CMS-PAS-HIG-17-006 | ||

Search for resonant and non-resonant Higgs boson pair production in the $\mathrm{b}\overline{\mathrm{b}} \ell\nu \ell\nu$ final state at $\sqrt{s} = $ 13 TeV | ||

CMS Collaboration | ||

March 2017 | ||

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Abstract:
Searches for resonant and non-resonant pair-produced Higgs bosons (hh) decaying respectively into $\mathrm{b}\overline{\mathrm{b}}$ and VV (with V either a W or a Z boson), with subsequent VV decays into two leptons and two neutrinos, are presented. The analyses are based on a sample of proton-proton collisions at $\sqrt{s} = $ 13 TeV at the LHC corresponding to an integrated luminosity of 36 fb$^{-1}$. Data and predictions from the standard model are in agreement within uncertainties. For the standard model hh hypothesis, the data are observed (expected) to exclude a production cross-section times branching ratio of 72 (81$^{+42}_{-25}$) fb, corresponding to 79 (89$^{+47}_{-28}$) times the SM cross section. Lack of deviation from the SM predictions in the observations is used to place constraints on different scenarios considering anomalous couplings which could affect the rate and kinematics of hh production. In the case of resonant production of a new particle $\mathrm{X}$, for mass hypotheses from ${\mathrm{m}}_{\mathrm{X}} = $ 300 GeV to ${\mathrm{m}}_{\mathrm{X}} = $ 900 GeV, the data are observed (expected) to exclude a production cross-section times branching ratio of narrow-width spin-0 particles from 434 to 17 (342$^{+135}_{-97}$ to 14$^{+6}_{-4}$) fb and narrow-width spin-2 particles from 448 to 14 (361$^{+140}_{-102}$ to 13$^{+5}_{-4}$) fb.
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Links:
CDS record (PDF) ;
inSPIRE record ;
CADI line (restricted) ;
These preliminary results are superseded in this paper, JHEP 01 (2018) 054.The superseded preliminary plots can be found here. |

Figures & Tables | Summary | Additional Figures & Tables | References | CMS Publications |
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Figures | |

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Figure 1:
Higgs pair production diagrams via gluon fusion in the SM. |

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Figure 1-a:
Higgs pair production diagram via gluon fusion in the SM. |

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Figure 1-b:
Higgs pair production diagram via gluon fusion in the SM. |

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Figure 2:
The di-jet $ {p_{\mathrm {T}}} $ distributions for data and simulated events after requiring two leptons, two b-tagged jets, and $ {m_{\ell \ell }} < {m}_{\mathrm{ Z } } \, - $ 15 GeV, for ee (left), e$\mu $ and $\mu$e (middle), and $\mu \mu $ (right) events. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

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Figure 2-a:
The di-jet $ {p_{\mathrm {T}}} $ distributions for data and simulated events after requiring two leptons, two b-tagged jets, and $ {m_{\ell \ell }} < {m}_{\mathrm{ Z } } \, - $ 15 GeV, for ee events. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

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Figure 2-b:
The di-jet $ {p_{\mathrm {T}}} $ distributions for data and simulated events after requiring two leptons, two b-tagged jets, and $ {m_{\ell \ell }} < {m}_{\mathrm{ Z } } \, - $ 15 GeV, for e$\mu and $\mu$e events. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

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Figure 2-c:
The di-jet $ {p_{\mathrm {T}}} $ distributions for data and simulated events after requiring two leptons, two b-tagged jets, and $ {m_{\ell \ell }} < {m}_{\mathrm{ Z } } \, - $ 15 GeV, for $\mu \mu $ events. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

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Figure 3:
The $ {m_{ {\mathrm {j}} {\mathrm {j}} }} $ distribution for data and simulated events after requiring all selection cuts in the ee (left), $\mathrm{ e } \mu $ and $\mu \mathrm{ e } $ (middle), and $\mu \mu $ (right) channels. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

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Figure 3-a:
The $ {m_{ {\mathrm {j}} {\mathrm {j}} }} $ distribution for data and simulated events after requiring all selection cuts in the ee channel. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

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Figure 3-b:
The $ {m_{ {\mathrm {j}} {\mathrm {j}} }} $ distribution for data and simulated events after requiring all selection cuts in the $\mathrm{ e } \mu $ and $\mu \mathrm{ e } $ channel. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

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Figure 3-c:
The $ {m_{ {\mathrm {j}} {\mathrm {j}} }} $ distribution for data and simulated events after requiring all selection cuts in the $\mu \mu $ channel. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

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Figure 4:
The DNN output distribution for data and simulated events after requiring all selection cuts, for the $\mu^{+} \mu^{-} $ channel. Output values towards 0 are background-like, while output values towards 1 are signal-like. The resonant DNN output (left) evaluated at $ {m_{\mathrm {X}}} = $ 400 GeV and the non-resonant DNN output (right) evaluated at $\kappa _{\lambda } =$ 1, $\kappa _{\mathrm{ t } } = $ 1. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

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Figure 4-a:
The DNN output distribution for data and simulated events after requiring all selection cuts, for the $\mu^{+} \mu^{-} $ channel. Output values towards 0 are background-like, while output values towards 1 are signal-like. The resonant DNN output evaluated at $ {m_{\mathrm {X}}} = $ 400 GeV. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

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Figure 4-b:
The DNN output distribution for data and simulated events after requiring all selection cuts, for the $\mu^{+} \mu^{-} $ channel. Output values towards 0 are background-like, while output values towards 1 are signal-like. The non-resonant DNN output evaluated at $\kappa _{\lambda } =$ 1, $\kappa _{\mathrm{ t } } = $ 1. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

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Figure 5:
The DNN output distribution for data and simulated events in three different $ {m_{ {\mathrm {j}} {\mathrm {j}} }} $ regions, for the $\mu^{+} \mu^{-} $ channel: $ {m_{ {\mathrm {j}} {\mathrm {j}} }} < $ 75 GeV, $ {m_{ {\mathrm {j}} {\mathrm {j}} }} \in $ [75, 140[ GeV and $ {m_{ {\mathrm {j}} {\mathrm {j}} }} \geq $ 140 GeV. The resonant DNN output (left) evaluated at $ {m_{\mathrm {X}}} = $ 400 GeV and the non-resonant DNN output (right) evaluated at $\kappa _{\lambda } =$ 1, $\kappa _{\mathrm{ t } } = $ 1. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

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Figure 5-a:
The DNN output distribution for data and simulated events in three different $ {m_{ {\mathrm {j}} {\mathrm {j}} }} $ regions, for the $\mu^{+} \mu^{-} $ channel: $ {m_{ {\mathrm {j}} {\mathrm {j}} }} < $ 75 GeV, $ {m_{ {\mathrm {j}} {\mathrm {j}} }} \in $ [75, 140[ GeV and $ {m_{ {\mathrm {j}} {\mathrm {j}} }} \geq $ 140 GeV. The resonant DNN output evaluated at $ {m_{\mathrm {X}}} = $ 400 GeV. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

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Figure 5-b:
The DNN output distribution for data and simulated events in three different $ {m_{ {\mathrm {j}} {\mathrm {j}} }} $ regions, for the $\mu^{+} \mu^{-} $ channel: $ {m_{ {\mathrm {j}} {\mathrm {j}} }} < $ 75 GeV, $ {m_{ {\mathrm {j}} {\mathrm {j}} }} \in $ [75, 140[ GeV and $ {m_{ {\mathrm {j}} {\mathrm {j}} }} \geq $ 140 GeV. The non-resonant DNN output (right) evaluated at $\kappa _{\lambda } =$ 1, $\kappa _{\mathrm{ t } } = $ 1. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

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Figure 6:
Expected and observed 95% CL upper limits on Higgs pair production cross section times branching ratio for $\mathrm{h} \mathrm{h} \to {\mathrm{ b \bar{b} } } {\mathrm {V}} {\mathrm {V}} \to {\mathrm{ b \bar{b} } } \ell \nu \ell \nu $ as a function of $ {m_{\mathrm {X}}} $. These limits are computed using the asymptotic CL$_s$ method, combining the $\mathrm{ e }^{+} \mathrm{ e }^{-} $, $\mu^{+} \mu^{-} $ and $\mathrm{ e } ^{\pm }\mu ^{\mp }$ channels, for spin-0 (left) and spin-2 (right) hypotheses. The dashed red lines represent possible expectations for new physics arising from a new spin-0 or spin-2 resonance (see text for details). The irregular behaviour of the observed limit is due to the limited statistics on data and to the parameterised learning technique, which results in a reshuffling of the observed data distributions for each point of the scan. The expected limits are evaluated with the same granularity as the observed limits. The DNN interpolates the expected analysis performance in a smooth fashion between the fully-simulated points. |

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Figure 6-a:
Expected and observed 95% CL upper limits on Higgs pair production cross section times branching ratio for $\mathrm{h} \mathrm{h} \to {\mathrm{ b \bar{b} } } {\mathrm {V}} {\mathrm {V}} \to {\mathrm{ b \bar{b} } } \ell \nu \ell \nu $ as a function of $ {m_{\mathrm {X}}} $. These limits are computed using the asymptotic CL$_s$ method, combining the $\mathrm{ e }^{+} \mathrm{ e }^{-} $, $\mu^{+} \mu^{-} $ and $\mathrm{ e } ^{\pm }\mu ^{\mp }$ channels, for the spin-0 hypothesis. The dashed red lines represent possible expectations for new physics arising from a new spin-0 resonance (see text for details). The irregular behaviour of the observed limit is due to the limited statistics on data and to the parameterised learning technique, which results in a reshuffling of the observed data distributions for each point of the scan. The expected limits are evaluated with the same granularity as the observed limits. The DNN interpolates the expected analysis performance in a smooth fashion between the fully-simulated points. |

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Figure 6-b:
Expected and observed 95% CL upper limits on Higgs pair production cross section times branching ratio for $\mathrm{h} \mathrm{h} \to {\mathrm{ b \bar{b} } } {\mathrm {V}} {\mathrm {V}} \to {\mathrm{ b \bar{b} } } \ell \nu \ell \nu $ as a function of $ {m_{\mathrm {X}}} $. These limits are computed using the asymptotic CL$_s$ method, combining the $\mathrm{ e }^{+} \mathrm{ e }^{-} $, $\mu^{+} \mu^{-} $ and $\mathrm{ e } ^{\pm }\mu ^{\mp }$ channels, for the spin-2 hypothesis. The dashed red lines represent possible expectations for new physics arising from a new spin-2 resonance (see text for details). The irregular behaviour of the observed limit is due to the limited statistics on data and to the parameterised learning technique, which results in a reshuffling of the observed data distributions for each point of the scan. The expected limits are evaluated with the same granularity as the observed limits. The DNN interpolates the expected analysis performance in a smooth fashion between the fully-simulated points. |

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Figure 7:
Expected and observed 95% CL upper limits on Higgs pair production cross section times branching ratio for $\mathrm{h} \mathrm{h} \to {\mathrm{ b \bar{b} } } {\mathrm {V}} {\mathrm {V}} \to {\mathrm{ b \bar{b} } } \ell \nu \ell \nu $ as a function of $\kappa _{\lambda } / \kappa _{\mathrm{ t } }$ (left). Observed (red region) and expected (dashed blue line) exclusion of the BSM parameter space at 95% CL in the $\kappa _{\lambda }$ vs $\kappa _{t}$ plane (right). Theoretical cross-section times branching fraction isolines for $\mathrm{h} \mathrm{h} \to {\mathrm{ b \bar{b} } } {\mathrm {V}} {\mathrm {V}} \to {\mathrm{ b \bar{b} } } \ell \nu \ell \nu $ are shown as dashed lines (right). These limits are computed using the asymptotic CL$_s$ method, combining the $\mathrm{ e }^{+} \mathrm{ e }^{-} $, $\mu^{+} \mu^{-} $ and $\mathrm{ e }^{+}m {\mu ^\mp } $ channels. Theory predictions are extracted from [68,10,11,12,13,14,69]. One can note that both theory predictions, expected and observed limits are symmetric through a $(\kappa _{\lambda } , \kappa _{\mathrm{ t } }) \leftrightarrow (-\kappa _{\lambda } , -\kappa _{\mathrm{ t } })$ transformation. |

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Figure 7-a:
Observed (red region) and expected (dashed blue line) exclusion of the BSM parameter space at 95% CL in the $\kappa _{\lambda }$ vs $\kappa _{t}$ plane. Theoretical cross-section times branching fraction isolines for $\mathrm{h} \mathrm{h} \to {\mathrm{ b \bar{b} } } {\mathrm {V}} {\mathrm {V}} \to {\mathrm{ b \bar{b} } } \ell \nu \ell \nu $ are shown as dashed lines. These limits are computed using the asymptotic CL$_s$ method, combining the $\mathrm{ e }^{+} \mathrm{ e }^{-} $, $\mu^{+} \mu^{-} $ and $\mathrm{ e }^{+}m {\mu ^\mp } $ channels. Theory predictions are extracted from [68,10,11,12,13,14,69]. One can note that both theory predictions, expected and observed limits are symmetric through a $(\kappa _{\lambda } , \kappa _{\mathrm{ t } }) \leftrightarrow (-\kappa _{\lambda } , -\kappa _{\mathrm{ t } })$ transformation. |

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Figure 7-b:
Expected and observed 95% CL upper limits on Higgs pair production cross section times branching ratio for $\mathrm{h} \mathrm{h} \to {\mathrm{ b \bar{b} } } {\mathrm {V}} {\mathrm {V}} \to {\mathrm{ b \bar{b} } } \ell \nu \ell \nu $ as a function of $\kappa _{\lambda } / \kappa _{\mathrm{ t } }$ (left). Observed (red region) and expected (dashed blue line) exclusion of the BSM parameter space at 95% CL in the $\kappa _{\lambda }$ vs $\kappa _{t}$ plane (right). Theoretical cross-section times branching fraction isolines for $\mathrm{h} \mathrm{h} \to {\mathrm{ b \bar{b} } } {\mathrm {V}} {\mathrm {V}} \to {\mathrm{ b \bar{b} } } \ell \nu \ell \nu $ are shown as dashed lines (right). These limits are computed using the asymptotic CL$_s$ method, combining the $\mathrm{ e }^{+} \mathrm{ e }^{-} $, $\mu^{+} \mu^{-} $ and $\mathrm{ e }^{+}m {\mu ^\mp } $ channels. Theory predictions are extracted from [68,10,11,12,13,14,69]. One can note that both theory predictions, expected and observed limits are symmetric through a $(\kappa _{\lambda } , \kappa _{\mathrm{ t } }) \leftrightarrow (-\kappa _{\lambda } , -\kappa _{\mathrm{ t } })$ transformation. |

Tables | |

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Table 1:
Summary of the systematic uncertainties and their impact range on total background yields and on the SM and $ {m_{\mathrm {X}}} = $ 400 GeV signal hypotheses in the signal region. |

Summary |

We have presented a search for resonant and non-resonant Higgs pair production, where one of the h decays as $\mathrm{h} \to \mathrm{ b \bar{b} }$, and the other as $\mathrm{h} \to \mathrm{ V }\mathrm{ V } \to \ell\nu \ell\nu$ using LHC proton-proton collision data at $\sqrt{s}$ = 13 TeV, corresponding to an integrated luminosity of 36 fb$^{-1}$. Masses are considered in the range between $m_{\mathrm{X}} = $ 260 GeV and 900 GeV for the resonant search, and anomalous couplings $\kappa_{\lambda}$, $\kappa_{\mathrm{ t }}$ are considered in addition to the standard model case for the non-resonant search. The results obtained by the analysis are in agreement with the predictions from the standard model within uncertainties. For mass hypotheses from $m_{\mathrm{X}} = $ 300 GeV to $m_{\mathrm{X}} = $ 900 GeV, the data are observed (expected) to exclude a production cross-section times branching ratio of narrow-width spin-0 particles from 434 to 17 (342$^{+135}_{-97}$ to 14$^{+6}_{-4}$) fb and narrow-width spin-2 particles from 448 to 14 (361$^{+140}_{-102}$ to 13$^{+5}_{-4}$) fb for the resonant search. For the SM hh hypothesis, the data are observed (expected) to exclude a production cross section times branching ratio of 72 (81$^{+42}_{-25}$) fb, corresponding to 79 (89$^{+47}_{-28}$) times the SM cross section. |

Additional Figures | |

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Additional Figure 1:
Expected and observed 95% CL upper limits on Higgs pair production cross section as a function of $ {\mathrm {m}_{\mathrm {X}}} $. These limits are computed using the asymptotic CL$_s$ method, combining the $\mathrm{ e }^{+} \mathrm{ e }^{-} $, $\mu^{+} \mu^{-} $ and $\mathrm{ e } ^{\pm }\mu ^{\mp }$ channels, for spin-0 hypotheses and divided by the branching ratio for $\mathrm{h} \mathrm{h} \to {\mathrm{ b \bar{b} } } {\mathrm {V}} {\mathrm {V}} \to {\mathrm{ b \bar{b} } } \ell \nu \ell \nu $. |

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Additional Figure 2:
Expected and observed 95% CL upper limits on Higgs pair production cross section as a function of $ {\mathrm {m}_{\mathrm {X}}} $. These limits are computed using the asymptotic CL$_s$ method, combining the $\mathrm{ e }^{+} \mathrm{ e }^{-} $, $\mu^{+} \mu^{-} $ and $\mathrm{ e } ^{\pm }\mu ^{\mp }$ channels, for spin-2 hypotheses and divided by the branching ratio for $\mathrm{h} \mathrm{h} \to {\mathrm{ b \bar{b} } } {\mathrm {V}} {\mathrm {V}} \to {\mathrm{ b \bar{b} } } \ell \nu \ell \nu $. |

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Additional Figure 3:
Expected and observed 95% CL upper limits on Higgs pair production cross section as a function of $\kappa _{\lambda } / \kappa _{\mathrm{ t } }$. These limits are computed using the asymptotic CL$_s$ method, combining the $\mathrm{ e }^{+} \mathrm{ e }^{-} $, $\mu^{+} \mu^{-} $ and $\mathrm{ e }^{+}m {\mu ^\mp } $ channels and divided by the branching ratio for $\mathrm{h} \mathrm{h} \to {\mathrm{ b \bar{b} } } {\mathrm {V}} {\mathrm {V}} \to {\mathrm{ b \bar{b} } } \ell \nu \ell \nu $. |

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Additional Figure 4:
The DNN output distribution for data and simulated events after requiring all selection cuts. Output values towards 0 are background-like, while output values towards 1 are signal-like. The resonant DNN output evaluated at $ {\mathrm {m}_{\mathrm {X}}} = $ 400 GeV. $\mathrm{ e }^{+} \mathrm{ e }^{-} $ channel only. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

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Additional Figure 5:
The DNN output distribution for data and simulated events after requiring all selection cuts. Output values towards 0 are background-like, while output values towards 1 are signal-like. The resonant DNN output evaluated at $ {\mathrm {m}_{\mathrm {X}}} = $ 400 GeV. $\mathrm{ e }^{+}m {} {\mu ^\mp } $ channel only. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

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Additional Figure 6:
The DNN output distribution for data and simulated events after requiring all selection cuts. Output values towards 0 are background-like, while output values towards 1 are signal-like. The resonant DNN output evaluated at $ {\mathrm {m}_{\mathrm {X}}} = $ 650 GeV. $\mathrm{ e }^{+} \mathrm{ e }^{-} $ channel only. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

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Additional Figure 7:
The DNN output distribution for data and simulated events after requiring all selection cuts. Output values towards 0 are background-like, while output values towards 1 are signal-like. The resonant DNN output evaluated at $ {\mathrm {m}_{\mathrm {X}}} = $ 650 GeV. $\mathrm{ e }^{+}m {} {\mu ^\mp } $ channel only. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

png pdf |
Additional Figure 8:
The DNN output distribution for data and simulated events after requiring all selection cuts. Output values towards 0 are background-like, while output values towards 1 are signal-like. The resonant DNN output evaluated at $ {\mathrm {m}_{\mathrm {X}}} = $ 650 GeV. $\mu^{+} {}\mu^{-} $ channel only. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

png pdf |
Additional Figure 9:
The DNN output distribution for data and simulated events after requiring all selection cuts. Output values towards 0 are background-like, while output values towards 1 are signal-like. The resonant DNN output evaluated at $ {\mathrm {m}_{\mathrm {X}}} = $ 900 GeV. $\mathrm{ e }^{+} \mathrm{ e }^{-} $ channel only. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

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Additional Figure 10:
The DNN output distribution for data and simulated events after requiring all selection cuts. Output values towards 0 are background-like, while output values towards 1 are signal-like. The resonant DNN output evaluated at $ {\mathrm {m}_{\mathrm {X}}} = $ 900 GeV. $\mathrm{ e }^{+}m {} {\mu ^\mp } $ channel only. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

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Additional Figure 11:
The DNN output distribution for data and simulated events after requiring all selection cuts. Output values towards 0 are background-like, while output values towards 1 are signal-like. The resonant DNN output evaluated at $ {\mathrm {m}_{\mathrm {X}}} = $ 900 GeV. $\mu^{+} {}\mu^{-} $ channel only. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

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Additional Figure 12:
DNN output distribution for data and simulated events in three different $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} $ regions: $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} < $ 75 GeV, $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \in $ [75, 140 [ GeV and $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \geq 140$ GeV. The resonant DNN output evaluated at $ {\mathrm {m}_{\mathrm {X}}} = $ 400 GeV. $\mathrm{ e }^{+} \mathrm{ e }^{-} $ channel only. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

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Additional Figure 13:
DNN output distribution for data and simulated events in three different $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} $ regions: $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} < $ 75 GeV, $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \in $ [75, 140 [ GeV and $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \geq 140$ GeV. The resonant DNN output evaluated at $ {\mathrm {m}_{\mathrm {X}}} = $ 400 GeV. $\mathrm{ e }^{+}m {} {\mu ^\mp } $ channel only. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

png pdf |
Additional Figure 14:
DNN output distribution for data and simulated events in three different $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} $ regions: $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} < $ 75 GeV, $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \in $ [75, 140 [ GeV and $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \geq 140$ GeV. The resonant DNN output evaluated at $ {\mathrm {m}_{\mathrm {X}}} = $ 650 GeV. $\mathrm{ e }^{+} \mathrm{ e }^{-} $ channel only. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

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Additional Figure 15:
DNN output distribution for data and simulated events in three different $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} $ regions: $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} < $ 75 GeV, $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \in $ [75, 140 [ GeV and $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \geq 140$ GeV. The resonant DNN output evaluated at $ {\mathrm {m}_{\mathrm {X}}} = $ 650 GeV. $\mathrm{ e }^{+}m {} {\mu ^\mp } $ channel only. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

png pdf |
Additional Figure 16:
DNN output distribution for data and simulated events in three different $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} $ regions: $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} < $ 75 GeV, $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \in $ [75, 140 [ GeV and $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \geq 140$ GeV. The resonant DNN output evaluated at $ {\mathrm {m}_{\mathrm {X}}} = $ 650 GeV. $\mu^{+} {}\mu^{-} $ channel only. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

png pdf |
Additional Figure 17:
DNN output distribution for data and simulated events in three different $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} $ regions: $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} < $ 75 GeV, $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \in $ [75, 140 [ GeV and $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \geq 140$ GeV. The resonant DNN output evaluated at $ {\mathrm {m}_{\mathrm {X}}} = $ 900 GeV. $\mathrm{ e }^{+} \mathrm{ e }^{-} $ channel only. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

png pdf |
Additional Figure 18:
DNN output distribution for data and simulated events in three different $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} $ regions: $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} < $ 75 GeV, $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \in $ [75, 140 [ GeV and $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \geq 140$ GeV. The resonant DNN output evaluated at $ {\mathrm {m}_{\mathrm {X}}} = $ 900 GeV. $\mathrm{ e }^{+}m {} {\mu ^\mp } $ channel only. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

png pdf |
Additional Figure 19:
DNN output distribution for data and simulated events in three different $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} $ regions: $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} < $ 75 GeV, $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \in $ [75, 140 [ GeV and $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \geq 140$ GeV. The resonant DNN output evaluated at $ {\mathrm {m}_{\mathrm {X}}} = $ 900 GeV. $\mu^{+} {}\mu^{-} $ channel only. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

png pdf |
Additional Figure 20:
The DNN output distribution for data and simulated events after requiring all selection cuts. Output values towards 0 are background-like, while output values towards 1 are signal-like. The non-resonant DNN output evaluated at $\kappa _{\lambda } = $ 1, $\kappa _{\mathrm{ t } } = $ 1. $\mathrm{ e }^{+} \mathrm{ e }^{-} $ channel only.The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

png pdf |
Additional Figure 21:
The DNN output distribution for data and simulated events after requiring all selection cuts. Output values towards 0 are background-like, while output values towards 1 are signal-like. The non-resonant DNN output evaluated at $\kappa _{\lambda } = $ 1, $\kappa _{\mathrm{ t } } = $ 1. $\mathrm{ e }^{+}m {} {\mu ^\mp } $ channel only.The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

png pdf |
Additional Figure 22:
The DNN output distribution for data and simulated events after requiring all selection cuts. Output values towards 0 are background-like, while output values towards 1 are signal-like. The non-resonant DNN output evaluated at $\kappa _{\lambda } = $ 5, $\kappa _{\mathrm{ t } } =2.5$. $\mathrm{ e }^{+} \mathrm{ e }^{-} $ channel only.The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

png pdf |
Additional Figure 23:
The DNN output distribution for data and simulated events after requiring all selection cuts. Output values towards 0 are background-like, while output values towards 1 are signal-like. The non-resonant DNN output evaluated at $\kappa _{\lambda } = $ 5, $\kappa _{\mathrm{ t } } =2.5$. $\mathrm{ e }^{+}m {} {\mu ^\mp } $ channel only.The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

png pdf |
Additional Figure 24:
The DNN output distribution for data and simulated events after requiring all selection cuts. Output values towards 0 are background-like, while output values towards 1 are signal-like. The non-resonant DNN output evaluated at $\kappa _{\lambda } = $ 5, $\kappa _{\mathrm{ t } } =2.5$. $\mu^{+} {}\mu^{-} $ channel only.The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

png pdf |
Additional Figure 25:
The DNN output distribution for data and simulated events after requiring all selection cuts. Output values towards 0 are background-like, while output values towards 1 are signal-like. The non-resonant DNN output evaluated at $\kappa _{\lambda } =-20$, $\kappa _{\mathrm{ t } } =0.5$. $\mathrm{ e }^{+} \mathrm{ e }^{-} $ channel only.The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

png pdf |
Additional Figure 26:
The DNN output distribution for data and simulated events after requiring all selection cuts. Output values towards 0 are background-like, while output values towards 1 are signal-like. The non-resonant DNN output evaluated at $\kappa _{\lambda } =-20$, $\kappa _{\mathrm{ t } } =0.5$. $\mathrm{ e }^{+}m {} {\mu ^\mp } $ channel only.The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

png pdf |
Additional Figure 27:
The DNN output distribution for data and simulated events after requiring all selection cuts. Output values towards 0 are background-like, while output values towards 1 are signal-like. The non-resonant DNN output evaluated at $\kappa _{\lambda } =-20$, $\kappa _{\mathrm{ t } } =0.5$. $\mu^{+} {}\mu^{-} $ channel only.The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

png pdf |
Additional Figure 28:
DNN output distribution for data and simulated events in three different $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} $ regions: $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} < $ 75 GeV, $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \in $ [75, 140 [ GeV and $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \geq 140$ GeV. The non-resonant DNN output evaluated at $\kappa _{\lambda } = $ 1, $\kappa _{\mathrm{ t } } = $ 1. $\mathrm{ e }^{+} \mathrm{ e }^{-} $ channel only. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

png pdf |
Additional Figure 29:
DNN output distribution for data and simulated events in three different $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} $ regions: $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} < $ 75 GeV, $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \in $ [75, 140 [ GeV and $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \geq 140$ GeV. The non-resonant DNN output evaluated at $\kappa _{\lambda } = $ 1, $\kappa _{\mathrm{ t } } = $ 1. $\mathrm{ e }^{+}m {} {\mu ^\mp } $ channel only. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

png pdf |
Additional Figure 30:
DNN output distribution for data and simulated events in three different $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} $ regions: $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} < $ 75 GeV, $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \in $ [75, 140 [ GeV and $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \geq 140$ GeV. The non-resonant DNN output evaluated at $\kappa _{\lambda } = $ 5, $\kappa _{\mathrm{ t } } =2.5$. $\mathrm{ e }^{+} \mathrm{ e }^{-} $ channel only. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

png pdf |
Additional Figure 31:
DNN output distribution for data and simulated events in three different $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} $ regions: $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} < $ 75 GeV, $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \in $ [75, 140 [ GeV and $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \geq 140$ GeV. The non-resonant DNN output evaluated at $\kappa _{\lambda } = $ 5, $\kappa _{\mathrm{ t } } =2.5$. $\mathrm{ e }^{+}m {} {\mu ^\mp } $ channel only. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

png pdf |
Additional Figure 32:
DNN output distribution for data and simulated events in three different $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} $ regions: $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} < $ 75 GeV, $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \in $ [75, 140 [ GeV and $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \geq 140$ GeV. The non-resonant DNN output evaluated at $\kappa _{\lambda } = $ 5, $\kappa _{\mathrm{ t } } =2.5$. $\mu^{+} {}\mu^{-} $ channel only. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

png pdf |
Additional Figure 33:
DNN output distribution for data and simulated events in three different $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} $ regions: $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} < $ 75 GeV, $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \in $ [75, 140 [ GeV and $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \geq 140$ GeV. The non-resonant DNN output evaluated at $\kappa _{\lambda } =-20$, $\kappa _{\mathrm{ t } } =0.5$. $\mathrm{ e }^{+} \mathrm{ e }^{-} $ channel only. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

png pdf |
Additional Figure 34:
DNN output distribution for data and simulated events in three different $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} $ regions: $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} < $ 75 GeV, $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \in $ [75, 140 [ GeV and $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \geq 140$ GeV. The non-resonant DNN output evaluated at $\kappa _{\lambda } =-20$, $\kappa _{\mathrm{ t } } =0.5$. $\mathrm{ e }^{+}m {} {\mu ^\mp } $ channel only. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

png pdf |
Additional Figure 35:
DNN output distribution for data and simulated events in three different $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} $ regions: $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} < $ 75 GeV, $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \in $ [75, 140 [ GeV and $ {\mathrm {m}_{ {\mathrm {j}} {\mathrm {j}} }} \geq 140$ GeV. The non-resonant DNN output evaluated at $\kappa _{\lambda } =-20$, $\kappa _{\mathrm{ t } } =0.5$. $\mu^{+} {}\mu^{-} $ channel only. The various signal hypotheses displayed have been scaled to a cross-section of 5 pb. |

png pdf |
Additional Figure 36:
Signal vs background efficiency curve comparing the non resonant DNN parameterised training, evaluated at $\kappa _{\lambda } = -20$, $\kappa _{\mathrm{ t } } = 0.5$ (dashed lines) and $\kappa _{\lambda } = 1$, $\kappa _{\mathrm{ t } } = 1$ (solid lines), with a dedicated non-parameterised training for each of the points. Both approaches show similar performance. |

png pdf |
Additional Figure 37:
Signal vs background efficiency curve showing the resonant DNN parameterised training, evaluated at $ {\mathrm {m}_{\mathrm {X}}} = $ 650 GeV. Blue line shows a parameterised training which includes $ {\mathrm {m}_{\mathrm {X}}} = $ 650 GeV , while the red line shows a parameterised training which does not include $ {\mathrm {m}_{\mathrm {X}}} = $ 650 GeV. |

png pdf |
Additional Figure 38:
The $\Delta R_{ll}$ distribution in Drell-Yan Monte Carlo events requiring two leptons and two jets ( blue line), two leptons and two b-tag jets by applying the b-tagging algorithm (red line), and two leptons and two b-tagged using the DY re-weighting method (violet line). |

Additional Tables | |

png pdf |
Additional Table 1:
Expected and observed 95% CL upper limits on Higgs pair production cross section times branching ratio for $\mathrm{h} \mathrm{h} \to {\mathrm{ b \bar{b} } } {\mathrm {V}} {\mathrm {V}} \to {\mathrm{ b \bar{b} } } \ell \nu \ell \nu $ as a function of $ {\mathrm {m}_{\mathrm {X}}} $. These limits are computed using the asymptotic CL$_s$ method, combining the $\mathrm{ e }^{+} \mathrm{ e }^{-} $, $\mu^{+} \mu^{-} $ and $\mathrm{ e } ^{\pm }\mu ^{\mp }$ channels, for spin-0 hypotheses. |

png pdf |
Additional Table 2:
Expected and observed 95% CL upper limits on Higgs pair production cross section times branching ratio for $\mathrm{h} \mathrm{h} \to {\mathrm{ b \bar{b} } } {\mathrm {V}} {\mathrm {V}} \to {\mathrm{ b \bar{b} } } \ell \nu \ell \nu $ as a function of $ {\mathrm {m}_{\mathrm {X}}} $. These limits are computed using the asymptotic CL$_s$ method, combining the $\mathrm{ e }^{+} \mathrm{ e }^{-} $, $\mu^{+} \mu^{-} $ and $\mathrm{ e } ^{\pm }\mu ^{\mp }$ channels, for spin-2 hypotheses. |

png pdf |
Additional Table 3:
Expected and observed 95% CL upper limits on Higgs pair production cross section times branching ratio for $\mathrm{h} \mathrm{h} \to {\mathrm{ b \bar{b} } } {\mathrm {V}} {\mathrm {V}} \to {\mathrm{ b \bar{b} } } \ell \nu \ell \nu $ as a function of $\kappa _{\lambda }$. These limits are computed using the asymptotic CL$_s$ method, combining the $\mathrm{ e }^{+} \mathrm{ e }^{-} $, $\mu^{+} \mu^{-} $ and $\mathrm{ e } ^{\pm }\mu ^{\mp }$ channels, for $\kappa _{\mathrm{ t } } = 1$. |

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