Upper 95% CL limits on HH signal cross section scanned over the $\kappa_{\lambda}$ parameter while fixing the $\kappa_{2V}$ and $\kappa_{V}$ to their SM-predicted values.

Upper 95% CL limits on VHH signal cross section scanned over the $\kappa_{2V}$ parameter while fixing the $\kappa_{\lambda}$ and $\kappa_{V}$ to their SM-predicted values.

Upper 95% CL limits on HH signal cross section scanned over the $\kappa_{2V}$ parameter while fixing the $\kappa_{\lambda}$ and $\kappa_{V}$ to their SM-predicted values.

Upper 95% CL limits on VHH signal cross section scanned over the $\kappa_{V}$ parameter while fixing the $\kappa_{2V}$ and $\kappa_{\lambda}$ to their SM-predicted values.

Upper 95% CL limits on HH signal cross section scanned over the $\kappa_{V}$ parameter while fixing the $\kappa_{2V}$ and $\kappa_{\lambda}$ to their SM-predicted values.

Differential cross sections normalized to the fiducial cross section as a function of the $p_T$ of the second-highest-$p_T$ jet

Differential cross sections normalized to the fiducial cross section as a function of the $|\eta|$ of the highest-$p_T$ jet

Differential cross sections normalized to the fiducial cross section as a function of the $|\eta|$ of the second-highest-$p_T$ jet

Differential cross sections normalized to the fiducial cross section as a function of the pseudorapidity difference between the two highest-$p_T$ jets in the event

Differential cross sections normalized to the fiducial cross section as a function of the invariant mass of the two highest-$p_T$ jets in the event

Differential cross sections normalized to the fiducial cross section as a function of the invariant mass of the four-lepton system, in the full $m_{4l}$ range

Differential cross sections normalized to the fiducial cross section as a function of the invariant mass of the four-lepton system in events with 0 jet, in the on-shell ZZ region

Differential cross sections normalized to the fiducial cross section as a function of the invariant mass of the four-lepton system in events with 1 jet, in the on-shell ZZ region

Differential cross sections normalized to the fiducial cross section as a function of the invariant mass of the four-lepton system in events with 2 jets, in the on-shell ZZ region

Differential cross sections normalized to the fiducial cross section as a function of the invariant mass of the four-lepton system in events with at least 3 jets, in the on-shell ZZ region

Differential cross sections normalized to the fiducial cross section as a function of the invariant mass of the four-lepton system in events with 0 jet, in the full $m_{4l}$ range

Differential cross sections normalized to the fiducial cross section as a function of the invariant mass of the four-lepton system in events with 1 jet, in the full $m_{4l}$ range

Differential cross sections normalized to the fiducial cross section as a function of the invariant mass of the four-lepton system in events with 2 jets, in the full $m_{4l}$ range

Differential cross sections normalized to the fiducial cross section as a function of the invariant mass of the four-lepton system in events with at least 3 jets, in the full $m_{4l}$ range

Fit results for the region 2 of pair produced resolved three jet mass ($m_{jjj}$) distribution, after $H_{\rm T}>600$ GeV, $|\eta|<2.4$, sixth jet $p_{\rm T}>50$ GeV, $D^2_{[(6,3)+(3,2)]}<1.0$, $A_m <0.175$, $\Delta>180$ GeV, $D^2_{[3,2]}<0.175$

Fit results for the region 3 of pair produced resolved three jet mass ($m_{jjj}$) distribution, after $H_{\rm T}>600$ GeV, $|\eta|<2.4$, sixth jet $p_{\rm T}>100$ GeV, $D^2_{[(6,3)+(3,2)]}<0.9$, $A_m <0.15$, $\Delta>150$ GeV, $D^2_{[3,2]}<0.2$

Expected and observed upper limits on the signal strength for the pair produced merged trijets. Acceptance after the selection $p_{\rm T}>300$ GeV, $|\eta|<2.4$, and $\tau_{32,\mathrm{DDT}}<0$ on both leading and subleading jet and $A_m<0.15$ between the two leading jets.

Expected and observed upper limits on the signal strength for the pair produced merged dijets. Acceptance after the selection $p_{\rm T}>300$ GeV, $|\eta|<2.4$, and $N^1_{2,\mathrm{DDT}}<0$ on both leading and subleading jet and $A_m<0.15$ between the two leading jets.

Expected and observed upper limits on the signal strength for the pair produced resolved trijets (including overlaps). Acceptance for three regions search requions described in table 1 of the paper.

Upper limits at 95% CL on $\sigma$B(pp→X→Y(bb)H) for combination as a function of m$_Y$.

Expected upper limits at 95% CL on the X → HH cross section as a function of mX from the combination of the three channels bbγγ, bbττ, and bbbb for an integrated luminosity of 3000 fb−1 with different assumptions on the systematic uncertainties.

Expected upper limits on the X → YH cross section times B(Y → bb) for mX ≤ 1000 GeV at 95 % CL as a function of m$_X$ and m$_Y$ from the combination of all considered channels projected to an integrated luminosity of 3000 fb$^{-1}$. Systematic uncertainties according to the ”S2” scenario are assumed.

Observed and expected 95% CL upper limits on the nonresonant HH production via vector boson fusion cross section obtained for both single-lepton and dilepton channels, and from their combination

Observed and expected 95% CL upper limits on the nonresonant HH production cross section for two different benchmark scenarios “JHEP04(2016)01” and “JHEP03(2020)91”

Observed and expected 95% CL upper limits on the nonresonant HH production cross section as a function of the Higgs boson self-coupling strength modifier κλ All Higgs boson couplings other than λ are assumed to have the values predicted by the SM

Observed and expected 95% CL upper limits on the nonresonant HH production via VBF cross section as a function of the effective coupling κ2V. The ggF contribution in this case is set to the SM expectation. All other Higgs boson couplings are assumed to have the values predicted by the SM.

Observed and expected 95% CL upper limits on the nonresonant HH production cross section as a function of the effective coupling c2. All other Higgs boson couplings are assumed to have the values predicted in the SM

The observed exclusions for the nominal $\sigma$ cross section in the plane of $m_{\phi}$ and $T_D$, for various $m_S$ values, for the case $m_{A'}=1.0$ GeV ($A' \rightarrow \pi^+\pi^-$ with $\mathcal{BR}=100\%$).

The expected exclusions for the nominal $\sigma$ cross section in the plane of $m_{\phi}$ and $T_D$, for various $m_S$ values, for the case $m_{A'}=1.0$ GeV ($A' \rightarrow \pi^+\pi^-$ with $\mathcal{BR}=100\%$).

The expected exclusions for the nominal $\sigma$ cross section in the plane of $m_{\phi}$ and $T_D$, for various $m_S$ values, for the case $m_{A'}=1.0$ GeV ($A' \rightarrow \pi^+\pi^-$ with $\mathcal{BR}=100\%$).

The expected upper $68\%$ exclusions for the nominal $\sigma$ cross section in the plane of $m_{\phi}$ and $T_D$, for various $m_S$ values, for the case $m_{A'}=1.0$ GeV ($A' \rightarrow \pi^+\pi^-$ with $\mathcal{BR}=100\%$).

The expected upper $68\%$ exclusions for the nominal $\sigma$ cross section in the plane of $m_{\phi}$ and $T_D$, for various $m_S$ values, for the case $m_{A'}=1.0$ GeV ($A' \rightarrow \pi^+\pi^-$ with $\mathcal{BR}=100\%$).

The expected lower $68\%$ exclusions for the nominal $\sigma$ cross section in the plane of $m_{\phi}$ and $T_D$, for various $m_S$ values, for the case $m_{A'}=1.0$ GeV ($A' \rightarrow \pi^+\pi^-$ with $\mathcal{BR}=100\%$).

The expected lower $68\%$ exclusions for the nominal $\sigma$ cross section in the plane of $m_{\phi}$ and $T_D$, for various $m_S$ values, for the case $m_{A'}=1.0$ GeV ($A' \rightarrow \pi^+\pi^-$ with $\mathcal{BR}=100\%$).

The $95\%$ CL observed upper limits on the cross section shown as a functions of $T_D$ and the pseudoscalar mass $m_{\phi}$ for $m_S = 300$ GeV, for the case $m_{A'}=1.0$ GeV ($A' \rightarrow \pi^+\pi^-$ with $\mathcal{BR}=100\%$).

The $95\%$ CL observed upper limits on the cross section shown as a functions of $T_D$ and the pseudoscalar mass $m_{\phi}$ for $m_S = 300$ GeV, for the case $m_{A'}=1.0$ GeV ($A' \rightarrow \pi^+\pi^-$ with $\mathcal{BR}=100\%$).

The $95\%$ CL observed upper limits on the cross section shown as a functions of $T_D$ and the pseudoscalar mass $m_{\phi}$ for $m_S = 600$ GeV, for the case $m_{A'}=1.0$ GeV ($A' \rightarrow \pi^+\pi^-$ with $\mathcal{BR}=100\%$).

The $95\%$ CL observed upper limits on the cross section shown as a functions of $T_D$ and the pseudoscalar mass $m_{\phi}$ for $m_S = 600$ GeV, for the case $m_{A'}=1.0$ GeV ($A' \rightarrow \pi^+\pi^-$ with $\mathcal{BR}=100\%$).

The $95\%$ CL observed upper limits on the cross section shown as a functions of $T_D$ and the pseudoscalar mass $m_{\phi}$ for $m_S = 1000$ GeV, for the case $m_{A'}=1.0$ GeV ($A' \rightarrow \pi^+\pi^-$ with $\mathcal{BR}=100\%$).

The $95\%$ CL observed upper limits on the cross section shown as a functions of $T_D$ and the pseudoscalar mass $m_{\phi}$ for $m_S = 1000$ GeV, for the case $m_{A'}=1.0$ GeV ($A' \rightarrow \pi^+\pi^-$ with $\mathcal{BR}=100\%$).

The observed exclusions for the nominal $\sigma$ cross section in the plane of $m_{\phi}$ and $T_D$, for various $m_S$ values, for the case $m_{A'} = 0.5$ GeV ($A' \rightarrow e^+e^-, \mu^+\mu^-, \pi^+\pi^-$ with $\mathcal{BR} = 40, 40, 20\%$).

The observed exclusions for the nominal $\sigma$ cross section in the plane of $m_{\phi}$ and $T_D$, for various $m_S$ values, for the case $m_{A'} = 0.5$ GeV ($A' \rightarrow e^+e^-, \mu^+\mu^-, \pi^+\pi^-$ with $\mathcal{BR} = 40, 40, 20\%$).

The expected exclusions for the nominal $\sigma$ cross section in the plane of $m_{\phi}$ and $T_D$, for various $m_S$ values, for the case $m_{A'} = 0.5$ GeV ($A' \rightarrow e^+e^-, \mu^+\mu^-, \pi^+\pi^-$ with $\mathcal{BR} = 40, 40, 20\%$).

The expected exclusions for the nominal $\sigma$ cross section in the plane of $m_{\phi}$ and $T_D$, for various $m_S$ values, for the case $m_{A'} = 0.5$ GeV ($A' \rightarrow e^+e^-, \mu^+\mu^-, \pi^+\pi^-$ with $\mathcal{BR} = 40, 40, 20\%$).

The expected upper $68\%$ exclusions for the nominal $\sigma$ cross section in the plane of $m_{\phi}$ and $T_D$, for various $m_S$ values, for the case $m_{A'} = 0.5$ GeV ($A' \rightarrow e^+e^-, \mu^+\mu^-, \pi^+\pi^-$ with $\mathcal{BR} = 40, 40, 20\%$).

The expected upper $68\%$ exclusions for the nominal $\sigma$ cross section in the plane of $m_{\phi}$ and $T_D$, for various $m_S$ values, for the case $m_{A'} = 0.5$ GeV ($A' \rightarrow e^+e^-, \mu^+\mu^-, \pi^+\pi^-$ with $\mathcal{BR} = 40, 40, 20\%$).

The expected lower $68\%$ exclusions for the nominal $\sigma$ cross section in the plane of $m_{\phi}$ and $T_D$, for various $m_S$ values, for the case $m_{A'} = 0.5$ GeV ($A' \rightarrow e^+e^-, \mu^+\mu^-, \pi^+\pi^-$ with $\mathcal{BR} = 40, 40, 20\%$).

The expected lower $68\%$ exclusions for the nominal $\sigma$ cross section in the plane of $m_{\phi}$ and $T_D$, for various $m_S$ values, for the case $m_{A'} = 0.5$ GeV ($A' \rightarrow e^+e^-, \mu^+\mu^-, \pi^+\pi^-$ with $\mathcal{BR} = 40, 40, 20\%$).

The observed exclusions for the nominal $\sigma$ cross section in the plane of $m_{\phi}$ and $T_D$, for various $m_S$ values, for the case $m_{A'} = 0.7$ GeV ($A' \rightarrow e^+e^-, \mu^+\mu^-, \pi^+\pi^-$ with $\mathcal{BR} = 15, 15, 70\%$).

The observed exclusions for the nominal $\sigma$ cross section in the plane of $m_{\phi}$ and $T_D$, for various $m_S$ values, for the case $m_{A'} = 0.7$ GeV ($A' \rightarrow e^+e^-, \mu^+\mu^-, \pi^+\pi^-$ with $\mathcal{BR} = 15, 15, 70\%$).

The expected exclusions for the nominal $\sigma$ cross section in the plane of $m_{\phi}$ and $T_D$, for various $m_S$ values, for the case $m_{A'} = 0.7$ GeV ($A' \rightarrow e^+e^-, \mu^+\mu^-, \pi^+\pi^-$ with $\mathcal{BR} = 15, 15, 70\%$).

The expected exclusions for the nominal $\sigma$ cross section in the plane of $m_{\phi}$ and $T_D$, for various $m_S$ values, for the case $m_{A'} = 0.7$ GeV ($A' \rightarrow e^+e^-, \mu^+\mu^-, \pi^+\pi^-$ with $\mathcal{BR} = 15, 15, 70\%$).

The expected upper $68\%$ exclusions for the nominal $\sigma$ cross section in the plane of $m_{\phi}$ and $T_D$, for various $m_S$ values, for the case $m_{A'} = 0.7$ GeV ($A' \rightarrow e^+e^-, \mu^+\mu^-, \pi^+\pi^-$ with $\mathcal{BR} = 15, 15, 70\%$).

The expected upper $68\%$ exclusions for the nominal $\sigma$ cross section in the plane of $m_{\phi}$ and $T_D$, for various $m_S$ values, for the case $m_{A'} = 0.7$ GeV ($A' \rightarrow e^+e^-, \mu^+\mu^-, \pi^+\pi^-$ with $\mathcal{BR} = 15, 15, 70\%$).

The expected lower $68\%$ exclusions for the nominal $\sigma$ cross section in the plane of $m_{\phi}$ and $T_D$, for various $m_S$ values, for the case $m_{A'} = 0.7$ GeV ($A' \rightarrow e^+e^-, \mu^+\mu^-, \pi^+\pi^-$ with $\mathcal{BR} = 15, 15, 70\%$).

The expected lower $68\%$ exclusions for the nominal $\sigma$ cross section in the plane of $m_{\phi}$ and $T_D$, for various $m_S$ values, for the case $m_{A'} = 0.7$ GeV ($A' \rightarrow e^+e^-, \mu^+\mu^-, \pi^+\pi^-$ with $\mathcal{BR} = 15, 15, 70\%$).

For a selection of signal samples in era 2018 with $m_{\phi} = T_D = 3$ GeV, the relative efficiencies and the total efficiency with respect to the selection on the generator-level $H_T$,$H^{gen}_T > 1000$ GeV.

For a selection of signal samples in era 2018 with $m_{\phi} = T_D = 3$ GeV, the relative efficiencies and the total efficiency with respect to the selection on the generator-level $H_T$,$H^{gen}_T > 1000$ GeV.

The $95\%$ CL cross section limit for all values of $m_{A'}$, $T_D$, $m_{\phi}$, and $m_S$ used in the scan.

The $95\%$ CL cross section limit for all values of $m_{A'}$, $T_D$, $m_{\phi}$, and $m_S$ used in the scan.

Expected and observed 95% CL upper limits on $|V_\mathrm{N}|^2$ as a function of $m_\mathrm{N}$ for the mixing scenario ($r_e$, $r_\mu$, $r_\tau$) = (0.33, 0.33, 0.33) and in the Majorana scenario.

Expected and observed 95% CL upper limits on $|V_\mathrm{N}|^2$ as a function of $m_\mathrm{N}$ for the mixing scenario ($r_e$, $r_\mu$, $r_\tau$) = (0.0, 1.0, 0.0) and in the Dirac-like scenario.

Expected and observed 95% CL upper limits on $|V_\mathrm{N}|^2$ as a function of $m_\mathrm{N}$ for the mixing scenario ($r_e$, $r_\mu$, $r_\tau$) = (0.0, 0.5, 0.5) and in the Dirac-like scenario.

Expected and observed 95% CL upper limits on $|V_\mathrm{N}|^2$ as a function of $m_\mathrm{N}$ for the mixing scenario ($r_e$, $r_\mu$, $r_\tau$) = (0.5, 0.5, 0.0) and in the Dirac-like scenario.

Expected and observed 95% CL upper limits on $|V_\mathrm{N}|^2$ as a function of $m_\mathrm{N}$ for the mixing scenario ($r_e$, $r_\mu$, $r_\tau$) = (0.33, 0.33, 0.33) and in the Dirac-like scenario.

Observed 95% CL lower limits on $c\tau_\mathrm{N}$ as functions of the mixing ratios ($r_e$, $r_\mu$, $r_\tau$) for a fixed N mass of 1.0 GeV in the Majorana scenario.

Observed 95% CL lower limits on $c\tau_\mathrm{N}$ as functions of the mixing ratios ($r_e$, $r_\mu$, $r_\tau$) for a fixed N mass of 1.5 GeV in the Majorana scenario.

Observed 95% CL lower limits on $c\tau_\mathrm{N}$ as functions of the mixing ratios ($r_e$, $r_\mu$, $r_\tau$) for a fixed N mass of 2.0 GeV in the Majorana scenario.

Observed 95% CL lower limits on $c\tau_\mathrm{N}$ as functions of the mixing ratios ($r_e$, $r_\mu$, $r_\tau$) for a fixed N mass of 1.0 GeV in the Dirac-like scenario.

Observed 95% CL lower limits on $c\tau_\mathrm{N}$ as functions of the mixing ratios ($r_e$, $r_\mu$, $r_\tau$) for a fixed N mass of 1.5 GeV in the Dirac-like scenario.

Observed 95% CL lower limits on $c\tau_\mathrm{N}$ as functions of the mixing ratios ($r_e$, $r_\mu$, $r_\tau$) for a fixed N mass of 2.0 GeV in the Dirac-like scenario.

The 95% CL limits on $|V_{eN}|^2$ as a function of the HNL mass for a Dirac HNL.

The 95% CL limits on $|V_{\mu N}|^2$ as a function of the HNL mass for a Dirac HNL.

The 95% CL limits on $|V_{\tau N}|^2$ as a function of the HNL mass for a Dirac HNL.

Comparison of the number of predicted background events and the observed events in search regions La. The predicted background yields are shown with the values of the normalizations and nuisance parameters obtained in the background-only fit applied.

Signal yields predicted in search regions La as function of HNL mass and coupling strength for a scenario with exclusive coupling between a Majorana HNL and an electron neutrino.

Signal yields predicted in search regions La as function of HNL mass and coupling strength for a scenario with exclusive coupling between a Majorana HNL and a muon neutrino.

Signal yields predicted in search regions La as function of HNL mass and coupling strength for a scenario with exclusive coupling between a Majorana HNL and a tau neutrino.

Comparison of the number of predicted background events and the observed events in search regions Lb. The predicted background yields are shown with the values of the normalizations and nuisance parameters obtained in the background-only fit applied.

Signal yields predicted in search regions Lb as function of HNL mass and coupling strength for a scenario with exclusive coupling between a Majorana HNL and an electron neutrino.

Signal yields predicted in search regions Lb as function of HNL mass and coupling strength for a scenario with exclusive coupling between a Majorana HNL and a muon neutrino.

Signal yields predicted in search regions Lb as function of HNL mass and coupling strength for a scenario with exclusive coupling between a Majorana HNL and a tau neutrino.

Comparison of the number of predicted background events and the observed events in search regions Ha. The predicted background yields are shown with the values of the normalizations and nuisance parameters obtained in the background-only fit applied.

Signal yields predicted in search regions Ha as function of HNL mass and coupling strength for a scenario with exclusive coupling between a Majorana HNL and an electron neutrino.

Signal yields predicted in search regions Ha as function of HNL mass and coupling strength for a scenario with exclusive coupling between a Majorana HNL and a muon neutrino.

Signal yields predicted in search regions Ha as function of HNL mass and coupling strength for a scenario with exclusive coupling between a Majorana HNL and a tau neutrino.

Comparison of the number of predicted background events and the observed events in search regions Hb. The predicted background yields are shown with the values of the normalizations and nuisance parameters obtained in the background-only fit applied. Search regions Hb2 and Hb3 are merged for final states including a hadronically decayed tau lepton. This is represented by the value of -1 in the Hb2 entry.

Signal yields predicted in search regions Hb as function of HNL mass and coupling strength for a scenario with exclusive coupling between a Majorana HNL and an electron neutrino. Search regions Hb2 and Hb3 are merged for final states including a hadronically decayed tau lepton. This is represented by the value of -1 in the Hb2 entry.

Signal yields predicted in search regions Hb as function of HNL mass and coupling strength for a scenario with exclusive coupling between a Majorana HNL and a muon neutrino. Search regions Hb2 and Hb3 are merged for final states including a hadronically decayed tau lepton. This is represented by the value of -1 in the Hb2 entry.

Signal yields predicted in search regions Hb as function of HNL mass and coupling strength for a scenario with exclusive coupling between a Majorana HNL and a tau neutrino. Search regions Hb2 and Hb3 are merged for final states including a hadronically decayed tau lepton. This is represented by the value of -1 in the Hb2 entry.

Covariance matrix for the postfit background prediction in signal region bins La.

Covariance matrix for the postfit background prediction in signal region bins Lb.

Covariance matrix for the postfit background prediction in signal region bins Ha.

Covariance matrix for the postfit background prediction in signal region bins Hb.

Simulated signal yields passing each stage of the low mass region selection as function of HNL mass and signal strength. Shown for exclusive coupling between a Majorana HNL and an electron neutrino.

Simulated signal yields passing each stage of the low mass region selection as function of HNL mass and signal strength. Shown for exclusive coupling between a Majorana HNL and a muon neutrino.

Simulated signal yields passing each stage of the low mass region selection as function of HNL mass and signal strength. Shown for exclusive coupling between a Majorana HNL and a tau neutrino.

Simulated signal yields passing each stage of the high mass region selection as function of HNL mass and signal strength. Shown for exclusive coupling between a Majorana HNL and an electron neutrino.

Simulated signal yields passing each stage of the high mass region selection as function of HNL mass and signal strength. Shown for exclusive coupling between a Majorana HNL and a muon neutrino.

Simulated signal yields passing each stage of the high mass region selection as function of HNL mass and signal strength. Shown for exclusive coupling between a Majorana HNL and a tau neutrino.

Observed upper limits at 95% CL on B($\text{H} \rightarrow \text{a}_{1}\text{a}_{1}$) in percent, obtained from the combination of the $\mu\mu$bb and $\tau\tau$bb channels. The results are obtained as functions of $m_{\text{a}_{1}}$ for 2HDM+S Type I (independent of tan$\beta$), Type II (tan$\beta$=2.0), Type III (tan$\beta$=2.0), and Type IV (tan$\beta$=0.6), respectively.