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CMS-PAS-B2G-17-019
Search for resonant and non-resonant production of Higgs boson pairs in the four b quark final state using boosted jets in proton-proton collisions at $\sqrt{s}= $ 13 TeV
Abstract: A search is presented for the pair production of the standard model Higgs boson using data from proton-proton collisions at a centre-of-mass energy of 13 TeV, collected by the CMS experiment at the CERN LHC in 2016, and corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The final state consists of two b quark-antiquark pairs, with at least one Higgs boson highly Lorentz-boosted and reconstructed as a single large-area jet. The observations are consistent with the standard model prediction. Upper limits on the product of the cross sections and branching fractions of narrow bulk gravitons and radions, in warped extra-dimensional models, are set between 67 and 1.1 fb at 95% confidence level, for masses in the range 750-3000 GeV. The upper limit on the product of the standard model Higgs boson pair production cross section and the branching fraction to b quark-antiquark pairs is 1980 fb at 95% confidence level. Limits are also set for twelve benchmark models of beyond standard model non-resonant Higgs boson pair production cross sections.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
For AK8 jets in semi-resolved events, the distributions of the soft-drop mass (upper left), $ {\tau _{21}} $ (upper right), and the double-b tagger (lower). The multijet and ${{\mathrm {t}\overline {\mathrm {t}}}} $+jets background components are shown separately, along with the simulated signals for bulk gravitons of masses 1000 and 1200 GeV and the non-resonant benchmark models 2 and 5. The distributions are normalized to unity. The selection is as follows: AK8 jets with $ {p_{\mathrm {T}}} > $ 300 GeV, AK4 jets with $ {p_{\mathrm {T}}} > $ 30 GeV, AK8 and AK4 jets with $|\eta | < 2.4$, AK8 jet soft-drop mass $ > $ 40 GeV, AK4 jets DeepCSV discriminator $ > 0.2219$, $\Delta R < 1.5$ separation between the AK4 jets, and $\Delta R > 0.8$ separation between the AK8 jet and each AK4 jet.

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Figure 1-a:
For AK8 jets in semi-resolved events, the distributions of the soft-drop mass (upper left), $ {\tau _{21}} $ (upper right), and the double-b tagger (lower). The multijet and ${{\mathrm {t}\overline {\mathrm {t}}}} $+jets background components are shown separately, along with the simulated signals for bulk gravitons of masses 1000 and 1200 GeV and the non-resonant benchmark models 2 and 5. The distributions are normalized to unity. The selection is as follows: AK8 jets with $ {p_{\mathrm {T}}} > $ 300 GeV, AK4 jets with $ {p_{\mathrm {T}}} > $ 30 GeV, AK8 and AK4 jets with $|\eta | < 2.4$, AK8 jet soft-drop mass $ > $ 40 GeV, AK4 jets DeepCSV discriminator $ > 0.2219$, $\Delta R < 1.5$ separation between the AK4 jets, and $\Delta R > 0.8$ separation between the AK8 jet and each AK4 jet.

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Figure 1-b:
For AK8 jets in semi-resolved events, the distributions of the soft-drop mass (upper left), $ {\tau _{21}} $ (upper right), and the double-b tagger (lower). The multijet and ${{\mathrm {t}\overline {\mathrm {t}}}} $+jets background components are shown separately, along with the simulated signals for bulk gravitons of masses 1000 and 1200 GeV and the non-resonant benchmark models 2 and 5. The distributions are normalized to unity. The selection is as follows: AK8 jets with $ {p_{\mathrm {T}}} > $ 300 GeV, AK4 jets with $ {p_{\mathrm {T}}} > $ 30 GeV, AK8 and AK4 jets with $|\eta | < 2.4$, AK8 jet soft-drop mass $ > $ 40 GeV, AK4 jets DeepCSV discriminator $ > 0.2219$, $\Delta R < 1.5$ separation between the AK4 jets, and $\Delta R > 0.8$ separation between the AK8 jet and each AK4 jet.

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Figure 1-c:
For AK8 jets in semi-resolved events, the distributions of the soft-drop mass (upper left), $ {\tau _{21}} $ (upper right), and the double-b tagger (lower). The multijet and ${{\mathrm {t}\overline {\mathrm {t}}}} $+jets background components are shown separately, along with the simulated signals for bulk gravitons of masses 1000 and 1200 GeV and the non-resonant benchmark models 2 and 5. The distributions are normalized to unity. The selection is as follows: AK8 jets with $ {p_{\mathrm {T}}} > $ 300 GeV, AK4 jets with $ {p_{\mathrm {T}}} > $ 30 GeV, AK8 and AK4 jets with $|\eta | < 2.4$, AK8 jet soft-drop mass $ > $ 40 GeV, AK4 jets DeepCSV discriminator $ > 0.2219$, $\Delta R < 1.5$ separation between the AK4 jets, and $\Delta R > 0.8$ separation between the AK8 jet and each AK4 jet.

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Figure 2:
The distributions of the DeepCSV discriminators for the leading j$_{1}$ (upper left) and $2^{\text {nd}}$ AK4 jets j$_{2}$ (upper right), ranked by the DeepCSV discriminator values, the invariant mass of j$_{1}$ and j$_{2}$ ($ {m_{\text {$jj$}}} (\text {j$_{1}$, j$_{2}$})$) (lower left), and the invariant mass of j$_{1}$, j$_{2}$, and their nearest AK4 jet j$_{3}$ ($ {m_{\text {$Jjj$}}} (\text {j$_{1}$, j$_{2}$, j$_{3}$})$) (lower right). The multijet and ${{\mathrm {t}\overline {\mathrm {t}}}} $+jets background components are shown separately, along with the simulated signals for bulk gravitons of masses 1000 and 1200 GeV and the non-resonant benchmark models 2 and 5. The distributions are normalized to unity. The selection is as follows: AK8 jets with $ {p_{\mathrm {T}}} > $ 300 GeV, AK4 jets with $ {p_{\mathrm {T}}} > $ 30 GeV, AK8 and AK4 jets with $|\eta | < 2.4$, AK8 jet soft-drop mass $ > $ 40 GeV, AK4 jets DeepCSV discriminator $ > 0.2219$, $\Delta R < 1.5$ separation between the AK4 jets, and $\Delta R > 0.8$ separation between the AK8 jet and each AK4 jet.

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Figure 2-a:
The distributions of the DeepCSV discriminators for the leading j$_{1}$ (upper left) and $2^{\text {nd}}$ AK4 jets j$_{2}$ (upper right), ranked by the DeepCSV discriminator values, the invariant mass of j$_{1}$ and j$_{2}$ ($ {m_{\text {$jj$}}} (\text {j$_{1}$, j$_{2}$})$) (lower left), and the invariant mass of j$_{1}$, j$_{2}$, and their nearest AK4 jet j$_{3}$ ($ {m_{\text {$Jjj$}}} (\text {j$_{1}$, j$_{2}$, j$_{3}$})$) (lower right). The multijet and ${{\mathrm {t}\overline {\mathrm {t}}}} $+jets background components are shown separately, along with the simulated signals for bulk gravitons of masses 1000 and 1200 GeV and the non-resonant benchmark models 2 and 5. The distributions are normalized to unity. The selection is as follows: AK8 jets with $ {p_{\mathrm {T}}} > $ 300 GeV, AK4 jets with $ {p_{\mathrm {T}}} > $ 30 GeV, AK8 and AK4 jets with $|\eta | < 2.4$, AK8 jet soft-drop mass $ > $ 40 GeV, AK4 jets DeepCSV discriminator $ > 0.2219$, $\Delta R < 1.5$ separation between the AK4 jets, and $\Delta R > 0.8$ separation between the AK8 jet and each AK4 jet.

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Figure 2-b:
The distributions of the DeepCSV discriminators for the leading j$_{1}$ (upper left) and $2^{\text {nd}}$ AK4 jets j$_{2}$ (upper right), ranked by the DeepCSV discriminator values, the invariant mass of j$_{1}$ and j$_{2}$ ($ {m_{\text {$jj$}}} (\text {j$_{1}$, j$_{2}$})$) (lower left), and the invariant mass of j$_{1}$, j$_{2}$, and their nearest AK4 jet j$_{3}$ ($ {m_{\text {$Jjj$}}} (\text {j$_{1}$, j$_{2}$, j$_{3}$})$) (lower right). The multijet and ${{\mathrm {t}\overline {\mathrm {t}}}} $+jets background components are shown separately, along with the simulated signals for bulk gravitons of masses 1000 and 1200 GeV and the non-resonant benchmark models 2 and 5. The distributions are normalized to unity. The selection is as follows: AK8 jets with $ {p_{\mathrm {T}}} > $ 300 GeV, AK4 jets with $ {p_{\mathrm {T}}} > $ 30 GeV, AK8 and AK4 jets with $|\eta | < 2.4$, AK8 jet soft-drop mass $ > $ 40 GeV, AK4 jets DeepCSV discriminator $ > 0.2219$, $\Delta R < 1.5$ separation between the AK4 jets, and $\Delta R > 0.8$ separation between the AK8 jet and each AK4 jet.

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Figure 2-c:
The distributions of the DeepCSV discriminators for the leading j$_{1}$ (upper left) and $2^{\text {nd}}$ AK4 jets j$_{2}$ (upper right), ranked by the DeepCSV discriminator values, the invariant mass of j$_{1}$ and j$_{2}$ ($ {m_{\text {$jj$}}} (\text {j$_{1}$, j$_{2}$})$) (lower left), and the invariant mass of j$_{1}$, j$_{2}$, and their nearest AK4 jet j$_{3}$ ($ {m_{\text {$Jjj$}}} (\text {j$_{1}$, j$_{2}$, j$_{3}$})$) (lower right). The multijet and ${{\mathrm {t}\overline {\mathrm {t}}}} $+jets background components are shown separately, along with the simulated signals for bulk gravitons of masses 1000 and 1200 GeV and the non-resonant benchmark models 2 and 5. The distributions are normalized to unity. The selection is as follows: AK8 jets with $ {p_{\mathrm {T}}} > $ 300 GeV, AK4 jets with $ {p_{\mathrm {T}}} > $ 30 GeV, AK8 and AK4 jets with $|\eta | < 2.4$, AK8 jet soft-drop mass $ > $ 40 GeV, AK4 jets DeepCSV discriminator $ > 0.2219$, $\Delta R < 1.5$ separation between the AK4 jets, and $\Delta R > 0.8$ separation between the AK8 jet and each AK4 jet.

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Figure 2-d:
The distributions of the DeepCSV discriminators for the leading j$_{1}$ (upper left) and $2^{\text {nd}}$ AK4 jets j$_{2}$ (upper right), ranked by the DeepCSV discriminator values, the invariant mass of j$_{1}$ and j$_{2}$ ($ {m_{\text {$jj$}}} (\text {j$_{1}$, j$_{2}$})$) (lower left), and the invariant mass of j$_{1}$, j$_{2}$, and their nearest AK4 jet j$_{3}$ ($ {m_{\text {$Jjj$}}} (\text {j$_{1}$, j$_{2}$, j$_{3}$})$) (lower right). The multijet and ${{\mathrm {t}\overline {\mathrm {t}}}} $+jets background components are shown separately, along with the simulated signals for bulk gravitons of masses 1000 and 1200 GeV and the non-resonant benchmark models 2 and 5. The distributions are normalized to unity. The selection is as follows: AK8 jets with $ {p_{\mathrm {T}}} > $ 300 GeV, AK4 jets with $ {p_{\mathrm {T}}} > $ 30 GeV, AK8 and AK4 jets with $|\eta | < 2.4$, AK8 jet soft-drop mass $ > $ 40 GeV, AK4 jets DeepCSV discriminator $ > 0.2219$, $\Delta R < 1.5$ separation between the AK4 jets, and $\Delta R > 0.8$ separation between the AK8 jet and each AK4 jet.

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Figure 3:
Left: The double-b tagger pass-fail ratio $R_\text {p/f}$ of the leading-$ {p_{\mathrm {T}}} $ AK8 jet in semi-resolved events as a function of the difference between the soft-drop mass and the Higgs boson mass, $m_{J} - {m_{{\mathrm {H}}}} $. The measured ratio in different bins of $m_{J} - {m_{{\mathrm {H}}}} $ is used in the fit (red solid line), except in the region around $m_{J} - {m_{{\mathrm {H}}}} = 0$, which corresponds to the signal region (blue markers). The fitted function is interpolated to obtain $R_\text {p/f}$ in the signal region. Right: The reduced mass distribution $ {m_{\text {$Jjj$,red}}} $ in the data (black markers) with the estimated background represented as the black histogram. The ${{\mathrm {t}\overline {\mathrm {t}}}} $+jets contribution from simulation is represented in green. The rest of the background is multijets, calculated by applying the $R_\text {p/f}$ to the antitag region. The total background, before fitting the background model to the data, is depicted using the shaded region. The signal distributions for a bulk graviton with a mass of 800 GeV (blue) and the non-resonant benchmark 2 model (red) are also shown. For the upper and lower figures, the pseudorapidity intervals are $ | \Delta \eta | < 1.0$ and 1.0 $ < | \Delta \eta | < 2.0$, respectively.

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Figure 3-a:
Left: The double-b tagger pass-fail ratio $R_\text {p/f}$ of the leading-$ {p_{\mathrm {T}}} $ AK8 jet in semi-resolved events as a function of the difference between the soft-drop mass and the Higgs boson mass, $m_{J} - {m_{{\mathrm {H}}}} $. The measured ratio in different bins of $m_{J} - {m_{{\mathrm {H}}}} $ is used in the fit (red solid line), except in the region around $m_{J} - {m_{{\mathrm {H}}}} = 0$, which corresponds to the signal region (blue markers). The fitted function is interpolated to obtain $R_\text {p/f}$ in the signal region. Right: The reduced mass distribution $ {m_{\text {$Jjj$,red}}} $ in the data (black markers) with the estimated background represented as the black histogram. The ${{\mathrm {t}\overline {\mathrm {t}}}} $+jets contribution from simulation is represented in green. The rest of the background is multijets, calculated by applying the $R_\text {p/f}$ to the antitag region. The total background, before fitting the background model to the data, is depicted using the shaded region. The signal distributions for a bulk graviton with a mass of 800 GeV (blue) and the non-resonant benchmark 2 model (red) are also shown. For the upper and lower figures, the pseudorapidity intervals are $ | \Delta \eta | < 1.0$ and 1.0 $ < | \Delta \eta | < 2.0$, respectively.

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Figure 3-b:
Left: The double-b tagger pass-fail ratio $R_\text {p/f}$ of the leading-$ {p_{\mathrm {T}}} $ AK8 jet in semi-resolved events as a function of the difference between the soft-drop mass and the Higgs boson mass, $m_{J} - {m_{{\mathrm {H}}}} $. The measured ratio in different bins of $m_{J} - {m_{{\mathrm {H}}}} $ is used in the fit (red solid line), except in the region around $m_{J} - {m_{{\mathrm {H}}}} = 0$, which corresponds to the signal region (blue markers). The fitted function is interpolated to obtain $R_\text {p/f}$ in the signal region. Right: The reduced mass distribution $ {m_{\text {$Jjj$,red}}} $ in the data (black markers) with the estimated background represented as the black histogram. The ${{\mathrm {t}\overline {\mathrm {t}}}} $+jets contribution from simulation is represented in green. The rest of the background is multijets, calculated by applying the $R_\text {p/f}$ to the antitag region. The total background, before fitting the background model to the data, is depicted using the shaded region. The signal distributions for a bulk graviton with a mass of 800 GeV (blue) and the non-resonant benchmark 2 model (red) are also shown. For the upper and lower figures, the pseudorapidity intervals are $ | \Delta \eta | < 1.0$ and 1.0 $ < | \Delta \eta | < 2.0$, respectively.

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Figure 3-c:
Left: The double-b tagger pass-fail ratio $R_\text {p/f}$ of the leading-$ {p_{\mathrm {T}}} $ AK8 jet in semi-resolved events as a function of the difference between the soft-drop mass and the Higgs boson mass, $m_{J} - {m_{{\mathrm {H}}}} $. The measured ratio in different bins of $m_{J} - {m_{{\mathrm {H}}}} $ is used in the fit (red solid line), except in the region around $m_{J} - {m_{{\mathrm {H}}}} = 0$, which corresponds to the signal region (blue markers). The fitted function is interpolated to obtain $R_\text {p/f}$ in the signal region. Right: The reduced mass distribution $ {m_{\text {$Jjj$,red}}} $ in the data (black markers) with the estimated background represented as the black histogram. The ${{\mathrm {t}\overline {\mathrm {t}}}} $+jets contribution from simulation is represented in green. The rest of the background is multijets, calculated by applying the $R_\text {p/f}$ to the antitag region. The total background, before fitting the background model to the data, is depicted using the shaded region. The signal distributions for a bulk graviton with a mass of 800 GeV (blue) and the non-resonant benchmark 2 model (red) are also shown. For the upper and lower figures, the pseudorapidity intervals are $ | \Delta \eta | < 1.0$ and 1.0 $ < | \Delta \eta | < 2.0$, respectively.

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Figure 3-d:
Left: The double-b tagger pass-fail ratio $R_\text {p/f}$ of the leading-$ {p_{\mathrm {T}}} $ AK8 jet in semi-resolved events as a function of the difference between the soft-drop mass and the Higgs boson mass, $m_{J} - {m_{{\mathrm {H}}}} $. The measured ratio in different bins of $m_{J} - {m_{{\mathrm {H}}}} $ is used in the fit (red solid line), except in the region around $m_{J} - {m_{{\mathrm {H}}}} = 0$, which corresponds to the signal region (blue markers). The fitted function is interpolated to obtain $R_\text {p/f}$ in the signal region. Right: The reduced mass distribution $ {m_{\text {$Jjj$,red}}} $ in the data (black markers) with the estimated background represented as the black histogram. The ${{\mathrm {t}\overline {\mathrm {t}}}} $+jets contribution from simulation is represented in green. The rest of the background is multijets, calculated by applying the $R_\text {p/f}$ to the antitag region. The total background, before fitting the background model to the data, is depicted using the shaded region. The signal distributions for a bulk graviton with a mass of 800 GeV (blue) and the non-resonant benchmark 2 model (red) are also shown. For the upper and lower figures, the pseudorapidity intervals are $ | \Delta \eta | < 1.0$ and 1.0 $ < | \Delta \eta | < 2.0$, respectively.

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Figure 4:
The upper limits for a bulk graviton (left) and radion (right), combining the fully-merged selection and the semi-resolved selection (where the events used in the fully-merged analysis are not considered in the semi-resolved analysis). The inner (green) and the outer (yellow) bands indicate the regions containing the 68% and 95%, respectively, of the distribution of limits expected under the background-only hypothesis. The theoretical prediction is shown as the blue line.

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Figure 4-a:
The upper limits for a bulk graviton (left) and radion (right), combining the fully-merged selection and the semi-resolved selection (where the events used in the fully-merged analysis are not considered in the semi-resolved analysis). The inner (green) and the outer (yellow) bands indicate the regions containing the 68% and 95%, respectively, of the distribution of limits expected under the background-only hypothesis. The theoretical prediction is shown as the blue line.

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Figure 4-b:
The upper limits for a bulk graviton (left) and radion (right), combining the fully-merged selection and the semi-resolved selection (where the events used in the fully-merged analysis are not considered in the semi-resolved analysis). The inner (green) and the outer (yellow) bands indicate the regions containing the 68% and 95%, respectively, of the distribution of limits expected under the background-only hypothesis. The theoretical prediction is shown as the blue line.

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Figure 5:
The observed and expected upper limits for non-resonant $ {\mathrm {H}} {\mathrm {H}} $ production in the standard model (Benchmark 0) and other benchmark models (1-12), combining the fully-merged selection and the semi-resolved selection (where the events used in the fully-merged analysis are not considered in the semi-resolved analysis). The inner (green) and the outer (yellow) bands indicate the regions containing the 68% and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.
Tables

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Table 1:
Parameter values of the final benchmark models selected with a twelve cluster model, along with the SM parameter values.

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Table 2:
Summary of the selection criteria for semi-resolved $ {\mathrm {H}} {\mathrm {H}} \to {{\mathrm {b}} {\overline {\mathrm {b}}}} {{\mathrm {b}} {\overline {\mathrm {b}}}} $ events.

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Table 3:
Summary of systematic uncertainties in the signal and background yields, for both the semi-resolved analysis and the fully merged analysis, taken from Ref.\nobreakspace {} [25].

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Table 4:
Observed and expected limits for the non-resonant benchmark models (1-12) and SM pair production (denoted 0), combining fully-merged and semi-resolved (where the events used in the fully-merged analysis are not considered in the semi-resolved analysis) results.

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Table 5:
Combined expected and observed upper limits of fully-merged and semi-resolved analyses for a bulk graviton (where the events used in the fully-merged analysis are not considered in the semi-resolved analysis).

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Table 6:
Combined expected and observed upper limits of fully-merged and semi-resolved channels for a radion (where the events used in the fully-merged analysis are not considered in the semi-resolved analysis).
Summary
A search is presented for the pair production of standard model Higgs bosons ($\mathrm{H}\mathrm{H}$), both decaying to a bottom quark-antiquark pair ($\mathrm{b\bar{b}}$), using data from proton-proton collisions at a centre-of-mass energy of 13 TeV, and corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The search is dedicated to the phase space where at least one of the Higgs bosons has a high transverse momentum, so that the $\mathrm{H}\to\mathrm{b\bar{b}}$ decay products are collimated to form a single jet, an $\mathrm{H}$ jet, adding sensitivity to the search for $\mathrm{H}\mathrm{H}\to\mathrm{b\bar{b}}\mathrm{b\bar{b}}$ by filling in the phase space between the fully resolved [26] and the fully merged regimes [25], in the search for a Kaluza-Klein bulk graviton and a Randall-Sundrum radion.



Such cases may arise either when a massive resonance produced in proton-proton collisions decays to $\mathrm{H}\mathrm{H}$, or through beyond standard model effects in the Higgs boson self-coupling, at a scale above the reach of the current collider energies. The events are classified according to whether both or only one Higgs boson is boosted enough to form a $\mathrm{H}$ jet. This paper augments the resonance search with the case where the events have a semi-resolved topology, with only one $\mathrm{H}$ jet, while the other ${\mathrm{H}\to\mathrm{b\bar{b}}} $ has a lower boost. The combined upper limits range from 67.0 to 1.4 fb at 95% confidence level for bulk gravitons and radions in the mass range 0.75-3 TeV. Depending on the mass of the resonance, these limits improve upon the results of the fully merged search [25] by up to 55% for the radion and up to 18% for the bulk graviton.



Furthermore, both the merged and semi-resolved events are used to search for non-resonant Higgs boson pair production and upper limits are set in a range from 4520 to 36.7 fb at 95% confidence level on the product of the production cross section and the branching fraction in different scenarios using an effective field theory approach for the anomalous Higgs boson self-couplings. Upper limits on the non-resonant standard model Higgs boson production cross section multiplied by the branching fraction are placed at 1980 fb at 95% confidence level. These are the first results on the limits on the Higgs boson self-couplings using boosted topologies and set the most stringent limits to date on benchmarks 2, 5, 8, 9, and 11 [16,75].
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