The total coherent $\mathrm{J}/\psi$ photoproduction cross section as a function of photon-nuclear center-of-mass energy per nucleon $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$, measured in PbPb ultra-peripheral collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV. The $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$ values used correspond to the center of each rapidity range. The theoretical uncertainties is due to the uncertainties in the photon flux.

The nuclear gluon suppression factor $R_{\mathrm{g}}^{\mathrm{Pb}}$ as a function of Bjorken $x$ extracted from the CMS measurement of the coherent $\mathrm{J}/\psi$ photoproduction in PbPb ultra-peripheral collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV. The $x$ values are evaluated at the centers of their corresponding rapidity ranges. The theoretical uncertainties are due to the uncertainties in the photon flux and the impulse approximation model.

The nuclear gluon suppression factor $R_{\mathrm{g}}^{\mathrm{Pb}}$ as a function of Bjorken $x$ extracted from the CMS measurement of the coherent $\mathrm{J}/\psi$ photoproduction in PbPb ultra-peripheral collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV. The $x$ values are evaluated at the centers of their corresponding rapidity ranges. The theoretical uncertainties are due to the uncertainties in the photon flux and the impulse approximation model.

The total covariance matrix of the total coherent photoproduction cross section as a function of photon-nuclear center-of-mass energy per nucleon $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$. The covariance matrix includes both the experimental and theoretical (photon flux) uncertainties. The bins are ordered as increasing in $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$.

The photon flux values from STARLight as a function of rapidity, in different neutron multiplicity classes: 0n0n, 0nXn, and XnXn.

The experimental covariance matrix of the total coherent photoproduction cross section as a function of photon-nuclear center-of-mass energy per nucleon $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$. The bins are ordered as increasing in $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$.

The covariance matrix for the flux in the 0n0n neutron multiplicity class.

The theoretical (photon flux) covariance matrix of the total coherent photoproduction cross section as a function of photon-nuclear center-of-mass energy per nucleon $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$. The bins are ordered as increasing in $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$.

The covariance matrix for the flux in the 0nXn neutron multiplicity class.

The covariance matrix for the flux in the XnXn neutron multiplicity class.

The total covariance matrix of the total coherent photoproduction cross section as a function of photon-nuclear center-of-mass energy per nucleon $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$. The covariance matrix includes both the experimental and theoretical (photon flux) uncertainties. The bins are ordered as increasing in $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$.

The experimental covariance matrix of the total coherent photoproduction cross section as a function of photon-nuclear center-of-mass energy per nucleon $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$. The bins are ordered as increasing in $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$.

The theoretical (photon flux) covariance matrix of the total coherent photoproduction cross section as a function of photon-nuclear center-of-mass energy per nucleon $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$. The bins are ordered as increasing in $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$.

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.

Expected $+ 1$ s.d. lower limit contour on the $m_{\mathrm{W}_{\mathrm{KK}}}$ and $m_{\mathrm{R}}$ plane after combinign with an analysis of the all-hadronic final state.

Expected - 1 s.d. lower limit contour on the $m_{\mathrm{W}_{\mathrm{KK}}}$ and $m_{\mathrm{R}}$ plane after combinign with an analysis of the all-hadronic final state.

Observed lower limit contour on the $m_{\mathrm{W}_{\mathrm{KK}}}$ and $m_{\mathrm{R}}$ plane after combinign with an analysis of the all-hadronic final state.

Post-fit distributions of the reconstructed $\ell\nu$+jets system ($m_{\mathrm{j}\ell\nu}$, $m_{\mathrm{jj}\ell\nu}$) in data and simulation for SR1.

Post-fit distributions of the reconstructed $\ell\nu$+jets system ($m_{\mathrm{j}\ell\nu}$, $m_{\mathrm{jj}\ell\nu}$) in data and simulation for SR2.

Post-fit distributions of the reconstructed $\ell\nu$+jets system ($m_{\mathrm{j}\ell\nu}$, $m_{\mathrm{jj}\ell\nu}$) in data and simulation for SR3.

Post-fit distributions of the reconstructed $\ell\nu$+jets system ($m_{\mathrm{j}\ell\nu}$, $m_{\mathrm{jj}\ell\nu}$) in data and simulation for SR5.

Post-fit distributions of the reconstructed $\ell\nu$+jets system ($m_{\mathrm{j}\ell\nu}$, $m_{\mathrm{jj}\ell\nu}$) in data and simulation for SR6.

Distribution of $m_{\mathrm{jjj}}$ for preselected events with $\mathrm{N}_{j}$ = 3

Distribution of $m_{\mathrm{j}}$ for preselected events with $\mathrm{N}_{j}$ = 3

Distribution of the deep-WH value of the highest-mass jet with 60 < $m_{\mathrm{j}}$ < 100 GeV for preselected events with $\mathrm{N}_{j}$ = 3

scale factors (SFs) for W, $t^{2}$, and q/g matched jets in the low-$m_{\mathrm{j}}$ and low-$p_{\mathrm{T}}$ (LL) bin, as functions of the deep-W discriminant value.

scale factors (SFs) for W, $t^{2}$, and q/g matched jets in the low-$m_{\mathrm{j}}$ and high-$p_{\mathrm{T}}$ (LH) bin, as functions of the deep-W discriminant value.

scale factors (SFs) for $t^{2}$, $t^{3,4}$, and q/g matched jets in the high-$m_{\mathrm{j}}$ and low-$p_{\mathrm{T}}$ (HL) bin, as functions of the deep-WH discriminant value.

scale factors (SFs) for $t^{2}$, $t^{3,4}$, and q/g matched jets in the high-$m_{\mathrm{j}}$ and high-$p_{\mathrm{T}}$ (HH) bin, as functions of the deep-WH discriminant value.

The deep-W discriminant of the jet with highest mass in the single-lepton sideband for LL samples.

The deep-W discriminant of the jet with highest mass in the single-lepton sideband for LH samples.

The deep-WH discriminant of the jet with highest mass in the single-lepton sideband for HL samples.

The deep-WH discriminant of the jet with highest mass in the single-lepton sideband for HH samples.

Comparison of the distribution of data and simulated backgrounds, as a function of the deep-W discriminant value for the highest-mass jet in CR1, after the scale factors have been applied.

Comparison of the distribution of data and simulated backgrounds, as a function of the deep-WH discriminant value for the highest-mass jet in CR2, after the scale factors have been applied.

Comparison of the distribution of data and simulated backgrounds, as a function of the deep-WH discriminant value for the highest-mass jet in CR3, after the scale factors have been applied.

Comparison of the distribution of data and simulated backgrounds, as a function of the deep-W discriminant value for the highest-mass jet in CR45, after the scale factors have been applied.

Comparison of the distribution of data and simulated backgrounds, as a function of the deep-W discriminant value for the highest-mass jet in CR6, after the scale factors have been applied.

The $m_{\mathrm{j}^{\mathrm{max}}}$ distributions for different jet types for SR1–3 events of the signal with $m_{\mathrm{W}_{\mathrm{KK}}}$ = 2.5 TeV, $m_{\mathrm{R}}$ = 0.2 TeV$ without deep-W (WH) constraints.

The deep-W distribution normalized to unity for the shown components of of the signal with $m_{\mathrm{W}_{\mathrm{KK}}}$ = 2.5 TeV, $m_{\mathrm{R}}$ = 0.2 TeV. The $t^{3,4}$ jets from the preselected sample, normalized to unity, are superimposed to compare shapes with the $R^{3q}$ and $R^{4q}$ distributions.

The deep-WH distribution normalized to unity for the shown components of of the signal with $m_{\mathrm{W}_{\mathrm{KK}}}$ = 2.5 TeV, $m_{\mathrm{R}}$ = 0.2 TeV. The $t^{3,4}$ jets from the preselected sample, normalized to unity, are superimposed to compare shapes with the $R^{3q}$ and $R^{4q}$ distributions.

The $m_{\mathrm{jj}}$ distribution for CR1 for data and simulation.

The $m_{\mathrm{jj}}$ distribution for CR2 for data and simulation.

The $m_{\mathrm{jj}}$ distribution for CR3 for data and simulation.

The $m_{\mathrm{jjj}}$ distribution for CR45 for data and simulation.

The $m_{\mathrm{jjj}}$ distribution for CR6 for data and simulation.

Post-fit distributions of the reconstructed triboson system ($m_{\mathrm{jj}}$) in data and simulation for SR1.

Post-fit distributions of the reconstructed triboson system ($m_{\mathrm{jj}}$) in data and simulation for SR2.

Post-fit distributions of the reconstructed triboson system ($m_{\mathrm{jj}}$) in data and simulation for SR3.

Post-fit distributions of the reconstructed triboson system ($m_{\mathrm{jjj}}$) in data and simulation for SR4.

Post-fit distributions of the reconstructed triboson system ($m_{\mathrm{jjj}}$) in data and simulation for SR5.

Post-fit distributions of the reconstructed triboson system ($m_{\mathrm{jjj}}$) in data and simulation for SR6.

Observed upper limits at $95\%$ CL on the signal cross section $\times$ branching fraction as functions of the $m_{\mathrm{W}_{\mathrm{KK}}}$ and $m_{\mathrm{R}}$ resonance masses.

Expected median lower limit contour on the $m_{\mathrm{W}_{\mathrm{KK}}}$ and $m_{\mathrm{R}}$ plane.

Expected $+ 1$ s.d. lower limit contour on the $m_{\mathrm{W}_{\mathrm{KK}}}$ and $m_{\mathrm{R}}$ plane.

Expected - 1 s.d. lower limit contour on the $m_{\mathrm{W}_{\mathrm{KK}}}$ and $m_{\mathrm{R}}$ plane.

Observed lower limit contour on the $m_{\mathrm{W}_{\mathrm{KK}}}$ and $m_{\mathrm{R}}$ plane.

Measured DPS effective cross section

pp -> J/psi J/psi J/psi X cross section

$pp \rightarrow J/\psi J/\psi J/\psi X~$ fiducial cross section

95% CL limits on the Lagrangian approach (a.k.a. LEP parametrization) parameters in Wgamma events.