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Comparison between the background model obtained with the hemisphere mixing technique and MC simulation of QCD multijet processes for $\pTjetind{1}$ (upper left), $\etaJetind{1}$ (upper right), \pTHone (lower left), and \MHH (lower right). Bias correction for the background model, described in Section~\ref{sec:bias_corr}, is applied by rescaling the weight of each event using the event yield ratio between corrected and uncorrected BDT distributions. Only statistical uncertainties are shown as the uncertainties related to the bias correction can not be propagated from the BDT classifier to a different variable.

Comparison between the background model obtained with the hemisphere mixing technique and MC simulation of QCD multijet processes for $\pTjetind{1}$ (upper left), $\etaJetind{1}$ (upper right), \pTHone (lower left), and \MHH (lower right). Bias correction for the background model, described in Section~\ref{sec:bias_corr}, is applied by rescaling the weight of each event using the event yield ratio between corrected and uncorrected BDT distributions. Only statistical uncertainties are shown as the uncertainties related to the bias correction can not be propagated from the BDT classifier to a different variable.

Comparison between the background model obtained with the hemisphere mixing technique and data in the \mHiggs\ CR for the variables $\pTjetind{1}$ (upper left), $\etaJetind{1}$ (upper right), \ctsHoneJone (lower left), and $\cmva{4}$ (lower right). Bias correction for the background model, described in Section~\ref{sec:bias_corr}, is applied by rescaling the weight of each event using the event yield ratio between corrected and uncorrected BDT distributions in this CR. Only statistical uncertainties are shown as the uncertainties related to the bias correction can not be propagated from the BDT classifier to a different variable.

Comparison between the background model obtained with the hemisphere mixing technique and data in the \cPqb\ tag CR for the variables $\pTjetind{1}$ (upper left), $\etaJetind{1}$ (upper right), \MHone (lower left), and \MHtwo (lower right). Bias correction for the background model, described in Section~\ref{sec:bias_corr}, is applied by rescaling the weight of each event using the event yield ratio between corrected and uncorrected BDT distributions in this CR. Only statistical uncertainties are shown as the uncertainties related to the bias correction can not be propagated from the BDT classifier to a different variable.

Comparison between the background model obtained with the hemisphere mixing technique and data in the \cPqb\ tag CR for the variables $\pTjetind{1}$ (upper left), $\etaJetind{1}$ (upper right), \MHone (lower left), and \MHtwo (lower right). Bias correction for the background model, described in Section~\ref{sec:bias_corr}, is applied by rescaling the weight of each event using the event yield ratio between corrected and uncorrected BDT distributions in this CR. Only statistical uncertainties are shown as the uncertainties related to the bias correction can not be propagated from the BDT classifier to a different variable.

Comparison between the background model obtained with the hemisphere mixing technique and data in the \mHiggs\ CR for the variables $\pTjetind{1}$ (upper left), $\etaJetind{1}$ (upper right), \ctsHoneJone (lower left), and $\cmva{4}$ (lower right). Bias correction for the background model, described in Section~\ref{sec:bias_corr}, is applied by rescaling the weight of each event using the event yield ratio between corrected and uncorrected BDT distributions in this CR. Only statistical uncertainties are shown as the uncertainties related to the bias correction can not be propagated from the BDT classifier to a different variable.

Comparison between the background model obtained with the hemisphere mixing technique and data in the \cPqb\ tag CR for the variables $\pTjetind{1}$ (upper left), $\etaJetind{1}$ (upper right), \MHone (lower left), and \MHtwo (lower right). Bias correction for the background model, described in Section~\ref{sec:bias_corr}, is applied by rescaling the weight of each event using the event yield ratio between corrected and uncorrected BDT distributions in this CR. Only statistical uncertainties are shown as the uncertainties related to the bias correction can not be propagated from the BDT classifier to a different variable.

Bias estimation by resampling, in relative units of the statistical uncertainty of the predicted background, used to correct the background estimation. The median (red line) and the upper and lower one \sd quantiles (green lines) have been computed from 200 subsamples of the re-mixed data comparing the predicted background $n^p_b$ with the observed $n^o_b$. The variability due to the limited number of subsamples is estimated by bootstrap and it is shown for each estimation using a coloured shadow around the quantile estimation. The light yellow shadow represents the uncertainty due to the limited statistics of the reference observed sample. The separation between the one \sd quantiles is compatible with the expected variance if the estimation was Poisson or Gaussian distributed.

95\% \CL cross section limits on \xsppToHHbbbb for values of \kappalambda in the [-20,20] range, assuming $\kappat = 1$; the theoretical prediction with $\kappat = 1$ is also shown.

An illustration of the hemisphere mixing procedure. The transverse thrust axis is defined as the axis on which the sum of the absolute values of the projections of the \pt of the jets is maximal. Once the thrust axis is identified, the event is divided into two halves by cutting along the axis perpendicular to the transverse thrust axis. One such half is called a hemisphere ($h$). In a preliminary step, each event in the original $N$-event data set is split into two hemispheres that are collected in a library of $2N$ hemispheres. Once the library is created, each event is used as a basis for creating artificial events. These are constructed by picking two hemispheres from the library that are similar to the two hemispheres that make up the original event.

Left: comparison of the distribution of BDT output for data (left) selected in a region of the leading versus trailing Higgs boson candidate mass plane that excludes a 60-\GeV-wide box around the most probable values of the dijet masses of signal events, with the corresponding output on an artificial sample obtained from the same data set by hemisphere mixing. Right: bin-by-bin differences between data and model, in \sd units before (upper right) and after (lower right) bias correction; pull distribution for the differences, fit to a Gaussian distribution. The bias correction uncertainty is increased to take the \sd of the residuals to 1.0.

The observed and expected upper limits at 95\% \CL on the \xsppToHHbbbb cross section for the 13 BSM models investigated. See Table~\ref{table:benchmarks} for their respective parameter values.

Comparison between the background model obtained with the hemisphere mixing technique and data in the \mHiggs\ CR for the variables $\pTjetind{1}$ (upper left), $\etaJetind{1}$ (upper right), \ctsHoneJone (lower left), and $\cmva{4}$ (lower right). Bias correction for the background model, described in Section~\ref{sec:bias_corr}, is applied by rescaling the weight of each event using the event yield ratio between corrected and uncorrected BDT distributions in this CR. Only statistical uncertainties are shown as the uncertainties related to the bias correction can not be propagated from the BDT classifier to a different variable.

Comparison between the background model obtained with the hemisphere mixing technique and data in the \cPqb\ tag CR for the variables $\pTjetind{1}$ (upper left), $\etaJetind{1}$ (upper right), \MHone (lower left), and \MHtwo (lower right). Bias correction for the background model, described in Section~\ref{sec:bias_corr}, is applied by rescaling the weight of each event using the event yield ratio between corrected and uncorrected BDT distributions in this CR. Only statistical uncertainties are shown as the uncertainties related to the bias correction can not be propagated from the BDT classifier to a different variable.

Comparison between the background model obtained with the hemisphere mixing technique and MC simulation of QCD multijet processes for $\pTjetind{1}$ (upper left), $\etaJetind{1}$ (upper right), \pTHone (lower left), and \MHH (lower right). Bias correction for the background model, described in Section~\ref{sec:bias_corr}, is applied by rescaling the weight of each event using the event yield ratio between corrected and uncorrected BDT distributions. Only statistical uncertainties are shown as the uncertainties related to the bias correction can not be propagated from the BDT classifier to a different variable.

Results of the fit to the BDT distribution for the SM \HH production signal. In the bottom panel a comparison is shown between the best fit signal and best fit background subtracted from measured data. The band, centred at zero, shows the total uncertainty.

Comparison between the background model obtained with the hemisphere mixing technique and MC simulation of QCD multijet processes for $\pTjetind{1}$ (upper left), $\etaJetind{1}$ (upper right), \pTHone (lower left), and \MHH (lower right). Bias correction for the background model, described in Section~\ref{sec:bias_corr}, is applied by rescaling the weight of each event using the event yield ratio between corrected and uncorrected BDT distributions. Only statistical uncertainties are shown as the uncertainties related to the bias correction can not be propagated from the BDT classifier to a different variable.

Post-fit distribution of \MHone\ (left) and \MHtwo\ (right). Bias correction for the background model is applied by rescaling the weight of each event using the event yield ratio between corrected and uncorrected BDT distributions.

Post-fit distribution of \MHone\ (left) and \MHtwo\ (right). Bias correction for the background model is applied by rescaling the weight of each event using the event yield ratio between corrected and uncorrected BDT distributions.

Feynman diagrams that contribute to \HH production via gluon-gluon fusion at LO. Diagrams (a) and (b) correspond to SM-like processes, while diagrams (c), (d), and (e) correspond to pure BSM effects: (c) and (d) describe contact interactions between the Higgs boson and gluons, and (e) describes the contact interaction of two Higgs bosons with top quarks.

Diagram describing the procedure used to estimate the background bias correction. All possible combinations of mixed hemispheres except those used for training are added together to create a large sample $M$ of $96N$ events from which we repeatedly subsample without replacement 200 replicas $M_i$ of $N$ events. The hemisphere mixing procedure is then carried out again for each of this replicas to produce a set of re-mixed data replicas $R_i$. The trained multivariate classifier trained is then evaluated over all the events of $M$ and each $R_i$. and the histograms of the classifier output are compared to obtain a the differences for each of the replicas. The median difference is taken as bias correction.

Comparison between the background model obtained with the hemisphere mixing technique and data in the \mHiggs\ CR for the variables $\pTjetind{1}$ (upper left), $\etaJetind{1}$ (upper right), \ctsHoneJone (lower left), and $\cmva{4}$ (lower right). Bias correction for the background model, described in Section~\ref{sec:bias_corr}, is applied by rescaling the weight of each event using the event yield ratio between corrected and uncorrected BDT distributions in this CR. Only statistical uncertainties are shown as the uncertainties related to the bias correction can not be propagated from the BDT classifier to a different variable.