Summary of observed and expected background yields in the SR after the likelihood fit under the background-only hypothesis.

Expected (dashed black line) and observed (solid red line) 95% CL exclusion limits on the higgsino simplified model being considered. These are shown with $\pm 1\sigma_{\mathrm{exp}}$ (yellow band) from experimental systematic and statistical uncertainties, and with $\pm 1\sigma_{\mathrm{theory}}^{\mathrm{SUSY}}$ (red dotted lines) from signal cross-section uncertainties, respectively. The limits set by the latest ATLAS searches using the soft lepton and disappearing track signatures are illustrated by the blue and green regions, respectively, while the limit imposed by the LEP experiments is shown in gray. The dot-dashed gray line indicates the predicted mass-splitting for the pure higgsino scenario.

Expected (dashed black line) and observed (solid red line) 95% CL exclusion limits on the higgsino simplified model being considered. These are shown with $\pm 1\sigma_{\mathrm{exp}}$ (yellow band) from experimental systematic and statistical uncertainties, and with $\pm 1\sigma_{\mathrm{theory}}^{\mathrm{SUSY}}$ (red dotted lines) from signal cross-section uncertainties, respectively. The limits set by the latest ATLAS searches using the soft lepton and disappearing track signatures are illustrated by the blue and green regions, respectively, while the limit imposed by the LEP experiments is shown in gray. The dot-dashed gray line indicates the predicted mass-splitting for the pure higgsino scenario.

Expected (dashed black line) and observed (solid red line) 95% CL exclusion limits on the higgsino simplified model being considered. These are shown with $\pm 1\sigma_{\mathrm{exp}}$ (yellow band) from experimental systematic and statistical uncertainties, and with $\pm 1\sigma_{\mathrm{theory}}^{\mathrm{SUSY}}$ (red dotted lines) from signal cross-section uncertainties, respectively. The limits set by the latest ATLAS searches using the soft lepton and disappearing track signatures are illustrated by the blue and green regions, respectively, while the limit imposed by the LEP experiments is shown in gray. The dot-dashed gray line indicates the predicted mass-splitting for the pure higgsino scenario.

Expected (dashed black line) and observed (solid red line) 95% CL exclusion limits on the higgsino simplified model being considered. These are shown with $\pm 1\sigma_{\mathrm{exp}}$ (yellow band) from experimental systematic and statistical uncertainties, and with $\pm 1\sigma_{\mathrm{theory}}^{\mathrm{SUSY}}$ (red dotted lines) from signal cross-section uncertainties, respectively. The limits set by the latest ATLAS searches using the soft lepton and disappearing track signatures are illustrated by the blue and green regions, respectively, while the limit imposed by the LEP experiments is shown in gray. The dot-dashed gray line indicates the predicted mass-splitting for the pure higgsino scenario.

Expected and observed CLs values per signal point represented by the grey numbers. The expected (dashed) and observed (solid) 95% CL exclusion limits are overlaid along with $\pm 1\sigma_{\mathrm{exp}}$ (yellow band) from experimental systematic and statistical uncertainties, and with $\pm 1\sigma_{\mathrm{theory}}^{\mathrm{SUSY}}$ (red dotted lines) from signal cross-section uncertainties, respectively.

Expected and observed CLs values per signal point represented by the grey numbers. The expected (dashed) and observed (solid) 95% CL exclusion limits are overlaid along with $\pm 1\sigma_{\mathrm{exp}}$ (yellow band) from experimental systematic and statistical uncertainties, and with $\pm 1\sigma_{\mathrm{theory}}^{\mathrm{SUSY}}$ (red dotted lines) from signal cross-section uncertainties, respectively.

Expected and observed cross-section upper-limit per signal point represented by the grey numbers. The expected (dashed) and observed (solid) 95% CL exclusion limits are overlaid along with $\pm 1\sigma_{\mathrm{exp}}$ (yellow band) from experimental systematic and statistical uncertainties, and with $\pm 1\sigma_{\mathrm{theory}}^{\mathrm{SUSY}}$ (red dotted lines) from signal cross-section uncertainties, respectively.

Expected and observed cross-section upper-limit per signal point represented by the grey numbers. The expected (dashed) and observed (solid) 95% CL exclusion limits are overlaid along with $\pm 1\sigma_{\mathrm{exp}}$ (yellow band) from experimental systematic and statistical uncertainties, and with $\pm 1\sigma_{\mathrm{theory}}^{\mathrm{SUSY}}$ (red dotted lines) from signal cross-section uncertainties, respectively.

Truth-level signal acceptances for each production process ($\tilde{\chi}_1^\pm \tilde{\chi}_1^0$, $\tilde{\chi}_1^\pm \tilde{\chi}_2^0$, $\tilde{\chi}_1^+ \tilde{\chi}_1^-$, and $\tilde{\chi}_2^0 \tilde{\chi}_1^0$) in a SR with the $S(d_0)$ requirement removed. The acceptance is defined as the fraction of accepted events divided by the total number of events in the generator-level signal Monte Carlo simulation, where the signal candidate track is identified as the charged particle with the largest distance between the interaction vertex and the secondary vertex of the higgsino decays.

Truth-level signal acceptances for each production process ($\tilde{\chi}_1^\pm \tilde{\chi}_1^0$, $\tilde{\chi}_1^\pm \tilde{\chi}_2^0$, $\tilde{\chi}_1^+ \tilde{\chi}_1^-$, and $\tilde{\chi}_2^0 \tilde{\chi}_1^0$) in a SR with the $S(d_0)$ requirement removed. The acceptance is defined as the fraction of accepted events divided by the total number of events in the generator-level signal Monte Carlo simulation, where the signal candidate track is identified as the charged particle with the largest distance between the interaction vertex and the secondary vertex of the higgsino decays.

Truth-level signal acceptances for each production process ($\tilde{\chi}_1^\pm \tilde{\chi}_1^0$, $\tilde{\chi}_1^\pm \tilde{\chi}_2^0$, $\tilde{\chi}_1^+ \tilde{\chi}_1^-$, and $\tilde{\chi}_2^0 \tilde{\chi}_1^0$) in a SR with the $S(d_0)$ requirement removed. The acceptance is defined as the fraction of accepted events divided by the total number of events in the generator-level signal Monte Carlo simulation, where the signal candidate track is identified as the charged particle with the largest distance between the interaction vertex and the secondary vertex of the higgsino decays.

Truth-level signal acceptances for each production process ($\tilde{\chi}_1^\pm \tilde{\chi}_1^0$, $\tilde{\chi}_1^\pm \tilde{\chi}_2^0$, $\tilde{\chi}_1^+ \tilde{\chi}_1^-$, and $\tilde{\chi}_2^0 \tilde{\chi}_1^0$) in a SR with the $S(d_0)$ requirement removed. The acceptance is defined as the fraction of accepted events divided by the total number of events in the generator-level signal Monte Carlo simulation, where the signal candidate track is identified as the charged particle with the largest distance between the interaction vertex and the secondary vertex of the higgsino decays.

Truth-level signal acceptances for each production process ($\tilde{\chi}_1^\pm \tilde{\chi}_1^0$, $\tilde{\chi}_1^\pm \tilde{\chi}_2^0$, $\tilde{\chi}_1^+ \tilde{\chi}_1^-$, and $\tilde{\chi}_2^0 \tilde{\chi}_1^0$) in a SR with the $S(d_0)$ requirement removed. The acceptance is defined as the fraction of accepted events divided by the total number of events in the generator-level signal Monte Carlo simulation, where the signal candidate track is identified as the charged particle with the largest distance between the interaction vertex and the secondary vertex of the higgsino decays.

Truth-level signal acceptances for each production process ($\tilde{\chi}_1^\pm \tilde{\chi}_1^0$, $\tilde{\chi}_1^\pm \tilde{\chi}_2^0$, $\tilde{\chi}_1^+ \tilde{\chi}_1^-$, and $\tilde{\chi}_2^0 \tilde{\chi}_1^0$) in a SR with the $S(d_0)$ requirement removed. The acceptance is defined as the fraction of accepted events divided by the total number of events in the generator-level signal Monte Carlo simulation, where the signal candidate track is identified as the charged particle with the largest distance between the interaction vertex and the secondary vertex of the higgsino decays.

Signal efficiencies in SR-Low for each production process ($\tilde{\chi}_1^\pm \tilde{\chi}_1^0$, $\tilde{\chi}_1^\pm \tilde{\chi}_2^0$, $\tilde{\chi}_1^+ \tilde{\chi}_1^-$, and $\tilde{\chi}_2^0 \tilde{\chi}_1^0$), defined by the number of events of reconstructed-level signal simulation divided by the number of events obtained at generator level, where the $S(d_0)$ selecton efficiency has the largest impact. The higgsino decay products from $\Delta \mathrm{m}(\tilde{\chi}_1^\pm,\tilde{\chi}_1^0) < 0.4$ GeV signal have $p_{\mathrm{T}}$ too low to be reconstructed as the signal candidate tracks, and therefore the identified signal candidate tracks are typically from pile-up collisions or underlying events similar to the QCD track background, causing a low $S(d_0)$ selection efficiency in these plots.

Signal efficiencies in SR-Low for each production process ($\tilde{\chi}_1^\pm \tilde{\chi}_1^0$, $\tilde{\chi}_1^\pm \tilde{\chi}_2^0$, $\tilde{\chi}_1^+ \tilde{\chi}_1^-$, and $\tilde{\chi}_2^0 \tilde{\chi}_1^0$), defined by the number of events of reconstructed-level signal simulation divided by the number of events obtained at generator level, where the $S(d_0)$ selecton efficiency has the largest impact. The higgsino decay products from $\Delta \mathrm{m}(\tilde{\chi}_1^\pm,\tilde{\chi}_1^0) < 0.4$ GeV signal have $p_{\mathrm{T}}$ too low to be reconstructed as the signal candidate tracks, and therefore the identified signal candidate tracks are typically from pile-up collisions or underlying events similar to the QCD track background, causing a low $S(d_0)$ selection efficiency in these plots.

Signal efficiencies in SR-Low for each production process ($\tilde{\chi}_1^\pm \tilde{\chi}_1^0$, $\tilde{\chi}_1^\pm \tilde{\chi}_2^0$, $\tilde{\chi}_1^+ \tilde{\chi}_1^-$, and $\tilde{\chi}_2^0 \tilde{\chi}_1^0$), defined by the number of events of reconstructed-level signal simulation divided by the number of events obtained at generator level, where the $S(d_0)$ selecton efficiency has the largest impact. The higgsino decay products from $\Delta \mathrm{m}(\tilde{\chi}_1^\pm,\tilde{\chi}_1^0) < 0.4$ GeV signal have $p_{\mathrm{T}}$ too low to be reconstructed as the signal candidate tracks, and therefore the identified signal candidate tracks are typically from pile-up collisions or underlying events similar to the QCD track background, causing a low $S(d_0)$ selection efficiency in these plots.

Signal efficiencies in SR-Low for each production process ($\tilde{\chi}_1^\pm \tilde{\chi}_1^0$, $\tilde{\chi}_1^\pm \tilde{\chi}_2^0$, $\tilde{\chi}_1^+ \tilde{\chi}_1^-$, and $\tilde{\chi}_2^0 \tilde{\chi}_1^0$), defined by the number of events of reconstructed-level signal simulation divided by the number of events obtained at generator level, where the $S(d_0)$ selecton efficiency has the largest impact. The higgsino decay products from $\Delta \mathrm{m}(\tilde{\chi}_1^\pm,\tilde{\chi}_1^0) < 0.4$ GeV signal have $p_{\mathrm{T}}$ too low to be reconstructed as the signal candidate tracks, and therefore the identified signal candidate tracks are typically from pile-up collisions or underlying events similar to the QCD track background, causing a low $S(d_0)$ selection efficiency in these plots.

Signal efficiencies in SR-Low for each production process ($\tilde{\chi}_1^\pm \tilde{\chi}_1^0$, $\tilde{\chi}_1^\pm \tilde{\chi}_2^0$, $\tilde{\chi}_1^+ \tilde{\chi}_1^-$, and $\tilde{\chi}_2^0 \tilde{\chi}_1^0$), defined by the number of events of reconstructed-level signal simulation divided by the number of events obtained at generator level, where the $S(d_0)$ selecton efficiency has the largest impact. The higgsino decay products from $\Delta \mathrm{m}(\tilde{\chi}_1^\pm,\tilde{\chi}_1^0) < 0.4$ GeV signal have $p_{\mathrm{T}}$ too low to be reconstructed as the signal candidate tracks, and therefore the identified signal candidate tracks are typically from pile-up collisions or underlying events similar to the QCD track background, causing a low $S(d_0)$ selection efficiency in these plots.

Signal efficiencies in SR-Low for each production process ($\tilde{\chi}_1^\pm \tilde{\chi}_1^0$, $\tilde{\chi}_1^\pm \tilde{\chi}_2^0$, $\tilde{\chi}_1^+ \tilde{\chi}_1^-$, and $\tilde{\chi}_2^0 \tilde{\chi}_1^0$), defined by the number of events of reconstructed-level signal simulation divided by the number of events obtained at generator level, where the $S(d_0)$ selecton efficiency has the largest impact. The higgsino decay products from $\Delta \mathrm{m}(\tilde{\chi}_1^\pm,\tilde{\chi}_1^0) < 0.4$ GeV signal have $p_{\mathrm{T}}$ too low to be reconstructed as the signal candidate tracks, and therefore the identified signal candidate tracks are typically from pile-up collisions or underlying events similar to the QCD track background, causing a low $S(d_0)$ selection efficiency in these plots.

Signal efficiencies in SR-High for each production process ($\tilde{\chi}_1^\pm \tilde{\chi}_1^0$, $\tilde{\chi}_1^\pm \tilde{\chi}_2^0$, $\tilde{\chi}_1^+ \tilde{\chi}_1^-$, and $\tilde{\chi}_2^0 \tilde{\chi}_1^0$), defined by the number of events of reconstructed-level signal simulation divided by the number of events obtained at generator level, where the $S(d_0)$ selecton efficiency has the largest impact. The higgsino decay products from $\Delta \mathrm{m}(\tilde{\chi}_1^\pm,\tilde{\chi}_1^0) < 0.4$ GeV signal have $p_{\mathrm{T}}$ too low to be reconstructed as the signal candidate tracks, and therefore the identified signal candidate tracks are typically from pile-up collisions or underlying events similar to the QCD track background, causing a low $S(d_0)$ selection efficiency in these plots.

Signal efficiencies in SR-High for each production process ($\tilde{\chi}_1^\pm \tilde{\chi}_1^0$, $\tilde{\chi}_1^\pm \tilde{\chi}_2^0$, $\tilde{\chi}_1^+ \tilde{\chi}_1^-$, and $\tilde{\chi}_2^0 \tilde{\chi}_1^0$), defined by the number of events of reconstructed-level signal simulation divided by the number of events obtained at generator level, where the $S(d_0)$ selecton efficiency has the largest impact. The higgsino decay products from $\Delta \mathrm{m}(\tilde{\chi}_1^\pm,\tilde{\chi}_1^0) < 0.4$ GeV signal have $p_{\mathrm{T}}$ too low to be reconstructed as the signal candidate tracks, and therefore the identified signal candidate tracks are typically from pile-up collisions or underlying events similar to the QCD track background, causing a low $S(d_0)$ selection efficiency in these plots.

Signal efficiencies in SR-High for each production process ($\tilde{\chi}_1^\pm \tilde{\chi}_1^0$, $\tilde{\chi}_1^\pm \tilde{\chi}_2^0$, $\tilde{\chi}_1^+ \tilde{\chi}_1^-$, and $\tilde{\chi}_2^0 \tilde{\chi}_1^0$), defined by the number of events of reconstructed-level signal simulation divided by the number of events obtained at generator level, where the $S(d_0)$ selecton efficiency has the largest impact. The higgsino decay products from $\Delta \mathrm{m}(\tilde{\chi}_1^\pm,\tilde{\chi}_1^0) < 0.4$ GeV signal have $p_{\mathrm{T}}$ too low to be reconstructed as the signal candidate tracks, and therefore the identified signal candidate tracks are typically from pile-up collisions or underlying events similar to the QCD track background, causing a low $S(d_0)$ selection efficiency in these plots.

Signal efficiencies in SR-High for each production process ($\tilde{\chi}_1^\pm \tilde{\chi}_1^0$, $\tilde{\chi}_1^\pm \tilde{\chi}_2^0$, $\tilde{\chi}_1^+ \tilde{\chi}_1^-$, and $\tilde{\chi}_2^0 \tilde{\chi}_1^0$), defined by the number of events of reconstructed-level signal simulation divided by the number of events obtained at generator level, where the $S(d_0)$ selecton efficiency has the largest impact. The higgsino decay products from $\Delta \mathrm{m}(\tilde{\chi}_1^\pm,\tilde{\chi}_1^0) < 0.4$ GeV signal have $p_{\mathrm{T}}$ too low to be reconstructed as the signal candidate tracks, and therefore the identified signal candidate tracks are typically from pile-up collisions or underlying events similar to the QCD track background, causing a low $S(d_0)$ selection efficiency in these plots.

Signal efficiencies in SR-High for each production process ($\tilde{\chi}_1^\pm \tilde{\chi}_1^0$, $\tilde{\chi}_1^\pm \tilde{\chi}_2^0$, $\tilde{\chi}_1^+ \tilde{\chi}_1^-$, and $\tilde{\chi}_2^0 \tilde{\chi}_1^0$), defined by the number of events of reconstructed-level signal simulation divided by the number of events obtained at generator level, where the $S(d_0)$ selecton efficiency has the largest impact. The higgsino decay products from $\Delta \mathrm{m}(\tilde{\chi}_1^\pm,\tilde{\chi}_1^0) < 0.4$ GeV signal have $p_{\mathrm{T}}$ too low to be reconstructed as the signal candidate tracks, and therefore the identified signal candidate tracks are typically from pile-up collisions or underlying events similar to the QCD track background, causing a low $S(d_0)$ selection efficiency in these plots.

Signal efficiencies in SR-High for each production process ($\tilde{\chi}_1^\pm \tilde{\chi}_1^0$, $\tilde{\chi}_1^\pm \tilde{\chi}_2^0$, $\tilde{\chi}_1^+ \tilde{\chi}_1^-$, and $\tilde{\chi}_2^0 \tilde{\chi}_1^0$), defined by the number of events of reconstructed-level signal simulation divided by the number of events obtained at generator level, where the $S(d_0)$ selecton efficiency has the largest impact. The higgsino decay products from $\Delta \mathrm{m}(\tilde{\chi}_1^\pm,\tilde{\chi}_1^0) < 0.4$ GeV signal have $p_{\mathrm{T}}$ too low to be reconstructed as the signal candidate tracks, and therefore the identified signal candidate tracks are typically from pile-up collisions or underlying events similar to the QCD track background, causing a low $S(d_0)$ selection efficiency in these plots.

Event selection cutflows for signal samples with $m(\tilde{\chi}_{1}^0)$ = 150 GeV and $\Delta m(\tilde{\chi}_{1}^\pm, \tilde{\chi}_{1}^0)$ = 1.5, 1.0, and 0.75 GeV, including all six production processes ($\tilde{\chi}_1^\pm \tilde{\chi}_1^0$, $\tilde{\chi}_1^\pm \tilde{\chi}_2^0$, $\tilde{\chi}_1^+ \tilde{\chi}_1^-$, and $\tilde{\chi}_2^0 \tilde{\chi}_1^0$). The cross-section used to obtain the initial number of events ($\sigma(\mathrm{n}_{\mathrm{jets}}) \geq 1$) refers to an emission of at least one gluon or quark with $p_{\mathrm{T}} > 50$ GeV at the parton level.

Event selection cutflows for signal samples with $m(\tilde{\chi}_{1}^0)$ = 150 GeV and $\Delta m(\tilde{\chi}_{1}^\pm, \tilde{\chi}_{1}^0)$ = 0.5, 0.35, and 0.25 GeV, including all six production processes ($\tilde{\chi}_1^\pm \tilde{\chi}_1^0$, $\tilde{\chi}_1^\pm \tilde{\chi}_2^0$, $\tilde{\chi}_1^+ \tilde{\chi}_1^-$, and $\tilde{\chi}_2^0 \tilde{\chi}_1^0$). The cross-section used to obtain the initial number of events ($\sigma(\mathrm{n}_{\mathrm{jets}}) \geq 1$) refers to an emission of at least one gluon or quark with $p_{\mathrm{T}} > 50$ GeV at the parton level.

Observed and expected distributions of the invariant mass of the four-lepton system in the $A\to ZH\to 4\ell+X$ search for SR1 under a background-only fit to data. The total background includes the $q\overline{q}\to ZZ$, $gg\to ZZ$, $q\overline{q}\to ZZ$ (EW), $VVV$, $t\overline{t}V$, $t\overline{t}$, $Z$+jets and $WZ$ processes. The distribution of the $(m_{A}, m_{H}) = (510, 380)$ GeV signal is normalised to the observed upper limit on the cross-section (29.9 fb).

Observed and expected distributions of the invariant mass of the four-lepton system in the $A\to ZH\to 4\ell+X$ search for SR2 under a background-only fit to data. The total background includes the $q\overline{q}\to ZZ$, $gg\to ZZ$, $q\overline{q}\to ZZ$ (EW), $VVV$, $t\overline{t}V$, $t\overline{t}$, $Z$+jets and $WZ$ processes. The distribution of the $(m_{A}, m_{H}) = (510, 380)$ GeV signal is normalised to the observed upper limit on the cross-section (29.9 fb).

Observed and expected distributions of the invariant mass of the four-lepton system in the $A\to ZH\to 4\ell+X$ search for SR3 under a background-only fit to data. The total background includes the $q\overline{q}\to ZZ$, $gg\to ZZ$, $q\overline{q}\to ZZ$ (EW), $VVV$, $t\overline{t}V$, $t\overline{t}$, $Z$+jets and $WZ$ processes. The distribution of the $(m_{A}, m_{H}) = (510, 380)$ GeV signal is normalised to the observed upper limit on the cross-section (29.9 fb).

Observed and expected distributions of the invariant mass of the four-lepton system in the $A\to ZH\to 4\ell+X$ search for SR4 under a background-only fit to data. The total background includes the $q\overline{q}\to ZZ$, $gg\to ZZ$, $q\overline{q}\to ZZ$ (EW), $VVV$, $t\overline{t}V$, $t\overline{t}$, $Z$+jets and $WZ$ processes. The distribution of the $(m_{A}, m_{H}) = (510, 380)$ GeV signal is normalised to the observed upper limit on the cross-section (29.9 fb).

Observed and expected distributions of the invariant mass of the four-lepton system in the $A\to ZH\to 4\ell+X$ search for SR5 under a background-only fit to data. The total background includes the $q\overline{q}\to ZZ$, $gg\to ZZ$, $q\overline{q}\to ZZ$ (EW), $VVV$, $t\overline{t}V$, $t\overline{t}$, $Z$+jets and $WZ$ processes. The distribution of the $(m_{A}, m_{H}) = (510, 380)$ GeV signal is normalised to the observed upper limit on the cross-section (29.9 fb).

Observed and expected distributions of the invariant mass of the four-lepton system in the $A\to ZH\to 4\ell+X$ search for SR6 under a background-only fit to data. The total background includes the $q\overline{q}\to ZZ$, $gg\to ZZ$, $q\overline{q}\to ZZ$ (EW), $VVV$, $t\overline{t}V$, $t\overline{t}$, $Z$+jets and $WZ$ processes. The distribution of the $(m_{A}, m_{H}) = (510, 380)$ GeV signal is normalised to the observed upper limit on the cross-section (29.9 fb).

Observed and expected distributions of the invariant mass of the four-lepton system in the $A\to ZH\to 4\ell+X$ search for SR7 under a background-only fit to data. The total background includes the $q\overline{q}\to ZZ$, $gg\to ZZ$, $q\overline{q}\to ZZ$ (EW), $VVV$, $t\overline{t}V$, $t\overline{t}$, $Z$+jets and $WZ$ processes. The distribution of the $(m_{A}, m_{H}) = (510, 380)$ GeV signal is normalised to the observed upper limit on the cross-section (29.9 fb).

Local p0-values in the $(m_{H}, m_{R})$ plane for the $R\to SH\to 4\ell+E^{\textrm{miss}}_{\textrm{T}}$ search with $m_{S} = 160$ GeV.

Local p0-values in the $(m_{H}, m_{A})$ plane for the $A\to ZH\to 4\ell+X$ search.

The observed upper limits at 95% confidence level on $\sigma(gg\to R)\times \mathcal{B}(R\to SH)\times (H\to ZZ)$ across the $(m_{H}, m_{R})$ plane with $m_{S} = 160$ GeV for the $R\to SH\to 4\ell+E^{\textrm{miss}}_{\textrm{T}}$ search.

The expected upper limits at 95% confidence level on $\sigma(gg\to R)\times \mathcal{B}(R\to SH)\times (H\to ZZ)$ across the $(m_{H}, m_{R})$ plane with $m_{S} = 160$ GeV for the $R\to SH\to 4\ell+E^{\textrm{miss}}_{\textrm{T}}$ search.

The observed upper limits at 95% confidence level on $\sigma(gg\to A)\times \mathcal{B}(A\to ZH)\times (H\to ZZ)$ across the $(m_{H}, m_{A})$ plane for the $A\to ZH\to 4\ell+X$ search.

The expected upper limits at 95% confidence level on $\sigma(gg\to A)\times \mathcal{B}(A\to ZH)\times (H\to ZZ)$ across the $(m_{H}, m_{A})$ plane for the $A\to ZH\to 4\ell+X$ search.

Cut-flow of the raw events at each selection stage for the $R\rightarrow SH\rightarrow 4\ell + E^{\textrm{miss}}_{\textrm{T}}$ signal with a mass point of $(m_R, m_H ) = (390, 220)$ GeV and $m_S = 160$ GeV. The events are shown for the individual and combined four-lepton channels. The SFOS denotes same flavour and opposite sign lepton pairs selection and the final selection is shown for each signal region. The final selection criteria for SR1 to SR3 are defined in Table 2 of the paper.

Cut-flow of the raw events at each selection stage for the $A\rightarrow Z(\rightarrow jj/\ell^+\ell^-/\textrm{invisible})H(\rightarrow 4\ell)$ signal with a mass point of $(m_A, m_H ) = (330, 220)$ GeV. The events are shown for the individual and combined four-lepton channels. The SFOS denotes same flavour and opposite sign lepton pairs selection and the final selection is shown for each signal region. The final selection criteria for SR1 to SR7 are defined in Table 2 of the paper.

Cut-flow of the raw events at each selection stage for the $A\rightarrow Z(\rightarrow 2\ell)H(\rightarrow 2\ell+jj/\textrm{invisible})$ signal with a mass point of $(m_A, m_H ) = (330, 220)$ GeV. The events are shown for the individual and combined four-lepton channels. The SFOS denotes same flavour and opposite sign lepton pairs selection and the final selection is shown for each signal region. The final selection criteria for SR1 to SR7 are defined in Table 2 of the paper.

Distribution of $m_{\mathrm{JJ}}$ in the SR (black points) compared to the background-only expectation, where the shape is derived from the CR and the normalisation is fitted in the SR.

Observed and expected limits at 95% CL on the cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model A (see the text for details). The darker and lighter shaded bands around the expected limits represent the $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty range, respectively.

The predicted theory cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model A (see the text for details). In the theory model, a universal coupling of the $Z^\prime$ to each SM quark $g_q$ is assumed and the dark quarks are all represented by one species with an effective coupling $g_{q_d}$ to the $Z^\prime$. For model A, the predicted cross-section is shown for $g_q=0.05$ and $g_{q_d} = 0.2$.

Observed and expected limits at 95% CL on the cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model B (see the text for details). The darker and lighter shaded bands around the expected limits represent the $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty range, respectively.

The predicted theory cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model B (see the text for details). In the theory model, a universal coupling of the $Z^\prime$ to each SM quark $g_q$ is assumed and the dark quarks are all represented by one species with an effective coupling $g_{q_d}$ to the $Z^\prime$. For model B, the predicted cross-section is shown for $g_q=0.15$ and $g_{q_d} = 0.5$.

Observed and expected limits at 95% CL on the cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model C (see the text for details). The darker and lighter shaded bands around the expected limits represent the $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty range, respectively.

The predicted theory cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model C (see the text for details). In the theory model, a universal coupling of the $Z^\prime$ to each SM quark $g_q$ is assumed and the dark quarks are all represented by one species with an effective coupling $g_{q_d}$ to the $Z^\prime$. For model C, the predicted cross-section is shown for $g_q=0.15$ and $g_{q_d}= 0.5$.

Observed and expected limits at 95% CL on the cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model D (see the text for details). The darker and lighter shaded bands around the expected limits represent the $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty range, respectively.

The predicted theory cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model D (see the text for details). In the theory model, a universal coupling of the $Z^\prime$ to each SM quark $g_q$ is assumed and the dark quarks are all represented by one species with an effective coupling $g_{q_d}$ to the $Z^\prime$. For model D, the predicted cross-section is shown for $g_q=0.05$ and $g_{q_d} = 0.2$.

Relative efficiency (in %) of each stage of the analysis selection with respect to the previous one for models A through D and $m_{Z^\prime}=2.5$ TeV. Approximately 90000 events were generated per signal mass hypothesis.

The distribution of the fit discriminant mTVH in the 3+ b-tag signal region of the vvbb channel for the mH=300 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The m(tt) distribution in the Lhi3_Zin region of the lltt channel. <br><br><a href="?table=overview">return to overview</a>

The m(bb) distribution in the 2 b-tag 0L region of the vvbb channel. <br><br><a href="?table=overview">return to overview</a>

The m(bb) distribution in the 3+ b-tag 0L region of the vvbb channel. <br><br><a href="?table=overview">return to overview</a>

Expected and observed upper limits at 95% CL on sigma(gg->A)*B(A->ZH)*B(H->tt) in the (mA,mH) plane. The limits are shown for tanbeta=1. The tanbeta value is relevant only for the choice of the A boson width. <br><a href="?table=overview">return to overview</a>

Expected and observed upper limits at 95% CL on sigma(bbA)*B(A->ZH)*B(H->tt)$ in the (mA,mH) plane. The limits are shown for tanbeta=10. The tanbeta value is relevant only for the choice of the A boson width. <br><br><a href="?table=overview">return to overview</a>

Expected and observed upper limits at 95% CL on sigma(gg->A)*B(A->ZH)*B(H->bb) in the (mA,mH) plane. The limits are shown for tanbeta=1. The tanbeta value is relevant only for the choice of the A boson width. <br><br><a href="?table=overview">return to overview</a>

Expected and observed upper limits at 95% CL on sigma(bbA)*B(A->ZH)*B(H->bb) in the (mA,mH) plane. The limits are shown for tanbeta=10. The tanbeta value is relevant only for the choice of the A boson width. <br><br><a href="?table=overview">return to overview</a>

Expected and observed upper limits at 95% CL on sigma(gg->A)*B(A->ZH)*B(H->tt) in he (mA,mH) plane. The limits are shown for tanbeta=0.5. The tanbeta value is relevant only for the choice of the A boson width. <br><a href="?table=overview">return to overview</a>

Expected and observed upper limits at 95% CL on sigma(gg->A)*B(A->ZH)*B(H->tt) in the (mA,mH) plane. The limits are shown for tanbeta=5. The tanbeta value is relevant only for the choice of the A boson width. <br><a href="?table=overview">return to overview</a>

Expected and observed upper limits at 95% CL on sigma(bbA)*B(A->ZH)*B(H->tt) in the (mA,mH) plane. The limits are shown for tanbeta=1. The tanbeta value is relevant only for the choice of the A boson width. <br><br><a href="?table=overview">return to overview</a>

Expected and observed upper limits at 95% CL on sigma(bbA)*B(A->ZH)*B(H->tt)$ in the (mA,mH) plane. The limits are shown for tanbeta=5. The tanbeta value is relevant only for the choice of the A boson width. <br><br><a href="?table=overview">return to overview</a>

Expected and observed upper limits at 95% CL on sigma(gg->A)*B(A->ZH)*B(H->bb) in the (mA,mH) plane. The limits are shown for tanbeta=0.5. The tanbeta value is relevant only for the choice of the A boson width. <br><br><a href="?table=overview">return to overview</a>

Expected and observed upper limits at 95% CL on sigma(gg->A)*B(A->ZH)*B(H->bb) in the (mA,mH) plane. The limits are shown for tanbeta=5. The tanbeta value is relevant only for the choice of the A boson width. <br><br><a href="?table=overview">return to overview</a>

Expected and observed upper limits at 95% CL on sigma(bbA)*B(A->ZH)*B(H->bb) in the (mA,mH) plane. The limits are shown for tanbeta=1. The tanbeta value is relevant only for the choice of the A boson width. <br><br><a href="?table=overview">return to overview</a>

Expected and observed upper limits at 95% CL on sigma(bbA)*B(A->ZH)*B(H->bb) in the (mA,mH) plane. The limits are shown for tanbeta=5. The tanbeta value is relevant only for the choice of the A boson width. <br><br><a href="?table=overview">return to overview</a>

Expected and observed upper limits at 95% CL on sigma(bbA)*B(A->ZH)*B(H->bb) in the (mA,mH) plane. The limits are shown for tanbeta=20. The tanbeta value is relevant only for the choice of the A boson width. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant m(lltt)-m(tt) in the signal region of the lltt channel for the mH=450 GeV hypothesis with the bbA signal shown for comparison. <br><br><a href="?table=overview">return to overview</a>

The m(tt) distribution in the L3hi_Zin region of the lltt channel for the mH=450 GeV hypothesis with the bbA signal shown for comparison. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant m(lltt)-m(tt) in the signal region of the lltt channel for the mH=350 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant m(lltt)-m(tt) in the signal region of the lltt channel for the mH=400 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant m(lltt)-m(tt) in the signal region of the lltt channel for the mH=500 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant m(lltt)-m(tt) in the signal region of the lltt channel for the mH=550 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant m(lltt)-m(tt) in the signal region of the lltt channel for the mH=600 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant m(lltt)-m(tt) in the signal region of the lltt channel for the mH=700 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant m(lltt)-m(tt) in the signal region of the lltt channel for the mH=800 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant mTVH in the 2 b-tag signal region of the vvbb channel for the mH=130 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant mTVH in the 2 b-tag signal region of the vvbb channel for the mH=150 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant mTVH in the 2 b-tag signal region of the vvbb channel for the mH=200 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant mTVH in the 2 b-tag signal region of the vvbb channel for the mH=250 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant mTVH in the 2 b-tag signal region of the vvbb channel for the mH=350 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant mTVH in the 2 b-tag signal region of the vvbb channel for the mH=400 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant mTVH in the 2 b-tag signal region of the vvbb channel for the mH=450 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant mTVH in the 2 b-tag signal region of the vvbb channel for the mH=500 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant mTVH in the 2 b-tag signal region of the vvbb channel for the mH=600 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant mTVH in the 2 b-tag signal region of the vvbb channel for the mH=700 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant mTVH in the 2 b-tag signal region of the vvbb channel for the mH=800 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant mTVH i+ the 3p b-tag signal region of the vvbb channel for the mH=130 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant mTVH in the 3+ b-tag signal region of the vvbb channel for the mH=150 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant mTVH in the 3+ b-tag signal region of the vvbb channel for the mH=200 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant mTVH in the 3+ b-tag signal region of the vvbb channel for the mH=250 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant mTVH in the 3+ b-tag signal region of the vvbb channel for the mH=350 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant mTVH in the 3+ b-tag signal region of the vvbb channel for the mH=400 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant mTVH in the 3+ b-tag signal region of the vvbb channel for the mH=450 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant mTVH in the 3+ b-tag signal region of the vvbb channel for the mH=500 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant mTVH in the 3+ b-tag signal region of the vvbb channel for the mH=600 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant mTVH in the 3+ b-tag signal region of the vvbb channel for the mH=700 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant mTVH in the 3+ b-tag signal region of the vvbb channel for the mH=800 GeV hypothesis. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant mTVH in the 2 b-tag 2L region of the vvbb channel. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant mTVH in the 2 b-tag em region of the vvbb channel. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant mTVH in the 3+ b-tag 2L region of the vvbb channel. <br><br><a href="?table=overview">return to overview</a>

The distribution of the fit discriminant mTVH in the 3+ b-tag em region of the vvbb channel. <br><br><a href="?table=overview">return to overview</a>

Local significance for lltt ggF signals for tanbeta=1. <br><br><a href="?table=overview">return to overview</a>

Local significance for lltt bbA signals for tanbeta=20. <br><br><a href="?table=overview">return to overview</a>

Local significance for vvbb ggF signals for tanbeta=1. <br><br><a href="?table=overview">return to overview</a>

Local significance for vvbb bbA signals for tanbeta=20. <br><br><a href="?table=overview">return to overview</a>

Signal acceptance times efficiency for lltt ggF signals. <br><br><a href="?table=overview">return to overview</a>

Signal acceptance times efficiency for lltt bbA signals. <br><br><a href="?table=overview">return to overview</a>

Signal acceptance times efficiency for vvbb ggF signals. <br><br><a href="?table=overview">return to overview</a>

Signal acceptance times efficiency for vvbb bbA signals. <br><br><a href="?table=overview">return to overview</a>

The pT distribution of the third lepton in the L3hi_Zin region of the lltt channel. <br><br><a href="?table=overview">return to overview</a>

The eta distribution of the H boson candidate in the rest frame of the A boson candidate in the L3hi_Zin region of the lltt channel. <br><br><a href="?table=overview">return to overview</a>

The ETmiss distribution in the 2 b-tag 0L region of the vvbb channel. <br><br><a href="?table=overview">return to overview</a>

The m_top_near distribution in the 2 b-tag 0L region of the vvbb channel. <br><br><a href="?table=overview">return to overview</a>

The ETmiss distribution in the 3+ b-tag 0L region of the vvbb channel. <br><br><a href="?table=overview">return to overview</a>

The m_top_near distribution in the 3+ b-tag 0L region of the vvbb channel. <br><br><a href="?table=overview">return to overview</a>

Expected (dashed line) value of $-2\ln\Lambda$ as a function of $\kappa_{2V}$, when all other coupling modifiers are fixed to their SM predictions.

Likelihood observed contours at 68% CL (solid line) and 95% CL (dashed line) in the $\kappa_{\lambda}$, $\kappa_{2V}$ parameter space, when all other coupling modifiers are fixed to their SM predictions. The best-fit value, denoted by a cross in the plot, corresponds to the very first entry in the table.

Likelihood expected contours at 68% CL (teal shaded region) and 95% CL (yellow shaded region) in the $\kappa_{\lambda}$, $\kappa_{2V}$ parameter space, when all other coupling modifiers are fixed to their SM predictions.In the plot, the SM prediction is indicated by the star.

Likelihood observed contours at 68% CL (solid line) and 95% CL (dashed line) in the $c_{gghh}$ versus $c_{hhh}$ HEFT parameter space, with the remaining coefficient fixed to its SM value. The best-fit value, denoted by a cross in the plot, corresponds to the very first entry in the table.

Likelihood expected contours at 68% CL (teal shaded region) 95% CL (yellow shaded region) in the $c_{gghh}$ versus $c_{hhh}$ HEFT parameter space, with the remaining coefficient fixed to its SM value. In the plot, the SM prediction is indicated by the star.

Likelihood observed contours at 68% CL (solid line) and 95% CL (dashed line) in the $c_{tthh}$ versus $c_{hhh}$ HEFT parameter space, with the remaining coefficient fixed to its SM value. The best-fit value, denoted by a cross in the plot, corresponds to the very first entry in the table.

Likelihood exptected contours at 68% CL (teal shaded region) and 95% CL (yellow shaded region) in the $c_{tthh}$ versus $c_{hhh}$ HEFT parameter space, with the remaining coefficient fixed to its SM value. In the plot, the SM prediction is indicated by the star.

The observed (filled circles) and expected (hollow circles) 95% CL upper limits on the $HH$ ggF production cross-section in the Standard Model and for seven HEFT benchmark points. The teal and yellow colored bands indicate the $\pm 1\sigma$ and $\pm 2\sigma$ variations on the expected limit due to statistical and systematic uncertainties. The predicted cross-sections of each of the models under consideration are shown by the red crosses. The contribution from VBF production to the total $HH$ production cross-section is neglected.

Likelihood observed contours at 68% CL (solid line) and 95% CL (dashed line) in the $c_{{H}\boxed{}}$ versus $c_{H}$ SMEFT parameter space, with the remaining coefficient fixed to its SM value. The best-fit value, denoted by a cross in the plot, corresponds to the very first entry in the table.

Likelihood expected contours at 68% CL (teal shaded region) 95% CL (yellow shaded region) in the $c_{{H}\boxed{}}$ versus $c_{H}$ SMEFT parameter space, with the remaining coefficient fixed to its SM value. In the plot, the SM prediction is indicated by the star.

The acceptance times efficiency for the signal ggF $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ in each analysis category. The other coupling modifiers affecting ggF $HH$ production are fixed to their SM predictions. The bands indicate the simulation statistical uncertainty.

The acceptance times efficiency for the signal VBF $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ in each analysis category. When varying $\kappa_{\lambda}$, the other coupling modifiers affecting the VBF $HH$ production mode are set to their SM predictions. The bands indicate the simulation statistical uncertainty.

The acceptance times efficiency for the signal VBF $HH$ process as a function of the coupling modifier $\kappa_{2V}$ in each analysis category. When varying $\kappa_{2V}$, the other coupling modifiers affecting the VBF $HH$ production mode are set to their SM predictions. The bands indicate the simulation statistical uncertainty.

Expected yields of the signal $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ after applying the analysis preselection and in each analysis category after the final selection. The $HH$ yield is obtained considering both the $ggF$ and $VBF$ contributions. The other coupling modifiers affecting $HH$ production are fixed to their SM predictions. The bands indicate the simulation statistical uncertainty.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{hhh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{tthh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{gghh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{H}$ SMEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{{H}\boxed{}}$ SMEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{hhh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{tthh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{gghh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{H}$ SMEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{{H}\boxed{}}$ SMEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the low mass 1 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the low mass 2 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the low mass 3 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the low mass 4 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the high mass 1 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the high mass 2 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the high mass 3 region.

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{hhh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{hhh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{gghh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{gghh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{tthh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{tthh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{H}$ SMEFT coefficients when all other coupling modifiers are fixed to the SM value.

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{H}$ SMEFT coefficients when all other coupling modifiers are fixed to the SM value.

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{{H}\boxed{}}$ SMEFT coefficients when all other coupling modifiers are fixed to the SM value.

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{{H}\boxed{}}$ SMEFT coefficients when all other coupling modifiers are fixed to the SM value.

Summary of the expected (blue) and observed (orange) one-dimensional constraints at 68% (solid error bars) and 95% (dashed error bars) CL on the coefficients of selected HEFT (top) and SMEFT (bottom) operators describing Higgs boson interactions affecting $HH$ production through gluon--gluon fusion. The results are obtained from one dimensional scans of the profile log-likelihood assuming that all other Wilson coefficients are fixed to their SM values. The contribution from VBF $HH$ production is neglected.

Unfolded $M(l^{-}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64822.9 $\pm$ 254.6, NPowHeg truth =634276.

Unfolded dR distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64273.2 $\pm$ 253.5, NPowHeg truth =338671.

Unfolded dR distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 65362.4 $\pm$ 255.7 , NPowHeg truth =634214.

Unfolded $P_{T}^{\gamma}$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63486.8 $\pm$ 252.0, NPowHeg truth =333348.

Unfolded $P_{T}^{\gamma}$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64432.6 $\pm$ 253.8, NPowHeg truth =624059.

Unfolded $M(l^{+}\gamma)$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57095.9 $\pm$ 254 , NPowHeg truth =301666, N Sherpa truth =76327.

Unfolded $M(l^{-}\gamma)$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57130 $\pm$ 254 , NPowHeg truth =301666, N Sherpa truth =763273.

Unfolded $M(l^{+}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58310.9 $\pm$ 245, NPowHeg truth =564672, N Sherpa truth =814016.

Unfolded $M(l^{-}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58320.9 $\pm$ 245, NPowHeg truth =564672, N Sherpa truth =814016.

Unfolded dR distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57705.4 $\pm$ 254 , NPowHeg truth =301655, N Sherpa truth =763259.

Unfolded dR distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58869.2 $\pm$ 256, NPowHeg truth =564660, NS herpa truth =813995.

Unfolded $P_{T}^{\gamma}$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57358.6 $\pm$ 254 , NPowHeg truth =298662, N Sherpa truth =756609.

Unfolded $P_{T}^{\gamma}$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58226.4 $\pm$ 254, NPowHeg truth =558949, N Sherpa truth =806988.

Unfolded $M(l^{+}\gamma)$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63717.4 $\pm$ 252.4, NPowHeg truth =338714.

Unfolded $M(l^{-}\gamma)$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63855.8 $\pm$ 252.7 , NPowHeg truth =338708.

Unfolded $M(l^{+}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64809.8 $\pm$ 254.6, NPowHeg truth =634285.

Unfolded $M(l^{-}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64822.9 $\pm$ 254.6, NPowHeg truth =634276.

Unfolded dR distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64273.2 $\pm$ 253.5, NPowHeg truth =338671.

Unfolded dR distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 65362.4 $\pm$ 255.7 , NPowHeg truth =634214.

Unfolded $P_{T}^{\gamma}$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63486.8 $\pm$ 252.0, NPowHeg truth =333348.

Unfolded $P_{T}^{\gamma}$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64432.6 $\pm$ 253.8, NPowHeg truth =624059.

Unfolded $M(l^{+}\gamma)$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57095.9 $\pm$ 254 , NPowHeg truth =301666, N Sherpa truth =76327.

Unfolded $M(l^{-}\gamma)$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57130 $\pm$ 254 , NPowHeg truth =301666, N Sherpa truth =763273.

Unfolded $M(l^{+}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58310.9 $\pm$ 245, NPowHeg truth =564672, N Sherpa truth =814016.

Unfolded $M(l^{-}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58320.9 $\pm$ 245, NPowHeg truth =564672, N Sherpa truth =814016.

Unfolded dR distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57705.4 $\pm$ 254 , NPowHeg truth =301655, N Sherpa truth =763259.

Unfolded dR distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58869.2 $\pm$ 256, NPowHeg truth =564660, NS herpa truth =813995.

Unfolded $P_{T}^{\gamma}$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57358.6 $\pm$ 254 , NPowHeg truth =298662, N Sherpa truth =756609.

Unfolded $P_{T}^{\gamma}$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58226.4 $\pm$ 254, NPowHeg truth =558949, N Sherpa truth =806988.

Truth $P_{T}^{Z}$ distribution after reweghting to data.

Combined Covariance Matrix for Unfolded $M(l^{+}\gamma)$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63717.4 $\pm$ 252.4, NPowHeg truth =338714.

Combined Covariance Matrix for Unfolded $M(l^{-}\gamma)$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63855.8 $\pm$ 252.7 , NPowHeg truth =338708.

Combined Covariance Matrix for Unfolded $M(l^{+}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64809.8 $\pm$ 254.6, NPowHeg truth =634285.

Combined Covariance Matrix for Unfolded $M(l^{-}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64822.9 $\pm$ 254.6, NPowHeg truth =634276.

Combined Covariance Matrix for Unfolded dR distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64273.2 $\pm$ 253.5, NPowHeg truth =338671.

Combined Covariance Matrix for Unfolded dR distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 65362.4 $\pm$ 255.7 , NPowHeg truth =634214.

Combined Covariance Matrix for Unfolded $P_{T}^{\gamma}$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63486.8 $\pm$ 252.0, NPowHeg truth =333348.

Combined Covariance Matrix for Unfolded $P_{T}^{\gamma}$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64432.6 $\pm$ 253.8, NPowHeg truth =624059.

Combined Covariance Matrix for Unfolded $M(l^{+}\gamma)$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57095.9 $\pm$ 254 , NPowHeg truth =301666, N Sherpa truth =76327.

Combined Covariance Matrix for Unfolded $M(l^{-}\gamma)$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57130 $\pm$ 254 , NPowHeg truth =301666, N Sherpa truth =763273.

Combined Covariance Matrix for Unfolded $M(l^{+}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58310.9 $\pm$ 245, NPowHeg truth =564672, N Sherpa truth =814016.

Combined Covariance Matrix for Unfolded $M(l^{-}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58320.9 $\pm$ 245, NPowHeg truth =564672, N Sherpa truth =814016.

Combined Covariance Matrix for Unfolded dR distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57705.4 $\pm$ 254 , NPowHeg truth =301655, N Sherpa truth =763259.

Combined Covariance Matrix for Unfolded dR distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58869.2 $\pm$ 256, NPowHeg truth =564660, NS herpa truth =813995.

Combined Covariance Matrix for Unfolded $P_{T}^{\gamma}$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57358.6 $\pm$ 254 , NPowHeg truth =298662, N Sherpa truth =756609.

Combined Covariance Matrix for Unfolded $P_{T}^{\gamma}$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58226.4 $\pm$ 254, NPowHeg truth =558949, N Sherpa truth =806988.

Combined Covariance Matrix for Unfolded $M(l^{+}\gamma)$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63717.4 $\pm$ 252.4, NPowHeg truth =338714.

Combined Covariance Matrix for Unfolded $M(l^{-}\gamma)$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63855.8 $\pm$ 252.7 , NPowHeg truth =338708.

Combined Covariance Matrix for Unfolded $M(l^{+}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64809.8 $\pm$ 254.6, NPowHeg truth =634285.

Combined Covariance Matrix for Unfolded $M(l^{-}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64822.9 $\pm$ 254.6, NPowHeg truth =634276.

Combined Covariance Matrix for Unfolded dR distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64273.2 $\pm$ 253.5, NPowHeg truth =338671.

Combined Covariance Matrix for Unfolded dR distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 65362.4 $\pm$ 255.7 , NPowHeg truth =634214.

Combined Covariance Matrix for Unfolded $P_{T}^{\gamma}$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63486.8 $\pm$ 252.0, NPowHeg truth =333348.

Combined Covariance Matrix for Unfolded $P_{T}^{\gamma}$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64432.6 $\pm$ 253.8, NPowHeg truth =624059.

Combined Covariance Matrix for Unfolded $M(l^{+}\gamma)$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57095.9 $\pm$ 254 , NPowHeg truth =301666, N Sherpa truth =76327.

Combined Covariance Matrix for Unfolded $M(l^{-}\gamma)$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57130 $\pm$ 254 , NPowHeg truth =301666, N Sherpa truth =763273.

Combined Covariance Matrix for Unfolded $M(l^{+}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58310.9 $\pm$ 245, NPowHeg truth =564672, N Sherpa truth =814016.

Combined Covariance Matrix for Unfolded $M(l^{-}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58320.9 $\pm$ 245, NPowHeg truth =564672, N Sherpa truth =814016.

Combined Covariance Matrix for Unfolded dR distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57705.4 $\pm$ 254 , NPowHeg truth =301655, N Sherpa truth =763259.

Combined Covariance Matrix for Unfolded dR distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58869.2 $\pm$ 256, NPowHeg truth =564660, NS herpa truth =813995.

Combined Covariance Matrix for Unfolded $P_{T}^{\gamma}$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57358.6 $\pm$ 254 , NPowHeg truth =298662, N Sherpa truth =756609.

Combined Covariance Matrix for Unfolded $P_{T}^{\gamma}$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58226.4 $\pm$ 254, NPowHeg truth =558949, N Sherpa truth =806988.

Unfolded $M(l^{+}\gamma\gamma)$ distribution for $Z \to ll\gamma\gamma$ process with dressed leptons.

Unfolded $M(l^{+}\gamma\gamma)$ distribution for $Z \to ll\gamma\gamma$ process with bare leptons.

Unfolded dR distribution for $Z \to ll\gamma\gamma$ process with dressed leptons for leading photon.

Unfolded dR distribution for $Z \to ll\gamma\gamma$ process with bare leptons for leading photon.

Unfolded dR distribution for $Z \to ll\gamma\gamma$ process with dressed leptons for second photon.

Unfolded dR distribution for $Z \to ll\gamma\gamma$ process with bare leptons for second photon.

Unfolded dRgg distribution for $Z \to ll\gamma\gamma$ process with dressed leptons.

Unfolded dRgg distribution for $Z \to ll\gamma\gamma$ process with bare leptons.

Unfolded $P_{T}^{\gamma 1}$ distribution for $Z \to ll\gamma\gamma$ process with dressed leptons for leading photon.

Unfolded $P_{T}^{\gamma 1}$ distribution for $Z \to ll\gamma\gamma$ process with bare leptons for leading photon.

Unfolded $P_{T}^{\gamma 2}$ distribution for $Z \to ll\gamma\gamma$ process with dressed leptons for second photon.

Unfolded $P_{T}^{\gamma 2}$ distribution for $Z \to ll\gamma\gamma$ process with bare leptons for second photon.

Summary of results for cross-section of non-prompt $\psi(2S)$ decaying to a muon pair for 13 TeV data in fb/GeV. Uncertainties are statistical and systematic, respectively.

Summary of results for non-prompt fraction of $J/\psi$ decaying to a muon pair as a percentage for 13 TeV data. Uncertainties are statistical and systematic, respectively.

Summary of results for non-prompt fraction of $\psi(2S)$ decaying to a muon pair as a percentage for 13 TeV data. Uncertainties are statistical and systematic, respectively.

Summary of results for prompt $\psi(2S)$ over $J/\psi$ ratio as a percentage for 13 TeV data. Uncertainties are statistical and systematic, respectively.

Summary of results for non-prompt $\psi(2S)$ over $J/\psi$ ratio as a percentage for 13 TeV data. Uncertainties are statistical and systematic, respectively.

Correction factors for an assumed angular dependence $\propto 1+\lambda_{\theta} \cos^2\theta $ in the helicity frame, for several values of the parameter $\lambda_{\theta}$. The correction factors were found to be the same (within 1% - 2%) for $J\psi$ and $\psi(2S)$ mesons, for prompt and non-prompt production mechanisms, and for the three rapidity intervals considered in this paper.