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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
png pdf	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} $.
png pdf	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} $.
png pdf	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} $.
png pdf	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} $.
png pdf	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} $.
png pdf	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} $.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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}}} $.
png pdf	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}}} $.
png pdf	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}}} $.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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).
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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}) $.
png pdf	Figure 19-a: Left: schematic diagram showing the regions used for the data-driven background estimation strategy used in the merged channel. The purity in QCD multijet events is reported in each of the background-enriched regions ($ \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}) $.
png pdf	Figure 19-b: Left: schematic diagram showing the regions used for the data-driven background estimation strategy used in the merged channel. The purity in QCD multijet events is reported in each of the background-enriched regions ($ \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}) $.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.

Additional Figures
png pdf	Additional Figure 1: 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{bb} $ VHP (top left), HP (top right), and MP (bottom left) 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 (bottom right). Each process considered in the fit is modeled via a parametric function as described in the text.
png pdf	Additional Figure 1-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{bb} $ VHP (top left), HP (top right), and MP (bottom left) 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 (bottom right). Each process considered in the fit is modeled via a parametric function as described in the text.
png pdf	Additional Figure 1-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{bb} $ VHP (top left), HP (top right), and MP (bottom left) 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 (bottom right). Each process considered in the fit is modeled via a parametric function as described in the text.
png pdf	Additional Figure 1-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{bb} $ VHP (top left), HP (top right), and MP (bottom left) 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 (bottom right). Each process considered in the fit is modeled via a parametric function as described in the text.
png pdf	Additional Figure 1-d: 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{bb} $ VHP (top left), HP (top right), and MP (bottom left) 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 (bottom right). Each process considered in the fit is modeled via a parametric function as described in the text.
png pdf	Additional Figure 2: 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{bb} $ VHP (top left), HP (top right), and MP (bottom left) categories. Data corresponds to the full integrated luminosity collected by the CMS detector in 2023. The same comparison is performed for the $m_{\mu\mu}$ distributions in the $ \mathrm{Z} \to \mu\mu $ region (bottom right). Each process considered in the fit is modeled via a parametric function as described in the text.
png pdf	Additional Figure 2-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{bb} $ VHP (top left), HP (top right), and MP (bottom left) categories. Data corresponds to the full integrated luminosity collected by the CMS detector in 2023. The same comparison is performed for the $m_{\mu\mu}$ distributions in the $ \mathrm{Z} \to \mu\mu $ region (bottom right). Each process considered in the fit is modeled via a parametric function as described in the text.
png pdf	Additional Figure 2-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{bb} $ VHP (top left), HP (top right), and MP (bottom left) categories. Data corresponds to the full integrated luminosity collected by the CMS detector in 2023. The same comparison is performed for the $m_{\mu\mu}$ distributions in the $ \mathrm{Z} \to \mu\mu $ region (bottom right). Each process considered in the fit is modeled via a parametric function as described in the text.
png pdf	Additional Figure 2-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{bb} $ VHP (top left), HP (top right), and MP (bottom left) categories. Data corresponds to the full integrated luminosity collected by the CMS detector in 2023. The same comparison is performed for the $m_{\mu\mu}$ distributions in the $ \mathrm{Z} \to \mu\mu $ region (bottom right). Each process considered in the fit is modeled via a parametric function as described in the text.
png pdf	Additional Figure 2-d: 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{bb} $ VHP (top left), HP (top right), and MP (bottom left) categories. Data corresponds to the full integrated luminosity collected by the CMS detector in 2023. The same comparison is performed for the $m_{\mu\mu}$ distributions in the $ \mathrm{Z} \to \mu\mu $ region (bottom right). Each process considered in the fit is modeled via a parametric function as described in the text.
png pdf	Additional Figure 3: Full suite of AK8 jet topologies used for the GloParT model training. Jet types are first categorized by the number of quarks and leptons in the final state, and then further separated by flavor. If the decay includes a V= W or Z boson, the class is further split based on whether the vector boson is on shell, leading to three versions of each $H\to\PV^{(\ast)}\PV^{(\ast)}$ class and two versions of each $\PQt\tob\PW^{(\ast)}$ class. Diagrams illustrating the corresponding jet topologies are also shown.
png pdf	Additional Figure 4: Transformed SvsB classifier output distribution for the reweighted $\mathrm{SR_{2b}}$ data events in the $\mathrm{SR_{4b}}$ region, shown for pre-ParkingHH (left) and post-ParkingHH (right) periods. Distributions correspond to the first analysis approach described in the note. In the upper panel, the solid blue line represents the nominal background prediction, obtained by averaging the event weights over the k-fold ensemble. The dashed lines indicate the background predictions obtained from each individual fold. In the lower panel, the red band shows the uncertainty in the $\mathrm{SR_{4b}}$ background prediction due to the limited size of the $\mathrm{SR_{2b}}$ sample, while the blue band corresponds to the symmetrized 68% CL interval around the nominal prediction as derived from the individual k-fold predictions. The statistical uncertainty from $\mathrm{SR_{2b}}$ data dominates in the highest SvsB score bins.
png pdf	Additional Figure 4-a: Transformed SvsB classifier output distribution for the reweighted $\mathrm{SR_{2b}}$ data events in the $\mathrm{SR_{4b}}$ region, shown for pre-ParkingHH (left) and post-ParkingHH (right) periods. Distributions correspond to the first analysis approach described in the note. In the upper panel, the solid blue line represents the nominal background prediction, obtained by averaging the event weights over the k-fold ensemble. The dashed lines indicate the background predictions obtained from each individual fold. In the lower panel, the red band shows the uncertainty in the $\mathrm{SR_{4b}}$ background prediction due to the limited size of the $\mathrm{SR_{2b}}$ sample, while the blue band corresponds to the symmetrized 68% CL interval around the nominal prediction as derived from the individual k-fold predictions. The statistical uncertainty from $\mathrm{SR_{2b}}$ data dominates in the highest SvsB score bins.
png pdf	Additional Figure 4-b: Transformed SvsB classifier output distribution for the reweighted $\mathrm{SR_{2b}}$ data events in the $\mathrm{SR_{4b}}$ region, shown for pre-ParkingHH (left) and post-ParkingHH (right) periods. Distributions correspond to the first analysis approach described in the note. In the upper panel, the solid blue line represents the nominal background prediction, obtained by averaging the event weights over the k-fold ensemble. The dashed lines indicate the background predictions obtained from each individual fold. In the lower panel, the red band shows the uncertainty in the $\mathrm{SR_{4b}}$ background prediction due to the limited size of the $\mathrm{SR_{2b}}$ sample, while the blue band corresponds to the symmetrized 68% CL interval around the nominal prediction as derived from the individual k-fold predictions. The statistical uncertainty from $\mathrm{SR_{2b}}$ data dominates in the highest SvsB score bins.
png pdf	Additional Figure 5: Data-driven shape uncertainties as a function of the SvsB classifier output for the reweighted $\mathrm{SR_{2b}}$ background events in the $\mathrm{SR_{4b}}$ region, shown for pre-ParkingHH (left) and post-ParkingHH (right) data. Distributions correspond to the first analysis approach described in the note. The solid (dashed) lines correspond to the +1$\sigma$ (-1$\sigma$) variations of the four Fourier basis components (azure, orange, red) and the bias (purple) uncertainty. The combined uncertainty, obtained by summing all components in quadrature, is shown as the solid gray filled band. Although the event selection and integrated luminosity differ between the two data-taking periods, the overall size of the shape uncertainties remains consistent. The overall uncertainty increases from 0.3% to 4.5% with increasing SvsB score.
png pdf	Additional Figure 5-a: Data-driven shape uncertainties as a function of the SvsB classifier output for the reweighted $\mathrm{SR_{2b}}$ background events in the $\mathrm{SR_{4b}}$ region, shown for pre-ParkingHH (left) and post-ParkingHH (right) data. Distributions correspond to the first analysis approach described in the note. The solid (dashed) lines correspond to the +1$\sigma$ (-1$\sigma$) variations of the four Fourier basis components (azure, orange, red) and the bias (purple) uncertainty. The combined uncertainty, obtained by summing all components in quadrature, is shown as the solid gray filled band. Although the event selection and integrated luminosity differ between the two data-taking periods, the overall size of the shape uncertainties remains consistent. The overall uncertainty increases from 0.3% to 4.5% with increasing SvsB score.
png pdf	Additional Figure 5-b: Data-driven shape uncertainties as a function of the SvsB classifier output for the reweighted $\mathrm{SR_{2b}}$ background events in the $\mathrm{SR_{4b}}$ region, shown for pre-ParkingHH (left) and post-ParkingHH (right) data. Distributions correspond to the first analysis approach described in the note. The solid (dashed) lines correspond to the +1$\sigma$ (-1$\sigma$) variations of the four Fourier basis components (azure, orange, red) and the bias (purple) uncertainty. The combined uncertainty, obtained by summing all components in quadrature, is shown as the solid gray filled band. Although the event selection and integrated luminosity differ between the two data-taking periods, the overall size of the shape uncertainties remains consistent. The overall uncertainty increases from 0.3% to 4.5% with increasing SvsB score.
png pdf	Additional Figure 6: Pre-fit and post b-only fit distributions of the SvsB classifier output for the ${\mathrm{VR_{4b,1}}}$ validation regions in pre-ParkingHH (left) and post-ParkingHH (right) data. Distributions correspond to the first analysis approach described in the note.
png pdf	Additional Figure 6-a: Pre-fit and post b-only fit distributions of the SvsB classifier output for the ${\mathrm{VR_{4b,1}}}$ validation regions in pre-ParkingHH (left) and post-ParkingHH (right) data. Distributions correspond to the first analysis approach described in the note.
png pdf	Additional Figure 6-b: Pre-fit and post b-only fit distributions of the SvsB classifier output for the ${\mathrm{VR_{4b,1}}}$ validation regions in pre-ParkingHH (left) and post-ParkingHH (right) data. Distributions correspond to the first analysis approach described in the note.
png pdf	Additional Figure 7: Pre-fit and post b-only fit distributions of the SvsB classifier output for the ${\mathrm{VR_{4b,2}}}$ validation regions in pre-ParkingHH (left) and post-ParkingHH (right) data. Distributions correspond to the first analysis approach described in the note.
png pdf	Additional Figure 7-a: Pre-fit and post b-only fit distributions of the SvsB classifier output for the ${\mathrm{VR_{4b,2}}}$ validation regions in pre-ParkingHH (left) and post-ParkingHH (right) data. Distributions correspond to the first analysis approach described in the note.
png pdf	Additional Figure 7-b: Pre-fit and post b-only fit distributions of the SvsB classifier output for the ${\mathrm{VR_{4b,2}}}$ validation regions in pre-ParkingHH (left) and post-ParkingHH (right) data. Distributions correspond to the first analysis approach described in the note.
png pdf	Additional Figure 8: Pre-fit and post b-only fit distributions of the SvsB classifier output for the ${\mathrm{VR_{4b,3}}}$ validation regions in pre-ParkingHH (left) and post-ParkingHH (right) data. Distributions correspond to the first analysis approach described in the note.
png pdf	Additional Figure 8-a: Pre-fit and post b-only fit distributions of the SvsB classifier output for the ${\mathrm{VR_{4b,3}}}$ validation regions in pre-ParkingHH (left) and post-ParkingHH (right) data. Distributions correspond to the first analysis approach described in the note.
png pdf	Additional Figure 8-b: Pre-fit and post b-only fit distributions of the SvsB classifier output for the ${\mathrm{VR_{4b,3}}}$ validation regions in pre-ParkingHH (left) and post-ParkingHH (right) data. Distributions correspond to the first analysis approach described in the note.
png pdf	Additional Figure 9: Pre-fit and post b-only fit distributions of the SvsB classifier output for the ${\mathrm{VR_{4b,4}}}$ validation regions in pre-ParkingHH (left) and post-ParkingHH (right) data. Distributions correspond to the first analysis approach described in the note.
png pdf	Additional Figure 9-a: Pre-fit and post b-only fit distributions of the SvsB classifier output for the ${\mathrm{VR_{4b,4}}}$ validation regions in pre-ParkingHH (left) and post-ParkingHH (right) data. Distributions correspond to the first analysis approach described in the note.
png pdf	Additional Figure 9-b: Pre-fit and post b-only fit distributions of the SvsB classifier output for the ${\mathrm{VR_{4b,4}}}$ validation regions in pre-ParkingHH (left) and post-ParkingHH (right) data. Distributions correspond to the first analysis approach described in the note.
png pdf	Additional Figure 10: Pre-fit and post b-only fit distributions of the SvsB classifier output for the ${\mathrm{VR_{4b,5}}}$ validation regions in pre-ParkingHH (left) and post-ParkingHH (right) data. Distributions correspond to the first analysis approach described in the note.
png pdf	Additional Figure 10-a: Pre-fit and post b-only fit distributions of the SvsB classifier output for the ${\mathrm{VR_{4b,5}}}$ validation regions in pre-ParkingHH (left) and post-ParkingHH (right) data. Distributions correspond to the first analysis approach described in the note.
png pdf	Additional Figure 10-b: Pre-fit and post b-only fit distributions of the SvsB classifier output for the ${\mathrm{VR_{4b,5}}}$ validation regions in pre-ParkingHH (left) and post-ParkingHH (right) data. Distributions correspond to the first analysis approach described in the note.
png pdf	Additional Figure 11: The observed (solid) and expected (dashed) 95% CL upper limits on the signal strength of the HH (left) and VBF (right) production (left) obtained as a function of $\mathrm{k}_{\lambda}$ (left) and $k_{VV}$(right) for the resolved $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analysis. 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. The observed (expected) allowed range, at 95% CL, for $\mathrm{k}_{\lambda}$ is {[-4.4,11.7]}~{([-3.8,11.0])}, while that for $k_{VV}$ is {[-0.08,2.20]}~{([-0.08,2.19])}. Results correspond to the first analysis approach described in the note.
png pdf	Additional Figure 11-a: The observed (solid) and expected (dashed) 95% CL upper limits on the signal strength of the HH (left) and VBF (right) production (left) obtained as a function of $\mathrm{k}_{\lambda}$ (left) and $k_{VV}$(right) for the resolved $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analysis. 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. The observed (expected) allowed range, at 95% CL, for $\mathrm{k}_{\lambda}$ is {[-4.4,11.7]}~{([-3.8,11.0])}, while that for $k_{VV}$ is {[-0.08,2.20]}~{([-0.08,2.19])}. Results correspond to the first analysis approach described in the note.
png pdf	Additional Figure 11-b: The observed (solid) and expected (dashed) 95% CL upper limits on the signal strength of the HH (left) and VBF (right) production (left) obtained as a function of $\mathrm{k}_{\lambda}$ (left) and $k_{VV}$(right) for the resolved $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analysis. 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. The observed (expected) allowed range, at 95% CL, for $\mathrm{k}_{\lambda}$ is {[-4.4,11.7]}~{([-3.8,11.0])}, while that for $k_{VV}$ is {[-0.08,2.20]}~{([-0.08,2.19])}. Results correspond to the first analysis approach described in the note.
png pdf	Additional Figure 12: The observed (solid) and expected (dashed) profile likelihood ratios as a function of $\mu_{HH}$ (left) and $\mu_{VBFHH}$ (right) from the resolved $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analysis. The expected curves are obtained from an Asimov dataset, defined by fixing the nuisances parameters to their maximum likelihood estimate obtained from data in which $\mu_{HH}=1$. The dashed red lines indicate the 68% and 95% CL ranges, expressed in units of $-2\Delta\ln(\mathcal{L})$. Best fit values for the signal strengths, along with their 68% CL intervals, are also reported. Results correspond to the first analysis approach described in the note.
png pdf	Additional Figure 12-a: The observed (solid) and expected (dashed) profile likelihood ratios as a function of $\mu_{HH}$ (left) and $\mu_{VBFHH}$ (right) from the resolved $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analysis. The expected curves are obtained from an Asimov dataset, defined by fixing the nuisances parameters to their maximum likelihood estimate obtained from data in which $\mu_{HH}=1$. The dashed red lines indicate the 68% and 95% CL ranges, expressed in units of $-2\Delta\ln(\mathcal{L})$. Best fit values for the signal strengths, along with their 68% CL intervals, are also reported. Results correspond to the first analysis approach described in the note.
png pdf	Additional Figure 12-b: The observed (solid) and expected (dashed) profile likelihood ratios as a function of $\mu_{HH}$ (left) and $\mu_{VBFHH}$ (right) from the resolved $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analysis. The expected curves are obtained from an Asimov dataset, defined by fixing the nuisances parameters to their maximum likelihood estimate obtained from data in which $\mu_{HH}=1$. The dashed red lines indicate the 68% and 95% CL ranges, expressed in units of $-2\Delta\ln(\mathcal{L})$. Best fit values for the signal strengths, along with their 68% CL intervals, are also reported. Results correspond to the first analysis approach described in the note.
png pdf	Additional Figure 13: The observed (solid) and expected (dashed) 95% CL upper limits on the signal strength of the HH (left) and VBF (right) production (left) obtained as a function of $\mathrm{k}_{\lambda}$ (left) and $k_{VV}$ (right) for the merged mass-fit $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analysis. 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. The observed (expected) allowed range, at 95% CL, for $\mathrm{k}_{\lambda}$ is {[-5.1,10.9]}~{([-6.8,12.8])}, while that for $k_{VV}$ is {[0.63,1.42]}~{([0.54,1.51])}. Results correspond to the first analysis approach described in the note.
png pdf	Additional Figure 13-a: The observed (solid) and expected (dashed) 95% CL upper limits on the signal strength of the HH (left) and VBF (right) production (left) obtained as a function of $\mathrm{k}_{\lambda}$ (left) and $k_{VV}$ (right) for the merged mass-fit $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analysis. 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. The observed (expected) allowed range, at 95% CL, for $\mathrm{k}_{\lambda}$ is {[-5.1,10.9]}~{([-6.8,12.8])}, while that for $k_{VV}$ is {[0.63,1.42]}~{([0.54,1.51])}. Results correspond to the first analysis approach described in the note.
png pdf	Additional Figure 13-b: The observed (solid) and expected (dashed) 95% CL upper limits on the signal strength of the HH (left) and VBF (right) production (left) obtained as a function of $\mathrm{k}_{\lambda}$ (left) and $k_{VV}$ (right) for the merged mass-fit $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analysis. 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. The observed (expected) allowed range, at 95% CL, for $\mathrm{k}_{\lambda}$ is {[-5.1,10.9]}~{([-6.8,12.8])}, while that for $k_{VV}$ is {[0.63,1.42]}~{([0.54,1.51])}. Results correspond to the first analysis approach described in the note.
png pdf	Additional Figure 14: The observed (solid) and expected (dashed) 95% CL upper limits on the signal strength of the HH (left) and VBF (right) production (left) obtained as a function of $\mathrm{k}_{\lambda}$ (left) and $k_{VV}$ (right) for the merged DNN-fit $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analysis. 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. The observed (expected) allowed range, at 95% CL, for $\mathrm{k}_{\lambda}$ is {[-6.5,13.4]}~{([-7.7,14.9])}, while that for $k_{VV}$is {[0.64,1.41]}~{([0.56,1.49])}. Results correspond to the first analysis approach described in the note.
png pdf	Additional Figure 14-a: The observed (solid) and expected (dashed) 95% CL upper limits on the signal strength of the HH (left) and VBF (right) production (left) obtained as a function of $\mathrm{k}_{\lambda}$ (left) and $k_{VV}$ (right) for the merged DNN-fit $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analysis. 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. The observed (expected) allowed range, at 95% CL, for $\mathrm{k}_{\lambda}$ is {[-6.5,13.4]}~{([-7.7,14.9])}, while that for $k_{VV}$is {[0.64,1.41]}~{([0.56,1.49])}. Results correspond to the first analysis approach described in the note.
png pdf	Additional Figure 14-b: The observed (solid) and expected (dashed) 95% CL upper limits on the signal strength of the HH (left) and VBF (right) production (left) obtained as a function of $\mathrm{k}_{\lambda}$ (left) and $k_{VV}$ (right) for the merged DNN-fit $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analysis. 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. The observed (expected) allowed range, at 95% CL, for $\mathrm{k}_{\lambda}$ is {[-6.5,13.4]}~{([-7.7,14.9])}, while that for $k_{VV}$is {[0.64,1.41]}~{([0.56,1.49])}. Results correspond to the first analysis approach described in the note.
png pdf	Additional Figure 15: The observed (solid) and expected (dashed) profile likelihood ratios as a function of $\mu_{HH}$ (left) and $\mu_{qqHH}$ (right) from the merged mass-fit $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analysis. The $\mu_{qqHH}$ likelihood scan is shown with $\mu_{\mathrm{ggHH}}$ fixed to one (blue) and with $\mu_{\mathrm{ggHH}}$ profiled (orange). The expected curves are obtained from an Asimov dataset, defined by fixing the nuisances parameters to their maximum likelihood estimate obtained from data in which $\mu_{HH}=1$. The dashed red lines indicate the 68% and 95% CL ranges, expressed in units of $-2\Delta\ln(\mathcal{L})$. Best fit values for the signal strengths, along with their 68% CL intervals, are also reported. Results correspond to the first analysis approach described in the note.
png pdf	Additional Figure 15-a: The observed (solid) and expected (dashed) profile likelihood ratios as a function of $\mu_{HH}$ (left) and $\mu_{qqHH}$ (right) from the merged mass-fit $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analysis. The $\mu_{qqHH}$ likelihood scan is shown with $\mu_{\mathrm{ggHH}}$ fixed to one (blue) and with $\mu_{\mathrm{ggHH}}$ profiled (orange). The expected curves are obtained from an Asimov dataset, defined by fixing the nuisances parameters to their maximum likelihood estimate obtained from data in which $\mu_{HH}=1$. The dashed red lines indicate the 68% and 95% CL ranges, expressed in units of $-2\Delta\ln(\mathcal{L})$. Best fit values for the signal strengths, along with their 68% CL intervals, are also reported. Results correspond to the first analysis approach described in the note.
png pdf	Additional Figure 15-b: The observed (solid) and expected (dashed) profile likelihood ratios as a function of $\mu_{HH}$ (left) and $\mu_{qqHH}$ (right) from the merged mass-fit $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analysis. The $\mu_{qqHH}$ likelihood scan is shown with $\mu_{\mathrm{ggHH}}$ fixed to one (blue) and with $\mu_{\mathrm{ggHH}}$ profiled (orange). The expected curves are obtained from an Asimov dataset, defined by fixing the nuisances parameters to their maximum likelihood estimate obtained from data in which $\mu_{HH}=1$. The dashed red lines indicate the 68% and 95% CL ranges, expressed in units of $-2\Delta\ln(\mathcal{L})$. Best fit values for the signal strengths, along with their 68% CL intervals, are also reported. Results correspond to the first analysis approach described in the note.
png pdf	Additional Figure 16: The observed (solid) and expected (dashed) profile likelihood ratios as a function of $\mu_{HH}$ (left) and $\mu_{qqHH}$ (right) from the merged DNN-fit $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analysis. The $\mu_{qqHH}$ likelihood scan is shown with $\mu_{\mathrm{ggHH}}$ fixed to one (blue) and with $\mu_{\mathrm{ggHH}}$ profiled (orange). The expected curves are obtained from an Asimov dataset, defined by fixing the nuisances parameters to their maximum likelihood estimate obtained from data in which $\mu_{HH}=1$. The dashed red lines indicate the 68% and 95% CL ranges, expressed in units of $-2\Delta\ln(\mathcal{L})$. Best fit values for the signal strengths, along with their 68% CL intervals, are also reported. Results correspond to the first analysis approach described in the note.
png pdf	Additional Figure 16-a: The observed (solid) and expected (dashed) profile likelihood ratios as a function of $\mu_{HH}$ (left) and $\mu_{qqHH}$ (right) from the merged DNN-fit $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analysis. The $\mu_{qqHH}$ likelihood scan is shown with $\mu_{\mathrm{ggHH}}$ fixed to one (blue) and with $\mu_{\mathrm{ggHH}}$ profiled (orange). The expected curves are obtained from an Asimov dataset, defined by fixing the nuisances parameters to their maximum likelihood estimate obtained from data in which $\mu_{HH}=1$. The dashed red lines indicate the 68% and 95% CL ranges, expressed in units of $-2\Delta\ln(\mathcal{L})$. Best fit values for the signal strengths, along with their 68% CL intervals, are also reported. Results correspond to the first analysis approach described in the note.
png pdf	Additional Figure 16-b: The observed (solid) and expected (dashed) profile likelihood ratios as a function of $\mu_{HH}$ (left) and $\mu_{qqHH}$ (right) from the merged DNN-fit $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analysis. The $\mu_{qqHH}$ likelihood scan is shown with $\mu_{\mathrm{ggHH}}$ fixed to one (blue) and with $\mu_{\mathrm{ggHH}}$ profiled (orange). The expected curves are obtained from an Asimov dataset, defined by fixing the nuisances parameters to their maximum likelihood estimate obtained from data in which $\mu_{HH}=1$. The dashed red lines indicate the 68% and 95% CL ranges, expressed in units of $-2\Delta\ln(\mathcal{L})$. Best fit values for the signal strengths, along with their 68% CL intervals, are also reported. Results correspond to the first analysis approach described in the note.
png pdf	Additional Figure 17: The observed (solid) and expected (dashed) profile likelihood ratios as a function of $\mu_{HH}$ (left) and $\mu_{qqHH}$ (right) for the combined fit of the resolved and merged $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analyses. The $\mu_{qqHH}$ likelihood scan is shown with $\mu_{\mathrm{ggHH}}$ fixed to one (blue) and with $\mu_{\mathrm{ggHH}}$ profiled (orange). The expected curves are obtained from an Asimov dataset, defined by fixing the nuisances parameters to their maximum likelihood estimate obtained from data in which $\mu_{HH}=1$. The dashed red lines indicate the 68% and 95% CL ranges, expressed in units of $-2\Delta\ln(\mathcal{L})$. Best fit values for the signal strengths, along with their 68% CL intervals, are also reported. Results correspond to the first analysis approach described in the note.
png pdf	Additional Figure 17-a: The observed (solid) and expected (dashed) profile likelihood ratios as a function of $\mu_{HH}$ (left) and $\mu_{qqHH}$ (right) for the combined fit of the resolved and merged $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analyses. The $\mu_{qqHH}$ likelihood scan is shown with $\mu_{\mathrm{ggHH}}$ fixed to one (blue) and with $\mu_{\mathrm{ggHH}}$ profiled (orange). The expected curves are obtained from an Asimov dataset, defined by fixing the nuisances parameters to their maximum likelihood estimate obtained from data in which $\mu_{HH}=1$. The dashed red lines indicate the 68% and 95% CL ranges, expressed in units of $-2\Delta\ln(\mathcal{L})$. Best fit values for the signal strengths, along with their 68% CL intervals, are also reported. Results correspond to the first analysis approach described in the note.
png pdf	Additional Figure 17-b: The observed (solid) and expected (dashed) profile likelihood ratios as a function of $\mu_{HH}$ (left) and $\mu_{qqHH}$ (right) for the combined fit of the resolved and merged $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analyses. The $\mu_{qqHH}$ likelihood scan is shown with $\mu_{\mathrm{ggHH}}$ fixed to one (blue) and with $\mu_{\mathrm{ggHH}}$ profiled (orange). The expected curves are obtained from an Asimov dataset, defined by fixing the nuisances parameters to their maximum likelihood estimate obtained from data in which $\mu_{HH}=1$. The dashed red lines indicate the 68% and 95% CL ranges, expressed in units of $-2\Delta\ln(\mathcal{L})$. Best fit values for the signal strengths, along with their 68% CL intervals, are also reported. Results correspond to the first analysis approach described in the note.
png pdf	Additional Figure 18: Schematic diagram of the signal and control regions used in the second analysis approach of the resolved topology described in the note.
png pdf	Additional Figure 19: A schematic of the FeynNet classifier architecture used in the second analysis approach of the resolved topology described in the note. For each unique assignment of final state jets, FeynNet builds a learned embedding which is used in linear combination with the rest to derive the final output classifier score.
png pdf	Additional Figure 20: The upper panel shows the ratio of the difference between the nominal background model and each of the 30 background model variations over the nominal background model in the $\text{SR}_{\text{3T1M}}$, as derived by reweighting the observed data in the $\text{SR}_{\text{3T1L}}$b, for the pre-ParkingHH (left) and post-ParkingHH (right) data sets as a function of the $D(\text{ggHH-vs-bkg})$ score. The lower panel shows the first three Fourier components (blue, orange, red), and the residual (purple) systematic uncertainties. The quadrature sum of the four background systematic uncertainties are illustrated with the gray envelope. Distributions correspond to the second analysis approach of the resolved topology described in the note.
png pdf	Additional Figure 20-a: The upper panel shows the ratio of the difference between the nominal background model and each of the 30 background model variations over the nominal background model in the $\text{SR}_{\text{3T1M}}$, as derived by reweighting the observed data in the $\text{SR}_{\text{3T1L}}$b, for the pre-ParkingHH (left) and post-ParkingHH (right) data sets as a function of the $D(\text{ggHH-vs-bkg})$ score. The lower panel shows the first three Fourier components (blue, orange, red), and the residual (purple) systematic uncertainties. The quadrature sum of the four background systematic uncertainties are illustrated with the gray envelope. Distributions correspond to the second analysis approach of the resolved topology described in the note.
png pdf	Additional Figure 20-b: The upper panel shows the ratio of the difference between the nominal background model and each of the 30 background model variations over the nominal background model in the $\text{SR}_{\text{3T1M}}$, as derived by reweighting the observed data in the $\text{SR}_{\text{3T1L}}$b, for the pre-ParkingHH (left) and post-ParkingHH (right) data sets as a function of the $D(\text{ggHH-vs-bkg})$ score. The lower panel shows the first three Fourier components (blue, orange, red), and the residual (purple) systematic uncertainties. The quadrature sum of the four background systematic uncertainties are illustrated with the gray envelope. Distributions correspond to the second analysis approach of the resolved topology described in the note.
png pdf	Additional Figure 21: The observed (solid) and expected (dashed) 95% CL upper limits on the signal strength of $ \mathrm{H}\mathrm{H} $ production from the ggHH $\text{SR}_{\text{3T1M}}$, ggHH $\text{SR}_{\text{3T1L}}$, qqHH $\text{SR}_{\text{3T1M}}$, and their combination, for the resolved analysis. The yellow and cyan bands represent, respectively, the 68 and 95% CL intervals around the expected limit. Results correspond to the second analysis approach of the resolved topology described in the note.
png pdf	Additional Figure 22: The observed (solid) and expected (dashed) 95% CL upper limits on the signal strength of $ \mathrm{H}\mathrm{H} $ production from the combination of the ggHH $\text{SR}_{\text{3T1M}}$, ggHH $\text{SR}_{\text{3T1L}}$, and qqHH $\text{SR}_{\text{3T1M}}$ in 2022 and 2023, for the resolved analysis. The yellow and cyan bands represent, respectively, the 68% and 95% CL intervals around the expected limit. Results correspond to the second analysis approach of the resolved topology described in the note.
png pdf	Additional Figure 23: The observed (solid) and expected (dashed) 95% CL upper limits on the signal strength of $ \mathrm{H}\mathrm{H} $ production obtained as a function of $\mathrm{k}_{\lambda}$ (left) and \kappaVV (right) for the resolved analysis. The yellow and cyan bands represent, respectively, the 68 and 95% CL intervals around the expected limit. The horizontal red lines indicate the SM prediction. The observed (expected) allowed range, at 95% CL, for $\mathrm{k}_{\lambda}$ is [-3.19, 10.0] ([-4.38, 11.6]), and for $\mathrm{k}_{VV}$ is [-0.05, 2.24] ([-0.25, 2.4]). Results correspond to the second analysis approach of the resolved topology described in the note.
png pdf	Additional Figure 23-a: The observed (solid) and expected (dashed) 95% CL upper limits on the signal strength of $ \mathrm{H}\mathrm{H} $ production obtained as a function of $\mathrm{k}_{\lambda}$ (left) and \kappaVV (right) for the resolved analysis. The yellow and cyan bands represent, respectively, the 68 and 95% CL intervals around the expected limit. The horizontal red lines indicate the SM prediction. The observed (expected) allowed range, at 95% CL, for $\mathrm{k}_{\lambda}$ is [-3.19, 10.0] ([-4.38, 11.6]), and for $\mathrm{k}_{VV}$ is [-0.05, 2.24] ([-0.25, 2.4]). Results correspond to the second analysis approach of the resolved topology described in the note.
png pdf	Additional Figure 23-b: The observed (solid) and expected (dashed) 95% CL upper limits on the signal strength of $ \mathrm{H}\mathrm{H} $ production obtained as a function of $\mathrm{k}_{\lambda}$ (left) and \kappaVV (right) for the resolved analysis. The yellow and cyan bands represent, respectively, the 68 and 95% CL intervals around the expected limit. The horizontal red lines indicate the SM prediction. The observed (expected) allowed range, at 95% CL, for $\mathrm{k}_{\lambda}$ is [-3.19, 10.0] ([-4.38, 11.6]), and for $\mathrm{k}_{VV}$ is [-0.05, 2.24] ([-0.25, 2.4]). Results correspond to the second analysis approach of the resolved topology described in the note.
png pdf	Additional Figure 24: The derivation of the $\mathrm{t}\mathrm{\bar{t}}$ scale factors as a function of $P_t^\mathrm{jj}$ (upper) in the $\mathrm{t}\mathrm{\bar{t}}$ fully hadronic CR, and $\tau_3/\tau_2$ (middle) and \TXbb (lower) in the $\mathrm{t}\mathrm{\bar{t}}$ semileptonic CR. The scale factors are derived separately in 2022 (left) and 2023 (right) data. Distributions correspond to the second analysis approach of the merged topology described in the note.
png pdf	Additional Figure 24-a: The derivation of the $\mathrm{t}\mathrm{\bar{t}}$ scale factors as a function of $P_t^\mathrm{jj}$ (upper) in the $\mathrm{t}\mathrm{\bar{t}}$ fully hadronic CR, and $\tau_3/\tau_2$ (middle) and \TXbb (lower) in the $\mathrm{t}\mathrm{\bar{t}}$ semileptonic CR. The scale factors are derived separately in 2022 (left) and 2023 (right) data. Distributions correspond to the second analysis approach of the merged topology described in the note.
png pdf	Additional Figure 24-b: The derivation of the $\mathrm{t}\mathrm{\bar{t}}$ scale factors as a function of $P_t^\mathrm{jj}$ (upper) in the $\mathrm{t}\mathrm{\bar{t}}$ fully hadronic CR, and $\tau_3/\tau_2$ (middle) and \TXbb (lower) in the $\mathrm{t}\mathrm{\bar{t}}$ semileptonic CR. The scale factors are derived separately in 2022 (left) and 2023 (right) data. Distributions correspond to the second analysis approach of the merged topology described in the note.
png pdf	Additional Figure 24-c: The derivation of the $\mathrm{t}\mathrm{\bar{t}}$ scale factors as a function of $P_t^\mathrm{jj}$ (upper) in the $\mathrm{t}\mathrm{\bar{t}}$ fully hadronic CR, and $\tau_3/\tau_2$ (middle) and \TXbb (lower) in the $\mathrm{t}\mathrm{\bar{t}}$ semileptonic CR. The scale factors are derived separately in 2022 (left) and 2023 (right) data. Distributions correspond to the second analysis approach of the merged topology described in the note.
png pdf	Additional Figure 24-d: The derivation of the $\mathrm{t}\mathrm{\bar{t}}$ scale factors as a function of $P_t^\mathrm{jj}$ (upper) in the $\mathrm{t}\mathrm{\bar{t}}$ fully hadronic CR, and $\tau_3/\tau_2$ (middle) and \TXbb (lower) in the $\mathrm{t}\mathrm{\bar{t}}$ semileptonic CR. The scale factors are derived separately in 2022 (left) and 2023 (right) data. Distributions correspond to the second analysis approach of the merged topology described in the note.
png pdf	Additional Figure 24-e: The derivation of the $\mathrm{t}\mathrm{\bar{t}}$ scale factors as a function of $P_t^\mathrm{jj}$ (upper) in the $\mathrm{t}\mathrm{\bar{t}}$ fully hadronic CR, and $\tau_3/\tau_2$ (middle) and \TXbb (lower) in the $\mathrm{t}\mathrm{\bar{t}}$ semileptonic CR. The scale factors are derived separately in 2022 (left) and 2023 (right) data. Distributions correspond to the second analysis approach of the merged topology described in the note.
png pdf	Additional Figure 24-f: The derivation of the $\mathrm{t}\mathrm{\bar{t}}$ scale factors as a function of $P_t^\mathrm{jj}$ (upper) in the $\mathrm{t}\mathrm{\bar{t}}$ fully hadronic CR, and $\tau_3/\tau_2$ (middle) and \TXbb (lower) in the $\mathrm{t}\mathrm{\bar{t}}$ semileptonic CR. The scale factors are derived separately in 2022 (left) and 2023 (right) data. Distributions correspond to the second analysis approach of the merged topology described in the note.
png pdf	Additional Figure 25: The $D$(ggHH-vs-bkg) (left) and $D$(qqHH-vs-bkg) (right) distributions in the $\mathrm{t}\mathrm{\bar{t}}$ fully hadronic CR for data and simulation prediction for the combined 2022 and 2023 data. The derived $\mathrm{t}\mathrm{\bar{t}}$ scale factors are shown in the bottom panel. Distributions correspond to the second analysis approach of the merged topology described in the note.
png pdf	Additional Figure 25-a: The $D$(ggHH-vs-bkg) (left) and $D$(qqHH-vs-bkg) (right) distributions in the $\mathrm{t}\mathrm{\bar{t}}$ fully hadronic CR for data and simulation prediction for the combined 2022 and 2023 data. The derived $\mathrm{t}\mathrm{\bar{t}}$ scale factors are shown in the bottom panel. Distributions correspond to the second analysis approach of the merged topology described in the note.
png pdf	Additional Figure 25-b: The $D$(ggHH-vs-bkg) (left) and $D$(qqHH-vs-bkg) (right) distributions in the $\mathrm{t}\mathrm{\bar{t}}$ fully hadronic CR for data and simulation prediction for the combined 2022 and 2023 data. The derived $\mathrm{t}\mathrm{\bar{t}}$ scale factors are shown in the bottom panel. Distributions correspond to the second analysis approach of the merged topology described in the note.
png pdf	Additional Figure 26: Postfit distribution of the regressed mass of the secondary H candidate $m_\text{reg}({H_2})$ in the QCD CR. Distribution corresponds to the second analysis approach of the merged topology described in the note.
png pdf	Additional Figure 27: The data in the ggHH SR 1 (upper left), qqHHSR (upper right), ggHH SR 2 (lower left), and ggHH SR 3 (lower right) after subtracting all background processes except the QCD multijet one compared to the QCD multijet background prediction derived from the QCD CR. The fitted shape and uncertainty are derived from a simultaneous background-only fit of all four SRs. Distributions corresponds to the second analysis approach of the merged topology described in the note.
png pdf	Additional Figure 27-a: The data in the ggHH SR 1 (upper left), qqHHSR (upper right), ggHH SR 2 (lower left), and ggHH SR 3 (lower right) after subtracting all background processes except the QCD multijet one compared to the QCD multijet background prediction derived from the QCD CR. The fitted shape and uncertainty are derived from a simultaneous background-only fit of all four SRs. Distributions corresponds to the second analysis approach of the merged topology described in the note.
png pdf	Additional Figure 27-b: The data in the ggHH SR 1 (upper left), qqHHSR (upper right), ggHH SR 2 (lower left), and ggHH SR 3 (lower right) after subtracting all background processes except the QCD multijet one compared to the QCD multijet background prediction derived from the QCD CR. The fitted shape and uncertainty are derived from a simultaneous background-only fit of all four SRs. Distributions corresponds to the second analysis approach of the merged topology described in the note.
png pdf	Additional Figure 27-c: The data in the ggHH SR 1 (upper left), qqHHSR (upper right), ggHH SR 2 (lower left), and ggHH SR 3 (lower right) after subtracting all background processes except the QCD multijet one compared to the QCD multijet background prediction derived from the QCD CR. The fitted shape and uncertainty are derived from a simultaneous background-only fit of all four SRs. Distributions corresponds to the second analysis approach of the merged topology described in the note.
png pdf	Additional Figure 27-d: The data in the ggHH SR 1 (upper left), qqHHSR (upper right), ggHH SR 2 (lower left), and ggHH SR 3 (lower right) after subtracting all background processes except the QCD multijet one compared to the QCD multijet background prediction derived from the QCD CR. The fitted shape and uncertainty are derived from a simultaneous background-only fit of all four SRs. Distributions corresponds to the second analysis approach of the merged topology described in the note.
png pdf	Additional Figure 28: The observed (solid) and expected (dashed) 95% CL upper limits on $ \mathrm{H}\mathrm{H} $ production with respect to the expectation for the SM (left) and $$\mathrm{k}_{\mathrm{VV}}$=0.5$ (right) scenarios in the individual ggHH and qqHHSRs and their combination. The yellow and cyan bands represent, respectively, the 68 and 95% CL intervals around the expected limit. Results correspond to the second analysis approach of the merged topology described in the note.
png pdf	Additional Figure 28-a: The observed (solid) and expected (dashed) 95% CL upper limits on $ \mathrm{H}\mathrm{H} $ production with respect to the expectation for the SM (left) and $$\mathrm{k}_{\mathrm{VV}}$=0.5$ (right) scenarios in the individual ggHH and qqHHSRs and their combination. The yellow and cyan bands represent, respectively, the 68 and 95% CL intervals around the expected limit. Results correspond to the second analysis approach of the merged topology described in the note.
png pdf	Additional Figure 28-b: The observed (solid) and expected (dashed) 95% CL upper limits on $ \mathrm{H}\mathrm{H} $ production with respect to the expectation for the SM (left) and $$\mathrm{k}_{\mathrm{VV}}$=0.5$ (right) scenarios in the individual ggHH and qqHHSRs and their combination. The yellow and cyan bands represent, respectively, the 68 and 95% CL intervals around the expected limit. Results correspond to the second analysis approach of the merged topology described in the note.
png pdf	Additional Figure 29: Profile likelihood test statistic $-2\Delta\log(L)$ scans as a function of $\mathrm{k}_{\lambda}$ (upper left), $\mathrm{k}_{\mathrm{VV}}$ (upper right), and in the ($\mathrm{k}_{\lambda}$, $\mathrm{k}_{\mathrm{VV}}$) plane (lower). Results correspond to the second analysis approach of the merged topology described in the note.
png pdf	Additional Figure 29-a: Profile likelihood test statistic $-2\Delta\log(L)$ scans as a function of $\mathrm{k}_{\lambda}$ (upper left), $\mathrm{k}_{\mathrm{VV}}$ (upper right), and in the ($\mathrm{k}_{\lambda}$, $\mathrm{k}_{\mathrm{VV}}$) plane (lower). Results correspond to the second analysis approach of the merged topology described in the note.
png pdf	Additional Figure 29-b: Profile likelihood test statistic $-2\Delta\log(L)$ scans as a function of $\mathrm{k}_{\lambda}$ (upper left), $\mathrm{k}_{\mathrm{VV}}$ (upper right), and in the ($\mathrm{k}_{\lambda}$, $\mathrm{k}_{\mathrm{VV}}$) plane (lower). Results correspond to the second analysis approach of the merged topology described in the note.
png pdf	Additional Figure 29-c: Profile likelihood test statistic $-2\Delta\log(L)$ scans as a function of $\mathrm{k}_{\lambda}$ (upper left), $\mathrm{k}_{\mathrm{VV}}$ (upper right), and in the ($\mathrm{k}_{\lambda}$, $\mathrm{k}_{\mathrm{VV}}$) plane (lower). Results correspond to the second analysis approach of the merged topology described in the note.
png pdf	Additional Figure 30: The observed (solid) and expected (dashed) 95% CL upper limits on the $ \mathrm{H}\mathrm{H} $ signal strength as a function of $\mathrm{k}_{\lambda}$ (left) and $\mathrm{k}_{\mathrm{VV}}$ (right). The yellow and cyan bands represent, respectively, the 68 and 95% CL intervals around the expected limit. The observed (expected) allowed range, at 95% CL for $\mathrm{k}_{\lambda}$ is [-11.0,19.2] ([-10.3,18.4]), and for $\mathrm{k}_{VV}$ is [0.30,1.74] ([0.47,1.58]). Results correspond to the second analysis approach of the merged topology described in the note.
png pdf	Additional Figure 30-a: The observed (solid) and expected (dashed) 95% CL upper limits on the $ \mathrm{H}\mathrm{H} $ signal strength as a function of $\mathrm{k}_{\lambda}$ (left) and $\mathrm{k}_{\mathrm{VV}}$ (right). The yellow and cyan bands represent, respectively, the 68 and 95% CL intervals around the expected limit. The observed (expected) allowed range, at 95% CL for $\mathrm{k}_{\lambda}$ is [-11.0,19.2] ([-10.3,18.4]), and for $\mathrm{k}_{VV}$ is [0.30,1.74] ([0.47,1.58]). Results correspond to the second analysis approach of the merged topology described in the note.
png pdf	Additional Figure 30-b: The observed (solid) and expected (dashed) 95% CL upper limits on the $ \mathrm{H}\mathrm{H} $ signal strength as a function of $\mathrm{k}_{\lambda}$ (left) and $\mathrm{k}_{\mathrm{VV}}$ (right). The yellow and cyan bands represent, respectively, the 68 and 95% CL intervals around the expected limit. The observed (expected) allowed range, at 95% CL for $\mathrm{k}_{\lambda}$ is [-11.0,19.2] ([-10.3,18.4]), and for $\mathrm{k}_{VV}$ is [0.30,1.74] ([0.47,1.58]). Results correspond to the second analysis approach of the merged topology described in the note.
png pdf	Additional Figure 31: The predicted QCD multijet HH probability, $\mathcal{P_\mathrm{H}\mathrm{H}}$, distributions for each of the 15 synthetic datasets in the signal region (yellow regions). The distribution from each synthetic data is offset by the data sample index number. The black points give the average of the 15 data samples. The solid blue curves show a fit to the individual distributions using an increasing number of basis functions from one in the upper left plot to six in the lowest right plot. The lower panels show the pulls before (yellow histogram) and after (blue histogram) adding the basis corrections. The correlation coefficient (r) for a fit testing for correlations is given in the legend, along with the p-value used to test for lack of correlation. Basis functions are added until the p-value is greater than 5%. Distributions correspond to the Run 2 analysis in the resolved topology described in the note
png pdf	Additional Figure 31-a: The predicted QCD multijet HH probability, $\mathcal{P_\mathrm{H}\mathrm{H}}$, distributions for each of the 15 synthetic datasets in the signal region (yellow regions). The distribution from each synthetic data is offset by the data sample index number. The black points give the average of the 15 data samples. The solid blue curves show a fit to the individual distributions using an increasing number of basis functions from one in the upper left plot to six in the lowest right plot. The lower panels show the pulls before (yellow histogram) and after (blue histogram) adding the basis corrections. The correlation coefficient (r) for a fit testing for correlations is given in the legend, along with the p-value used to test for lack of correlation. Basis functions are added until the p-value is greater than 5%. Distributions correspond to the Run 2 analysis in the resolved topology described in the note
png pdf	Additional Figure 31-b: The predicted QCD multijet HH probability, $\mathcal{P_\mathrm{H}\mathrm{H}}$, distributions for each of the 15 synthetic datasets in the signal region (yellow regions). The distribution from each synthetic data is offset by the data sample index number. The black points give the average of the 15 data samples. The solid blue curves show a fit to the individual distributions using an increasing number of basis functions from one in the upper left plot to six in the lowest right plot. The lower panels show the pulls before (yellow histogram) and after (blue histogram) adding the basis corrections. The correlation coefficient (r) for a fit testing for correlations is given in the legend, along with the p-value used to test for lack of correlation. Basis functions are added until the p-value is greater than 5%. Distributions correspond to the Run 2 analysis in the resolved topology described in the note
png pdf	Additional Figure 31-c: The predicted QCD multijet HH probability, $\mathcal{P_\mathrm{H}\mathrm{H}}$, distributions for each of the 15 synthetic datasets in the signal region (yellow regions). The distribution from each synthetic data is offset by the data sample index number. The black points give the average of the 15 data samples. The solid blue curves show a fit to the individual distributions using an increasing number of basis functions from one in the upper left plot to six in the lowest right plot. The lower panels show the pulls before (yellow histogram) and after (blue histogram) adding the basis corrections. The correlation coefficient (r) for a fit testing for correlations is given in the legend, along with the p-value used to test for lack of correlation. Basis functions are added until the p-value is greater than 5%. Distributions correspond to the Run 2 analysis in the resolved topology described in the note
png pdf	Additional Figure 31-d: The predicted QCD multijet HH probability, $\mathcal{P_\mathrm{H}\mathrm{H}}$, distributions for each of the 15 synthetic datasets in the signal region (yellow regions). The distribution from each synthetic data is offset by the data sample index number. The black points give the average of the 15 data samples. The solid blue curves show a fit to the individual distributions using an increasing number of basis functions from one in the upper left plot to six in the lowest right plot. The lower panels show the pulls before (yellow histogram) and after (blue histogram) adding the basis corrections. The correlation coefficient (r) for a fit testing for correlations is given in the legend, along with the p-value used to test for lack of correlation. Basis functions are added until the p-value is greater than 5%. Distributions correspond to the Run 2 analysis in the resolved topology described in the note
png pdf	Additional Figure 31-e: The predicted QCD multijet HH probability, $\mathcal{P_\mathrm{H}\mathrm{H}}$, distributions for each of the 15 synthetic datasets in the signal region (yellow regions). The distribution from each synthetic data is offset by the data sample index number. The black points give the average of the 15 data samples. The solid blue curves show a fit to the individual distributions using an increasing number of basis functions from one in the upper left plot to six in the lowest right plot. The lower panels show the pulls before (yellow histogram) and after (blue histogram) adding the basis corrections. The correlation coefficient (r) for a fit testing for correlations is given in the legend, along with the p-value used to test for lack of correlation. Basis functions are added until the p-value is greater than 5%. Distributions correspond to the Run 2 analysis in the resolved topology described in the note
png pdf	Additional Figure 31-f: The predicted QCD multijet HH probability, $\mathcal{P_\mathrm{H}\mathrm{H}}$, distributions for each of the 15 synthetic datasets in the signal region (yellow regions). The distribution from each synthetic data is offset by the data sample index number. The black points give the average of the 15 data samples. The solid blue curves show a fit to the individual distributions using an increasing number of basis functions from one in the upper left plot to six in the lowest right plot. The lower panels show the pulls before (yellow histogram) and after (blue histogram) adding the basis corrections. The correlation coefficient (r) for a fit testing for correlations is given in the legend, along with the p-value used to test for lack of correlation. Basis functions are added until the p-value is greater than 5%. Distributions correspond to the Run 2 analysis in the resolved topology described in the note
png pdf	Additional Figure 32: Distributions of the HH signal probability, $\mathcal{P_\mathrm{H}\mathrm{H}}$, for the average observed signal region yields from the synthetic dataset models. The yellow and blue regions give the distributions of the average of the QCD multijet models and the tt simulation, respectively. The red histogram displays the post-fit results of the data fit to the background model with 0 (left) and 1 unconstrained parameter (right) in the fit. The $\chi^2$ / dof and the p-value from the fit are shown in the legend. The lower panels give the pre- (black histograms) and post-fit (red histograms) pulls. Distributions correspond to the Run 2 analysis in the resolved topology described in the note.
png pdf	Additional Figure 32-a: Distributions of the HH signal probability, $\mathcal{P_\mathrm{H}\mathrm{H}}$, for the average observed signal region yields from the synthetic dataset models. The yellow and blue regions give the distributions of the average of the QCD multijet models and the tt simulation, respectively. The red histogram displays the post-fit results of the data fit to the background model with 0 (left) and 1 unconstrained parameter (right) in the fit. The $\chi^2$ / dof and the p-value from the fit are shown in the legend. The lower panels give the pre- (black histograms) and post-fit (red histograms) pulls. Distributions correspond to the Run 2 analysis in the resolved topology described in the note.
png pdf	Additional Figure 32-b: Distributions of the HH signal probability, $\mathcal{P_\mathrm{H}\mathrm{H}}$, for the average observed signal region yields from the synthetic dataset models. The yellow and blue regions give the distributions of the average of the QCD multijet models and the tt simulation, respectively. The red histogram displays the post-fit results of the data fit to the background model with 0 (left) and 1 unconstrained parameter (right) in the fit. The $\chi^2$ / dof and the p-value from the fit are shown in the legend. The lower panels give the pre- (black histograms) and post-fit (red histograms) pulls. Distributions correspond to the Run 2 analysis in the resolved topology described in the note.
png pdf	Additional Figure 33: The prefit, background-only fit, and signal plus background distributions of the signal probability, $\mathcal{P_\mathrm{H}\mathrm{H}}$. The black points show one of the synthetic datasets. The yellow and blue regions show the predictions from the QCD multijet model and the $\mathrm{t}\mathrm{\bar{t}}$ simulation, respectively. The predictions for the $ \mathrm{H}\mathrm{H} $ signal distributions are given by the red histograms, multiplied by 100. The lower panels show the data-to-background ratio, with the hatched area representing the background uncertainty. Distributions correspond to the Run 2 analysis in the resolved topology described in the note.
png pdf	Additional Figure 33-a: The prefit, background-only fit, and signal plus background distributions of the signal probability, $\mathcal{P_\mathrm{H}\mathrm{H}}$. The black points show one of the synthetic datasets. The yellow and blue regions show the predictions from the QCD multijet model and the $\mathrm{t}\mathrm{\bar{t}}$ simulation, respectively. The predictions for the $ \mathrm{H}\mathrm{H} $ signal distributions are given by the red histograms, multiplied by 100. The lower panels show the data-to-background ratio, with the hatched area representing the background uncertainty. Distributions correspond to the Run 2 analysis in the resolved topology described in the note.
png pdf	Additional Figure 33-b: The prefit, background-only fit, and signal plus background distributions of the signal probability, $\mathcal{P_\mathrm{H}\mathrm{H}}$. The black points show one of the synthetic datasets. The yellow and blue regions show the predictions from the QCD multijet model and the $\mathrm{t}\mathrm{\bar{t}}$ simulation, respectively. The predictions for the $ \mathrm{H}\mathrm{H} $ signal distributions are given by the red histograms, multiplied by 100. The lower panels show the data-to-background ratio, with the hatched area representing the background uncertainty. Distributions correspond to the Run 2 analysis in the resolved topology described in the note.
png pdf	Additional Figure 33-c: The prefit, background-only fit, and signal plus background distributions of the signal probability, $\mathcal{P_\mathrm{H}\mathrm{H}}$. The black points show one of the synthetic datasets. The yellow and blue regions show the predictions from the QCD multijet model and the $\mathrm{t}\mathrm{\bar{t}}$ simulation, respectively. The predictions for the $ \mathrm{H}\mathrm{H} $ signal distributions are given by the red histograms, multiplied by 100. The lower panels show the data-to-background ratio, with the hatched area representing the background uncertainty. Distributions correspond to the Run 2 analysis in the resolved topology described in the note.
png pdf	Additional Figure 34: Distribution of the signal probability for HH, $\mathcal{P_\mathrm{H}\mathrm{H}}$, in the control region (left) and signal region (right). The 4b data events, with slightly different trigger requirements, are shown as black points. The QCD multijet distribution before kinematic corrections is shown as the yellow-filled histogram, and the simulated $\mathrm{t}\mathrm{\bar{t}}$ distribution is shown as the blue-filled histogram. The average of the synthetic datasets (red) provides a high-event-count proxy for the 4b background (black), allowing the background model to be extrapolated and tested precisely. The lower panels display the ratio of the 4b data to the average of the synthetic datasets (red) and to the QCD multijet distribution (black). Distributions correspond to the Run 2 analysis in the resolved topology described in the note.
png pdf	Additional Figure 34-a: Distribution of the signal probability for HH, $\mathcal{P_\mathrm{H}\mathrm{H}}$, in the control region (left) and signal region (right). The 4b data events, with slightly different trigger requirements, are shown as black points. The QCD multijet distribution before kinematic corrections is shown as the yellow-filled histogram, and the simulated $\mathrm{t}\mathrm{\bar{t}}$ distribution is shown as the blue-filled histogram. The average of the synthetic datasets (red) provides a high-event-count proxy for the 4b background (black), allowing the background model to be extrapolated and tested precisely. The lower panels display the ratio of the 4b data to the average of the synthetic datasets (red) and to the QCD multijet distribution (black). Distributions correspond to the Run 2 analysis in the resolved topology described in the note.
png pdf	Additional Figure 34-b: Distribution of the signal probability for HH, $\mathcal{P_\mathrm{H}\mathrm{H}}$, in the control region (left) and signal region (right). The 4b data events, with slightly different trigger requirements, are shown as black points. The QCD multijet distribution before kinematic corrections is shown as the yellow-filled histogram, and the simulated $\mathrm{t}\mathrm{\bar{t}}$ distribution is shown as the blue-filled histogram. The average of the synthetic datasets (red) provides a high-event-count proxy for the 4b background (black), allowing the background model to be extrapolated and tested precisely. The lower panels display the ratio of the 4b data to the average of the synthetic datasets (red) and to the QCD multijet distribution (black). Distributions correspond to the Run 2 analysis in the resolved topology described in the note.
png pdf	Additional Figure 35: Distributions of the signal probabilities, $\mathcal{P_\mathrm{H}\mathrm{H}}$, in the control region. The points show the 4b events. The QCD multijet distribution (yellow region) is from the 3b data control region, before kinematic corrections (FvT reweighting) on the left and after those corrections on the right. The tt distribution (blue region) is from simulations. The lower panels display the ratio of the 4b data to the total background, which is the sum of the QCD multijet and $\mathrm{t}\mathrm{\bar{t}}$ distributions. The hatched area gives the statistical uncertainty in the background. Distributions correspond to the Run 2 analysis in the resolved topology described in the note.
png pdf	Additional Figure 35-a: Distributions of the signal probabilities, $\mathcal{P_\mathrm{H}\mathrm{H}}$, in the control region. The points show the 4b events. The QCD multijet distribution (yellow region) is from the 3b data control region, before kinematic corrections (FvT reweighting) on the left and after those corrections on the right. The tt distribution (blue region) is from simulations. The lower panels display the ratio of the 4b data to the total background, which is the sum of the QCD multijet and $\mathrm{t}\mathrm{\bar{t}}$ distributions. The hatched area gives the statistical uncertainty in the background. Distributions correspond to the Run 2 analysis in the resolved topology described in the note.
png pdf	Additional Figure 35-b: Distributions of the signal probabilities, $\mathcal{P_\mathrm{H}\mathrm{H}}$, in the control region. The points show the 4b events. The QCD multijet distribution (yellow region) is from the 3b data control region, before kinematic corrections (FvT reweighting) on the left and after those corrections on the right. The tt distribution (blue region) is from simulations. The lower panels display the ratio of the 4b data to the total background, which is the sum of the QCD multijet and $\mathrm{t}\mathrm{\bar{t}}$ distributions. The hatched area gives the statistical uncertainty in the background. Distributions correspond to the Run 2 analysis in the resolved topology described in the note.
png pdf	Additional Figure 36: The prefit and background only fit signal probability, $\mathcal{P_\mathrm{H}\mathrm{H}}$, distributions. The black points show the 4b events from data. The yellow and blue regions show the predictions from the QCD multijet model and the $\mathrm{t}\mathrm{\bar{t}}$ simulation, respectively. The predictions for the $ \mathrm{H}\mathrm{H} $ signal distributions are given by the red histograms, multiplied by 100. The lower panels show the data-to-background ratio, with the hatched area representing the background uncertainty. Distributions correspond to the Run 2 analysis in the resolved topology described in the note.
png pdf	Additional Figure 36-a: The prefit and background only fit signal probability, $\mathcal{P_\mathrm{H}\mathrm{H}}$, distributions. The black points show the 4b events from data. The yellow and blue regions show the predictions from the QCD multijet model and the $\mathrm{t}\mathrm{\bar{t}}$ simulation, respectively. The predictions for the $ \mathrm{H}\mathrm{H} $ signal distributions are given by the red histograms, multiplied by 100. The lower panels show the data-to-background ratio, with the hatched area representing the background uncertainty. Distributions correspond to the Run 2 analysis in the resolved topology described in the note.
png pdf	Additional Figure 36-b: The prefit and background only fit signal probability, $\mathcal{P_\mathrm{H}\mathrm{H}}$, distributions. The black points show the 4b events from data. The yellow and blue regions show the predictions from the QCD multijet model and the $\mathrm{t}\mathrm{\bar{t}}$ simulation, respectively. The predictions for the $ \mathrm{H}\mathrm{H} $ signal distributions are given by the red histograms, multiplied by 100. The lower panels show the data-to-background ratio, with the hatched area representing the background uncertainty. Distributions correspond to the Run 2 analysis in the resolved topology described in the note.

Additional Tables
png pdf	Additional Table 1 : Efficiency, jet mass scale (JMS), and jet mass resolution (JMR) data-to-simulation scale factors measured for the GloParT mass regression separately between data collected in 2022 and 2023. Only $ \mathrm{Z} \to \mathrm{bb} $ candidates with ${P_T > 450$ GeV} are considered. Corrections for scale and resolution are applied as multiplicative factors to the predictions from simulation in the merged $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analysis, while efficiency scale factors are applied as per-event weights.
png pdf	Additional Table 2 : The complete set of input features per AK8 jet used for the GloParT model training. Three types of inputs are considered: charged PF candidates and ``lost tracks'' not associated with a charged PF candidate, neutral PF candidates, and secondary vertices (SVs)
png pdf	Additional Table 3: Major sources of uncertainty in the measurement of the $\mu_{HH}$ signal strength in the resolved $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analysis. The post-fit uncertainty on $\mu_{HH}$ is first separated into statistical and systematic components. The systematic component is further divided into uncertainties affecting the data-driven background prediction -- primarily driven by the sample size in the regSRTwob, regCRTwob, and regCRFourb regions -- and those associated with the simulation of HH signal events. Results correspond to the first analysis approach described in the note.
png pdf	Additional Table 4: Major sources of uncertainty in the measurement of the $\mu_{HH}$ signal strength in the merged mass-fit $ \mathrm{H}\mathrm{H} \to 4\mathrm{b} $ analysis. The post-fit uncertainty on $\mu_{HH}$ is first separated into statistical and systematic components. The systematic component is further divided into uncertainties affecting the data-driven prediction of the leading backgrounds -- primarily driven by the statistics in the QCD and $\mathrm{t}\mathrm{\bar{t}}$ control regions -- and those associated with the simulation of HH signal events. Results correspond to the first analysis approach described in the note.
png pdf	Additional Table 5: Input observables used in the FeynNet models, for the second analysis approach of the resolved topology described in the note.
png pdf	Additional Table 6 : Efficiency of each signal process in the HH, ZZ, and ZH categories defined by the maximum FeynNet probability score in the second analysis approach of the resolved topology described in the note.
png pdf	Additional Table 7 : Input observables used in the second analysis approach of the merged topology described in the note.

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