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| CMS-HIG-17-017 ; CERN-EP-2018-269 | ||
| Search for nonresonant Higgs boson pair production in the ${\mathrm{b\bar{b}}\mathrm{b\bar{b}}}$ final state at $\sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 29 October 2018 | ||
| JHEP 04 (2019) 112 | ||
| Abstract: Results of a search for nonresonant production of Higgs boson pairs, with each Higgs boson decaying to a $ \mathrm{b\bar{b}} $ pair, are presented. This search uses data from proton-proton collisions at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$, collected by the CMS detector at the LHC. No signal is observed, and a 95% confidence level upper limit of 847fb is set on the cross section for standard model nonresonant Higgs boson pair production times the squared branching fraction of the Higgs boson decay to a $ \mathrm{b\bar{b}} $ pair. The same signature is studied, and upper limits are set, in the context of models of physics beyond the standard model that predict modified couplings of the Higgs boson. | ||
| Links: e-print arXiv:1810.11854 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
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. |
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Figure 2:
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 $ {p_{\mathrm {T}}} $ 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. |
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Figure 3:
Comparison between the background model obtained with the hemisphere mixing technique and MC simulation of QCD multijet processes for $ {{{{p_{\mathrm {T}}}}_{\mathrm {j}}} ^{1}} $ (upper left), $ {\eta ^{1}_{\text {j}}} $ (upper right), ${{{p_{\mathrm {T}}} ^{{{\mathrm {H}} _1}}}}$ (lower left), and $ {M_{{\mathrm {H}} {\mathrm {H}}}} $ (lower right). Bias correction for the background model, described in Section 8.2, 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. |
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Figure 3-a:
Comparison between the background model obtained with the hemisphere mixing technique and MC simulation of QCD multijet processes for $ {{{{p_{\mathrm {T}}}}_{\mathrm {j}}} ^{1}} $. Bias correction for the background model, described in Section 8.2, 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. |
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Figure 3-b:
Comparison between the background model obtained with the hemisphere mixing technique and MC simulation of QCD multijet processes for $ {\eta ^{1}_{\text {j}}} $. Bias correction for the background model, described in Section 8.2, 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. |
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Figure 3-c:
Comparison between the background model obtained with the hemisphere mixing technique and MC simulation of QCD multijet processes for ${{{p_{\mathrm {T}}} ^{{{\mathrm {H}} _1}}}}$. Bias correction for the background model, described in Section 8.2, 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. |
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Figure 3-d:
Comparison between the background model obtained with the hemisphere mixing technique and MC simulation of QCD multijet processes for $ {M_{{\mathrm {H}} {\mathrm {H}}}} $. Bias correction for the background model, described in Section 8.2, 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. |
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Figure 4:
Comparison between the background model obtained with the hemisphere mixing technique and data in the ${m_{{\mathrm {H}}}} $ CR for the variables $ {{{{p_{\mathrm {T}}}}_{\mathrm {j}}} ^{1}} $ (upper left), $ {\eta ^{1}_{\text {j}}} $ (upper right), ${\cos {\theta ^{*}} _{{{\mathrm {H}} _1} \text {-}\mathrm {j}_1}}$ (lower left), and $CMVA_{4} $ (lower right). Bias correction for the background model, described in Section 8.2, 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. |
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Figure 4-a:
Comparison between the background model obtained with the hemisphere mixing technique and data in the ${m_{{\mathrm {H}}}} $ CR for the $ {{{{p_{\mathrm {T}}}}_{\mathrm {j}}} ^{1}} $ variable. Bias correction for the background model, described in Section 8.2, 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. |
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Figure 4-b:
Comparison between the background model obtained with the hemisphere mixing technique and data in the ${m_{{\mathrm {H}}}} $ CR for the $ {\eta ^{1}_{\text {j}}} $ variable. Bias correction for the background model, described in Section 8.2, 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. |
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Figure 4-c:
Comparison between the background model obtained with the hemisphere mixing technique and data in the ${m_{{\mathrm {H}}}} $ CR for the ${\cos {\theta ^{*}} _{{{\mathrm {H}} _1} \text {-}\mathrm {j}_1}}$ variable. |
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Figure 4-d:
Comparison between the background model obtained with the hemisphere mixing technique and data in the ${m_{{\mathrm {H}}}} $ CR for the $CMVA_{4} $ variable. Bias correction for the background model, described in Section 8.2, 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. |
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Figure 5:
Comparison between the background model obtained with the hemisphere mixing technique and data in the b tag CR for the variables $ {{{{p_{\mathrm {T}}}}_{\mathrm {j}}} ^{1}} $ (upper left), $ {\eta ^{1}_{\text {j}}} $ (upper right), ${M_{{{\mathrm {H}} _1}}}$ (lower left), and ${M_{{{\mathrm {H}} _2}}}$ (lower right). Bias correction for the background model, described in Section 8.2, 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. |
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Figure 5-a:
Comparison between the background model obtained with the hemisphere mixing technique and data in the b tag CR for the $ {{{{p_{\mathrm {T}}}}_{\mathrm {j}}} ^{1}} $ variable. Bias correction for the background model, described in Section 8.2, 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. |
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Figure 5-b:
Comparison between the background model obtained with the hemisphere mixing technique and data in the b tag CR for the $ {\eta ^{1}_{\text {j}}} $ variable. Bias correction for the background model, described in Section 8.2, 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. |
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Figure 5-c:
Comparison between the background model obtained with the hemisphere mixing technique and data in the b tag CR for the ${M_{{{\mathrm {H}} _1}}}$ variable. Bias correction for the background model, described in Section 8.2, 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. |
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Figure 5-d:
Comparison between the background model obtained with the hemisphere mixing technique and data in the b tag CR for the ${M_{{{\mathrm {H}} _2}}}$ variable. Bias correction for the background model, described in Section 8.2, 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. |
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Figure 6:
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 s.d. 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 s.d. of the residuals to 1.0. |
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Figure 7:
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. |
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Figure 8:
Post-fit distribution of ${M_{{{\mathrm {H}} _1}}} $ (left) and ${M_{{{\mathrm {H}} _2}}} $ (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. |
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Figure 8-a:
Post-fit distribution of ${M_{{{\mathrm {H}} _1}}} $. 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. |
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Figure 8-b:
Post-fit distribution of ${M_{{{\mathrm {H}} _2}}} $. 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. |
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Figure 9:
The observed and expected upper limits at 95% CL on the ${\sigma {({{\mathrm {p}} {\mathrm {p}} \to {{\mathrm {H}} {\mathrm {H}} \to {{\mathrm {b}} {\overline {\mathrm {b}}}} {{\mathrm {b}} {\overline {\mathrm {b}}}}}})}}$ cross section for the 13 BSM models investigated. See Table 9 for their respective parameter values. |
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Figure 10:
95% CL cross section limits on ${\sigma {({{\mathrm {p}} {\mathrm {p}} \to {{\mathrm {H}} {\mathrm {H}} \to {{\mathrm {b}} {\overline {\mathrm {b}}}} {{\mathrm {b}} {\overline {\mathrm {b}}}}}})}}$ for values of ${\kappa _{{{\lambda}}}}$ in the [-20,20] range, assuming $ {\kappa _{{\mathrm {t}}}} = $ 1; the theoretical prediction with $ {\kappa _{{\mathrm {t}}}} = $ 1 is also shown. |
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Figure 11:
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. |
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Figure 12:
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 s.d. 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 s.d. quantiles is compatible with the expected variance if the estimation was Poisson or Gaussian distributed. |
| Tables | |
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Table 1:
The values of the anomalous coupling parameters for the 13 benchmark models studied [28]. For reference, the values of the parameters in the SM are also included. |
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Table 2:
Cut-flow efficiency for the SM signal $ {{\mathrm {p}} {\mathrm {p}} \to {{\mathrm {H}} {\mathrm {H}} \to {{\mathrm {b}} {\overline {\mathrm {b}}}} {{\mathrm {b}} {\overline {\mathrm {b}}}}}} $; the efficiency and the relative reduction of each successive selection step is shown. The number of expected SM signal events for an integrated luminosity of 1 fb$^{-1}$ is also reported. |
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Table 3:
List of BDT input variables. |
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Table 4:
Systematic uncertainties considered in the analysis and relative impact on the expected limit for the SM HH production. The relative impact is obtained by fixing the nuisance parameters corresponding to each source and recalculating the expected limit. |
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Table 5:
The observed and expected upper limits on ${\sigma {({{\mathrm {p}} {\mathrm {p}} \to {{\mathrm {H}} {\mathrm {H}} \to {{\mathrm {b}} {\overline {\mathrm {b}}}} {{\mathrm {b}} {\overline {\mathrm {b}}}}}})}}$ in the SM at 95% CL in units of fb. |
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Table 6:
The observed and expected upper limits on the ${\sigma {({{\mathrm {p}} {\mathrm {p}} \to {{\mathrm {H}} {\mathrm {H}} \to {{\mathrm {b}} {\overline {\mathrm {b}}}} {{\mathrm {b}} {\overline {\mathrm {b}}}}}})}}$ cross section for the 13 BSM benchmark models at 95% CL in units of fb. |
| Summary |
| This paper presents a search for nonresonant Higgs boson pair (HH) production with both Higgs bosons decaying into $ \mathrm{b\bar{b}} $ pairs. The standard model (SM) production has been studied along with 13 beyond the SM (BSM) benchmark models, using a data set of $\sqrt{s} = $ 13 TeV proton-proton collision events, corresponding to an integrated luminosity of 35.9 fb$^{-1}$ collected by the CMS detector during the 2016 LHC run. The analysis of events acquired by a hadronic multijet trigger includes the selection of events with 4 b-tagged jets and a classification using boosted decision trees, optimized for discovery of the SM HH signal. Limits at 95% confidence level on the HH production cross section times the square of the branching fraction for the Higgs boson decay to b quark pairs are extracted for the SM and each BSM model considered, using binned likelihood fits of the shape of the boosted decision tree classifier output. The background model is derived from a novel technique based on data that provides a multidimensional representation of the dominant quantum chromodynamics multijet background and also models well the overall background distribution. The expected upper limit on ${\sigma{(\mathrm{pp\to HH \to b\bar{b}b\bar{b}})}}$ is 419 fb, corresponding to 37 times the expected value for the SM process. The observed upper limit is 847 fb. Anomalous couplings of the Higgs boson are also investigated. The upper limits extracted for the HH production cross section in the 13 BSM benchmark models range from 508 to 3513 fb. |
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