Lower limits at 95$\%$ CL on $\Lambda$ for the dimuon channel for different signal chiralities in the (constructive/destructive interference) SRs of the analysis.

Lower limits at 95$\%$ CL on $\Lambda$ for the dilepton combination for different signal chiralities in the (constructive/destructive interference) SRs of the analysis.

The dielectron data events passing the full selection.

The dimuon data events passing the full selection.

Distribution of the NN output in the $\geq$1fj$\,$SR in data and the expected contribution of the signal and background processes after the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions considering the correlations of the uncertainties as obtained by the fit.

Distribution of the NN output in the $t\bar{t}\gamma\,$CR in data and the expected contribution of the signal and background processes after the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions considering the correlations of the uncertainties as obtained by the fit.

Total event yield in the $W\gamma\,$CR in data and the expected contribution of the signal and background processes after the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions considering the correlations of the uncertainties as obtained by the fit.

Distribution of the scalar sum of the jet transverse momenta in the 0fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions. The first and last bins include the underflow and overflow, respectively.

Distribution of the $\eta$ of the $b$-tagged jet in the 0fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions.

Distribution of the reconstructed top-quark mass in the 0fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions. The first and last bins include the underflow and overflow, respectively.

Distribution of the $p_{\mathrm{T}}$ of the top-quark+photon system in the 0fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions and the last bin includes the overflow.

Distribution of the photon $p_{\mathrm{T}}$ in the 0fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions and the last bin includes the overflow.

Distribution of the photon $\eta$ in the 0fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions.

Distribution of the scalar sum of the jet transverse momenta in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions and the last bin includes the overflow.

Distribution of the invariant mass of the $b$-tagged jet and the highest-$p_{\mathrm{T}}$ forward jet in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions and the last bin includes the overflow.

Distribution of $p_{\mathrm{T}}$ of the highest-$p_{\mathrm{T}}$ forward jet in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions and the last bin includes the overflow.

Distribution of the difference in $\eta$ between the highest-$p_{\mathrm{T}}$ forward jet and the photon in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions and the last bin includes the overflow.

Distribution of the energy of the system formed by the highest-$p_{\mathrm{T}}$ forward jet and the photon in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions. The first and last bins include the underflow and overflow, respectively.

Distribution of the $\eta$ of the $b$-tagged jet in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions.

Distribution of the reconstructed top-quark mass in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions. The first and last bins include the underflow and overflow, respectively.

Distribution of the $p_{\mathrm{T}}$ of the top-quark and photon system in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions and the last bin includes the overflow.

Distribution of the photon $p_{\mathrm{T}}$ in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions and the last bin includes the overflow.

Distribution of the photon $\eta$ in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions.

Ordered list of the 30 systematic uncertainties with the largest impact on the measured signal normalisation in the fit to data in the parton-level measurement considered as nuisance parameters (NPs) in the profile-likelihood fit. The column "NP value, error" corresponds to the nominal best-fit values and the corresponding uncertainties. The impact of each NP, $\Delta\sigma$/$\sigma_{\mathrm{pred}}$, is computed by comparing the nominal best-fit value of the POI ($\sigma$/$\sigma_{\mathrm{pred}}$) with the result of the fits when fixing the considered NP to its best-fit value shifted by its pre-fit and post-fit uncertainties. The corresponding impacts are listed in the "POI impact prefit high/low" and "POI impact high/low" columns, respectively. The "MC stat." NPs represent the MC statistical uncertainty and they enter the likelihood with a Poisson term, while all the other NPs enter the likelihood via a Gaussian term.

Ordered list of the 30 systematic uncertainties with the largest impact on the measured signal normalisation in the fit to data in the particle-level measurement considered as nuisance parameters (NPs) in the profile-likelihood fit. The column "NP value, error" corresponds to the nominal best-fit values and the corresponding uncertainties. The impact of each NP, $\Delta\sigma$/$\sigma_{\mathrm{pred}}$, is computed by comparing the nominal best-fit value of the POI ($\sigma$/$\sigma_{\mathrm{pred}}$) with the result of the fits when fixing the considered NP to its best-fit value shifted by its pre-fit and post-fit uncertainties. The corresponding impacts are listed in the "POI impact prefit high/low" and "POI impact high/low" columns, respectively. The "MC stat." NPs represent the MC statistical uncertainty and they enter the likelihood with a Poisson term, while all the other NPs enter the likelihood via a Gaussian term.

This table lists the kinematic requirements on parton-level objects used to define of the fiducial phase space for the parton-level measurement. Frixione isolation ($\href{https://arxiv.org/abs/hep-ph/9801442}{\text{hep-ph/9801442}}$) with a chosen radius of $\Delta R = 0.2$ is applied to photons ($\gamma$). The measured fiducial parton-level cross section is $\sigma_{tq\gamma}\times\mathcal{B}(t\rightarrow l\nu b) = 688\pm 23(\text{stat.})^{+75}_{-71}(\text{syst.})\,$fb.

This table lists the kinematic requirements on particle-level objects used to define of the fiducial phase space for the particle-level measurement. The particle level objects are photons ($\gamma$) not from a hadron decay, neutrinos not from a hadron decay ($\nu$), prompt electrons and muons ($\ell$) "dressed" by adding close-by ($\Delta R < 0.1$) photons, and anti-$k_t$ $R = 0.4$ jets built from stable particles ($\tau > 30\,$ps) and tau leptons excluding neutrinos and prompt dressed muons. Jets are $b$-tagged ($b$-jet) using ghost-matched $b$-hadrons with $p_{\text{T}} > 5\,$GeV. Apart from the kinematic requirements, isolation and overlap removal criteria are applied. Jets within $\Delta R = 0.4$ of a photon are removed if the $p_{\text{T}}$ of charged particles within $\Delta R = 0.3$ of the photon is smaller than $10\,\%$ of its $p_{\text{T}}$. Jets within $\Delta R = 0.4$ of a lepton are removed. Events are removed where a photon is close ($\Delta R < 0.4$) to a lepton or a surviving jet. The measured fiducial particle-level cross section is $\sigma_{tq\gamma}\times\mathcal{B}(t\rightarrow l\nu b)+\sigma_{t(\rightarrow l\nu b\gamma)q} = 303\pm 9(\text{stat.})^{+33}_{-32}(\text{syst.})\,$fb.

Number of data events for the 2-tag category with the loose selection in bins of diphoton mass.

Number of data events for the 1-tag category with the tight selection in bins of diphoton mass.

Number of data events for the 2-tag category with the tight selection in bins of diphoton mass.

Number of data events for the 1-tag category with the loose selection in bins of four-body mass.

Number of data events for the 2-tag category with the loose selection in bins of four-body mass.

Number of data events for the 1-tag category with the tight selection in bins of four-body mass.

Number of data events for the 2-tag category with the tight selection in bins of four-body mass.

Expected and observed upper limits at the 95% CL on the cross-section of gluon-fusion initiated Higgs boson pair production as a function of $\kappa_{\lambda}$.

Expected and observed upper limits at the 95% CL on the cross-section of gluon-fusion initiated resonant production of a Higgs boson pair as a function of the mass of the resonance, $m_X$.

Observed and expected limits on $\tan\beta$ as a function of $m_{H^+}$ in the $M_h^{125}(\tilde{\chi})$ scenario. Limits are shown for $\tan\beta$ values in the range of 0.5-60 due to the availability of the model prediction. The bands surrounding the expected limits show the 68% and 95% confidence intervals. Uncertainties in the predicted $H^+$ cross-sections or branching ratios are not considered.

Observed and expected limits on $\tan\beta$ as a function of $m_{H^+}$ in the $M_h^{125}(\tilde{\tau})$ scenario. Limits are shown for $\tan\beta$ values in the range of 0.5-60 due to the availability of the model prediction. The bands surrounding the expected limits show the 68% and 95% confidence intervals. Uncertainties in the predicted $H^+$ cross-sections or branching ratios are not considered.

Observed and expected limits on $\tan\beta$ as a function of $m_{H^+}$ in the $M_h^{125}$(alignment) scenario. Limits are shown for $\tan\beta$ values in the range of 0.5-60 due to the availability of the model prediction. The bands surrounding the expected limits show the 68% and 95% confidence intervals. Uncertainties in the predicted $H^+$ cross-sections or branching ratios are not considered.

Observed and expected limits on $\tan\beta$ as a function of $m_{H^+}$ in the $M_{h_1}^{125}$(CPV) scenario. Limits are shown for $\tan\beta$ values in the range of 0.5-60 due to the availability of the model prediction. The bands surrounding the expected limits show the 68% and 95% confidence intervals. Uncertainties in the predicted $H^+$ cross-sections or branching ratios are not considered.

Event yields of the SM background processes and the 800 GeV $H^{+}$ sample in the four analysis regions before the fit to the data. Uncertainties include both statistical and systematic uncertainties. The yields of the $H^{+}$ signal sample correspond to a cross-section times branching fraction of 10 pb.

Event acceptance for the different $H^+$ mass signal samples.

Transverse profile for 70 GeV < pT < 100 GeV.

Longitudinal profile for pT > 100 GeV.

Transverse profile for pT > 100 GeV.

Average longitudinal profile

Transverse profile for pT > 100 GeV.

Total efficiencies for the selection of signal events after categorization and application of the tighter photon $E_{\mathrm{T}}^{\gamma}$ selection used to optimize the signal significance spin-1 $q\bar{q'}\to X^{\pm} \to W^{\pm}\gamma$. In addition to the total efficiency, contributions to the signal selection from each of the separate event categories are shown. The efficiencies calculated from MC samples with $W/Z$ hadronic decays are shown as the points on each curve. The line presents interpolated results.

Total efficiencies for the selection of signal events after categorization and application of the tighter photon $E_{\mathrm{T}}^{\gamma}$ selection used to optimize the signal significance spin-2 $q\bar{q}\to X^0 \to Z\gamma$. In addition to the total efficiency, contributions to the signal selection from each of the separate event categories are shown. The efficiencies calculated from MC samples with $W/Z$ hadronic decays are shown as the points on each curve. The line presents interpolated results.

Total efficiencies for the selection of signal events after categorization and application of the tighter photon $E_{\mathrm{T}}^{\gamma}$ selection used to optimize the signal significance spin-2 $gg\to X^0 \to Z\gamma$. In addition to the total efficiency, contributions to the signal selection from each of the separate event categories are shown. The efficiencies calculated from MC samples with $W/Z$ hadronic decays are shown as the points on each curve. The line presents interpolated results.

The $m_{J\gamma}$ distributions of data events selected for the spin-1 $q\bar{q'}\to X^{\pm} \to W^{\pm}\gamma$ search in the D2 category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-1 $q\bar{q'}\to X^{\pm} \to W^{\pm}\gamma$ search in the WMASS category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-0 $gg \to X^{0} \to Z\gamma$ search in the BTAG category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-0 $gg \to X^{0} \to Z\gamma$ search in the D2 category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-0 $gg \to X^{0} \to Z\gamma$ search in the ZMASS category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-2 $gg \to X^{0} \to Z\gamma$ search in the BTAG category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-2 $gg \to X^{0} \to Z\gamma$ search in the D2 category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-2 $gg \to X^{0} \to Z\gamma$ search in the ZMASS category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-2 $q\bar{q} \to X^{0} \to Z\gamma$ search in the BTAG category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-2 $q\bar{q} \to X^{0} \to Z\gamma$ search in the D2 category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-2 $q\bar{q} \to X^{0} \to Z\gamma$ search in the ZMASS category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The 95% CL upper limits on $\sigma(pp\to X)\times B(X\to W/Z\gamma)$ as a function of $m_{X}$ for spin-0 $gg \to X^{0} \to Z\gamma$. The observed limits are shown as a solid black line and the expected ones are shown as a dashed line with the 1$\sigma$ (2$\sigma$) uncertainty band presented as the green (yellow) band.

The 95% CL upper limits on $\sigma(pp\to X)\times B(X\to W/Z\gamma)$ as a function of $m_{X}$ for spin-2 $gg \to X^{0} \to Z\gamma$. The observed limits are shown as a solid black line and the expected ones are shown as a dashed line with the 1$\sigma$ (2$\sigma$) uncertainty band presented as the green (yellow) band.

The 95% CL upper limits on $\sigma(pp\to X)\times B(X\to W/Z\gamma)$ as a function of $m_{X}$ for spin-2 $q\bar{q} \to X^{0} \to Z\gamma$. The observed limits are shown as a solid black line and the expected ones are shown as a dashed line with the 1$\sigma$ (2$\sigma$) uncertainty band presented as the green (yellow) band.

The 95% CL upper limits on $\sigma(pp\to X)\times B(X\to W/Z\gamma)$ as a function of $m_{X}$ for spin-1 $q\bar{q'}\to X^{\pm} \to W^{\pm}\gamma$. The observed limits are shown as a solid black line and the expected ones are shown as a dashed line with the 1$\sigma$ (2$\sigma$) uncertainty band presented as the green (yellow) band.

The jet mass distribution of large-$R$ jets originating from the hadronic decay of $W$ and $Z$ bosons produced from the decay of BSM bosons with mass $m_X = 2000$ GeV. The decays simulated are for the production models $q\bar{q'}\to X^{\pm} \to W^{\pm}\gamma$ with a spin-1 resonance $X^{\pm}$ and $gg\to X^0 \to Z\gamma$ with a spin-0 resonance $X^{0}$.

The photon $E_{T}$ selection criteria as a function of resonance mass for D2 categories. Selections for four different signal channels are shown together.

The photon $E_{T}$ selection criteria as a function of resonance mass for ZMASS or WMASS categories. Selections for four different signal channels are shown together.

Upper limits on $\mathcal{B}(H\rightarrow aa\rightarrow 4\gamma)$ at 95% CL as a function of the axion mass and for ALP-photon coupling $C_{a\gamma\gamma}=0.01$.

Upper limits on $\mathcal{B}(H\rightarrow aa\rightarrow 4\gamma)$ at 95% CL as a function of the axion mass and for ALP-photon coupling $C_{a\gamma\gamma}=5\times10^{-4}$

Upper limits on $\mathcal{B}(H\rightarrow aa\rightarrow 4\gamma)$ at 95% CL as a function of the axion mass and for ALP-photon coupling $C_{a\gamma\gamma}=10^{-5}$

Upper limits on $B(H\rightarrow 4\gamma)$ at 95% CL as a function of the signal mass hypothesis and for the assumption of promptly decaying ALPs.

Identification efficiency for isolated photons that pass the tight photon ID requirements in dependence of the opening angle in $\Delta R$ of both decay photons of the axion and the decay radius of the originating axion from the primary vertex for axions with masses between 100 MeV and 300 MeV. All four axion decay photons on MC truth level are required to fulfil $|\eta|<2.5$ and $p_T>5$ GeV. Only a mild dependency on the decay radius can be seen, since the distance between the two photons is small and hence the combined decay signature in the calorimeter still points to the primary vertex.

Efficiency for classified merged isolated photons in dependence of the opening angle in $\Delta R$ of both decay photons of the axion and the decay radius of the originating axion from the primary vertex for axions with masses between 100 MeV and 300 MeV. All four axion decay photons on MC truth level are required to fulfil $|\eta|<2.5$ and $p_T>5$ GeV. Only a mild dependency on the decay radius can be seen, since the distance between the two photons is small and hence the combined decay signature in the calorimeter still points to the primary vertex.

Limits on the ALP mass and coupling to photons at 95\%~CL, assuming $\mathcal{B}(a\rightarrow\gamma\gamma) = 1$, $\Lambda = 1\,TeV$ with $|C_{aH}^{\text{eff}}|$ = $1$ (solid line) and $|C_{aH}^{\text{eff}}|$ = $0.1$.

The number of data and estimated background events in the signal region of the most sensitive categories..

A comparison of the measured cell $E_T^{miss}$ distribution with that predicted by the two-component model for two pile-up scenarios. The magenta points extend the measured distribution using L1 $E_T^{miss} > 30\,$GeV and L1 $E_T^{miss} > 50\,$GeV data. The red curve is the prediction from the calorimeter-resolution part of the model. The green curve is the high $E_T^{miss}$ tail's probability distribution for the mean number of $pp$ interactions $\mu$ in each figure. The blue curve is the full model prediction computed by combining the $E_T^{miss}$ from these two individual sources shown in red and green, each calculated for $\mu=\langle\mu\rangle$. The black points show the unbiased $E_T^{miss}$ distribution measured in data. Corresponds to a prediction for $\langle\mu\rangle = 25$.

A comparison of the measured cell $E_T^{miss}$ distribution with that predicted by the two-component model for two pile-up scenarios. The magenta points extend the measured distribution using L1 $E_T^{miss} > 30\,$GeV and L1 $E_T^{miss} > 50\,$GeV data. The red curve is the prediction from the calorimeter-resolution part of the model. The green curve is the high $E_T^{miss}$ tail's probability distribution for the mean number of $pp$ interactions $\mu$ in each figure. The blue curve is the full model prediction computed by combining the $E_T^{miss}$ from these two individual sources shown in red and green, each calculated for $\mu=\langle\mu\rangle$. The black points show the unbiased $E_T^{miss}$ distribution measured in data. Corresponds to a prediction for $\langle\mu\rangle = 25$.

A comparison of the measured cell $E_T^{miss}$ distribution with that predicted by the two-component model for two pile-up scenarios. The magenta points extend the measured distribution using L1 $E_T^{miss} > 30\,$GeV and L1 $E_T^{miss} > 50\,$GeV data. The red curve is the prediction from the calorimeter-resolution part of the model. The green curve is the high $E_T^{miss}$ tail's probability distribution for the mean number of $pp$ interactions $\mu$ in each figure. The blue curve is the full model prediction computed by combining the $E_T^{miss}$ from these two individual sources shown in red and green, each calculated for $\mu=\langle\mu\rangle$. The black points show the unbiased $E_T^{miss}$ distribution measured in data. Corresponds to a prediction for $\langle\mu\rangle = 55$.

A comparison of the measured cell $E_T^{miss}$ distribution with that predicted by the two-component model for two pile-up scenarios. The magenta points extend the measured distribution using L1 $E_T^{miss} > 30\,$GeV and L1 $E_T^{miss} > 50\,$GeV data. The red curve is the prediction from the calorimeter-resolution part of the model. The green curve is the high $E_T^{miss}$ tail's probability distribution for the mean number of $pp$ interactions $\mu$ in each figure. The blue curve is the full model prediction computed by combining the $E_T^{miss}$ from these two individual sources shown in red and green, each calculated for $\mu=\langle\mu\rangle$. The black points show the unbiased $E_T^{miss}$ distribution measured in data. Corresponds to a prediction for $\langle\mu\rangle = 55$.

A comparison of the measured cell $E_T^{miss}$ distribution with that predicted by the two-component model for two pile-up scenarios. The magenta points extend the measured distribution using L1 $E_T^{miss} > 30\,$GeV and L1 $E_T^{miss} > 50\,$GeV data. The red curve is the prediction from the calorimeter-resolution part of the model. The green curve is the high $E_T^{miss}$ tail's probability distribution for the mean number of $pp$ interactions $\mu$ in each figure. The blue curve is the full model prediction computed by combining the $E_T^{miss}$ from these two individual sources shown in red and green, each calculated for $\mu=\langle\mu\rangle$. The black points show the unbiased $E_T^{miss}$ distribution measured in data. Corresponds to a prediction for $\langle\mu\rangle = 55$.

A comparison of the measured cell $E_T^{miss}$ distribution with that predicted by the two-component model for two pile-up scenarios. The magenta points extend the measured distribution using L1 $E_T^{miss} > 30\,$GeV and L1 $E_T^{miss} > 50\,$GeV data. The red curve is the prediction from the calorimeter-resolution part of the model. The green curve is the high $E_T^{miss}$ tail's probability distribution for the mean number of $pp$ interactions $\mu$ in each figure. The blue curve is the full model prediction computed by combining the $E_T^{miss}$ from these two individual sources shown in red and green, each calculated for $\mu=\langle\mu\rangle$. The black points show the unbiased $E_T^{miss}$ distribution measured in data. Corresponds to a prediction for $\langle\mu\rangle = 55$.

A comparison of the measured cell $E_T^{miss}$ distribution with that predicted by the two-component model for two pile-up scenarios. The magenta points extend the measured distribution using L1 $E_T^{miss} > 30\,$GeV and L1 $E_T^{miss} > 50\,$GeV data. The red curve is the prediction from the calorimeter-resolution part of the model. The green curve is the high $E_T^{miss}$ tail's probability distribution for the mean number of $pp$ interactions $\mu$ in each figure. The blue curve is the full model prediction computed by combining the $E_T^{miss}$ from these two individual sources shown in red and green, each calculated for $\mu=\langle\mu\rangle$. The black points show the unbiased $E_T^{miss}$ distribution measured in data. Corresponds to a prediction for $\langle\mu\rangle = 55$.

The L1 $E_T^{miss}$ trigger efficiency, shown as a function of $p_T(\mu\mu)$ in $Z\rightarrow\mu\mu$ events.

The efficiencies in the plot are shown for events satisfying a $Z\rightarrow\mu\mu$ selection and with $p_T(\mu\mu)$ larger than $150\,$GeV vs pile-up for each of the four years of data taking.

Background acceptance vs signal efficiency for each of four individual HLT $E_T^{miss}$ algorithms for a $Z\rightarrow\mu\mu$ selection with $p_T(\mu\mu) > 175\,$GeV for data recorded in the year 2017. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger. $0\leq\langle\mu\rangle < 20$.

Background acceptance vs signal efficiency for each of four individual HLT $E_T^{miss}$ algorithms for a $Z\rightarrow\mu\mu$ selection with $p_T(\mu\mu) > 175\,$GeV for data recorded in the year 2017. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger. $0\leq\langle\mu\rangle < 20$.

Background acceptance vs signal efficiency for each of four individual HLT $E_T^{miss}$ algorithms for a $Z\rightarrow\mu\mu$ selection with $p_T(\mu\mu) > 175\,$GeV for data recorded in the year 2017. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger. $0\leq\langle\mu\rangle < 20$.

Background acceptance vs signal efficiency for each of four individual HLT $E_T^{miss}$ algorithms for a $Z\rightarrow\mu\mu$ selection with $p_T(\mu\mu) > 175\,$GeV for data recorded in the year 2017. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger. $0\leq\langle\mu\rangle < 20$.

Background acceptance vs signal efficiency for each of four individual HLT $E_T^{miss}$ algorithms for a $Z\rightarrow\mu\mu$ selection with $p_T(\mu\mu) > 175\,$GeV for data recorded in the year 2017. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger. $0\leq\langle\mu\rangle < 20$.

Background acceptance vs signal efficiency for each of four individual HLT $E_T^{miss}$ algorithms for a $Z\rightarrow\mu\mu$ selection with $p_T(\mu\mu) > 175\,$GeV for data recorded in the year 2017. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger. $20\leq\langle\mu\rangle < 30$.

Background acceptance vs signal efficiency for each of four individual HLT $E_T^{miss}$ algorithms for a $Z\rightarrow\mu\mu$ selection with $p_T(\mu\mu) > 175\,$GeV for data recorded in the year 2017. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger. $20\leq\langle\mu\rangle < 30$.

Background acceptance vs signal efficiency for each of four individual HLT $E_T^{miss}$ algorithms for a $Z\rightarrow\mu\mu$ selection with $p_T(\mu\mu) > 175\,$GeV for data recorded in the year 2017. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger. $20\leq\langle\mu\rangle < 30$.

Background acceptance vs signal efficiency for each of four individual HLT $E_T^{miss}$ algorithms for a $Z\rightarrow\mu\mu$ selection with $p_T(\mu\mu) > 175\,$GeV for data recorded in the year 2017. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger. $20\leq\langle\mu\rangle < 30$.

Background acceptance vs signal efficiency for each of four individual HLT $E_T^{miss}$ algorithms for a $Z\rightarrow\mu\mu$ selection with $p_T(\mu\mu) > 175\,$GeV for data recorded in the year 2017. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger. $20\leq\langle\mu\rangle < 30$.

Background acceptance vs signal efficiency for each of four individual HLT $E_T^{miss}$ algorithms for a $Z\rightarrow\mu\mu$ selection with $p_T(\mu\mu) > 175\,$GeV for data recorded in the year 2017. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger. $30\leq\langle\mu\rangle < 40$.

Background acceptance vs signal efficiency for each of four individual HLT $E_T^{miss}$ algorithms for a $Z\rightarrow\mu\mu$ selection with $p_T(\mu\mu) > 175\,$GeV for data recorded in the year 2017. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger. $30\leq\langle\mu\rangle < 40$.

Background acceptance vs signal efficiency for each of four individual HLT $E_T^{miss}$ algorithms for a $Z\rightarrow\mu\mu$ selection with $p_T(\mu\mu) > 175\,$GeV for data recorded in the year 2017. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger. $30\leq\langle\mu\rangle < 40$.

Background acceptance vs signal efficiency for each of four individual HLT $E_T^{miss}$ algorithms for a $Z\rightarrow\mu\mu$ selection with $p_T(\mu\mu) > 175\,$GeV for data recorded in the year 2017. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger. $30\leq\langle\mu\rangle < 40$.

Background acceptance vs signal efficiency for each of four individual HLT $E_T^{miss}$ algorithms for a $Z\rightarrow\mu\mu$ selection with $p_T(\mu\mu) > 175\,$GeV for data recorded in the year 2017. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger. $30\leq\langle\mu\rangle < 40$.

Background acceptance vs signal efficiency for each of four individual HLT $E_T^{miss}$ algorithms for a $Z\rightarrow\mu\mu$ selection with $p_T(\mu\mu) > 175\,$GeV for data recorded in the year 2017. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger. $40\leq\langle\mu\rangle$.

Background acceptance vs signal efficiency for each of four individual HLT $E_T^{miss}$ algorithms for a $Z\rightarrow\mu\mu$ selection with $p_T(\mu\mu) > 175\,$GeV for data recorded in the year 2017. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger. $40\leq\langle\mu\rangle$.

Background acceptance vs signal efficiency for each of four individual HLT $E_T^{miss}$ algorithms for a $Z\rightarrow\mu\mu$ selection with $p_T(\mu\mu) > 175\,$GeV for data recorded in the year 2017. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger. $40\leq\langle\mu\rangle$.

Background acceptance vs signal efficiency for each of four individual HLT $E_T^{miss}$ algorithms for a $Z\rightarrow\mu\mu$ selection with $p_T(\mu\mu) > 175\,$GeV for data recorded in the year 2017. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger. $40\leq\langle\mu\rangle$.

Background acceptance vs signal efficiency for each of four individual HLT $E_T^{miss}$ algorithms for a $Z\rightarrow\mu\mu$ selection with $p_T(\mu\mu) > 175\,$GeV for data recorded in the year 2017. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger. $40\leq\langle\mu\rangle$.

Relative background acceptance fraction vs. relative efficiency for two different $p_T(\mu\mu)>150\,$GeV threshold for data recorded in the year 2018. Two of the curves show the performance of the stand-alone cell algorithm and the stand-alone pufit algorithm. The other two show combined algorithms each formed by requiring that the event satisfy both a fixed threshold (either 65 GeV or 70 GeV as shown in the legend) for the cell algorithm and a pufit threshold which varies along the curve. In each plot the background acceptance fractions and the efficiencies are relative to those of the pufit $E_T^{miss} > 110\,$GeV trigger and thus can be greater than one. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger while the cross indicates the performance of the combined (pufit $E_T^{miss}>110\,$GeV and cell $E_T^{miss}>50\,$GeV) trigger.

Relative background acceptance fraction vs. relative efficiency for two different $p_T(\mu\mu)>150\,$GeV threshold for data recorded in the year 2018. Two of the curves show the performance of the stand-alone cell algorithm and the stand-alone pufit algorithm. The other two show combined algorithms each formed by requiring that the event satisfy both a fixed threshold (either 65 GeV or 70 GeV as shown in the legend) for the cell algorithm and a pufit threshold which varies along the curve. In each plot the background acceptance fractions and the efficiencies are relative to those of the pufit $E_T^{miss} > 110\,$GeV trigger and thus can be greater than one. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger while the cross indicates the performance of the combined (pufit $E_T^{miss}>110\,$GeV and cell $E_T^{miss}>50\,$GeV) trigger.

Relative background acceptance fraction vs. relative efficiency for two different $p_T(\mu\mu)>150\,$GeV threshold for data recorded in the year 2018. Two of the curves show the performance of the stand-alone cell algorithm and the stand-alone pufit algorithm. The other two show combined algorithms each formed by requiring that the event satisfy both a fixed threshold (either 65 GeV or 70 GeV as shown in the legend) for the cell algorithm and a pufit threshold which varies along the curve. In each plot the background acceptance fractions and the efficiencies are relative to those of the pufit $E_T^{miss} > 110\,$GeV trigger and thus can be greater than one. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger while the cross indicates the performance of the combined (pufit $E_T^{miss}>110\,$GeV and cell $E_T^{miss}>50\,$GeV) trigger.

Relative background acceptance fraction vs. relative efficiency for two different $p_T(\mu\mu)>150\,$GeV threshold for data recorded in the year 2018. Two of the curves show the performance of the stand-alone cell algorithm and the stand-alone pufit algorithm. The other two show combined algorithms each formed by requiring that the event satisfy both a fixed threshold (either 65 GeV or 70 GeV as shown in the legend) for the cell algorithm and a pufit threshold which varies along the curve. In each plot the background acceptance fractions and the efficiencies are relative to those of the pufit $E_T^{miss} > 110\,$GeV trigger and thus can be greater than one. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger while the cross indicates the performance of the combined (pufit $E_T^{miss}>110\,$GeV and cell $E_T^{miss}>50\,$GeV) trigger.

Relative background acceptance fraction vs. relative efficiency for two different $p_T(\mu\mu)>150\,$GeV threshold for data recorded in the year 2018. Two of the curves show the performance of the stand-alone cell algorithm and the stand-alone pufit algorithm. The other two show combined algorithms each formed by requiring that the event satisfy both a fixed threshold (either 65 GeV or 70 GeV as shown in the legend) for the cell algorithm and a pufit threshold which varies along the curve. In each plot the background acceptance fractions and the efficiencies are relative to those of the pufit $E_T^{miss} > 110\,$GeV trigger and thus can be greater than one. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger while the cross indicates the performance of the combined (pufit $E_T^{miss}>110\,$GeV and cell $E_T^{miss}>50\,$GeV) trigger.

Relative background acceptance fraction vs. relative efficiency for two different $p_T(\mu\mu)>150\,$GeV threshold for data recorded in the year 2018. Two of the curves show the performance of the stand-alone cell algorithm and the stand-alone pufit algorithm. The other two show combined algorithms each formed by requiring that the event satisfy both a fixed threshold (either 65 GeV or 70 GeV as shown in the legend) for the cell algorithm and a pufit threshold which varies along the curve. In each plot the background acceptance fractions and the efficiencies are relative to those of the pufit $E_T^{miss} > 110\,$GeV trigger and thus can be greater than one. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger while the cross indicates the performance of the combined (pufit $E_T^{miss}>110\,$GeV and cell $E_T^{miss}>50\,$GeV) trigger.

Relative background acceptance fraction vs. relative efficiency for two different $p_T(\mu\mu)>150\,$GeV threshold for data recorded in the year 2018. Two of the curves show the performance of the stand-alone cell algorithm and the stand-alone pufit algorithm. The other two show combined algorithms each formed by requiring that the event satisfy both a fixed threshold (either 65 GeV or 70 GeV as shown in the legend) for the cell algorithm and a pufit threshold which varies along the curve. In each plot the background acceptance fractions and the efficiencies are relative to those of the pufit $E_T^{miss} > 110\,$GeV trigger and thus can be greater than one. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger while the cross indicates the performance of the combined (pufit $E_T^{miss}>110\,$GeV and cell $E_T^{miss}>50\,$GeV) trigger.

Relative background acceptance fraction vs. relative efficiency for two different $p_T(\mu\mu)>150\,$GeV threshold for data recorded in the year 2018. Two of the curves show the performance of the stand-alone cell algorithm and the stand-alone pufit algorithm. The other two show combined algorithms each formed by requiring that the event satisfy both a fixed threshold (either 65 GeV or 70 GeV as shown in the legend) for the cell algorithm and a pufit threshold which varies along the curve. In each plot the background acceptance fractions and the efficiencies are relative to those of the pufit $E_T^{miss} > 110\,$GeV trigger and thus can be greater than one. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger while the cross indicates the performance of the combined (pufit $E_T^{miss}>110\,$GeV and cell $E_T^{miss}>50\,$GeV) trigger.

Relative background acceptance fraction vs. relative efficiency for two different $p_T(\mu\mu)>150\,$GeV threshold for data recorded in the year 2018. Two of the curves show the performance of the stand-alone cell algorithm and the stand-alone pufit algorithm. The other two show combined algorithms each formed by requiring that the event satisfy both a fixed threshold (either 65 GeV or 70 GeV as shown in the legend) for the cell algorithm and a pufit threshold which varies along the curve. In each plot the background acceptance fractions and the efficiencies are relative to those of the pufit $E_T^{miss} > 110\,$GeV trigger and thus can be greater than one. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger while the cross indicates the performance of the combined (pufit $E_T^{miss}>110\,$GeV and cell $E_T^{miss}>50\,$GeV) trigger.

Relative background acceptance fraction vs. relative efficiency for two different $p_T(\mu\mu)>150\,$GeV threshold for data recorded in the year 2018. Two of the curves show the performance of the stand-alone cell algorithm and the stand-alone pufit algorithm. The other two show combined algorithms each formed by requiring that the event satisfy both a fixed threshold (either 65 GeV or 70 GeV as shown in the legend) for the cell algorithm and a pufit threshold which varies along the curve. In each plot the background acceptance fractions and the efficiencies are relative to those of the pufit $E_T^{miss} > 110\,$GeV trigger and thus can be greater than one. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger while the cross indicates the performance of the combined (pufit $E_T^{miss}>110\,$GeV and cell $E_T^{miss}>50\,$GeV) trigger.

Relative background acceptance fraction vs. relative efficiency for two different $p_T(\mu\mu)>150\,$GeV threshold for data recorded in the year 2018. Two of the curves show the performance of the stand-alone cell algorithm and the stand-alone pufit algorithm. The other two show combined algorithms each formed by requiring that the event satisfy both a fixed threshold (either 65 GeV or 70 GeV as shown in the legend) for the cell algorithm and a pufit threshold which varies along the curve. In each plot the background acceptance fractions and the efficiencies are relative to those of the pufit $E_T^{miss} > 110\,$GeV trigger and thus can be greater than one. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger while the cross indicates the performance of the combined (pufit $E_T^{miss}>110\,$GeV and cell $E_T^{miss}>50\,$GeV) trigger.

Relative background acceptance fraction vs. relative efficiency for two different $p_T(\mu\mu)>150\,$GeV threshold for data recorded in the year 2018. Two of the curves show the performance of the stand-alone cell algorithm and the stand-alone pufit algorithm. The other two show combined algorithms each formed by requiring that the event satisfy both a fixed threshold (either 65 GeV or 70 GeV as shown in the legend) for the cell algorithm and a pufit threshold which varies along the curve. In each plot the background acceptance fractions and the efficiencies are relative to those of the pufit $E_T^{miss} > 110\,$GeV trigger and thus can be greater than one. The diamond indicates the performance of the pufit $E_T^{miss}>110\,$GeV trigger while the cross indicates the performance of the combined (pufit $E_T^{miss}>110\,$GeV and cell $E_T^{miss}>50\,$GeV) trigger.

Turn-on efficiency curves are shown for $Z\rightarrow\mu\mu$ events for three algorithms: the cell algorithm alone, the pufit algorithm alone and the combined cell+pufit algorithm. The thresholds are set such that the algorithms have equal rates, and the data were recorded in the year 2018. Here the trigger efficiency is shown with respect to $p_T(\mu\mu)$.

Turn-on efficiency curves are shown for $Z\rightarrow\mu\mu$ events for three algorithms: the cell algorithm alone, the pufit algorithm alone and the combined cell+pufit algorithm. The thresholds are set such that the algorithms have equal rates, and the data were recorded in the year 2018. Here the trigger efficiency is shown with respect to the offline $E_T^{miss}$ calculation with muons treated as being invisible.

Full-chain trigger efficiencies for each year as a function of $p_T(\mu\mu)$. The efficiency corresponds to that of the lowest unprescaled trigger that is adjusted throughout each year.

Full-chain trigger efficiencies for 2015, 2016, 2017 and 2018 as a function of $\langle\mu\rangle$ for $p_T(\mu\mu)>150$ GeV. The efficiency corresponds to that of the lowest unprescaled trigger that is adjusted throughout the year.

The observed 95% CL upper limit on $\sigma( p p \rightarrow H) \cdot (H\rightarrow Z \gamma)$