Distribution of the missing transverse energy in CRTop. The Z+HF and $t\bar{t}$ scale factors, described in the text, have been applied to the simulated samples. The distribution labeled "Signal" is for the model with ($m_a$, $m_{\tilde{\chi}_{1}^{0}}$, $m_{\tilde{\chi}_{2}^{0}}$) = (45 GeV, 10 GeV, 80 GeV).

Distribution of the dijet invariant mass in the signal region, shown together with the parameterized background model (labelled "Bkg Model"). For reference, the MC prediction for the SM background is also shown (labelled "SM MC"). The Z+HF and $t\bar{t}$ scale factors, described in the text, have been applied to the simulated samples. The signal region is defined to have dijet invariant mass > 20 GeV. The distribution labeled "Signal" is for the model with ($m_a$, $m_{\tilde{\chi}_{1}^{0}}$, $m_{\tilde{\chi}_{2}^{0}}$) = (45 GeV, 10 GeV, 80 GeV).

Upper limits at 95% CL on the $pp \rightarrow ZH$ cross section times the branching ratio for $Z \rightarrow \ell^{+}\ell^{-}$ (where $\ell = e, \mu \;\mathrm{or}\; \tau$) and $H \rightarrow \tilde{\chi}_{2}^{0}\tilde{\chi}_{1}^{0} \rightarrow a \tilde{\chi}_{1}^{0}\tilde{\chi}_{1}^{0} \rightarrow b\bar{b} \tilde{\chi}_{1}^{0}\tilde{\chi}_{1}^{0}$ as a function of $m_{a}$ for $m_{\tilde{\chi}_{1}^{0}} = 10$ GeV and $m_{\tilde{\chi}_{2}^{0}} = 65$ GeV in the NMSSM scenario described in the text. All branching ratios in the Higgs boson decay chain after the decay $H \rightarrow \tilde{\chi}_{2}^{0}\tilde{\chi}_{1}^{0}$ are set to 100%.

Upper limits at 95% CL on the $pp \rightarrow ZH$ cross section times the branching ratio for $Z \rightarrow \ell^{+}\ell^{-}$ (where $\ell = e, \mu \;\mathrm{or}\; \tau$) and $H \rightarrow \tilde{\chi}_{2}^{0}\tilde{\chi}_{1}^{0} \rightarrow a \tilde{\chi}_{1}^{0}\tilde{\chi}_{1}^{0} \rightarrow b\bar{b} \tilde{\chi}_{1}^{0}\tilde{\chi}_{1}^{0}$ as a function of $m_{a}$ for $m_{\tilde{\chi}_{1}^{0}} = 10$ GeV and $m_{\tilde{\chi}_{2}^{0}} = 80$ GeV in the NMSSM scenario described in the text. All branching ratios in the Higgs boson decay chain after the decay $H \rightarrow \tilde{\chi}_{2}^{0}\tilde{\chi}_{1}^{0}$ are set to 100%.

Upper limits at 95% CL on the $pp \rightarrow ZH$ cross section times the branching ratio for $Z \rightarrow \ell^{+}\ell^{-}$ (where $\ell = e, \mu\; \mathrm{or}\; \tau$) and $H \rightarrow \tilde{\chi}_{2}^{0}\tilde{\chi}_{1}^{0} \rightarrow a \tilde{\chi}_{1}^{0}\tilde{\chi}_{1}^{0} \rightarrow b\bar{b} \tilde{\chi}_{1}^{0}\tilde{\chi}_{1}^{0}$ as a function of $m_{a}$ for $m_{\tilde{\chi}_{1}^{0}} = 10$ GeV and $m_{\tilde{\chi}_{2}^{0}} = 95$ GeV in the NMSSM scenario described in the text. All branching ratios in the Higgs boson decay chain after the decay $H \rightarrow \tilde{\chi}_{2}^{0}\tilde{\chi}_{1}^{0}$ are set to 100%.

Upper limits at 95% CL on the $pp \rightarrow ZH$ cross section times the branching ratio for $Z \rightarrow \ell^{+}\ell^{-}$ (where $\ell = e, \mu\; \mathrm{or}\; \tau$) and $H \rightarrow \tilde{\chi}_{2}^{0}\tilde{\chi}_{1}^{0} \rightarrow a \tilde{\chi}_{1}^{0}\tilde{\chi}_{1}^{0} \rightarrow b\bar{b} \tilde{\chi}_{1}^{0}\tilde{\chi}_{1}^{0}$ as a function of $m_{a}$ for $m_{\tilde{\chi}_{1}^{0}} = 10$ GeV and $m_{\tilde{\chi}_{2}^{0}} = 110$ GeV in the NMSSM scenario described in the text. All branching ratios in the Higgs boson decay chain after the decay $H \rightarrow \tilde{\chi}_{2}^{0}\tilde{\chi}_{1}^{0}$ are set to 100%.

Upper limits at 95% CL on the $pp \rightarrow ZH$ cross section times the branching ratio for $Z \rightarrow \ell^{+}\ell^{-}$ (where $\ell = e, \mu\; \mathrm{or}\; \tau$) and $H \rightarrow \tilde{\chi}_{2}^{0}\tilde{\chi}_{1}^{0} \rightarrow a \tilde{\chi}_{1}^{0}\tilde{\chi}_{1}^{0} \rightarrow b\bar{b} \tilde{\chi}_{1}^{0}\tilde{\chi}_{1}^{0}$ as a function of $m_{a}$ for $m_{\tilde{\chi}_{1}^{0}} = 20$ GeV and $m_{\tilde{\chi}_{2}^{0}} = 80$ GeV in the NMSSM scenario described in the text. All branching ratios in the Higgs boson decay chain after the decay $H \rightarrow \tilde{\chi}_{2}^{0}\tilde{\chi}_{1}^{0}$ are set to 100%.

Upper limits at 95% CL on the $pp \rightarrow ZH$ cross section times the branching ratio for $Z \rightarrow \ell^{+}\ell^{-}$ (where $\ell = e, \mu \;\mathrm{or}\; \tau$) and $H \rightarrow \tilde{\chi}_{2}^{0}\tilde{\chi}_{1}^{0} \rightarrow a \tilde{\chi}_{1}^{0}\tilde{\chi}_{1}^{0} \rightarrow b\bar{b} \tilde{\chi}_{1}^{0}\tilde{\chi}_{1}^{0}$ as a function of $m_{a}$ for $m_{\tilde{\chi}_{1}^{0}} = 30$ GeV and $m_{\tilde{\chi}_{2}^{0}} = 80$ GeV in the NMSSM scenario described in the text. All branching ratios in the Higgs boson decay chain after the decay $H \rightarrow \tilde{\chi}_{2}^{0}\tilde{\chi}_{1}^{0}$ are set to 100%.

Unweighted and weighted number of events after each stage of selection for the NMSSM scenario with $pp \rightarrow ZH$, $Z \rightarrow \ell^{+}\ell^{-}$, $H \rightarrow \tilde{\chi}_{2}^{0}\tilde{\chi}_{1}^{0} \rightarrow a \tilde{\chi}_{1}^{0}\tilde{\chi}_{1}^{0} \rightarrow b\bar{b} \tilde{\chi}_{1}^{0}\tilde{\chi}_{1}^{0}$ where $(m_{a}, m_{\tilde{\chi}_{1}^{0}}, m_{\tilde{\chi}_{2}^{0}}) = (45,10,80)$ GeV and the Z boson decaying to $e^{+}e^{-}, \;\mu^{+}\mu^{-} \;\mathrm{or}\; \tau^{+}\tau^{-}$. All branching ratios in the Higgs boson decay chain are set to 100%. The weighted number of events corresponds to an integrated luminosity of $139 \;\mathrm{fb}^{-1}$. The "skimming selection" required either a single electron or muon with $p_{T} > 100\;$ GeV or a pair of electrons or muons each with $p_{T} > 20\;$ GeV. The preselection requirements include the trigger, absence of a bad jet or bad muon, and two leptons, where a lepton is either an electron or a muon.

Acceptance and efficiency of this analysis for the signal models considered in this paper. The signal is an NMSSM scenario with $pp \rightarrow ZH$, $Z \rightarrow \ell^{+}\ell^{-}$, $H \rightarrow \tilde{\chi}_{2}^{0}\tilde{\chi}_{1}^{0} \rightarrow a \tilde{\chi}_{1}^{0}\tilde{\chi}_{1}^{0} \rightarrow b\bar{b} \tilde{\chi}_{1}^{0}\tilde{\chi}_{1}^{0}$ where the values of $(m_{a}, m_{\tilde{\chi}_{1}^{0}}, m_{\tilde{\chi}_{2}^{0}})$ are varied. The Z boson decays to $e^{+}e^{-}, \mu^{+}\mu^{-} \;\mathrm{or}\; \tau^{+}\tau^{-}$. All branching ratios in the Higgs boson decay chain are set to 100%. The product of acceptance times efficiency is defined by the fraction of simulated events that pass all the selection criteria of this analysis. The acceptance is defined by the fraction of simulated events that pass all the selection criteria as applied to Monte Carlo truth-level quantities. The efficiency is then defined as the acceptance times efficiency, divided by the acceptance.

Acceptance and efficiency of this analysis for the signal models considered in this paper. The signal is an NMSSM scenario with $pp \rightarrow ZH$, $Z \rightarrow \ell^{+}\ell^{-}$, $H \rightarrow \tilde{\chi}_{2}^{0}\tilde{\chi}_{1}^{0} \rightarrow a \tilde{\chi}_{1}^{0}\tilde{\chi}_{1}^{0} \rightarrow b\bar{b} \tilde{\chi}_{1}^{0}\tilde{\chi}_{1}^{0}$ where the values of $(m_{a}, m_{\tilde{\chi}_{1}^{0}}, m_{\tilde{\chi}_{2}^{0}})$ are varied. The Z boson decays to $e^{+}e^{-}, \mu^{+}\mu^{-} \;\mathrm{or}\; \tau^{+}\tau^{-}$. All branching ratios in the Higgs boson decay chain are set to 100%. The product of acceptance times efficiency is defined by the fraction of simulated events that pass all the selection criteria of this analysis. The acceptance is defined by the fraction of simulated events that pass all the selection criteria as applied to Monte Carlo truth-level quantities. The efficiency is then defined as the acceptance times efficiency, divided by the acceptance.

Trigger efficiency for simulated signal events as a function of the LLP decay position in the x–y plane (L_xy) for LLPs decaying in the barrel (|η|<1.4) for one of the low-E_T signal samples for HLT CalRatio triggers seeded by the high-E_T L1 triggers with E_T thresholds of 60 GeV and 100 GeV and by the two versions of the low-E_T L1 triggers. Only statistical uncertainties are shown.

Trigger efficiency for simulated signal events as a function of the LLP decay position in the x–y plane (L_xy) for LLPs decaying in the barrel (|η|<1.4) for one of the high-E_T signal samples for HLT CalRatio triggers seeded by the high-E_T L1 triggers with E_T thresholds of 60 GeV and 100 GeV and by the two versions of the low-E_T L1 triggers. Only statistical uncertainties are shown.

The NN output scores in the dijet control region for the low-E_T training with no adversary network. Statistical uncertainties are shown in all plots. In cases where training with adversary networks is considered, the systematic uncertainty related to modelling discrepancies is included as well.

The NN output scores in the dijet control region for the low-E_T training with an adversary network included. Statistical uncertainties are shown in all plots. In cases where training with adversary networks is considered, the systematic uncertainty related to modelling discrepancies is included as well.

The NN output scores in the dijet control region for the high-E_T training with no adversary network. Statistical uncertainties are shown in all plots. In cases where training with adversary networks is considered, the systematic uncertainty related to modelling discrepancies is included as well.

The NN output scores in the dijet control region for the high-E_T training with an adversary network included. Statistical uncertainties are shown in all plots. In cases where training with adversary networks is considered, the systematic uncertainty related to modelling discrepancies is included as well.

Distribution of the low-E_T per-event BDT in main data, BIB data and some of the benchmark signal samples after preselection. Only statistical uncertainties are shown.

Distribution of the high-E_T per-event BDT outputs in main data, BIB data and some of the benchmark signal samples after preselection. Only statistical uncertainties are shown.

Sequential impact of each requirement on the number of events passing the selection for the high-E_T selections. The signal columns represent the cumulative fraction of events passing the selection than the number of events.

Sequential impact of each requirement on the number of events passing the selection for the low-E_T selections. The signal columns represent the cumulative fraction of events passing the selection than the number of events.

Application of the modified ABCD method to the final high-E_T selections. The a priori estimate refers to the "pre-unblinding" case, where the data in region A are ignored by removing the Poisson constraint in that region and the signal strength is fixed to zero. This matches the simple N^bkg_A=(N^bkg_B· N^bkg_C)/N^bkg_D relation. The a posteriori estimate refers to the "post-unblinding" case, including the observed data in region A in the background-only global fit, obtained by fixing the signal strength to 0 (background-only fit) or allowing it to float (signal-plus-background fit). The table also shows one set of representative signal yields in each selection for the signal-plus-background fit. Only statistical uncertainties are included in the quoted error of the background, while the uncertainties in the signal include those from both statistical and experimental sources.

Application of the modified ABCD method to the final low-E_T selections. The a priori estimate refers to the "pre-unblinding" case, where the data in region A are ignored by removing the Poisson constraint in that region and the signal strength is fixed to zero. This matches the simple N^bkg_A=(N^bkg_B· N^bkg_C)/N^bkg_D relation. The a posteriori estimate refers to the "post-unblinding" case, including the observed data in region A in the background-only global fit, obtained by fixing the signal strength to 0 (background-only fit) or allowing it to float (signal-plus-background fit). The table also shows one set of representative signal yields in each selection for the signal-plus-background fit. Only statistical uncertainties are included in the quoted error of the background, while the uncertainties in the signal include those from both statistical and experimental sources.

95% CL expected and observed limits on the BR of SM Higgs bosons to pairs of neutral LLPs (B_{H→ ss}), showing the ± 1 σ (green) and ± 2 σ (yellow) expected limit bands, as well as a comparison with the results from previous ATLAS searches [36,78]. The cross-section for SM Higgs boson gluon--gluon fusion production is assumed to be 48.6 pb.

Trigger efficiency of simulated signal events as a function of the LLP decay position in the z direction for LLPs decaying in the calorimeter endcaps (1.4 ≤ |η| < 2.5) for one of the low-E_T signal samples for HLT CalRatio triggers seeded by the 60 GeV-high-E_T trigger and by the two versions of the low-E_T triggers.

Trigger efficiency of simulated signal events as a function of the LLP decay position in the z direction for LLPs decaying in the calorimeter endcaps (1.4 ≤ |η| < 2.5) for one of the high-E_T signal samples for HLT CalRatio triggers seeded by the 60 GeV-high-E_T trigger and by the two versions of the low-E_T triggers.

The simulated efficiencies as a function of c times the mean proper lifetime (cτ) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (cτ) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (cτ) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (cτ) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (cτ) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (cτ) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (cτ) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (cτ) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (cτ) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (cτ) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (cτ) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (cτ) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (cτ) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (cτ) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The event BDT in the dijet control region for the low-E_T training training. The uncertainties are combined statistical and ML modelling systematic uncertainty.

The event BDT in the dijet control region for the high-E_T training. The uncertainties are combined statistical and ML modelling systematic uncertainty.

The 95% CL observed limits, expected limits and ± 1 σ and 2 σ bands for the Φ mass of 60 GeV compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and ± 1 σ and 2 σ bands for the Φ mass of 60 GeV compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and ± 1 σ and 2 σ bands for the Φ mass 125 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and ± 1 σ and 2 σ bands for the Φ mass 125 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available. The 125 GeV mediator is assumed to be the SM Higgs boson.

The 95% CL observed limits, expected limits and ± 1 σ and 2 σ bands for the Φ mass 125 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available. The 125 GeV mediator is assumed to be the SM Higgs boson.

The 95% CL observed limits, expected limits and ± 1 σ and 2 σ bands for the Φ mass of 200 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and ± 1 σ and 2 σ bands for the Φ mass of 400 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and ± 1 σ and 2 σ bands for the Φ mass 600 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and ± 1 σ and 2 σ bands for the Φ mass of 600 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and ± 1 σ and 2 σ bands for the Φ masses of of 1000 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and ± 1 σ and 2 σ bands for the Φ masses of of 1000 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and ± 1 σ and 2 σ bands for the Φ masses of of 1000 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and ± 1 σ and 2 σ bands for the Φ masses of of 1000 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available.

Efficiency for an event to enter Region A of the high-E_T selection, as a function of the two LLP kinematics, decay type and decay position. LLP p_T is binned in the ranges of [0, 50 , 100, 200 , 400, 1600] GeV (5 bins), the LLP decay position is binned in decay position in L_xy in [0, 1.5, 2, 2.5, 3, 3.5, 3.9, ∞] m for LLPs with |η| < 1.5 and L_z in [0, 3.6, 4.2, 4.8, 5.5, 6, ∞ ] m for LLPs with |η|geq1.5, 13 bins in all. Finally, four decay types are considered: LLPs decaying to pairs of c, b, t, or τ in bins 0, 1, 2, 3 respectively. The efficiency is presented as a function of "Bin Index", which is calculated as follows: Bin Index = (decay position bin index ) × (number of p_T bins × number of decay type bins) + p_T bin index * (number of decay type bin) + decay type bin index. The efficiency for a given pair-produced LLP sample can be obtained by summing the efficiency values for each event as extracted from this map, and dividing it by the total number of events in the sample. The efficiency map is symmetric between the LLPs, so the choice of LLP1 and LLP2 is arbitrary. For the high-E_T selections, for overall efficiencies above 0.5%, the results are typically accurate to around 25%, but below this the efficiency can be overestimated and therefore should not be used for re-interpration.

Efficiency for an event to enter Region A of the low-E_T selection, as a function of the two LLP kinematics, decay type and decay position. LLP p_T is binned in the ranges of [0, 50 , 100, 200 , 400, 1600] GeV (5 bins), the LLP decay position is binned in L_xy in [0, 1.5, 2, 2.5, 3, 3.5, 3.9, ∞] m for LLPs with |η| < 1.5 and L_z in [0, 3.6, 4.2, 4.8, 5.5, 6, ∞ ] m for LLPs with |η|geq1.5, 13 bins in all. Finally, four decay types are considered: LLPs decaying to pairs of c, b, t, or τ in bins 0, 1, 2, 3 respectively. The efficiency is presented as a function of "Bin Index", which is calculated as follows: Bin Index = (decay position bin index ) × (number of p_T bins × number of decay type bins) + p_T bin index * (number of decay type bin) + decay type bin index. The efficiency for a given pair-produced LLP sample can be obtained by summing the efficiency values for each event as extracted from this map, and dividing it by the total number of events in the sample. The efficiency map is symmetric between the LLPs, so the choice of LLP1 and LLP2 is arbitrary. For the low-E_T selections, for overall efficiencies above 0.15%, the results are typically accurate to around 33%, and below this the efficiency is typically accurate up to a factor of 3.