706.03762 
77  R. A. Fisher  On the interpretation of $ \chi^2 $ from contingency tables, and the calculation of $ p $  J. Royal Stat. Soc. (1922)  
78  T. Junk  Confidence level computation for combining searches with small statistics  NIM A 434 (1999) 435  hepex/9902006 
79  A. L. Read  Presentation of search results: The CL$ _{\text{s}} $ technique  JPG 28 (2002) 2693 
Compact Muon Solenoid LHC, CERN 