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| CMS-PAS-HIG-24-010 | ||
| Improved results on Higgs boson pair production in the 4b final state | ||
| CMS Collaboration | ||
| 2025-10-29 | ||
| Abstract: Measurements of Higgs boson pair (HH) production in the four bottom quark final state are presented using a data set of proton-proton (pp) collisions at $ \sqrt{s}= $ 13.6 TeV collected by the CMS experiment during 2022-2023 and corresponding to an integrated luminosity of 62 fb$ ^{-1} $. Events in which each Higgs boson decay is separately reconstructed as a pair of small-radius jets (resolved), as well as events in which each $ \mathrm{H}\to\mathrm{b}\bar{\mathrm{b}} $ decay is reconstructed as a single large-radius jet (merged) are analyzed exclusively. Benefiting from novel analysis techniques, the combination of resolved and merged channels gives an observed (expected) upper limit at 95% confidence level (CL) on the HH signal strength $ \mu_{\mathrm{HH}} $, defined as the observed HH production cross section divided by the standard model (SM) prediction, of 4.4 (4.4). Compared to previous LHC results, the expected limit with an equivalent integrated luminosity is improved by more than a factor two in the resolved topology and significantly improved in the merged topology as well. The allowed ranges at 95% CL for the Higgs trilinear self-coupling and quartic coupling between two Higgs bosons and two vector bosons, relative to the standard model expectation, are observed (expected, in absence of signal) to be $ [-3.3,9.7] $ ($ [-3.4,10.0] $) and $ [0.63,1.43] $ ($ [0.54,1.51] $), respectively. An updated analysis of the resolved topology using a 13 TeV pp collision data set corresponding to 138 fb$ ^{-1} $ and collected in 2016-2018, reports an observed (expected) 95% CL upper limit on $ \mu_{\mathrm{HH}} $ of 10.0 (5.9), an improvement of about 25% in the expected limit compared to the published results using the same data. | ||
| Links: CDS record (PDF) ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Feynman diagrams that contribute to ggF and VBF HH production at leading order with coupling modifiers affecting the Higgs-to-fermion coupling $ \kappa_f $, to vector-boson coupling $ \kappa_{\text{V}} $, to two-vector-boson vertices $ \kappa_{\text{2V}} $ and self-coupling $ \kappa_{\lambda} $. |
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Figure 1-a:
Feynman diagrams that contribute to ggF and VBF HH production at leading order with coupling modifiers affecting the Higgs-to-fermion coupling $ \kappa_f $, to vector-boson coupling $ \kappa_{\text{V}} $, to two-vector-boson vertices $ \kappa_{\text{2V}} $ and self-coupling $ \kappa_{\lambda} $. |
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Figure 1-b:
Feynman diagrams that contribute to ggF and VBF HH production at leading order with coupling modifiers affecting the Higgs-to-fermion coupling $ \kappa_f $, to vector-boson coupling $ \kappa_{\text{V}} $, to two-vector-boson vertices $ \kappa_{\text{2V}} $ and self-coupling $ \kappa_{\lambda} $. |
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Figure 1-c:
Feynman diagrams that contribute to ggF and VBF HH production at leading order with coupling modifiers affecting the Higgs-to-fermion coupling $ \kappa_f $, to vector-boson coupling $ \kappa_{\text{V}} $, to two-vector-boson vertices $ \kappa_{\text{2V}} $ and self-coupling $ \kappa_{\lambda} $. |
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Figure 1-d:
Feynman diagrams that contribute to ggF and VBF HH production at leading order with coupling modifiers affecting the Higgs-to-fermion coupling $ \kappa_f $, to vector-boson coupling $ \kappa_{\text{V}} $, to two-vector-boson vertices $ \kappa_{\text{2V}} $ and self-coupling $ \kappa_{\lambda} $. |
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Figure 1-e:
Feynman diagrams that contribute to ggF and VBF HH production at leading order with coupling modifiers affecting the Higgs-to-fermion coupling $ \kappa_f $, to vector-boson coupling $ \kappa_{\text{V}} $, to two-vector-boson vertices $ \kappa_{\text{2V}} $ and self-coupling $ \kappa_{\lambda} $. |
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Figure 2:
Left: the b tagging performance of the Run 3 PNET@HLT algorithm (in blue) compared to the best-performing algorithm deployed at HLT in Run 2 (DEEPCSV, in red), as evaluated from $ \mathrm{t} \overline{\mathrm{t}} $ simulation on trigger-level AK4 jets with $ p_{\mathrm{T}} > $ 30 GeV and $ {|\eta| < 2.5} $. Right: efficiency of the triggers targeting the resolved $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ topology as a function of the generator-level $ m_{\mathrm{H}\mathrm{H}} $ in simulated SM $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ signal events in which the generator-level jets from the b quarks produced by $ \mathrm{H}\to \mathrm{b}\overline{\mathrm{b}} $ decays have $ p_{\mathrm{T}} $ larger than 25 GeV and $ {|\eta| < 2.5} $. The teal histogram shows the expected distribution for the SM $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ signal prior to any trigger selections. |
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Figure 2-a:
Left: the b tagging performance of the Run 3 PNET@HLT algorithm (in blue) compared to the best-performing algorithm deployed at HLT in Run 2 (DEEPCSV, in red), as evaluated from $ \mathrm{t} \overline{\mathrm{t}} $ simulation on trigger-level AK4 jets with $ p_{\mathrm{T}} > $ 30 GeV and $ {|\eta| < 2.5} $. Right: efficiency of the triggers targeting the resolved $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ topology as a function of the generator-level $ m_{\mathrm{H}\mathrm{H}} $ in simulated SM $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ signal events in which the generator-level jets from the b quarks produced by $ \mathrm{H}\to \mathrm{b}\overline{\mathrm{b}} $ decays have $ p_{\mathrm{T}} $ larger than 25 GeV and $ {|\eta| < 2.5} $. The teal histogram shows the expected distribution for the SM $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ signal prior to any trigger selections. |
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Figure 2-b:
Left: the b tagging performance of the Run 3 PNET@HLT algorithm (in blue) compared to the best-performing algorithm deployed at HLT in Run 2 (DEEPCSV, in red), as evaluated from $ \mathrm{t} \overline{\mathrm{t}} $ simulation on trigger-level AK4 jets with $ p_{\mathrm{T}} > $ 30 GeV and $ {|\eta| < 2.5} $. Right: efficiency of the triggers targeting the resolved $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ topology as a function of the generator-level $ m_{\mathrm{H}\mathrm{H}} $ in simulated SM $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ signal events in which the generator-level jets from the b quarks produced by $ \mathrm{H}\to \mathrm{b}\overline{\mathrm{b}} $ decays have $ p_{\mathrm{T}} $ larger than 25 GeV and $ {|\eta| < 2.5} $. The teal histogram shows the expected distribution for the SM $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ signal prior to any trigger selections. |
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Figure 3:
Left: the $ \mathrm{b}\overline{\mathrm{b}} $ tagging performance of the PNET@HLT algorithm (in blue) compared to the highest-performing Run 2 algorithm (DOUBLEBB, in red), as evaluated on AK8 jets in the HLT from simulated $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ and QCD multijet events with $ p_{\mathrm{T}} > $ 300 GeV and $ {|\eta| < 2.5} $. Right: efficiency of the logical or of the trigger paths developed for the merged topology, as a function of the generator-level leading H candidate $ p_{\mathrm{T}} $ in simulated SM $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ events in which $ {\Delta R(\mathrm{b},\overline{\mathrm{b}}) < 0.8} $. The teal histogram shows the expected distribution for the SM $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ signal prior to any selections. |
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Figure 3-a:
Left: the $ \mathrm{b}\overline{\mathrm{b}} $ tagging performance of the PNET@HLT algorithm (in blue) compared to the highest-performing Run 2 algorithm (DOUBLEBB, in red), as evaluated on AK8 jets in the HLT from simulated $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ and QCD multijet events with $ p_{\mathrm{T}} > $ 300 GeV and $ {|\eta| < 2.5} $. Right: efficiency of the logical or of the trigger paths developed for the merged topology, as a function of the generator-level leading H candidate $ p_{\mathrm{T}} $ in simulated SM $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ events in which $ {\Delta R(\mathrm{b},\overline{\mathrm{b}}) < 0.8} $. The teal histogram shows the expected distribution for the SM $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ signal prior to any selections. |
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Figure 3-b:
Left: the $ \mathrm{b}\overline{\mathrm{b}} $ tagging performance of the PNET@HLT algorithm (in blue) compared to the highest-performing Run 2 algorithm (DOUBLEBB, in red), as evaluated on AK8 jets in the HLT from simulated $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ and QCD multijet events with $ p_{\mathrm{T}} > $ 300 GeV and $ {|\eta| < 2.5} $. Right: efficiency of the logical or of the trigger paths developed for the merged topology, as a function of the generator-level leading H candidate $ p_{\mathrm{T}} $ in simulated SM $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ events in which $ {\Delta R(\mathrm{b},\overline{\mathrm{b}}) < 0.8} $. The teal histogram shows the expected distribution for the SM $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ signal prior to any selections. |
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Figure 4:
Left: invariant mass distributions for the leading ($ m_{\mathrm{H}_1} $) and subleading ($ m_{\mathrm{H}_2} $) $ p_{\mathrm{T}} \mathrm{H} $ candidates in SM $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ events obtained before and after the application of the PNET jet $ p_{\mathrm{T}} $ regression. Right: distribution of the $ p_{\mathrm{T}} $ balance, $ r=p_{\mathrm{T}}^{\mathrm{j_{1}}}/p_{\mathrm{T}}^{\mu\mu} $, in 2023 data and simulated events for the selected $ \mathrm{Z}(\mu\mu)+\mathrm{b}\text{-jet} $ region with $ \alpha=p_{\mathrm{T}}^{\mathrm{j_{2}}}/p_{\mathrm{T}}^{\mu\mu} < $ 0.15, obtained after applying the PNET jet $ p_{\mathrm{T}} $ regression. The $ \mu $ values quoted in the legend correspond to the mean of the distributions. |
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Figure 4-a:
Left: invariant mass distributions for the leading ($ m_{\mathrm{H}_1} $) and subleading ($ m_{\mathrm{H}_2} $) $ p_{\mathrm{T}} \mathrm{H} $ candidates in SM $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ events obtained before and after the application of the PNET jet $ p_{\mathrm{T}} $ regression. Right: distribution of the $ p_{\mathrm{T}} $ balance, $ r=p_{\mathrm{T}}^{\mathrm{j_{1}}}/p_{\mathrm{T}}^{\mu\mu} $, in 2023 data and simulated events for the selected $ \mathrm{Z}(\mu\mu)+\mathrm{b}\text{-jet} $ region with $ \alpha=p_{\mathrm{T}}^{\mathrm{j_{2}}}/p_{\mathrm{T}}^{\mu\mu} < $ 0.15, obtained after applying the PNET jet $ p_{\mathrm{T}} $ regression. The $ \mu $ values quoted in the legend correspond to the mean of the distributions. |
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Figure 4-b:
Left: invariant mass distributions for the leading ($ m_{\mathrm{H}_1} $) and subleading ($ m_{\mathrm{H}_2} $) $ p_{\mathrm{T}} \mathrm{H} $ candidates in SM $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ events obtained before and after the application of the PNET jet $ p_{\mathrm{T}} $ regression. Right: distribution of the $ p_{\mathrm{T}} $ balance, $ r=p_{\mathrm{T}}^{\mathrm{j_{1}}}/p_{\mathrm{T}}^{\mu\mu} $, in 2023 data and simulated events for the selected $ \mathrm{Z}(\mu\mu)+\mathrm{b}\text{-jet} $ region with $ \alpha=p_{\mathrm{T}}^{\mathrm{j_{2}}}/p_{\mathrm{T}}^{\mu\mu} < $ 0.15, obtained after applying the PNET jet $ p_{\mathrm{T}} $ regression. The $ \mu $ values quoted in the legend correspond to the mean of the distributions. |
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Figure 5:
The ROC curve for GLOPART and PNET for discriminating $ \mathrm{H}\to\mathrm{b}\overline{\mathrm{b}} $ from QCD jets with 400 $ < p_{\mathrm{T}} < $ 600 GeV, $ |\eta| < $ 2.4, and 60 $ < m_\text{SD} < $ 150 GeV (left). The mass regression performance for GLOPART and PNET for jets with $ p_{\mathrm{T}} > $ 200 GeV, $ |\eta| < $ 2.4, and satisfying a PNET selection corresponding to 30% signal efficiency (right). The conditions correspond to those during data collection in 2023. |
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Figure 5-a:
The ROC curve for GLOPART and PNET for discriminating $ \mathrm{H}\to\mathrm{b}\overline{\mathrm{b}} $ from QCD jets with 400 $ < p_{\mathrm{T}} < $ 600 GeV, $ |\eta| < $ 2.4, and 60 $ < m_\text{SD} < $ 150 GeV (left). The mass regression performance for GLOPART and PNET for jets with $ p_{\mathrm{T}} > $ 200 GeV, $ |\eta| < $ 2.4, and satisfying a PNET selection corresponding to 30% signal efficiency (right). The conditions correspond to those during data collection in 2023. |
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Figure 5-b:
The ROC curve for GLOPART and PNET for discriminating $ \mathrm{H}\to\mathrm{b}\overline{\mathrm{b}} $ from QCD jets with 400 $ < p_{\mathrm{T}} < $ 600 GeV, $ |\eta| < $ 2.4, and 60 $ < m_\text{SD} < $ 150 GeV (left). The mass regression performance for GLOPART and PNET for jets with $ p_{\mathrm{T}} > $ 200 GeV, $ |\eta| < $ 2.4, and satisfying a PNET selection corresponding to 30% signal efficiency (right). The conditions correspond to those during data collection in 2023. |
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Figure 6:
Comparison between data and fit prediction from a simultaneous signal-plus-background fit to the GLOPART regressed jet mass distributions in $ \mathrm{Z} \to \mathrm{b}\overline{\mathrm{b}} $ VHP (left) and HP (middle) categories. Data corresponds to the full integrated luminosity collected by the CMS detector in 2022. The same comparison is performed for the $ m_{\mu\mu} $ distributions in the $ \mathrm{Z} \to \mu\mu $ region (right). Each process considered in the fit is modeled via a parametric function as described in the text. |
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Figure 6-a:
Comparison between data and fit prediction from a simultaneous signal-plus-background fit to the GLOPART regressed jet mass distributions in $ \mathrm{Z} \to \mathrm{b}\overline{\mathrm{b}} $ VHP (left) and HP (middle) categories. Data corresponds to the full integrated luminosity collected by the CMS detector in 2022. The same comparison is performed for the $ m_{\mu\mu} $ distributions in the $ \mathrm{Z} \to \mu\mu $ region (right). Each process considered in the fit is modeled via a parametric function as described in the text. |
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Figure 6-b:
Comparison between data and fit prediction from a simultaneous signal-plus-background fit to the GLOPART regressed jet mass distributions in $ \mathrm{Z} \to \mathrm{b}\overline{\mathrm{b}} $ VHP (left) and HP (middle) categories. Data corresponds to the full integrated luminosity collected by the CMS detector in 2022. The same comparison is performed for the $ m_{\mu\mu} $ distributions in the $ \mathrm{Z} \to \mu\mu $ region (right). Each process considered in the fit is modeled via a parametric function as described in the text. |
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Figure 6-c:
Comparison between data and fit prediction from a simultaneous signal-plus-background fit to the GLOPART regressed jet mass distributions in $ \mathrm{Z} \to \mathrm{b}\overline{\mathrm{b}} $ VHP (left) and HP (middle) categories. Data corresponds to the full integrated luminosity collected by the CMS detector in 2022. The same comparison is performed for the $ m_{\mu\mu} $ distributions in the $ \mathrm{Z} \to \mu\mu $ region (right). Each process considered in the fit is modeled via a parametric function as described in the text. |
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Figure 7:
Left: schematic diagram of the signal regions (dark shaded circles) and control regions (annular regions) in the $ m_{\mathrm{H}_1} $--$ m_{\mathrm{H}_2} $ mass plane as a function of $N_{\mathrm{b jet}}$. Right: schematic diagram showing the background estimation strategy, which applies a multidimensional reweighting of events from $ \mathrm{SR_{2\mathrm{b}}} $ to $ \mathrm{SR_{4\mathrm{b}}} $. |
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Figure 7-a:
Left: schematic diagram of the signal regions (dark shaded circles) and control regions (annular regions) in the $ m_{\mathrm{H}_1} $--$ m_{\mathrm{H}_2} $ mass plane as a function of $N_{\mathrm{b jet}}$. Right: schematic diagram showing the background estimation strategy, which applies a multidimensional reweighting of events from $ \mathrm{SR_{2\mathrm{b}}} $ to $ \mathrm{SR_{4\mathrm{b}}} $. |
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Figure 7-b:
Left: schematic diagram of the signal regions (dark shaded circles) and control regions (annular regions) in the $ m_{\mathrm{H}_1} $--$ m_{\mathrm{H}_2} $ mass plane as a function of $N_{\mathrm{b jet}}$. Right: schematic diagram showing the background estimation strategy, which applies a multidimensional reweighting of events from $ \mathrm{SR_{2\mathrm{b}}} $ to $ \mathrm{SR_{4\mathrm{b}}} $. |
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Figure 8:
Distribution of the SvsB classifier score in the $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ category for $ \mathrm{SR_{3\mathrm{b}}} $ data (black points) compared to the data-driven background prediction (blue histogram), for the pre-ParkingHH (left) and post-ParkingHH (right) data sets. The middle panel shows the ratio of data to the pre-fit (red open markers) and post b-only fit (black solid markers) background prediction, with the gray band indicating the background post-fit uncertainty. The lower panel show the distribution of the pulls, defined as the difference between the data and the post-fit background prediction, divided by the statistical uncertainty in the data. |
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Figure 8-a:
Distribution of the SvsB classifier score in the $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ category for $ \mathrm{SR_{3\mathrm{b}}} $ data (black points) compared to the data-driven background prediction (blue histogram), for the pre-ParkingHH (left) and post-ParkingHH (right) data sets. The middle panel shows the ratio of data to the pre-fit (red open markers) and post b-only fit (black solid markers) background prediction, with the gray band indicating the background post-fit uncertainty. The lower panel show the distribution of the pulls, defined as the difference between the data and the post-fit background prediction, divided by the statistical uncertainty in the data. |
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Figure 8-b:
Distribution of the SvsB classifier score in the $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ category for $ \mathrm{SR_{3\mathrm{b}}} $ data (black points) compared to the data-driven background prediction (blue histogram), for the pre-ParkingHH (left) and post-ParkingHH (right) data sets. The middle panel shows the ratio of data to the pre-fit (red open markers) and post b-only fit (black solid markers) background prediction, with the gray band indicating the background post-fit uncertainty. The lower panel show the distribution of the pulls, defined as the difference between the data and the post-fit background prediction, divided by the statistical uncertainty in the data. |
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Figure 9:
A schematic diagram of the 4b validation regions defined in the $ m_{\mathrm{H}_1} $--$ m_{\mathrm{H}_2} $ mass plane and orthogonal to the $ \mathrm{SR_{4\mathrm{b}}} $. In each validation region, the solid blue area identifies the signal region, while the dashed blue lines indicate the corresponding control region. The ``leading'' H candidate is the one with largest $ p_{\mathrm{T}} $(H). |
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Figure 10:
Pre-fit and post b-only fit distributions of the SvsB classifier output for the sum of all 4b validation regions in pre-ParkingHH (left) and post-ParkingHH (right) data. |
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Figure 10-a:
Pre-fit and post b-only fit distributions of the SvsB classifier output for the sum of all 4b validation regions in pre-ParkingHH (left) and post-ParkingHH (right) data. |
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Figure 10-b:
Pre-fit and post b-only fit distributions of the SvsB classifier output for the sum of all 4b validation regions in pre-ParkingHH (left) and post-ParkingHH (right) data. |
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Figure 11:
Post-fit distributions of the SvsB classifier score in the $ \mathrm{SR_{4\mathrm{b}}} $ of the $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ resolved analysis for data (black points) and the predicted background (blue filled histograms), for pre-ParkingHH (left) and post-ParkingHH (right) data. The distributions of the SM $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ (orange line) and $ \text{qq}\mathrm{H}\mathrm{H} $ (red line) signals, scaled to improve their visibility, are overlaid. |
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Figure 11-a:
Post-fit distributions of the SvsB classifier score in the $ \mathrm{SR_{4\mathrm{b}}} $ of the $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ resolved analysis for data (black points) and the predicted background (blue filled histograms), for pre-ParkingHH (left) and post-ParkingHH (right) data. The distributions of the SM $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ (orange line) and $ \text{qq}\mathrm{H}\mathrm{H} $ (red line) signals, scaled to improve their visibility, are overlaid. |
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Figure 11-b:
Post-fit distributions of the SvsB classifier score in the $ \mathrm{SR_{4\mathrm{b}}} $ of the $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ resolved analysis for data (black points) and the predicted background (blue filled histograms), for pre-ParkingHH (left) and post-ParkingHH (right) data. The distributions of the SM $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ (orange line) and $ \text{qq}\mathrm{H}\mathrm{H} $ (red line) signals, scaled to improve their visibility, are overlaid. |
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Figure 12:
Post-fit distributions of the SvsB output score in the $ \mathrm{SR_{4\mathrm{b}}} $ of the $ \text{qq}\mathrm{H}\mathrm{H} $ resolved analysis reported for data (black points) and the predicted background (blue filled histograms) for pre-ParkingHH (left) and post-ParkingHH (right) data. The distributions of the SM $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ (orange line) and $ \text{qq}\mathrm{H}\mathrm{H} $(red line) signals, scaled to improve their visibility, are overlaid. |
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Figure 12-a:
Post-fit distributions of the SvsB output score in the $ \mathrm{SR_{4\mathrm{b}}} $ of the $ \text{qq}\mathrm{H}\mathrm{H} $ resolved analysis reported for data (black points) and the predicted background (blue filled histograms) for pre-ParkingHH (left) and post-ParkingHH (right) data. The distributions of the SM $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ (orange line) and $ \text{qq}\mathrm{H}\mathrm{H} $(red line) signals, scaled to improve their visibility, are overlaid. |
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Figure 12-b:
Post-fit distributions of the SvsB output score in the $ \mathrm{SR_{4\mathrm{b}}} $ of the $ \text{qq}\mathrm{H}\mathrm{H} $ resolved analysis reported for data (black points) and the predicted background (blue filled histograms) for pre-ParkingHH (left) and post-ParkingHH (right) data. The distributions of the SM $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ (orange line) and $ \text{qq}\mathrm{H}\mathrm{H} $(red line) signals, scaled to improve their visibility, are overlaid. |
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Figure 13:
The expected HH, ZH, and ZZ signal yields as estimated from simulation (left) and the observed data (right) for the Run 3 dataset, in the 3T1M region, as a function of the reconstructed masses of the leading and subleading in $ p_{\mathrm{T}} \mathrm{H} $ candidates. The signal region is defined by the union of the regions enclosed by the dashed red lines. |
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Figure 13-a:
The expected HH, ZH, and ZZ signal yields as estimated from simulation (left) and the observed data (right) for the Run 3 dataset, in the 3T1M region, as a function of the reconstructed masses of the leading and subleading in $ p_{\mathrm{T}} \mathrm{H} $ candidates. The signal region is defined by the union of the regions enclosed by the dashed red lines. |
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Figure 13-b:
The expected HH, ZH, and ZZ signal yields as estimated from simulation (left) and the observed data (right) for the Run 3 dataset, in the 3T1M region, as a function of the reconstructed masses of the leading and subleading in $ p_{\mathrm{T}} \mathrm{H} $ candidates. The signal region is defined by the union of the regions enclosed by the dashed red lines. |
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Figure 14:
Distribution of the $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $, $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $, ZZ, and ZH signal processes, normalized to unity, as a function of the three FEYNNET probability scores. |
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Figure 15:
Postfit distribution of the $ D $ ($\mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H}$-vs-bkg) (upper left), $ D $ ($\mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H}$-vs-bkg) (upper right), $ D $ ($\mathrm{Z}\mathrm{Z}$-vs-bkg) (lower left), and $ D $ ($\mathrm{Z}\mathrm{H}$-vs-bkg) (lower right) scores in the validation region $ \text{SR}_{\text{3MnT}} $ for data (black points) and the predicted background (cyan filled histograms) with the Run 3 dataset. |
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Figure 15-a:
Postfit distribution of the $ D $ ($\mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H}$-vs-bkg) (upper left), $ D $ ($\mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H}$-vs-bkg) (upper right), $ D $ ($\mathrm{Z}\mathrm{Z}$-vs-bkg) (lower left), and $ D $ ($\mathrm{Z}\mathrm{H}$-vs-bkg) (lower right) scores in the validation region $ \text{SR}_{\text{3MnT}} $ for data (black points) and the predicted background (cyan filled histograms) with the Run 3 dataset. |
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Figure 15-b:
Postfit distribution of the $ D $ ($\mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H}$-vs-bkg) (upper left), $ D $ ($\mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H}$-vs-bkg) (upper right), $ D $ ($\mathrm{Z}\mathrm{Z}$-vs-bkg) (lower left), and $ D $ ($\mathrm{Z}\mathrm{H}$-vs-bkg) (lower right) scores in the validation region $ \text{SR}_{\text{3MnT}} $ for data (black points) and the predicted background (cyan filled histograms) with the Run 3 dataset. |
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Figure 15-c:
Postfit distribution of the $ D $ ($\mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H}$-vs-bkg) (upper left), $ D $ ($\mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H}$-vs-bkg) (upper right), $ D $ ($\mathrm{Z}\mathrm{Z}$-vs-bkg) (lower left), and $ D $ ($\mathrm{Z}\mathrm{H}$-vs-bkg) (lower right) scores in the validation region $ \text{SR}_{\text{3MnT}} $ for data (black points) and the predicted background (cyan filled histograms) with the Run 3 dataset. |
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Figure 15-d:
Postfit distribution of the $ D $ ($\mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H}$-vs-bkg) (upper left), $ D $ ($\mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H}$-vs-bkg) (upper right), $ D $ ($\mathrm{Z}\mathrm{Z}$-vs-bkg) (lower left), and $ D $ ($\mathrm{Z}\mathrm{H}$-vs-bkg) (lower right) scores in the validation region $ \text{SR}_{\text{3MnT}} $ for data (black points) and the predicted background (cyan filled histograms) with the Run 3 dataset. |
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Figure 16:
Postfit distributions of the transformed $ D $ ($\mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H}$-vs-bkg) score in the $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} \text{SR}_{\text{3T1M}} $ (left) and $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} \text{SR}_{\text{3T1L}} $ (middle) categories, and $ D $ ($\mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H}$-vs-bkg) score in the $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} \text{SR}_{\text{3T1M}} $ (right) category for data (black points) and the predicted background (cyan filled histograms) for the Run 3 dataset. The distributions of the SM $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ (orange line) and $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ (red line) signal processes, scaled to improve their visibility, are also overlaid. |
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Figure 16-a:
Postfit distributions of the transformed $ D $ ($\mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H}$-vs-bkg) score in the $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} \text{SR}_{\text{3T1M}} $ (left) and $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} \text{SR}_{\text{3T1L}} $ (middle) categories, and $ D $ ($\mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H}$-vs-bkg) score in the $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} \text{SR}_{\text{3T1M}} $ (right) category for data (black points) and the predicted background (cyan filled histograms) for the Run 3 dataset. The distributions of the SM $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ (orange line) and $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ (red line) signal processes, scaled to improve their visibility, are also overlaid. |
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Figure 16-b:
Postfit distributions of the transformed $ D $ ($\mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H}$-vs-bkg) score in the $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} \text{SR}_{\text{3T1M}} $ (left) and $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} \text{SR}_{\text{3T1L}} $ (middle) categories, and $ D $ ($\mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H}$-vs-bkg) score in the $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} \text{SR}_{\text{3T1M}} $ (right) category for data (black points) and the predicted background (cyan filled histograms) for the Run 3 dataset. The distributions of the SM $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ (orange line) and $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ (red line) signal processes, scaled to improve their visibility, are also overlaid. |
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Figure 16-c:
Postfit distributions of the transformed $ D $ ($\mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H}$-vs-bkg) score in the $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} \text{SR}_{\text{3T1M}} $ (left) and $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} \text{SR}_{\text{3T1L}} $ (middle) categories, and $ D $ ($\mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H}$-vs-bkg) score in the $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} \text{SR}_{\text{3T1M}} $ (right) category for data (black points) and the predicted background (cyan filled histograms) for the Run 3 dataset. The distributions of the SM $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ (orange line) and $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ (red line) signal processes, scaled to improve their visibility, are also overlaid. |
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Figure 17:
Postfit distribution of the transformed $ D $ ($\mathrm{Z}\mathrm{Z}$-vs-bkg) score in the $ \mathrm{Z}\mathrm{Z} \text{SR}_{\text{3T1M}} $ (upper left) and $ \mathrm{Z}\mathrm{Z} \text{SR}_{\text{3T1L}} $ (upper right) categories, and $ D $ ($\mathrm{Z}\mathrm{H}$-vs-bkg) score in the $ \mathrm{Z}\mathrm{H} \text{SR}_{\text{3T1M}} $ (lower left) and $ \mathrm{Z}\mathrm{H} \text{SR}_{\text{3T1L}} $ (lower right) SR for data (black points) and the predicted background (cyan filled histograms) for the Run 3 dataset. The distributions of the SM ZZ (green line) and ZH (purple line) processes are also overlaid. |
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Figure 17-a:
Postfit distribution of the transformed $ D $ ($\mathrm{Z}\mathrm{Z}$-vs-bkg) score in the $ \mathrm{Z}\mathrm{Z} \text{SR}_{\text{3T1M}} $ (upper left) and $ \mathrm{Z}\mathrm{Z} \text{SR}_{\text{3T1L}} $ (upper right) categories, and $ D $ ($\mathrm{Z}\mathrm{H}$-vs-bkg) score in the $ \mathrm{Z}\mathrm{H} \text{SR}_{\text{3T1M}} $ (lower left) and $ \mathrm{Z}\mathrm{H} \text{SR}_{\text{3T1L}} $ (lower right) SR for data (black points) and the predicted background (cyan filled histograms) for the Run 3 dataset. The distributions of the SM ZZ (green line) and ZH (purple line) processes are also overlaid. |
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Figure 17-b:
Postfit distribution of the transformed $ D $ ($\mathrm{Z}\mathrm{Z}$-vs-bkg) score in the $ \mathrm{Z}\mathrm{Z} \text{SR}_{\text{3T1M}} $ (upper left) and $ \mathrm{Z}\mathrm{Z} \text{SR}_{\text{3T1L}} $ (upper right) categories, and $ D $ ($\mathrm{Z}\mathrm{H}$-vs-bkg) score in the $ \mathrm{Z}\mathrm{H} \text{SR}_{\text{3T1M}} $ (lower left) and $ \mathrm{Z}\mathrm{H} \text{SR}_{\text{3T1L}} $ (lower right) SR for data (black points) and the predicted background (cyan filled histograms) for the Run 3 dataset. The distributions of the SM ZZ (green line) and ZH (purple line) processes are also overlaid. |
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Figure 17-c:
Postfit distribution of the transformed $ D $ ($\mathrm{Z}\mathrm{Z}$-vs-bkg) score in the $ \mathrm{Z}\mathrm{Z} \text{SR}_{\text{3T1M}} $ (upper left) and $ \mathrm{Z}\mathrm{Z} \text{SR}_{\text{3T1L}} $ (upper right) categories, and $ D $ ($\mathrm{Z}\mathrm{H}$-vs-bkg) score in the $ \mathrm{Z}\mathrm{H} \text{SR}_{\text{3T1M}} $ (lower left) and $ \mathrm{Z}\mathrm{H} \text{SR}_{\text{3T1L}} $ (lower right) SR for data (black points) and the predicted background (cyan filled histograms) for the Run 3 dataset. The distributions of the SM ZZ (green line) and ZH (purple line) processes are also overlaid. |
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Figure 17-d:
Postfit distribution of the transformed $ D $ ($\mathrm{Z}\mathrm{Z}$-vs-bkg) score in the $ \mathrm{Z}\mathrm{Z} \text{SR}_{\text{3T1M}} $ (upper left) and $ \mathrm{Z}\mathrm{Z} \text{SR}_{\text{3T1L}} $ (upper right) categories, and $ D $ ($\mathrm{Z}\mathrm{H}$-vs-bkg) score in the $ \mathrm{Z}\mathrm{H} \text{SR}_{\text{3T1M}} $ (lower left) and $ \mathrm{Z}\mathrm{H} \text{SR}_{\text{3T1L}} $ (lower right) SR for data (black points) and the predicted background (cyan filled histograms) for the Run 3 dataset. The distributions of the SM ZZ (green line) and ZH (purple line) processes are also overlaid. |
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Figure 18:
The fitted signal+background distribution of the signal probability, $ \mathcal{P_{\mathrm{H}\mathrm{H}}} $, in the $ \mathrm{H}\mathrm{H} \mathrm{SR_{4\mathrm{b}}} $. The black points show the 4b events from data. The yellow and blue regions show the predictions from the QCD multijet model and the $ \mathrm{t} \overline{\mathrm{t}} $ simulation, respectively. The prediction for the SM $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ signal distribution is given by the red histogram, multiplied by 100. The lower panel shows the data-to-background ratio, with the hatched area representing the background uncertainty. |
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Figure 19:
Left: schematic diagram showing the regions used for the data-driven background estimation strategy used in the merged channel. The purity in QCD multijet events is reported in each of the background-enriched regions ($ \mathrm{CR_{QCD,A}} $, $ \mathrm{CR_{QCD,B}} $, and $ \mathrm{CR_{QCD,C}} $). Right: schematic diagram of the signal (orange area) and control regions (QCD in green, $ \mathrm{t} \overline{\mathrm{t}} $ in azure) in the plane defined by the $ m_\text{reg}({\mathrm{H}_1}) $ and $ m_\text{reg}({\mathrm{H}_2}) $. |
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Figure 19-a:
Left: schematic diagram showing the regions used for the data-driven background estimation strategy used in the merged channel. The purity in QCD multijet events is reported in each of the background-enriched regions ($ \mathrm{CR_{QCD,A}} $, $ \mathrm{CR_{QCD,B}} $, and $ \mathrm{CR_{QCD,C}} $). Right: schematic diagram of the signal (orange area) and control regions (QCD in green, $ \mathrm{t} \overline{\mathrm{t}} $ in azure) in the plane defined by the $ m_\text{reg}({\mathrm{H}_1}) $ and $ m_\text{reg}({\mathrm{H}_2}) $. |
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Figure 19-b:
Left: schematic diagram showing the regions used for the data-driven background estimation strategy used in the merged channel. The purity in QCD multijet events is reported in each of the background-enriched regions ($ \mathrm{CR_{QCD,A}} $, $ \mathrm{CR_{QCD,B}} $, and $ \mathrm{CR_{QCD,C}} $). Right: schematic diagram of the signal (orange area) and control regions (QCD in green, $ \mathrm{t} \overline{\mathrm{t}} $ in azure) in the plane defined by the $ m_\text{reg}({\mathrm{H}_1}) $ and $ m_\text{reg}({\mathrm{H}_2}) $. |
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Figure 20:
Pre-fit and post-fit distributions of the fitted observables for the $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $-inclusive HPSR (left) and LPSR (right) categories of the merged analysis following the mass-fit method. Distributions are shown for data (black points) and the different background contributions from QCD multijet, $ \mathrm{t} \overline{\mathrm{t}} $, $ \mathrm{V}+\text{jets} $, dibosons, and ZH productions. The expected distributions for SM $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ (orange) and $ \text{qq}\mathrm{H}\mathrm{H} $ (red) signals are overlaid and scaled by a multiplicative factor to improve their visibility. |
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Figure 20-a:
Pre-fit and post-fit distributions of the fitted observables for the $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $-inclusive HPSR (left) and LPSR (right) categories of the merged analysis following the mass-fit method. Distributions are shown for data (black points) and the different background contributions from QCD multijet, $ \mathrm{t} \overline{\mathrm{t}} $, $ \mathrm{V}+\text{jets} $, dibosons, and ZH productions. The expected distributions for SM $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ (orange) and $ \text{qq}\mathrm{H}\mathrm{H} $ (red) signals are overlaid and scaled by a multiplicative factor to improve their visibility. |
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Figure 20-b:
Pre-fit and post-fit distributions of the fitted observables for the $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $-inclusive HPSR (left) and LPSR (right) categories of the merged analysis following the mass-fit method. Distributions are shown for data (black points) and the different background contributions from QCD multijet, $ \mathrm{t} \overline{\mathrm{t}} $, $ \mathrm{V}+\text{jets} $, dibosons, and ZH productions. The expected distributions for SM $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ (orange) and $ \text{qq}\mathrm{H}\mathrm{H} $ (red) signals are overlaid and scaled by a multiplicative factor to improve their visibility. |
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Figure 21:
Pre-fit and post-fit distributions of the fitted observables for the $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $-inclusive HPSR (left) and LPSR (right) categories of the merged analysis following the DNN-fit method. Distributions are shown for data (black points) and the different background contributions from QCD multijet, $ \mathrm{t} \overline{\mathrm{t}} $, $ \mathrm{V}+\text{jets} $, dibosons, and ZH productions. The expected distributions for SM $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ (orange) and $ \text{qq}\mathrm{H}\mathrm{H} $ (red) signals are overlaid and scaled by a multiplicative factor to improve their visibility. |
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Figure 21-a:
Pre-fit and post-fit distributions of the fitted observables for the $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $-inclusive HPSR (left) and LPSR (right) categories of the merged analysis following the DNN-fit method. Distributions are shown for data (black points) and the different background contributions from QCD multijet, $ \mathrm{t} \overline{\mathrm{t}} $, $ \mathrm{V}+\text{jets} $, dibosons, and ZH productions. The expected distributions for SM $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ (orange) and $ \text{qq}\mathrm{H}\mathrm{H} $ (red) signals are overlaid and scaled by a multiplicative factor to improve their visibility. |
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Figure 21-b:
Pre-fit and post-fit distributions of the fitted observables for the $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $-inclusive HPSR (left) and LPSR (right) categories of the merged analysis following the DNN-fit method. Distributions are shown for data (black points) and the different background contributions from QCD multijet, $ \mathrm{t} \overline{\mathrm{t}} $, $ \mathrm{V}+\text{jets} $, dibosons, and ZH productions. The expected distributions for SM $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ (orange) and $ \text{qq}\mathrm{H}\mathrm{H} $ (red) signals are overlaid and scaled by a multiplicative factor to improve their visibility. |
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Figure 22:
Pre-fit and post-fit distributions of the fitted observables for the $ \text{qq}\mathrm{H}\mathrm{H} $ HPSR (left) and LPSR (right) categories of the merged analysis. Distributions are shown for data (black points) and the different background contributions from QCD multijet, $ \mathrm{t} \overline{\mathrm{t}} $, $ \mathrm{V}+\text{jets} $, dibosons, and ZH productions. The expected distributions for SM $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ (orange) and $ \text{qq}\mathrm{H}\mathrm{H} $ (red) signals are overlaid and scaled by a multiplicative factor to improve their visibility. |
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Figure 22-a:
Pre-fit and post-fit distributions of the fitted observables for the $ \text{qq}\mathrm{H}\mathrm{H} $ HPSR (left) and LPSR (right) categories of the merged analysis. Distributions are shown for data (black points) and the different background contributions from QCD multijet, $ \mathrm{t} \overline{\mathrm{t}} $, $ \mathrm{V}+\text{jets} $, dibosons, and ZH productions. The expected distributions for SM $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ (orange) and $ \text{qq}\mathrm{H}\mathrm{H} $ (red) signals are overlaid and scaled by a multiplicative factor to improve their visibility. |
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Figure 22-b:
Pre-fit and post-fit distributions of the fitted observables for the $ \text{qq}\mathrm{H}\mathrm{H} $ HPSR (left) and LPSR (right) categories of the merged analysis. Distributions are shown for data (black points) and the different background contributions from QCD multijet, $ \mathrm{t} \overline{\mathrm{t}} $, $ \mathrm{V}+\text{jets} $, dibosons, and ZH productions. The expected distributions for SM $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ (orange) and $ \text{qq}\mathrm{H}\mathrm{H} $ (red) signals are overlaid and scaled by a multiplicative factor to improve their visibility. |
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Figure 23:
Schematic diagrams showing the SRs and QCD CR (gray) used in the merged analysis described in Section 6.3. Left: the $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ SR 1 (red), 2 (blue), and 3 (orange) are defined based on successively lower selections on the $ T_\text{Xbb} $ score of the \HepParticleHu candidate and the D(\text$ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $-vs-bkg) score. Right: the $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ SR (purple) is defined based on a Tight selection on D(\text$ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $-vs-bkg) and a Loose selection on $ T_\text{Xbb} $ of the \HepParticleHu candidate. |
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Figure 24:
The fitted signal+background distributions in the regressed mass of the secondary Higgs boson candidate $ m_\text{reg}(\mathrm{H_u}) $ in $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ SR 1 (upper left), the $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ SR (upper right), $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ SR 2 (lower left), and $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ SR 3 (lower right). The SM $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ and $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ signal are overlaid in the $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ SRs scaled by different factors. The targeted $ \kappa_{2\mathrm{V}}= $ 0 $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ signal is also overlaid in the $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ SR. |
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Figure 24-a:
The fitted signal+background distributions in the regressed mass of the secondary Higgs boson candidate $ m_\text{reg}(\mathrm{H_u}) $ in $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ SR 1 (upper left), the $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ SR (upper right), $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ SR 2 (lower left), and $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ SR 3 (lower right). The SM $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ and $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ signal are overlaid in the $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ SRs scaled by different factors. The targeted $ \kappa_{2\mathrm{V}}= $ 0 $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ signal is also overlaid in the $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ SR. |
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Figure 24-b:
The fitted signal+background distributions in the regressed mass of the secondary Higgs boson candidate $ m_\text{reg}(\mathrm{H_u}) $ in $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ SR 1 (upper left), the $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ SR (upper right), $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ SR 2 (lower left), and $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ SR 3 (lower right). The SM $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ and $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ signal are overlaid in the $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ SRs scaled by different factors. The targeted $ \kappa_{2\mathrm{V}}= $ 0 $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ signal is also overlaid in the $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ SR. |
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Figure 24-c:
The fitted signal+background distributions in the regressed mass of the secondary Higgs boson candidate $ m_\text{reg}(\mathrm{H_u}) $ in $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ SR 1 (upper left), the $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ SR (upper right), $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ SR 2 (lower left), and $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ SR 3 (lower right). The SM $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ and $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ signal are overlaid in the $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ SRs scaled by different factors. The targeted $ \kappa_{2\mathrm{V}}= $ 0 $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ signal is also overlaid in the $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ SR. |
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Figure 24-d:
The fitted signal+background distributions in the regressed mass of the secondary Higgs boson candidate $ m_\text{reg}(\mathrm{H_u}) $ in $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ SR 1 (upper left), the $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ SR (upper right), $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ SR 2 (lower left), and $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ SR 3 (lower right). The SM $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ and $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ signal are overlaid in the $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $ SRs scaled by different factors. The targeted $ \kappa_{2\mathrm{V}}= $ 0 $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ signal is also overlaid in the $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ SR. |
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Figure 25:
Left: the observed (solid) and expected (dashed) 95% CL upper limits on the signal strength of HH production from the resolved analysis with overlap removed, the merged HPSR mass-fit category, and their combination. The cyan and blue bands represent, respectively, the 68 and 95% CL intervals around the expected limit. Right: the same breakdown of 95% CL upper limits on the signal strength of $ \text{qq}\mathrm{H}\mathrm{H} $ production. |
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Figure 25-a:
Left: the observed (solid) and expected (dashed) 95% CL upper limits on the signal strength of HH production from the resolved analysis with overlap removed, the merged HPSR mass-fit category, and their combination. The cyan and blue bands represent, respectively, the 68 and 95% CL intervals around the expected limit. Right: the same breakdown of 95% CL upper limits on the signal strength of $ \text{qq}\mathrm{H}\mathrm{H} $ production. |
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Figure 25-b:
Left: the observed (solid) and expected (dashed) 95% CL upper limits on the signal strength of HH production from the resolved analysis with overlap removed, the merged HPSR mass-fit category, and their combination. The cyan and blue bands represent, respectively, the 68 and 95% CL intervals around the expected limit. Right: the same breakdown of 95% CL upper limits on the signal strength of $ \text{qq}\mathrm{H}\mathrm{H} $ production. |
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Figure 26:
The observed (solid) and expected (dashed) 95% CL upper limits on the signal strength of the HH production ($ \mu_{\mathrm{H}\mathrm{H}} $) obtained as a function of $ \kappa_{\lambda} $ (left) and $ \kappa_{\text{2V}} $ (right) for the combined fit of resolved and merged $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analyses. The cyan and blue bands represent, respectively, the 68 and 95% CL intervals around the expected limit. The horizontal red lines indicate the SM prediction. |
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Figure 26-a:
The observed (solid) and expected (dashed) 95% CL upper limits on the signal strength of the HH production ($ \mu_{\mathrm{H}\mathrm{H}} $) obtained as a function of $ \kappa_{\lambda} $ (left) and $ \kappa_{\text{2V}} $ (right) for the combined fit of resolved and merged $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analyses. The cyan and blue bands represent, respectively, the 68 and 95% CL intervals around the expected limit. The horizontal red lines indicate the SM prediction. |
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Figure 26-b:
The observed (solid) and expected (dashed) 95% CL upper limits on the signal strength of the HH production ($ \mu_{\mathrm{H}\mathrm{H}} $) obtained as a function of $ \kappa_{\lambda} $ (left) and $ \kappa_{\text{2V}} $ (right) for the combined fit of resolved and merged $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analyses. The cyan and blue bands represent, respectively, the 68 and 95% CL intervals around the expected limit. The horizontal red lines indicate the SM prediction. |
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Figure 27:
The observed (solid) and expected (dashed) profile likelihood ratios as a function of $ \kappa_{\lambda} $ (left) and $ \kappa_{\text{2V}} $ (right) for the combined fit of resolved and merged $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analyses, where the expected is obtained from an Asimov dataset [100] defined by fixing the nuisances parameters to their maximum likelihood estimate obtained from data in which $ \mu_{\mathrm{H}\mathrm{H}}= $ 1. The 68 and 95% CL levels are indicated with the dashed red lines. |
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Figure 27-a:
The observed (solid) and expected (dashed) profile likelihood ratios as a function of $ \kappa_{\lambda} $ (left) and $ \kappa_{\text{2V}} $ (right) for the combined fit of resolved and merged $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analyses, where the expected is obtained from an Asimov dataset [100] defined by fixing the nuisances parameters to their maximum likelihood estimate obtained from data in which $ \mu_{\mathrm{H}\mathrm{H}}= $ 1. The 68 and 95% CL levels are indicated with the dashed red lines. |
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Figure 27-b:
The observed (solid) and expected (dashed) profile likelihood ratios as a function of $ \kappa_{\lambda} $ (left) and $ \kappa_{\text{2V}} $ (right) for the combined fit of resolved and merged $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analyses, where the expected is obtained from an Asimov dataset [100] defined by fixing the nuisances parameters to their maximum likelihood estimate obtained from data in which $ \mu_{\mathrm{H}\mathrm{H}}= $ 1. The 68 and 95% CL levels are indicated with the dashed red lines. |
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Figure 28:
The observed (blue) and expected (orange) 2D exclusion range for ($ \mu_{\mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H}} $, $ \mu_{\text{qq}\mathrm{H}\mathrm{H}} $) (left) and ($ \kappa_{\lambda} $,$ \kappa_{\text{2V}} $) (right) for the combination of resolved and merged $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analyses. The solid and dashed lines represent the 68 and 95% CL exclusion contours, respectively. The red circle indicates the SM prediction, while the black cross shows the best-fit result. |
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Figure 28-a:
The observed (blue) and expected (orange) 2D exclusion range for ($ \mu_{\mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H}} $, $ \mu_{\text{qq}\mathrm{H}\mathrm{H}} $) (left) and ($ \kappa_{\lambda} $,$ \kappa_{\text{2V}} $) (right) for the combination of resolved and merged $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analyses. The solid and dashed lines represent the 68 and 95% CL exclusion contours, respectively. The red circle indicates the SM prediction, while the black cross shows the best-fit result. |
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Figure 28-b:
The observed (blue) and expected (orange) 2D exclusion range for ($ \mu_{\mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H}} $, $ \mu_{\text{qq}\mathrm{H}\mathrm{H}} $) (left) and ($ \kappa_{\lambda} $,$ \kappa_{\text{2V}} $) (right) for the combination of resolved and merged $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analyses. The solid and dashed lines represent the 68 and 95% CL exclusion contours, respectively. The red circle indicates the SM prediction, while the black cross shows the best-fit result. |
| Tables | |
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Table 1:
The observed (expected) upper limits at 95% CL on the $ \mu_{\mathrm{Z}\mathrm{Z}} $ and $ \mu_{\mathrm{Z}\mathrm{H}} $, observed signal strength and significance. The upper limits are obtained from a fit on the $ D $ ($\mathrm{Z}\mathrm{Z}$-vs-bkg) and $ D $ ($\mathrm{Z}\mathrm{H}$-vs-bkg) scores under the hypothesis of no $ \mathrm{Z}\mathrm{Z} \rightarrow4\mathrm{b} $ or $ \mathrm{Z}\mathrm{H} \rightarrow4\mathrm{b} $ signal. |
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Table 2:
Expected best-fit values and 95% CL upper limits (``U.L.'') for $ \mu_{\mathrm{HH}} $, $ \mu_{\mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H}} $, and $ \mu_{\text{qq}\mathrm{H}\mathrm{H}} $ in the $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ resolved analysis following the two approaches described in Secs. 5.2 and 5.3, respectively. The uncertainties given for the best-fit signal strengths correspond to the 68% CL intervals. The best-fit signal strengths are calculated with a SM $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ signal injected, while the upper limits are calculated in the absence of signal. |
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Table 3:
Observed best-fit values and 95% CL upper limits (``U.L.'') for $ \mu_{\mathrm{HH}} $, $ \mu_{\mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H}} $, and $ \mu_{\text{qq}\mathrm{H}\mathrm{H}} $ in the $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ resolved analysis following the two approaches described in Secs. 5.2 and 5.3, respectively. The uncertainties given for the best-fit signal strengths correspond to the 68% CL intervals. |
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Table 4:
Observed and expected, in absence of signal, 95% CL intervals for $ \kappa_{\lambda} $ and $ \kappa_{\text{2V}} $ in the $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ resolved analysis, following the two approaches described in Secs. 5.2 and 5.3, respectively. |
png pdf |
Table 5:
Expected and observed $ \mu_{\mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H}} $ and their corresponding upper limits at 95% CL in the $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ resolved channel with Run 2 data (described in Section 5.4). The observed and expected 95% CL intervals for $ \kappa_{\lambda} $ are also reported. |
png pdf |
Table 6:
The expected best-fit signal strengths and 95% CL upper limits on the inclusive, $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $, and $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ signal strengths for the SM scenario for the two approaches described in Sections 6.2 and 6.3, respectively. The expected best-fit signal strength and 95% CL upper limit on the HH signal strength for the non-SM $ \kappa_{2\mathrm{V}}= $ 0.5 scenario are also reported. The uncertainties given for the best-fit signal strengths correspond to the 68% CL intervals. The best-fit signal strengths are calculated with a SM $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ signal injected, while the upper limits are calculated in the absence of signal. |
png pdf |
Table 7:
The observed best-fit signal strengths and 95% CL upper limits on the inclusive, $ \mathrm{g}\mathrm{g}\mathrm{H}\mathrm{H} $, and $ \mathrm{q}\mathrm{q}\mathrm{H}\mathrm{H} $ signal strengths for the SM scenario for the two approaches described in Sections 6.2 and 6.3, respectively. The best-fit and observed 95% CL upper limits on the HH signal strength for the non-SM $ \kappa_{2\mathrm{V}}= $ 0.5 are also reported. The uncertainties given for the best-fit signal strengths correspond to the 68% CL intervals. |
png pdf |
Table 8:
The observed and expected 95% CL intervals for $ \kappa_\lambda $ and $ \kappa_{2\mathrm{V}} $ in the merged channel for the two approaches described in Sections 6.2 and 6.3, respectively. |
png pdf |
Table 9:
Expected and observed best-fit values for the signal strengths, $ \kappa_{\lambda} $, and $ \kappa_{\text{2V}} $ from the combined fit of the $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ resolved and merged analyses. The uncertainties given correspond to the 68% CL intervals. The expected results are calculated with a SM $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ signal injected. |
| Summary |
| Measurements of Higgs boson pair (HH) production in the four bottom quark final state are presented using a data set of proton-proton (pp) collisions at $ \sqrt{s}= $ 13.6 TeV collected by the CMS experiment during 2022-2023 and corresponding to an integrated luminosity of 62 fb$ ^{-1} $. Events in which each Higgs boson decay is separately reconstructed as a pair of small-radius jets (resolved), as well as events in which each $ \mathrm{H}\to\mathrm{b}\overline{\mathrm{b}} $ decay is reconstructed as a single large-radius jet (merged) are analyzed exclusively. Benefiting from novel analysis techniques, the combination of resolved and merged channels gives an observed (expected) upper limit at 95% confidence level (CL) on the HH signal strength $ \mu_{\mathrm{H}\mathrm{H}} $, defined as the observed HH production cross section divided by the standard model (SM) prediction, of 4.4 (4.4). Compared to previous LHC results, the expected limit with an equivalent integrated luminosity is improved by more than a factor two in the resolved topology and significantly improved in the merged topology as well. The allowed ranges at 95% CL for the Higgs trilinear self-coupling and quartic coupling between two Higgs bosons and two vector bosons, relative to the standard model expectation, are observed (expected, in absence of signal) to be $ [-3.3,9.7] $ ($ [-3.4,10.0] $) and $ [0.63,1.43] $ ($ [0.54,1.51] $), respectively. An updated analysis of the resolved topology using a 13 TeV pp collision data set corresponding to 138 fb$ ^{-1} $ and collected in 2016-2018, reports an observed (expected) 95% CL upper limit on $ \mu_{\mathrm{H}\mathrm{H}} $ of 10.0 (5.9), an improvement of about 25% in the expected limit compared to the published results using the same data. |
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