Observed and theoretical cross sections. In the observed, the first uncertainty is statistical, the second is the systematic, and the third the luminosity. In the theoretical, the first uncertainty is due to scale variations, the second due to the choice of PDF. The theoretical cross section has been computed at approximate next-to-next-to-leading order (aNNLO) assuming a top quark mass of 172.5 GeV.

The number of observed and MC predicted events after the fit in the 1j1b, 2j1b, and 2j2b regions. The statistical uncertainties in the data and the total uncertainties in the predictions are given.

Normalised fiducial differential tW production cross section as a function of the $Leading$ $lepton$ $p_{T}$. The vertical bars on the points give the statistical uncertainty in the data, the horizontal bars show the bin width. Predictions from POWHEG (PH) + PYTHIA 8 (P8) DR and DS, POWHEG + HERWIG 7 (H7) DR, MADGRAPH5_aMC@NLO (aMC) + PYTHIA 8 DR, DR2, DS and DS with a dynamic factor are also shown. The grey band represents the statistical uncertainty and the orange band the total uncertainty. In the lower panels, the ratio of the predictions to the data is shown.

Normalised fiducial differential tW production cross section as a function of the $p_{Z}(e^{\pm}, \mu^{\pm}, j)$. The vertical bars on the points give the statistical uncertainty in the data, the horizontal bars show the bin width. Predictions from POWHEG (PH) + PYTHIA 8 (P8) DR and DS, POWHEG + HERWIG 7 (H7) DR, MADGRAPH5_aMC@NLO (aMC) + PYTHIA 8 DR, DR2, DS and DS with a dynamic factor are also shown. The grey band represents the statistical uncertainty and the orange band the total uncertainty. In the lower panels, the ratio of the predictions to the data is shown.

Normalised fiducial differential tW production cross section as a function of the $Jet$ $p_{T}$. The vertical bars on the points give the statistical uncertainty in the data, the horizontal bars show the bin width. Predictions from POWHEG (PH) + PYTHIA 8 (P8) DR and DS, POWHEG + HERWIG 7 (H7) DR, MADGRAPH5_aMC@NLO (aMC) + PYTHIA 8 DR, DR2, DS and DS with a dynamic factor are also shown. The grey band represents the statistical uncertainty and the orange band the total uncertainty. In the lower panels, the ratio of the predictions to the data is shown.

Normalised fiducial differential tW production cross section as a function of the $m(e^{\pm}, \mu^{\pm}, j)$. The vertical bars on the points give the statistical uncertainty in the data, the horizontal bars show the bin width. Predictions from POWHEG (PH) + PYTHIA 8 (P8) DR and DS, POWHEG + HERWIG 7 (H7) DR, MADGRAPH5_aMC@NLO (aMC) + PYTHIA 8 DR, DR2, DS and DS with a dynamic factor are also shown. The grey band represents the statistical uncertainty and the orange band the total uncertainty. In the lower panels, the ratio of the predictions to the data is shown.

Normalised fiducial differential tW production cross section as a function of the $\Delta\phi(e^{\pm}, \mu^{\pm})/\pi$. The vertical bars on the points give the statistical uncertainty in the data, the horizontal bars show the bin width. Predictions from POWHEG (PH) + PYTHIA 8 (P8) DR and DS, POWHEG + HERWIG 7 (H7) DR, MADGRAPH5_aMC@NLO (aMC) + PYTHIA 8 DR, DR2, DS and DS with a dynamic factor are also shown. The grey band represents the statistical uncertainty and the orange band the total uncertainty. In the lower panels, the ratio of the predictions to the data is shown.

Normalised fiducial differential tW production cross section as a function of the $m_{T}(e^{\pm}, \mu^{\pm}, j, p_{T}^{miss})$. The vertical bars on the points give the statistical uncertainty in the data, the horizontal bars show the bin width. Predictions from POWHEG (PH) + PYTHIA 8 (P8) DR and DS, POWHEG + HERWIG 7 (H7) DR, MADGRAPH5_aMC@NLO (aMC) + PYTHIA 8 DR, DR2, DS and DS with a dynamic factor are also shown. The grey band represents the statistical uncertainty and the orange band the total uncertainty. In the lower panels, the ratio of the predictions to the data is shown.

The p-values from the goodness-of-fit tests comparing the six differential cross section measurements with the predictions from POWHEG (PH) + PYTHIA 8 (P8) DR and DS, POWHEG + HERWIG 7 (H7) DR, MADGRAPH5 aMC@NLO (aMC) + PYTHIA 8 DR, DR2, DS, and DS with a dynamic factor. The complete covariance matrix from the results and the statistical uncertainties of the predictions are taken into account.

Response matrix between detector and particle level for the $Leading$ $lepton$ $p_{T}$.

Response matrix between detector and particle level for the $p_{Z}(e^{\pm}, \mu^{\pm}, j)$.

Response matrix between detector and particle level for the $Jet$ $p_{T}$.

Response matrix between detector and particle level for the $m(e^{\pm}, \mu^{\pm}, j)$.

Response matrix between detector and particle level for the $\Delta\phi(e^{\pm}, \mu^{\pm})/\pi$.

Response matrix between detector and particle level for the $m_{T}(e^{\pm}, \mu^{\pm}, j, p_{T}^{miss})$.

Covariance matrix including all uncertainties of the differential result for the $Leading$ $lepton$ $p_{T}$.

Covariance matrix including all uncertainties of the differential result for the $p_{Z}(e^{\pm}, \mu^{\pm}, j)$.

Covariance matrix including all uncertainties of the differential result for the $Jet$ $p_{T}$.

Covariance matrix including all uncertainties of the differential result for the $m(e^{\pm}, \mu^{\pm}, j)$.

Covariance matrix including all uncertainties of the differential result for the $\Delta\phi(e^{\pm}, \mu^{\pm})/\pi$.

Covariance matrix including all uncertainties of the differential result for the $m_{T}(e^{\pm}, \mu^{\pm}, j, p_{T}^{miss})$.

'Identified transverse momentum spectra of $\pi^{-}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV'

'Identified transverse momentum spectra of $K^{-}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV'

'Identified transverse momentum spectra of $\bar{p}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV'

'Average transverse momentum as a function of $\langle$N$_{part}$$\rangle$ for $\pi^{+}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'Average transverse momentum as a function of $\langle$N$_{part}$$\rangle$ for $K^{+}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'Average transverse momentum as a function of $\langle$N$_{part}$$\rangle$ for p at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'dN/dy scaled by 0.5 × $\langle$N$_{part}$$\rangle$ as a function of $\langle$N$_{part}$$\rangle$ for $\pi^{+}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'dN/dy scaled by 0.5 × $\langle$N$_{part}$$\rangle$ as a function of $\langle$N$_{part}$$\rangle$ for $K^{+}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'dN/dy scaled by 0.5 × $\langle$N$_{part}$$\rangle$ as a function of $\langle$N$_{part}$$\rangle$ for p at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'dN/dy scaled by 0.5 × $\langle$N$_{part}$$\rangle$ as a function of $\langle$N$_{part}$$\rangle$ for $\bar{p}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'$\pi^{−}$/$\pi^{+}$ ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'$K^{−}$/$K^{+}$ ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'$\bar{p}$/p ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'$K^{+}$/$\pi^{+}$ ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'$K^{-}$/$\pi^{-}$ ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'p/$\pi^{+}$ ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'$\bar{p}$/$\pi^{-}$ ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

Number of data events and the number of background events in the best-fit signal-plus-background model for the ggH Tag 2 category, in bins of $m_{ee}$. The number of signal events in the SM and at the observed limit are also provided in the same bins.

Number of data events and the number of background events in the best-fit signal-plus-background model for the ggH Tag 3 category, in bins of $m_{ee}$. The number of signal events in the SM and at the observed limit are also provided in the same bins.

Number of data events and the number of background events in the best-fit signal-plus-background model for the VBF Tag 0 category, in bins of $m_{ee}$. The number of signal events in the SM and at the observed limit are also provided in the same bins.

Number of data events and the number of background events in the best-fit signal-plus-background model for the VBF Tag 1 category, in bins of $m_{ee}$. The number of signal events in the SM and at the observed limit are also provided in the same bins.

Expected and observed limits at the 95%% C.L. on the branching fraction to an electron pair ($e^{+}e^{-}$) for a Higgs boson mass between 120 and 130 GeV.

Expected and observed limits at the 95%% C.L. on the branching fraction to an electron pair ($e^{+}e^{-}$) for each analysis category, and all categories combined. The results here are computed for $m_{H}=125.38$ GeV.

Proton factorial cumulants K4, K5 and K6 in 0-40$\%$ and 50-60$\%$ Au+Au collisions from $\sqrt{s_{NN}}$ = 3 - 200 GeV. At $\sqrt{s_{NN}}$ = 3 GeV, measurement is done with halfrapdity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5).

Proton factorial cumulants K4, K5 and K6 in 0-40$\%$ and 50-60$\%$ Au+Au collisions from $\sqrt{s_{NN}}$ = 3 - 200 GeV. At $\sqrt{s_{NN}}$ = 3 GeV, measurement is done with halfrapdity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5).

Proton factorial cumulants K4, K5 and K6 in 0-40$\%$ and 50-60$\%$ Au+Au collisions from $\sqrt{s_{NN}}$ = 3 - 200 GeV. At $\sqrt{s_{NN}}$ = 3 GeV, measurement is done with halfrapdity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5).

Proton factorial cumulants K4, K5 and K6 from UrQMD model (0-40$\%$ and 50-60$\%$ centrality) for Au+Au collisions from $\sqrt{s_{NN}}$ = 3 - 200 GeV. UrQMD calculation for 3 GeVis with rapidity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5). In addition, two-component model (0-40$\%$) calculations for facorial cumulants are also given.

Proton factorial cumulants K4, K5 and K6 from UrQMD model (0-40$\%$ and 50-60$\%$ centrality) for Au+Au collisions from $\sqrt{s_{NN}}$ = 3 - 200 GeV. UrQMD calculation for 3 GeVis with rapidity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5). In addition, two-component model (0-40$\%$) calculations for facorial cumulants are also given.

Proton factorial cumulants K4, K5 and K6 from UrQMD model (0-40$\%$ and 50-60$\%$ centrality) for Au+Au collisions from $\sqrt{s_{NN}}$ = 3 - 200 GeV. UrQMD calculation for 3 GeVis with rapidity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5). In addition, two-component model (0-40$\%$) calculations for facorial cumulants are also given.

Net-proton cumulant ratios C4/C2, C5/C1, C6/C2 (0-40$\%$ and 50-60$\%$ centrality) and C3/C1 (0-40$\%$ centrality) in Au+Au collisions from $\sqrt{s_{NN}}$ = 3 - 200 GeV. At $\sqrt{s_{NN}}$ = 3 GeV, measurement is done for protons instead of net-protons, and with halfrapdity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5).

Net-proton cumulant ratios C4/C2, C5/C1, C6/C2 (0-40$\%$ and 50-60$\%$ centrality) and C3/C1 (0-40$\%$ centrality) in Au+Au collisions from $\sqrt{s_{NN}}$ = 3 - 200 GeV. At $\sqrt{s_{NN}}$ = 3 GeV, measurement is done for protons instead of net-protons, and with halfrapdity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5).

Net-proton cumulant ratios C4/C2, C5/C1, C6/C2 (0-40$\%$ and 50-60$\%$ centrality) and C3/C1 (0-40$\%$ centrality) in Au+Au collisions from $\sqrt{s_{NN}}$ = 3 - 200 GeV. At $\sqrt{s_{NN}}$ = 3 GeV, measurement is done for protons instead of net-protons, and with halfrapdity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5).

Net-proton cumulant ratios C4/C2, C5/C1, C6/C2 (0-40$\%$ and 50-60$\%$ centrality) and C3/C1 (0-40$\%$ centrality) from UrQMD model in Au+Au collisions from $\sqrt{s_{NN}}$ = 3 -200 GeV. At $\sqrt{s_{NN}}$ = 3 GeV, UrQMD calculation is done for protons instead of net-protons, and with halfrapdity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5).

Net-proton cumulant ratios C4/C2, C5/C1, C6/C2 (0-40$\%$ and 50-60$\%$ centrality) and C3/C1 (0-40$\%$ centrality) from UrQMD model in Au+Au collisions from $\sqrt{s_{NN}}$ = 3 -200 GeV. At $\sqrt{s_{NN}}$ = 3 GeV, UrQMD calculation is done for protons instead of net-protons, and with halfrapdity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5).

Net-proton cumulant ratios C4/C2, C5/C1, C6/C2 (0-40$\%$ and 50-60$\%$ centrality) and C3/C1 (0-40$\%$ centrality) from UrQMD model in Au+Au collisions from $\sqrt{s_{NN}}$ = 3 -200 GeV. At $\sqrt{s_{NN}}$ = 3 GeV, UrQMD calculation is done for protons instead of net-protons, and with halfrapdity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5).

Fifth-to-first (KS5/KS1) and sixth-to-second (KS6/KS2) order K-statistic ratios of net-proton distributions in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV for 0-40$\%$ and 50-60$\%$ centrality.

Fifth-to-first (KS5/KS1) and sixth-to-second (KS6/KS2) order K-statistic ratios of net-proton distributions in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV for 0-40$\%$ and 50-60$\%$ centrality.

Fifth-to-first (KS5/KS1) and sixth-to-second (KS6/KS2) order K-statistic ratios of net-proton distributions in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV for 0-40$\%$ and 50-60$\%$ centrality.

Net-proton cumulant ratio C6/C2 and corresponding K-statistic ratio (0-40$\%$) in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV as a function of sample size. Uncertainties are only statistical.

Net-proton cumulant ratio C6/C2 and corresponding K-statistic ratio (0-40$\%$) in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV as a function of sample size. Uncertainties are only statistical.

Net-proton cumulant ratio C6/C2 and corresponding K-statistic ratio (0-40$\%$) in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV as a function of sample size. Uncertainties are only statistical.

Cumulant ratios C4/C2, C5/C1 and C6/C2 of net-proton distributions measured with half rapdity coverage (-0.5 $<$ y $<$ 0) in 0-40$\%$ central Au+Au collisions for collider energies from $\sqrt{s_{NN}}$ = 7.7 - 54.4 GeV.

Cumulant ratios C4/C2, C5/C1, C6/C2 and C3/C1 of net-proton distributions measured with half rapdity coverage (-0.5 $<$ y $<$ 0) in 0-40$\%$ central Au+Au collisions for collider energies from $\sqrt{s_{NN}}$ = 7.7 - 54.4 GeV.

Cumulant ratios C4/C2, C5/C1, C6/C2 and C3/C1 of net-proton distributions measured with half rapdity coverage (-0.5 $<$ y $<$ 0) in 0-40$\%$ central Au+Au collisions for collider energies from $\sqrt{s_{NN}}$ = 7.7 - 54.4 GeV.

Cumulant ratios C5/C1 of net-proton distributions measured in 40-50$\%$, 60-70$\%$, and 70-80$\%$ Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. This is supplemental data and was not part of the original paper.

Inclusive Y(2S) $R_{AA}$ as a function of centrality in Au+Au collisions at 200 GeV. The bin corresponding to $N_{part}$ = 162 is for 0-60% centrality. Global uncertainty of 20.5% not shown.

Upper limit of inclusive Y(3S) $R_{AA}$ with 95% confidence level in 0-60% Au+Au collisions at 200 GeV

Upper limit of inclusive Y(3S) $R_{AA}$ with 95% confidence level in 0-60% Au+Au collisions at 200 GeV

Inclusive Y(1S) $R_{AA}$ as a function of $p_{T}$ in Au+Au collisions at 200 GeV. Global uncertainty of 6.8% not shown.

Inclusive Y(1S) $R_{AA}$ as a function of $p_{T}$ in 0-60% Au+Au collisions at 200 GeV. Global uncertainty of 6.8% not shown.

Inclusive Y(2S) R_{AA} as a function of p_{T} in Au+Au collisions at 200 GeV. Global uncertainty of 6.8% not shown.

Inclusive Y(2S) $R_{AA}$ as a function of $p_{T}$ in 0-60% Au+Au collisions at 200 GeV. Global uncertainty of 6.8% not shown.

Inclusive Y(1S) yield as a function of centrality in Au+Au collisions at 200 GeV. The bin corresponding to $N_{part}$ = 162 is for 0-60% centrality.

Inclusive Y(2S) yield as a function of centrality in Au+Au collisions at 200 GeV. The bin corresponding to $N_{part}$ = 162 is for 0-60% centrality.

Upper limit of inclusive Y(3S) yield with 95% confidence level in 0-60% Au+Au collisions at 200 GeV

Inclusive Y(1S) yield as a function of $p_{T}$ in 0-60% Au+Au collisions at 200 GeV.

Inclusive Y(2S) yield as a function of p_{T} in 0-60% Au+Au collisions at 200 GeV.

Y(2S)/Y(1S) ratio as a function of centrality in Au+Au collisions at 200 GeV. The bin corresponding to $N_{part}$ = 162 is for 0-60% centrality.

Upper limit of Y(3S)/Y(1S) ratio with 95% confidence level in 0-60% Au+Au collisions at 200 GeV

Y(2S)/Y(1S) ratio as a function of $p_{T}$ in 0-60% Au+Au collisions at 200 GeV.

Covariance matrix for the total uncertainty (i.e. fit including stat., not extrapolation) for the measurement of the absolute differential cross section as a function of the rho observable at parton level.

Covariance matrix for the statistical uncertainty for the measurement of the absolute differential cross section as a function of the rho observable at parton level.

Covariance matrix for the statistical uncertainty for the measurement of the absolute differential cross section as a function of the rho observable at parton level.

Covariance matrix for the extrapolation uncertainty for the measurement of the absolute differential cross section as a function of the rho observable at parton level.

Covariance matrix for the extrapolation uncertainty for the measurement of the absolute differential cross section as a function of the rho observable at parton level.

Normalized differential cross section as a function of the rho observable at parton level.

Normalized differential cross section as a function of the rho observable at parton level.

Covariance matrix for the total uncertainty for the measurement of the normalized differential cross section as a function of the rho observable at parton level.

Covariance matrix for the total uncertainty (i.e. fit including stat., not extrapolation) for the measurement of the normalized differential cross section as a function of the rho observable at parton level.

Covariance matrix for the statistical uncertainty for the measurement of the normalized differential cross section as a function of the rho observable at parton level.

Covariance matrix for the statistical uncertainty for the measurement of the normalized differential cross section as a function of the rho observable at parton level.

Covariance matrix for the extrapolation uncertainty for the measurement of the normalized differential cross section as a function of the rho observable at parton level.

Covariance matrix for the extrapolation uncertainty for the measurement of the normalized differential cross section as a function of the rho observable at parton level.

Correlation matrix for all nuisance parameters and parameters of interest of the Likelihood fit.

Correlation matrix for all nuisance parameters and parameters of interest of the Likelihood fit.

This table is a numerical representation of Fig. 8 for all nuisance parameters.

This table is a numerical representation of Fig. 8 for all nuisance parameters.

Simultaneous coupling measurement $\kappa_V/\kappa_f$

Simultaneous coupling measurement $\kappa_V/\kappa_f$

Simultaneous coupling measurement $\kappa_V/\kappa_f$

Couplings resolved loops. Numbers are in $\kappa_i$.

Couplings effective loops.

Upper limits at 95% CL on the SM strength modifier for the HH production, per final state and combined.

Upper limits at 95% CL on the HH production cross section for different values of $\kappa_\lambda$.

Upper limits at 95% CL on the HH production cross section for different values of $\kappa_{2V}$.

Signal strength modifiers per production channel tims decay mode $\mu_i^f$.

Couplings effective loops including the invisible and undetermined branching fractions.

$\kappa_{\lambda}$ 68 and 95% confidence intervals, from single and double Higgs productions.

Simultaneous coupling measurement $\kappa_\lambda/\kappa_{2V}$

Simultaneous coupling measurement $\kappa_\lambda/\kappa_{2V}$

Simultaneous coupling measurement $\kappa_\lambda/\kappa_{2V}$

Observed correlations between the signal strength modifiers per production mode, $\mu_i$

Observed correlations between the signal strength modifiers per decay channel, $\mu^f$

Observed correlations between the signal strength modifiers per production mode times decay channel $\mu_i^f$.

Observed correlations between the coupling modifiers in the resolved loop model

Observed correlations between the coupling modifiers in the effective loop model

Distribution of an input to the BDT classifier in the $3\ell$ category: The linear discrimminant $p_{T}^{miss,LD}$. The discriminant is defined by the relation $p_{T}^{miss,LD} = 0.6 p_{T}^{miss} + 0.4 H_{T}^{miss}$, where $H_{T}^{miss}$ corresponds to the magnitude of the vector $p_{T}$ sum of all electrons, muons, taus and small radius jets passing the selection critertia, and $p_{T}^{miss}$ represents the missing transverse momentum vector computed as the negative vector $p_{T}$ sum of all the particles reconstructed by the PF algorithm in the event.

Distributions of the transverse mass $m_{T}$ of the lepton that is not originating from the Z boson decay and the missing transverse momentum in the $3\ell$/WZ control region. The distributions expected for the WZ and ZZ as well as for other background processes are shown for the values of nuisance parameters obtained from the ML fit used in the signal extraction.

Distributions of the four lepton invariant mass $m_{4\ell}$ in the $4\ell$/ZZ control region. The distributions expected for the ZZ as well as for other background processes are shown for the values of nuisance parameters obtained from the ML fit used in the signal extraction.

Distributions of the transverse mass $m_{T}$ of the leading lepton and the missing transverse momentum in the $2\ell$(ss) control region. The distributions expected for the misidentified $\ell$ background as well as for other background processes is shown for the values of nuisance parameters obtained from the background-only ML fit, in which the HH signal is constrained to be zero.

Distributions of the reconstructed HH mass $m_{HH}$ in the $2\ell+2 au_{h}$ control region. The distributions expected for the misidentified $\ell/ au_{h}$ background as well as for other background processes is shown for the values of nuisance parameters obtained from the background-only ML fit, in which the HH signal is constrained to be zero.

Distribution in the output of the BDT trained for nonresonant HH production and evaluated for the benchmark scenario JHEP04 BM7 for the $2\ell$(ss) category. The SM HH signal is shown for a cross section amounting to $30$ times the value predicted in the SM. The distributions expected for the background processes are shown for the values of nuisance parameters obtained from the ML fit of the signal+background hypothesis to the data. The binning is chosen to approximate signal quantiles.

Distribution in the output of the BDT trained for nonresonant HH production and evaluated for the benchmark scenario JHEP04 BM7 for the $3\ell$ category. The SM HH signal is shown for a cross section amounting to $30$ times the value predicted in the SM. The distributions expected for the background processes are shown for the values of nuisance parameters obtained from the ML fit of the signal+background hypothesis to the data. The binning is chosen to approximate signal quantiles.

Distribution in the output of the BDT trained for nonresonant HH production and evaluated for the benchmark scenario JHEP04 BM7 for the $4\ell$ category. The SM HH signal is shown for a cross section amounting to $30$ times the value predicted in the SM. The distributions expected for the background processes are shown for the values of nuisance parameters obtained from the ML fit of the signal+background hypothesis to the data. The binning is chosen to approximate signal quantiles.

Distribution in the output of the BDT trained for nonresonant HH production and evaluated for the benchmark scenario JHEP04 BM7 for the $3\ell+1 au_{h}$ category. The SM HH signal is shown for a cross section amounting to $30$ times the value predicted in the SM. The distributions expected for the background processes are shown for the values of nuisance parameters obtained from the ML fit of the signal+background hypothesis to the data. The binning is chosen to approximate background quantiles.

Distribution in the output of the BDT trained for nonresonant HH production and evaluated for the benchmark scenario JHEP04 BM7 for the $2\ell+2 au_{h}$ category. The SM HH signal is shown for a cross section amounting to $30$ times the value predicted in the SM. The distributions expected for the background processes are shown for the values of nuisance parameters obtained from the ML fit of the signal+background hypothesis to the data. The binning is chosen to approximate background quantiles.

Distribution in the output of the BDT trained for nonresonant HH production and evaluated for the benchmark scenario JHEP04 BM7 for the $1\ell+3 au_{h}$ category. The SM HH signal is shown for a cross section amounting to $30$ times the value predicted in the SM. The distributions expected for the background processes are shown for the values of nuisance parameters obtained from the ML fit of the signal+background hypothesis to the data. The binning is chosen to approximate background quantiles.

Distribution in the output of the BDT trained for nonresonant HH production and evaluated for the benchmark scenario JHEP04 BM7 for the $4 au_{h}$ category. The SM HH signal is shown for a cross section amounting to $30$ times the value predicted in the SM. The distributions expected for the background processes are shown for the values of nuisance parameters obtained from the ML fit of the signal+background hypothesis to the data. The binning is chosen to approximate background quantiles.

Observed and expected $95\%$ CL upper limits on the SM HH production cross section, obtained for both individual search categories and from a simultaneous fit of all seven categories combined.

Observed and expected $95\%$ CL upper limits on the HH production cross section as a function of the Higgs boson self-coupling strength modifier $\kappa_\lambda$ for the combination of all seven categories. All Higgs boson couplings other than $\lambda$ are assumed to have the values predicted in the SM.

Observed and expected $95\%$ CL upper limits on the HH production cross section as a function of the Higgs boson self-coupling strength modifier $\kappa_\lambda$ for the seven different categories as well as their combination. All Higgs boson couplings other than $\lambda$ are assumed to have the values predicted in the SM.

Observed and expected $95\%$ CL upper limits on the HH production cross section for the twelve benchmark scenarios from doi:10.1007/JHEP04(2016)126, the additional benchmark scenario 8a from doi:10.1007/JHEP09(2018)057, the seven benchmark scenarios from doi:10.1007/JHEP03(2020)091, and for the SM.

Observed and expected $95\%$ CL upper limits on the HH production cross section for the twelve benchmark scenarios from doi:10.1007/JHEP04(2016)126, the additional benchmark scenario 8a from doi:10.1007/JHEP09(2018)057, the seven benchmark scenarios from doi:10.1007/JHEP03(2020)091, and for the SM. The limits are shown for all seven search categories as well as for their combination.

Observed and expected $95\%$ CL upper limits on the HH production cross section as a function of the effective coupling $c_{2}$ for the combination of all seven categories. All Higgs boson couplings other than $c_{2}$ are assumed to have the values predicted in the SM.

Observed and expected $95\%$ CL upper limits on the HH production cross section as a function of the effective coupling $c_{2}$ and the top Yukawa coupling modifier $\kappa_{t}$ for the combination of all seven categories. All Higgs boson couplings other than $c_{2}$ and $\kappa_{t}$ are assumed to have the values predicted in the SM. The position of the SM in the ($c_{2}-\kappa_{t}$) plane, as well as the best fit value of $(c_{2},\kappa_{t})=(1.05, 1.74)$ together with contours for the theory cross section are shown as well.

Observed and expected $95\%$ CL upper limits on the HH production cross section as a function of the Higgs boson self-coupling modifier $\kappa_{\lambda}$ and the top Yukawa coupling modifier $\kappa_{t}$ for the combination of all seven categories. All Higgs boson couplings other than $\kappa_{\lambda}$ and $\kappa_{t}$ are assumed to have the values predicted in the SM. The position of the SM in the ($\kappa_{\lambda}-\kappa_{t}$) plane, as well as the best fit value of $(\kappa_{\lambda},\kappa_{t})=(-3.54, -1.70)$ together with contours for the theory cross section are shown as well.

Observed and expected $95\%$ CL upper limits on the HH production cross section as a function of the effective coupling $c_{2}$ and the Higgs boson self-coupling modifier $\kappa_{\lambda}$ for the combination of all seven categories. All Higgs boson couplings other than $c_{2}$ and $\kappa_{\lambda}$ are assumed to have the values predicted in the SM. The position of the SM in the ($c_{2}-\kappa_{\lambda}$) plane, as well as the best fit value of $(c_{2},\kappa_{\lambda})=(-0.66, 5.33)$ together with contours for the theory cross section are shown as well.

Observed and expected $95\%$ CL upper limits on the production of new particles X of spin $0$ and mass $m_{X}$ in the range $250$-$1000$ GeV, which decay to Higgs boson pairs.

Observed and expected $95\%$ CL upper limits on the production of new particles X of spin $0$ and mass $m_{X}$ in the range $250$-$1000$ GeV, which decay to Higgs boson pairs. The Limit is shown for the seven different search categories as well as their combination.

Observed and expected $95\%$ CL upper limits on the production of new particles X of spin $2$ and mass $m_{X}$ in the range $250$-$1000$ GeV, which decay to Higgs boson pairs.

Observed and expected $95\%$ CL upper limits on the production of new particles X of spin $2$ and mass $m_{X}$ in the range $250$-$1000$ GeV, which decay to Higgs boson pairs. The Limit is shown for the seven different search categories as well as their combination.

Distribution in the output of the BDT trained for resonances of spin 2 and mass $750\,$GeV production for the $2\ell$(ss) category. The resonant HH signal is shown for a cross section amounting to $1\,$pb. The distributions expected for the background processes are shown for the values of nuisance parameters obtained from the ML fit of the signal+background hypothesis to the data. The binning is chosen to approximate signal quantiles.

Distribution in the output of the BDT trained for resonances of spin 2 and mass $750\,$GeV production for the $3\ell$ category. The resonant HH signal is shown for a cross section amounting to $1\,$pb. The distributions expected for the background processes are shown for the values of nuisance parameters obtained from the ML fit of the signal+background hypothesis to the data. The binning is chosen to approximate signal quantiles.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances decaying to a quark-gluon pair, with $M(X)/M(Y) = 0.17$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to predictions for a scalar diquark with couplings to pairs of up quarks, $y_{uu}$ = 0.4, and to pairs of vector-like quarks, $y_{χ}$ = 0.6.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances decaying to a quark-gluon pair, with $M(X)/M(Y) = 0.19$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to predictions for a scalar diquark with couplings to pairs of up quarks, $y_{uu}$ = 0.4, and to pairs of vector-like quarks, $y_{χ}$ = 0.6.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances decaying to a quark-gluon pair, with $M(X)/M(Y) = 0.21$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to predictions for a scalar diquark with couplings to pairs of up quarks, $y_{uu}$ = 0.4, and to pairs of vector-like quarks, $y_{χ}$ = 0.6.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances decaying to a quark-gluon pair, with $M(X)/M(Y) = 0.23$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to predictions for a scalar diquark with couplings to pairs of up quarks, $y_{uu}$ = 0.4, and to pairs of vector-like quarks, $y_{χ}$ = 0.6.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances decaying to a quark-gluon pair, with $M(X)/M(Y) = 0.25$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to predictions for a scalar diquark with couplings to pairs of up quarks, $y_{uu}$ = 0.4, and to pairs of vector-like quarks, $y_{χ}$ = 0.6.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances decaying to a quark-gluon pair, with $M(X)/M(Y) = 0.27$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to predictions for a scalar diquark with couplings to pairs of up quarks, $y_{uu}$ = 0.4, and to pairs of vector-like quarks, $y_{χ}$ = 0.6.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances decaying to a quark-gluon pair, with $M(X)/M(Y) = 0.29$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to predictions for a scalar diquark with couplings to pairs of up quarks, $y_{uu}$ = 0.4, and to pairs of vector-like quarks, $y_{χ}$ = 0.6.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances decaying to a quark-gluon pair, with $M(X)/M(Y) = 0.31$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to predictions for a scalar diquark with couplings to pairs of up quarks, $y_{uu}$ = 0.4, and to pairs of vector-like quarks, $y_{χ}$ = 0.6.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances decaying to a quark-gluon pair, with $M(X)/M(Y) = 0.33$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to predictions for a scalar diquark with couplings to pairs of up quarks, $y_{uu}$ = 0.4, and to pairs of vector-like quarks, $y_{χ}$ = 0.6.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances decaying to a quark-gluon pair, with $M(X)/M(Y) = 0.42$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to predictions for a scalar diquark with couplings to pairs of up quarks, $y_{uu}$ = 0.4, and to pairs of vector-like quarks, $y_{χ}$ = 0.6.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for the non-resonant production of top squark pairs in the RPV SUSY decay scenario. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to the top squark model cross section.

Observed differential four-jet mass spectrum for 0.22 < $\\a$ < 0.24. The cross-section is calculated by dividing the event yield by the bin width and luminosity.

Observed differential four-jet mass spectrum for 0.24 < $\\a$ < 0.26. The cross-section is calculated by dividing the event yield by the bin width and luminosity.

Observed differential four-jet mass spectrum for 0.26 < $\\a$ < 0.28. The cross-section is calculated by dividing the event yield by the bin width and luminosity.

Observed differential four-jet mass spectrum for all $\\a$ bins together. The cross-section is calculated by dividing the event yield by the bin width and luminosity.

Observed differential average dijet mass spectrum within three $\\a$ bins of the non-resonant search. The cross-section is calculated by dividing the event yield by the bin width and luminosity.