Invariant mass distribution of the diphoton pairs for the elastic selection region with events satisfying a < 0.005 (signal contribution is magnified by a factor 5000).

Predicted number of events having an elastic diphoton pair in association with a pair of protons observed within the range where the proton detectors have a radiation inefficiency less than 10%. The yields where the two-photon and two-proton systems mass and rapidity are matching at 2 and 3$\sigma$ are also quoted. This corresponds to a search region of $m_{\gamma\gamma} > 350$ GeV, $0.070 < \xi^+ < 0.111$, and $0.070 < \xi^- < 0.138$.

Predicted number of events having an elastic diphoton pair in association with a pair of protons observed within the range where the proton detectors have a radiation inefficiency less than 10%. The yields where the two-photon and two-proton systems mass and rapidity are matching at 2 and 3$\sigma$ are also quoted. This corresponds to a search region of $m_{\gamma\gamma} > 350$ GeV, $0.070 < \xi^+ < 0.111$, and $0.070 < \xi^- < 0.138$.

95% CL expected and observed frequentist upper limit for the LbL cross section within the $m_{\gamma\gamma} > 350$ GeV, $0.070 < \xi^+ < 0.111$, and $0.070 < \xi^- < 0.138$ search region.

95% CL expected and observed frequentist upper limit for the LbL cross section within the $m_{\gamma\gamma} > 350$ GeV, $0.070 < \xi^+ < 0.111$, and $0.070 < \xi^- < 0.138$ search region.

95% expected and observed one-dimensional limits on $\zeta_1$ and $\zeta_2$ anomalous LbyL production parameters, when the other parameter is set to zero. This corresponds to a search region of $m_{\gamma\gamma} > 350$ GeV, $0.070 < \xi^+ < 0.111$, and $0.070 < \xi^- < 0.138$.

95% expected and observed one-dimensional limits on $\zeta_1$ and $\zeta_2$ anomalous LbyL production parameters, when the other parameter is set to zero. This corresponds to a search region of $m_{\gamma\gamma} > 350$ GeV, $0.070 < \xi^+ < 0.111$, and $0.070 < \xi^- < 0.138$.

95% expected and observed limits on $\zeta_1$ and $\zeta_2$ anomalous LbyL production parameters. The parametric elliptic form is assumed: $a_0\zeta_1^2+a_1\zeta_1\zeta_2+a_2\zeta_2^2=1$. This corresponds to a search region of $m_{\gamma\gamma} > 350$ GeV, $0.070 < \xi^+ < 0.111$, and $0.070 < \xi^- < 0.138$.

95% expected and observed limits on $\zeta_1$ and $\zeta_2$ anomalous LbyL production parameters. The parametric elliptic form is assumed: $a_0\zeta_1^2+a_1\zeta_1\zeta_2+a_2\zeta_2^2=1$. This corresponds to a search region of $m_{\gamma\gamma} > 350$ GeV, $0.070 < \xi^+ < 0.111$, and $0.070 < \xi^- < 0.138$.

Correlation coefficients $\rho_{i,j}$ for the statistical and systematic uncertainties between the $i$-th and $j$-th bin of the differential $A_E$ measurement as a function of the jet scattering angle $\theta_j$

The effects on the energy asymmetry of $1\sigma$ variations in its influencing nuisance parameters for the three $\theta_j$ bins. These are extracted from the samples of the posterior distribution with $\sigma_i^{(j)} = c_{ij}/\sqrt{c_{jj}}$ being the estimated shift of bin $i$ in conjunction with a shift $\Delta\theta_j$ of nuisance parameter $j$. The data statistical (Data stat.) uncertainty is obtained from running the unfolding with all nuisance parameters being fixed to their post-marginalised values, the MC statistical uncertainty on the response matrix ($t\bar{t}$ response MC stat.) is evaluated using a bootstrapping method from the covariance matrix of the ensemble of repeated unfolding results with varied response matrices. The $\gamma$ variations denote the statistical uncertainties of the background predictions in the corresponding bin of the $\Delta E$ vs $\theta_{j}$ distribution. The numbers appended to the $W$+jets PDF variations denote the corresponding NNPDF3.0 PDF sets.

The effects on the energy asymmetry of $1\sigma$ variations in its influencing nuisance parameters for the three $\theta_j$ bins. These are extracted from the samples of the posterior distribution with $\sigma_i^{(j)} = c_{ij}/\sqrt{c_{jj}}$ being the estimated shift of bin $i$ in conjunction with a shift $\Delta\theta_j$ of nuisance parameter $j$. The data statistical (Data stat.) uncertainty is obtained from running the unfolding with all nuisance parameters being fixed to their post-marginalised values, the MC statistical uncertainty on the response matrix ($t\bar{t}$ response MC stat.) is evaluated using a bootstrapping method from the covariance matrix of the ensemble of repeated unfolding results with varied response matrices. The $\gamma$ variations denote the statistical uncertainties of the background predictions in the corresponding bin of the $\Delta E$ vs $\theta_{j}$ distribution. The numbers appended to the $W$+jets PDF variations denote the corresponding NNPDF3.0 PDF sets.

Covariances $c_{ij}$ for the highest ranked systematic uncertainties in the energy asymmetry measurement differential in $\theta_j$.

Covariances $c_{ij}$ for the highest ranked systematic uncertainties in the energy asymmetry measurement differential in $\theta_j$.

Definition of the fiducial phase space with lepton candidate ($\ell$), hadronic top candidate ($j_h$), leptonic top candidate ($j_l$) and associated jet candidate ($j_a$).

Definition of the fiducial phase space with lepton candidate ($\ell$), hadronic top candidate ($j_h$), leptonic top candidate ($j_l$) and associated jet candidate ($j_a$).

Bounds on individual Wilson coefficients $C($TeV$/\Lambda)^2$ from the energy asymmetry, obtained from a combined fit to its values in all three $\theta_j$ bins.

Bounds on individual Wilson coefficients $C($TeV$/\Lambda)^2$ from the energy asymmetry, obtained from a combined fit to its values in all three $\theta_j$ bins.

$M_{p\eta}$ invariant mass distribution for $E_\gamma$ = 1400-1500 MeV.

$M_{p\eta}$ invariant mass distribution for $E_\gamma$ = 1500-1600 MeV.

$M_{p\eta}$ invariant mass distribution under the conditions: $E_\gamma$ = 1400-1500 MeV; 1120 MeV $\leq M_{p\pi^0} \leq$ 1220 MeV; $\theta_p^{lab} \leq$ 25°; 25° $\leq \theta_\gamma^{lab} \leq$ 155°.

$M_{p\eta}$ invariant mass distribution under the conditions: $E_\gamma$ = 1400-1500 MeV; 1120 MeV $\leq M_{p\pi^0} \leq$ 1220 MeV; $\theta_p^{lab} \leq$ 25°; 1° $\leq \theta_\gamma^{lab} \leq$ 155°.

$M_{p\eta}$ invariant mass distribution for $E_\gamma$ = 1400-1500 MeV and $M_{p\pi^0} \leq$ 1190 MeV, allowing for all proton and photon laboratory angles.

$M_{p\eta}$ invariant mass distribution for the incident photon energy range $E_\gamma$ = 1420-1540 MeV and $M_{p\pi^0} \leq$ 1170 MeV.

$M_{p\eta}$ invariant mass distribution for the incident photon energy range $E_\gamma$ = 1420-1540 MeV and $M_{p\pi^0} \leq$ 1180 MeV.

$M_{p\eta}$ invariant mass distribution for the incident photon energy range $E_\gamma$ = 1420-1540 MeV and $M_{p\pi^0} \leq$ 1190 MeV.

$M_{p\eta}$ invariant mass distribution for the incident photon energy range $E_\gamma$ = 1420-1540 MeV and $M_{p\pi^0} \leq$ 1200 MeV.

$M_{p\eta}$ invariant mass distribution for the incident photon energy range $E_\gamma$ = 1420-1540 MeV and $M_{p\pi^0} \leq$ 1210 MeV.

$M_{p\eta}$ invariant mass distribution for the incident photon energy range $E_\gamma$ = 1420-1540 MeV and $M_{p\pi^0} \leq$ 1220 MeV.

$M_{p\eta}$ invariant mass distribution for the incident photon energy range $E_\gamma$ = 1400-1420 MeV and $M_{p\pi^0} \leq$ 1190 MeV.

$M_{p\eta}$ invariant mass distribution for the incident photon energy range $E_\gamma$ = 1420-1460 MeV and $M_{p\pi^0} \leq$ 1190 MeV.

$M_{p\eta}$ invariant mass distribution for the incident photon energy range $E_\gamma$ = 1460-1500 MeV and $M_{p\pi^0} \leq$ 1190 MeV.

$M_{p\eta}$ invariant mass distribution for the incident photon energy range $E_\gamma$ = 1500-1540 MeV and $M_{p\pi^0} \leq$ 1190 MeV.

$M_{p\eta}$ invariant mass distribution for the incident photon energy range $E_\gamma$ = 1540-1600 MeV and $M_{p\pi^0} \leq$ 1190 MeV.

$M_{p\eta}$ invariant mass distribution for the incident photon energy range $E_\gamma$ = 1420-1540 MeV and $M_{p\pi^0} \leq$ 1190 MeV.

Excess yield relative to the PWA distributions in the invariant mass distributions $M^2_{p\eta}$.

Excess yield relative to the PWA distributions in the invariant mass distributions $M^2_{\pi^0\eta}$.

Excess yield relative to the PWA distributions in the invariant mass distributions $M^2_{p\pi^0}$, with a cut on the structure in the $M^2_{p\eta}$ invariant mass distribution.

Excess yield relative to the PWA distributions in the $p-\eta$ opening angle distribution in the $\gamma p$ centre-of-mass system.

Excess yield relative to the PWA distributions in the $p-\eta$ opening angle distribution in the $\gamma p$ centre-of-mass system.

Excess yield relative to the PWA distributions in the $\pi^0-\eta$ opening angle distribution in the $\gamma p$ centre-of-mass system.

Excess yield relative to the PWA distributions in the $\pi^0-\eta$ opening angle distribution in the $\gamma p$ centre-of-mass system.

Differential cross section $d\sigma/dM_{\pi^0\eta}$ for $E_\gamma$ = 1540-1600 MeV.

$M_{p\eta}$ invariant mass distribution, taken as difference to the PWA calculations (s. Fig. 11).

$M_{\pi^0\eta}$ invariant mass distribution, taken as difference to the PWA calculations (s. Fig. 11).

$\theta_{p\eta}$ opening angle distribution, taken as difference to the PWA calculations (s. Fig. 12).

$\theta_{\pi^0\eta}$ opening angle distribution, taken as difference to the PWA calculations (s. Fig. 12).

Observed likelihood scan in the ($\kappa_\tau$, $\tilde{\kappa}_\tau$) plane.

Observed likelihood scan in the ($\alpha^{\mathrm{H}\tau\tau}$, $\mu_{\text{ggH}}$) plane. The $\mu_{\text{qqH}}$ signal strength modifier is profiled.

Observed likelihood scan in the ($\alpha^{\mathrm{H}\tau\tau}$, $\mu_{\text{qqH}}$) plane. The $\mu_{\text{ggH}}$ signal strength modifier is profiled.

Observed likelihood scan in the ($\mu_{\text{qqH}}$, $\mu_{\text{ggH}}$) plane. The value of $\alpha^{\mathrm{H}\tau\tau}$ is profiled.

Two-dimensional distributions of the leading electron vs the leading muon $|d_{0}|$, for the events that pass the e$\mu$ preselection. Data events and $\tilde{t} \to b\ell$ signal events with a $\tilde{t}$ mass of 700 GeV and a proper decay length of 10 mm that correspond to 2018 data-taking conditions are shown. In each $|d_{0}|$-$|d_{0}|$ bin, the number of events divided by the bin area is plotted. The inclusive signal region covers the region between 100 $\mu$m and 10 cm in each $|d_{0}|$ variable shown.

Two-dimensional distributions of the leading vs the subleading electron $|d_0|$, for the events that pass the ee preselection. Data events and $\tilde{t} \to b\ell$ signal events with a $\tilde{t}$ mass of 700 GeV and a proper decay length of 10 mm that correspond to 2018 data-taking conditions are shown. In each $|d_{0}|$-$|d_{0}|$ bin, the number of events divided by the bin area is plotted. The inclusive signal region covers the region between 100 $\mu$m and 10 cm in each $|d_{0}|$ variable shown.

Two-dimensional distributions of the leading vs the subleading muon $|d_{0}|$, for the events that pass the $\mu\mu$ preselection. Data events and $\tilde{t} \to b\ell$ signal events with a $\tilde{t}$ mass of 700 GeV and a proper decay length of 10 mm that correspond to 2018 data-taking conditions are shown. In each $|d_{0}|$-$|d_{0}|$ bin, the number of events divided by the bin area is plotted. The inclusive signal region covers the region between 100 $\mu$m and 10 cm in each $|d_{0}|$ variable shown.

The number of observed and estimated background events in each channel and SR, with a representative signal overlaid. For each background estimate and signal yield, the total uncertainty (statistical plus systematic) is given. The distributions shown correspond to the events before the final maximum likelihood fit to the data.

The number of observed and estimated background events in each channel and SR in 2016, with a representative signal overlaid. For each background estimate and signal yield, the total uncertainty is given. The distributions shown correspond to the events before the final maximum likelihood fit to the data.

The number of observed and estimated background events in each channel and SR in 2017 and 2018, with a representative signal overlaid. For each background estimate and signal yield, the total uncertainty is given. The distributions shown correspond to the events before the final maximum likelihood fit to the data.

The observed 95% CL upper limits on the long-lived top squark production cross section, in the $c\tau_0$ -- mass plane, for the three channels combined. The $\tilde{t} \to b\ell $ process is shown. These limits assume $\mathcal{B}(\tilde{t} \to b\ell)$ is 100%, and each lepton has an equal probability of being an electron, a muon, or a tau lepton. The area to the left of the black curve represents the observed exclusion region, and the dashed red lines indicate the expected limits and their 68% confidence intervals.

The observed 95% CL upper limits on the long-lived top squark production cross section, in the $c\tau_0$ -- mass plane, for the three channels combined. The $\tilde{t} \to d\ell$ process is shown. These limits assume $\mathcal{B}(\tilde{t} \to d\ell)$ is 100%, and each lepton has an equal probability of being an electron, a muon, or a tau lepton. The area to the left of the black curve represents the observed exclusion region, and the dashed red lines indicate the expected limits and their 68% confidence intervals.

The observed 95% CL upper limits on the long-lived top squark production cross section, in the $c\tau_0$ -- mass plane, for the three channels combined. The $\tilde{t} \to b\ell $ process is shown. These limits assume $\mathcal{B}(\tilde{t} \to b\ell)$ is 100%, and each lepton has an equal probability of being an electron, a muon, or a tau lepton. The area to the left of the black curve represents the observed exclusion region, and the dashed red lines indicate the expected limits and their 68% confidence intervals.

The observed 95% CL upper limits on the long-lived top squark production cross section, in the $c\tau_0$ -- mass plane, for the three channels combined. The $\tilde{t} \to d\ell$ process is shown. These limits assume $\mathcal{B}(\tilde{t} \to d\ell)$ is 100%, and each lepton has an equal probability of being an electron, a muon, or a tau lepton. The area to the left of the black curve represents the observed exclusion region, and the dashed red lines indicate the expected limits and their 68% confidence intervals.

The 95% CL upper limits on the long-lived top squark proper decay length ($c\tau_0$) as a function of its mass, for the e$\mu$, ee, and $\mu\mu$ channels, and their combination. The $\tilde{t} \to b\ell $ process is shown. These limits assume $\mathcal{B}(\tilde{t} \to b\ell)$ is 100%, and each lepton has an equal probability of being an electron, a muon, or a tau lepton.

The 95% CL upper limits on the long-lived top squark proper decay length ($c\tau_0$) as a function of its mass, for the e$\mu$, ee, and $\mu\mu$ channels, and their combination. The $\tilde{t} \to d\ell$ process is shown. These limits assume $\mathcal{B}(\tilde{t} \to d\ell)$ is 100%, and each lepton has an equal probability of being an electron, a muon, or a tau lepton.

The 95% CL constraints on the long-lived slepton $c\tau_{0}$ and mass. The $\tilde{\tau}$ and co-NLSP limits are shown for the three channels combined, while the $\tilde{e}$ and $\tilde{\mu}$ NLSP limits are shown for the ee and $\mu\mu$ channels, respectively. These limits assume that the superpartners of the left- and right-handed leptons are degenerate in mass and $\mathcal{B}(\tilde{\ell} \to \ell\tilde{G})$ is 100%. The area to the left of the solid curves represents the observed exclusion region, and the dashed lines indicate the expected limits.

The observed 95% CL upper limits on the long-lived slepton production cross section, in the $c\tau_0$ -- mass plane. The co-NLSP limits are shown for the three channels combined. These limits assume that the superpartners of the left- and right-handed leptons are degenerate in mass and $\mathcal{B}(\tilde{\ell} \to \ell\tilde{G})$ is 100%. The area to the left of the black curve represents the observed exclusion region, and the dashed red lines indicate the expected limits and their 68% confidence intervals.

The observed 95% CL upper limits on the long-lived slepton production cross section, in the $c\tau_0$ -- mass plane. The co-NLSP limits are shown for the three channels combined. These limits assume that the superpartners of the left- and right-handed leptons are degenerate in mass and $\mathcal{B}(\tilde{\ell} \to \ell\tilde{G})$ is 100%. The area to the left of the black curve represents the observed exclusion region, and the dashed red lines indicate the expected limits and their 68% confidence intervals.

The 95% CL upper limits on the $\mathrm{H} \to \mathrm{S}\mathrm{S}, \mathrm{S} \to \ell^{+}\ell^{-}$ branching fraction as a function of $c\tau_0$, for a Higgs boson with a mass of 125 GeV and a long-lived scalar with a mass of 30 GeV or 50 GeV, for the three channels combined. These limits assume that $\mathcal{B}(H \to SS)=100\%$ and each S has a 50% probability of decaying to two electrons or two muons. The area above the solid (dashed) curve represents the observed (expected) exclusion region.

The 95% CL upper limits on the product of the cross section and branching fraction $\mathrm{H} \to \mathrm{S}\mathrm{S}, \mathrm{S} \to \ell^{+}\ell^{-}$ as a function of $c\tau_0$, for a 300 GeV Higgs boson and several long-lived scalar masses, for the three channels combined. These limits assume that $\mathcal{B}(H \to SS)=100\%$ and each S has a 50% probability of decaying to two electrons or two muons. The area above the solid (dashed) curves represents the observed (expected) exclusion region.

The 95% CL upper limits on the product of the cross section and branching fraction $\mathrm{H} \to \mathrm{S}\mathrm{S}, \mathrm{S} \to \ell^{+}\ell^{-}$ as a function of $c\tau_0$, for a 400 GeV Higgs boson and several long-lived scalar masses, for the three channels combined. These limits assume that $\mathcal{B}(H \to SS)=100\%$ and each S has a 50% probability of decaying to two electrons or two muons. The area above the solid (dashed) curves represents the observed (expected) exclusion region.

The 95% CL upper limits on the product of the cross section and branching fraction $\mathrm{H} \to \mathrm{S}\mathrm{S}, \mathrm{S} \to \ell^{+}\ell^{-}$ as a function of $c\tau_0$, for a 600 GeV Higgs boson and several long-lived scalar masses, for the three channels combined. These limits assume that $\mathcal{B}(H \to SS)=100\%$ and each S has a 50% probability of decaying to two electrons or two muons. The area above the solid (dashed) curves represents the observed (expected) exclusion region.

The 95% CL upper limits on the product of the cross section and branching fraction $\mathrm{H} \to \mathrm{S}\mathrm{S}, \mathrm{S} \to \ell^{+}\ell^{-}$ as a function of $c\tau_0$, for a 800 GeV Higgs boson and several long-lived scalar masses, for the three channels combined. These limits assume that $\mathcal{B}(H \to SS)=100\%$ and each S has a 50% probability of decaying to two electrons or two muons. The area above the solid (dashed) curves represents the observed (expected) exclusion region.

The 95% CL upper limits on the product of the cross section and branching fraction $\mathrm{H} \to \mathrm{S}\mathrm{S}, \mathrm{S} \to \ell^{+}\ell^{-}$ as a function of $c\tau_0$, for a 1000 GeV Higgs boson and several long-lived scalar masses, for the three channels combined. These limits assume that $\mathcal{B}(H \to SS)=100\%$ and each S has a 50% probability of decaying to two electrons or two muons. The area above the solid (dashed) curves represents the observed (expected) exclusion region.

The 95% CL upper limits on the $\mathrm{H} \to \mathrm{S}\mathrm{S} \to 4\ell$ branching fraction as a function of $c\tau_0$, for a Higgs boson with a mass of 125 GeV and a long-lived scalar with a mass of 30 GeV or 50 GeV, for the ee channel only. These limits assume that $\mathcal{B}(H \to SS)=100\%$ and each S has a 50% probability of decaying to two electrons. The area above the solid (dashed) curve represents the observed (expected) exclusion region. The curves are not smooth because very few ee channel events pass the preselection for the Higgs boson and scalar masses shown in this figure.

The 95% CL upper limits on the product of the cross section and branching fraction $\mathrm{H} \to \mathrm{S}\mathrm{S} \to 4\ell$ as a function of $c\tau_0$, for a 600 GeV Higgs boson and several long-lived scalar masses, for the ee channel only. These limits assume that $\mathcal{B}(H \to SS)=100\%$ and each S has a 50% probability of decaying to two electrons. The area above the solid (dashed) curves represents the observed (expected) exclusion region.

The 95% CL upper limits on the product of the cross section and branching fraction $\mathrm{H} \to \mathrm{S}\mathrm{S} \to 4\ell$ as a function of $c\tau_0$, for a 1000 GeV Higgs boson and several long-lived scalar masses, for the ee channel only. These limits assume that $\mathcal{B}(H \to SS)=100\%$ and each S has a 50% probability of decaying to two electrons. The area above the solid (dashed) curves represents the observed (expected) exclusion region.

The 95% CL upper limits on the $\mathrm{H} \to \mathrm{S}\mathrm{S} \to 4\ell$ branching fraction as a function of $c\tau_0$, for a Higgs boson with a mass of 125 GeV and a long-lived scalar with a mass of 30 GeV or 50 GeV, for the $\mu\mu$ channel only. These limits assume that $\mathcal{B}(H \to SS)=100\%$ and each S has a 50% probability of decaying to two muons. The area above the solid (dashed) curve represents the observed (expected) exclusion region.

The 95% CL upper limits on the product of the cross section and branching fraction $\mathrm{H} \to \mathrm{S}\mathrm{S} \to 4\ell$ as a function of $c\tau_0$, for a 600 GeV Higgs boson and several long-lived scalar masses, for the $\mu\mu$ channel only. These limits assume that $\mathcal{B}(H \to SS)=100\%$ and each S has a 50% probability of decaying to two muons. The area above the solid (dashed) curves represents the observed (expected) exclusion region.

The 95% CL upper limits on the product of the cross section and branching fraction $\mathrm{H} \to \mathrm{S}\mathrm{S} \to 4\ell$ as a function of $c\tau_0$, for a 1000 GeV Higgs boson and several long-lived scalar masses, for the $\mu\mu$ channel only. These limits assume that $\mathcal{B}(H \to SS)=100\%$ and each S has a 50% probability of decaying to two muons. The area above the solid (dashed) curves represents the observed (expected) exclusion region.

Upper limits on $\mathcal{B}(H\rightarrow aa\rightarrow bb\mu\mu)$ at 95% CL including the BDT cut as a function of the signal mass.

Upper limits on $\mathcal{B}(H\rightarrow aa\rightarrow bb\mu\mu)$ at 95% CL without the BDT cut as a function of the signal mass.

The number of events when applying each cut in the analysis for $m_a$ = 16 GeV. The first row shows the approximate total number of events scaled to the theoretical signal cross-section and luminosity of the full Run 2 dataset, assuming $ \mathcal{B}(H\rightarrow aa\rightarrow bb\mu\mu)$ = 0.16%.

The number of events when applying each cut in the analysis for $m_a$ = 20 GeV. The first row shows the approximate total number of events scaled to the theoretical signal cross-section and luminosity of the full Run 2 dataset, assuming $ \mathcal{B}(H\rightarrow aa\rightarrow bb\mu\mu)$ = 0.16%.

The number of events when applying each cut in the analysis for $m_a$ = 30 GeV. The first row shows the approximate total number of events scaled to the theoretical signal cross-section and luminosity of the full Run 2 dataset, assuming $ \mathcal{B}(H\rightarrow aa\rightarrow bb\mu\mu)$ = 0.16%.

The number of events when applying each cut in the analysis for $m_a$ = 40 GeV. The first row shows the approximate total number of events scaled to the theoretical signal cross-section and luminosity of the full Run 2 dataset, assuming $ \mathcal{B}(H\rightarrow aa\rightarrow bb\mu\mu)$ = 0.16%.

The number of events when applying each cut in the analysis for $m_a$ = 50 GeV. The first row shows the approximate total number of events scaled to the theoretical signal cross-section and luminosity of the full Run 2 dataset, assuming $ \mathcal{B}(H\rightarrow aa\rightarrow bb\mu\mu)$ = 0.16%.

The number of events when applying each cut in the analysis for $m_a$ = 60 GeV. The first row shows the approximate total number of events scaled to the theoretical signal cross-section and luminosity of the full Run 2 dataset, assuming $ \mathcal{B}(H\rightarrow aa\rightarrow bb\mu\mu)$ = 0.16%.

Data/MC ratio as a function of reconstructed $\pi^0$ momentum for the 2$\gamma$0p selection

Energy spectra for the 1$\gamma$1p selected events. The figure shows the unconstrained background prediction and breakdowns as a function of reconstructed shower energy.

Energy spectra for the 1$\gamma$1p selected events. This figure shows the total background prediction with systematic uncertainty both before and after the 2$\gamma$ constraint.

Energy spectra for the 1$\gamma$0p selected events. The figure shows the unconstrained background prediction and breakdowns as a function of reconstructed shower energy.

Energy spectra for the 1$\gamma$0p selected events. This figure shows the total background prediction with systematic uncertainty both before and after the 2$\gamma$ constraint.

The observed event rate for the 1$\gamma$1p event sample, and comparisons to unconstrained (left) and constrained (right) background and LEE model predictions.

The observed event rate for the 1$\gamma$0p event sample, and comparisons to unconstrained (left) and constrained (right) background and LEE model predictions.

The fractional systematic covariance matrix for the final selected 1$\gamma$1p, 1$\gamma$0p, 2$\gamma$1p, and 2$\gamma$0p event samples, in bins of reconstructed shower energy for the 1$\gamma$ distributions, and reconstructed $\pi^{0}$ momentum for the 2$\gamma$ distributions. The bin boundaries are defined in Sec. II in supplementary material. This covariance matrix is evaluated at central value prediction and all variances have been rounded to three significant digits.

The fractional systematic covariance matrix for the final selected 1$\gamma$1p, 1$\gamma$0p, 2$\gamma$1p, and 2$\gamma$0p event samples, in bins of reconstructed shower energy for the 1$\gamma$1p signal, 1$\gamma$1p background, 1$\gamma$0p signal and 1$\gamma$0p background distributions, and reconstructed $\pi^{0}$ momentum for the 2$\gamma$ distributions. The bin boundaries are defined in Sec. II in supplementary material. This covariance matrix is evaluated at central value prediction and variances have been rounded to three significant digits.

Post-fit event yields in the signal and control regions obtained from a scan over $\epsilon_{VV}$ exploiting both shape and rate information. The quoted uncertainties include the theoretical and experimental systematic sources and those due to sample statistics. The fit constrains the total expected yield to the observed yield. The diboson background is split into $W W$ and non-$W W$ contributions.

Best-fit values and their uncertainties as obtained from the shape-only and shape-plus-rate likelihood fits to the Asimov dataset and to ATLAS data. Results of both shape-only and shape+rate fits for $a_L$ and $a_T$ are shown. Results of fits to one parameter with the other one fixed or profiled are presented.

Best-fit values and their uncertainties as obtained from the shape-only and shape-plus-rate likelihood fits to the Asimov dataset and to ATLAS data. Results of both shape-only and shape+rate fits for $\epsilon_{VV}$ and $\kappa_{VV}$ are shown. Results of fits to one parameter with the other one fixed or profiled are presented.

The contributions of the leading individual systematic uncertainties together with the data statistical uncertainties, in the one dimensional fit for the pseudo-observables $\kappa_{VV}$ (a) and $\epsilon_{VV}$ (b) for electroweak-boson polarisation in the VBF $H\to WW$ channel. Both shape and rate informations are exploited in the fit. The theoretical and experimental uncertainties are subdivided further into categories.

The contributions of the leading individual systematic uncertainties together with the data statistical uncertainties, in the one dimensional fit for the pseudo-observables $\kappa_{VV}$ (a) and $\epsilon_{VV}$ (b) for electroweak-boson polarisation in the VBF $H\to WW$ channel. Both shape and rate informations are exploited in the fit. The theoretical and experimental uncertainties are subdivided further into categories.

Post-fit distribution of the BDT response observable presented in the four $|\Delta \eta jj|$ categories of the ggF +2 jets signal region, with signal and background yields fixed from the fit for $\mu^{\text{ggF+2jets}}$. The distributions of the ggF + 2 jets and VBF processes are overlaid with their respective contributions multiplied by 50.

The weighted $\Delta \Phi_{jj}$ post-fit distribution in the ggF +2 jets signal region, with signal and background yields fixed from the fit to $\tan \alpha$ using shape and rate information.

Expected and observed likelihood curves for scans over $\tan \alpha$ where only the shape is taken into account in the fit, $\mu_{VBF}$ is fixed.

Expected and observed likelihood curves for scans over $\tan \alpha$ where both shape and normalisation are taken into account in the fit, $\mu_{VBF}$ is fixed.

68% and 95% CL two-dimensional likelihood contours of the CP-even and CP-odd coupling parameters $K_{gg} \cos(\alpha)$ and $K_{gg} \sin(\alpha)$. The minima are represented by black stars, while the SM value is shown as a red star.

The weighted $\Delta \Phi jj$ distribution in the VBF signal region, with signal and background yields fixed from the fit for $\epsilon_{VV}$ using shape and rate information.

Likelihood scans over the transversally polarised couplings. The fit is using shape-only information. All relevant experimental and modelling systematic uncertainties are considered in the fit.

Likelihood scans over the transversally polarised couplings. The fit is using shape + rate information. All relevant experimental and modelling systematic uncertainties are considered in the fit.

Likelihood scans over the longitudinally polarised couplings. The fit is using shape + rate information. All relevant experimental and modelling systematic uncertainties are considered in the fit.

Likelihood scans over $\kappa_{VV}$ with the $\epsilon_{VV}$ profiled. The fit is performed using both shape and rate information. All relevant experimental and theoretical systematic uncertainties are considered in the fit.

Likelihood scans over $\epsilon_{VV}$ with the $\kappa_{VV}$ profiled. The fit is performed using both shape and rate information. All relevant experimental and theoretical systematic uncertainties are considered in the fit.

The contributions of the leading individual systematic uncertainties together with the data statistical uncertainties, in the one dimensional fit for electroweak-boson polarisation in the VBF $H\to WW$ channel, using (aL, aT) parametrisation. Both shape and rate informations are exploited in the fit. The theoretical and experimental uncertainties are subdivided further into categories.

The contributions of the leading individual systematic uncertainties together with the data statistical uncertainties, in the one dimensional fit for electroweak-boson polarisation in the VBF $H\to WW$ channel, using (aL, aT) parametrisation.. Both shape and rate informations are exploited in the fit. The theoretical and experimental uncertainties are subdivided further into categories.

Comparison of the pT spectrum for the fourth-leading from data to different PYTHIA8 (P8),HERWIG++ (H++),and HERWIG7 (H7) tunes.

Comparison of the eta spectrum for the leading jet from data to different PYTHIA8 (P8),HERWIG++ (H++),and HERWIG7 (H7) tunes.

Comparison of the eta spectrum for the sub-leading from data to different PYTHIA8 (P8),HERWIG++ (H++),and HERWIG7 (H7) tunes.

Comparison of the eta spectrum for the third-leading from data to different PYTHIA8 (P8),HERWIG++ (H++),and HERWIG7 (H7) tunes.

Comparison of the eta spectrum for the fourth-leading from data to different PYTHIA8 (P8),HERWIG++ (H++),and HERWIG7 (H7) tunes.

Comparison of the DeltaPhiSoft distribution from data to different PYTHIA8 (P8),HERWIG++ (H++), and HERWIG7 (H7) tunes. All distributions have been normalized to regions where a reduced DPS contribution is expected.

Comparison of the DeltaPhiMin distribution from data to different PYTHIA8 (P8),HERWIG++ (H++), and HERWIG7 (H7) tunes. All distributions have been normalized to regions where a reduced DPS contribution is expected.

Comparison of the DeltaY distribution from data to different PYTHIA8 (P8),HERWIG++ (H++), and HERWIG7 (H7) tunes. All distributions have been normalized to regions where a reduced DPS contribution is expected.

Comparison of the phi_ij distribution from data to different PYTHIA8 (P8),HERWIG++ (H++), and HERWIG7 (H7) tunes. All distributions have been normalized to regions where a reduced DPS contribution is expected.

Comparison of the Deltap_{T,Soft} distribution from data to different PYTHIA 8 (P8), HERWIG ++ (H++), and HERWIG 7 (H7) tunes. All distributions have been normalized to regions where a reduced DPS contribution is expected.

Comparison of the DeltaS distribution from data to different PYTHIA 8 (P8), HERWIG ++ (H++), and HERWIG 7 (H7) tunes. All distributions have been normalized to regions where a reduced DPS contribution is expected.

Comparison of the pT spectrum for the leading jet from data with different KATIE(KT), MADGRAPH5aMC@NLO(MG5), and POWHEG(PW) models

Comparison of the pT spectrum for the sub-leading from data with different KATIE(KT), MADGRAPH5aMC@NLO(MG5), and POWHEG(PW) models

Comparison of the pT spectrum for the third-leading from data to different PYTHIA8 (P8),HERWIG++ (H++),and HERWIG7 (H7) tunes.

Comparison of the pT spectrum for the fourth-leading from data with different KATIE(KT), MADGRAPH5aMC@NLO(MG5), and POWHEG(PW) models

Comparison of the eta spectrum for the leading jet from data with different KATIE(KT), MADGRAPH5aMC@NLO(MG5), and POWHEG(PW) models

Comparison of the eta spectrum for the sub-leading from data with different KATIE(KT), MADGRAPH5aMC@NLO(MG5), and POWHEG(PW) models

Comparison of the eta spectrum for the third-leading from data with different KATIE(KT), MADGRAPH5aMC@NLO(MG5), and POWHEG(PW) models

Comparison of the eta spectrum for the fourth-leading from data with different KATIE(KT), MADGRAPH5aMC@NLO(MG5), and POWHEG(PW) models

Comparison of the DeltaPhiSoft distribution from data to differentKATIE(KT), MADGRAPH5aMC@NLO(MG5), andPOWHEG(PW) implementations. All distributions have been normalized to regions where a reduced DPS sensitivity is expected.

Comparison of the DeltaPhiMin, distribution from data to differentKATIE(KT), MADGRAPH5aMC@NLO(MG5), andPOWHEG(PW) implementations. All distributions have been normalized to regions where a reduced DPS sensitivity is expected.

Comparison of the DeltaY and distribution from data to differentKATIE(KT), MADGRAPH5aMC@NLO(MG5), andPOWHEG(PW) implementations. All distributions have been normalized to regions where a reduced DPS sensitivity is expected.

Comparison of the phi_ij distribution from data to differentKATIE(KT), MADGRAPH5aMC@NLO(MG5), andPOWHEG(PW) implementations. All distributions have been normalized to regions where a reduced DPS sensitivity is expected.

Comparison of the Deltap_{T,Soft} distribution from data to different KATIE(KT),MADGRAPH5aMC@NLO(MG5), andPOWHEG(PW) implementations. All distributions havebeen normalized to regions where a reduced DPS sensitivity is expected.

Comparison of the DeltaS distribution from data to different KATIE(KT),MADGRAPH5aMC@NLO(MG5), andPOWHEG(PW) implementations. All distributions havebeen normalized to regions where a reduced DPS sensitivity is expected.

Comparison of the pT spectrum for the leading jet from data with different SPS+DPS KATIE( KT) and PYTHIA8 (P8) models.

Comparison of the pT spectrum for the sub-leading from data with different SPS+DPS KATIE( KT) and PYTHIA8 (P8) models.

Comparison of the pT spectrum for the third-leading from data with different SPS+DPS KATIE( KT) and PYTHIA8 (P8) models.

Comparison of the pT spectrum for the fourth-leading from data with different SPS+DPS KATIE( KT) and PYTHIA8 (P8) models.

Comparison of the eta spectrum for the leading jet from data with different SPS+DPS KATIE( KT) and PYTHIA8 (P8) models.

Comparison of the eta spectrum for the sub-leading from data with different SPS+DPS KATIE( KT) and PYTHIA8 (P8) models.

Comparison of the eta spectrum for the third-leading from data with different SPS+DPS KATIE( KT) and PYTHIA8 (P8) models.

Comparison of the eta spectrum for the fourth-leading from data with different SPS+DPS KATIE( KT) and PYTHIA8 (P8) models.

Comparison of the DeltaPhiSoft distribution from data to different SPS+DPS KATIE (KT) and PYTHIA 8 (P8) models. All distributions have been normalized to regions where a reduced DPS sensitivity is expected.

Comparison of the DeltaPhiMin distribution from data to different SPS+DPS KATIE (KT) and PYTHIA 8 (P8) models. All distributions have been normalized to regions where a reduced DPS sensitivity is expected.

Comparison of the DeltaY distribution from data to different SPS+DPS KATIE (KT) and PYTHIA 8 (P8) models. All distributions have been normalized to regions where a reduced DPS sensitivity is expected.

Comparison of the phi_ij distribution from data to different SPS+DPS KATIE (KT) and PYTHIA 8 (P8) models. All distributions have been normalized to regions where a reduced DPS sensitivity is expected.

Comparison of the Deltap_{T,Soft} distributions from data to different SPS+DPS KATIE (KT) and PYTHIA 8 (P8) models. All distributions havebeen normalized to regions where a reduced DPS sensitivity is expected.

Comparison of the DeltaS distributions from data to different SPS+DPS KATIE (KT) and PYTHIA 8 (P8) models. All distributions have been normalized to regions where a reduced DPS contribution is expected.

The DeltaS distribution obtained from the mixed data sample compared to predictions from the pure DPS sample in PYTHIA 8 (P8) and KATIE (KT). The distributions are normalized to unity.

The results of the template fit for the POWHEG (PW) NLO 2 -> 2 model without the hard MPI removed. As the DeltaS distribution obtained from the mixed data sample carries a statistical and systematic uncertainty, so does the total fitted sample.

Comparison of the DeltaPhiSoft distribution from data to different PYTHIA8 (P8),HERWIG++ (H++), and HERWIG7 (H7) tunes.

Comparison of the DeltaPhiMin distribution from data to different PYTHIA8 (P8),HERWIG++ (H++), and HERWIG7 (H7) tunes.

Comparison of the DeltaY distribution from data to different PYTHIA8 (P8),HERWIG++ (H++), and HERWIG7 (H7) tunes.

Comparison of the phi_ij distribution from data to different PYTHIA8 (P8),HERWIG++ (H++), and HERWIG7 (H7) tunes.

Comparison of the Deltap_{T,Soft} distribution from data to different PYTHIA 8 (P8), HERWIG ++ (H++), and HERWIG 7 (H7) tunes.

Comparison of the DeltaS distribution from data to different PYTHIA 8 (P8), HERWIG ++ (H++), and HERWIG 7 (H7) tunes.

Comparison of the DeltaPhiSoft distribution from data to different KATIE(KT),MADGRAPH5aMC@NLO(MG5), andPOWHEG(PW) implementations.

Comparison of the DeltaPhiMin distribution from data to different KATIE(KT),MADGRAPH5aMC@NLO(MG5), andPOWHEG(PW) implementations.

Comparison of the DeltaY distribution from data to different KATIE(KT),MADGRAPH5aMC@NLO(MG5), andPOWHEG(PW) implementations.

Comparison of the phi_ij distribution from data to different KATIE(KT),MADGRAPH5aMC@NLO(MG5), andPOWHEG(PW) implementations.

Comparison of the Deltap_{T,Soft} distribution from data to different KATIE(KT),MADGRAPH5aMC@NLO(MG5), andPOWHEG(PW) implementations.

Comparison of the DeltaS distribution from data to different KATIE(KT),MADGRAPH5aMC@NLO(MG5), andPOWHEG(PW) implementations.

Comparison of the DeltaPhiSoft distribution from data to different SPS+DPS KATIE (KT) and PYTHIA 8 (P8) models.

Comparison of the DeltaPhiMin distribution from data to different SPS+DPS KATIE (KT) and PYTHIA 8 (P8) models.

Comparison of the DeltaY distribution from data to different SPS+DPS KATIE (KT) and PYTHIA 8 (P8) models.

Comparison of the phi_ij distribution from data to different SPS+DPS KATIE (KT) and PYTHIA 8 (P8) models.

Comparison of the Deltap_{T,Soft} distribution from data to different SPS+DPS KATIE (KT) and PYTHIA 8 (P8) models.

Comparison of the DeltaS distributions from data to different SPS+DPS KATIE (KT) and PYTHIA 8 (P8) models.

(a) The HFE (electrons from semileptonic decays of heavy-flavor hadrons) cross section at STAR in $p$+$p$ collisions at $\sqrt{s}=200$ GeV from $2012$ (filled circles) and the FONLL calculations (curves). (b) Ratio of data over FONLL calculations. The vertical bars and the boxes represent statistical and systematic uncertainties, respectively.