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.

Parametrization of the $A_{X}$ factor, defined as the fraction of diphoton resonances satisfying the fiducial acceptance at the particle level, as function of $m_{X}$ obtained from the narrow width simulated signal samples produced in gluon fusion.

The correction factor, $C_{X}$, defined as the ratio between the number of reconstructed signal events passing the analysis cuts and the number of signal events at the particle level generated within the fiducial volume, and acceptance correction factor, $A_{X}$, defined as the fraction of diphoton resonances satisfying the fiducial acceptance at the particle level. Both are computed for NWA spin-0 models as a function of $m_{X}$.

Effect of event selections on a scalar MC signal sample generated for $m_{X}$ = 15 GeV and on the data. For the MC sample, the efficiencies are shown after applying event weights and a truth level filter that requires two photons with $p^{\gamma\gamma}_{T}>40$ GeV; for the data, the absolute yields are shown. The initial yields for data include a trigger preselection that is the OR of a list of single photon and diphoton triggers. The "2 $loose$ photons" step includes the kinematic acceptance cuts.

Parameterization of the Double Sided Crystal Ball function parameters describing the scalar mass resolution model as a function of $m_{X}$ [GeV].

The correlation matrix for the Higgs pT measurements, both for the unregularized and regularized fits. The last bin is inclusive.

The correlation matrix for the jet multiplicity measurements, both for the unregularized and regularized fits. The last bin is inclusive.

The correlation matrix for the leading jet pT measurements, both for the unregularized and regularized fits. The last bin is inclusive.

The fiducial integrated signal strength and cross section.

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

The absolute differential cross-section measured in the fiducial phase-space as a function of the minimum $\Delta R$ between the photon and the leptons in the electron-muon channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.

The absolute differential cross-section measured in the fiducial phase-space as a function of the $\Delta\phi$ between the two leptons in the electron-muon channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.

The absolute differential cross-section measured in the fiducial phase-space as a function of the $|\Delta\eta|$ between the two leptons in the electron-muon channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.

The normalised differential cross-section measured in the fiducial phase-space as a function of the photon pT in the electron-muon channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.

The normalised differential cross-section measured in the fiducial phase-space as a function of the photon $|\eta|$ in the electron-muon channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.

The normalised differential cross-section measured in the fiducial phase-space as a function of the minimum $\Delta R$ between the photon and the leptons in the electron-muon channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.

The normalised differential cross-section measured in the fiducial phase-space as a function of the $\Delta\phi$ between the two leptons in the electron-muon channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.

The normalised differential cross-section measured in the fiducial phase-space as a function of the $|\Delta\eta|$ between the two leptons in the electron-muon channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.

The total correlation matrix of the absolute differential cross-section measured in the fiducial phase-space as a function of the photon pT in the electron-muon channel. The individual systematic uncertainties are symmetrized before deriving the correlation matrix.

The total correlation matrix of the absolute differential cross-section measured in the fiducial phase-space as a function of the photon $|\eta|$ in the electron-muon channel. The individual systematic uncertainties are symmetrized before deriving the correlation matrix.

The total correlation matrix of the absolute differential cross-section measured in the fiducial phase-space as a function of the minimum $\Delta R$ between the photon and the leptons in the electron-muon channel. The individual systematic uncertainties are symmetrized before deriving the correlation matrix.

The total correlation matrix of the absolute differential cross-section measured in the fiducial phase-space as a function of the $\Delta\phi$ between the two leptons in the electron-muon channel. The individual systematic uncertainties are symmetrized before deriving the correlation matrix.

The total correlation matrix of the absolute differential cross-section measured in the fiducial phase-space as a function of the $|\Delta\eta|$ between the two leptons in the electron-muon channel. The individual systematic uncertainties are symmetrized before deriving the correlation matrix.

The total correlation matrix of the normalised differential cross-section measured in the fiducial phase-space as a function of the photon pT in the electron-muon channel. The individual systematic uncertainties are symmetrized before deriving the correlation matrix.

The total correlation matrix of the normalised differential cross-section measured in the fiducial phase-space as a function of the photon $|\eta|$ in the electron-muon channel. The individual systematic uncertainties are symmetrized before deriving the correlation matrix.

The total correlation matrix of the normalised differential cross-section measured in the fiducial phase-space as a function of the minimum $\Delta R$ between the photon and the leptons in the electron-muon channel. The individual systematic uncertainties are symmetrized before deriving the correlation matrix.

The total correlation matrix of the normalised differential cross-section measured in the fiducial phase-space as a function of the $\Delta\phi$ between the two leptons in the electron-muon channel. The individual systematic uncertainties are symmetrized before deriving the correlation matrix.

The total correlation matrix of the normalised differential cross-section measured in the fiducial phase-space as a function of the $|\Delta\eta|$ between the two leptons in the electron-muon channel. The individual systematic uncertainties are symmetrized before deriving the correlation matrix.

The statistical correlation matrix of all the absolute differential cross-sections measured in the fiducial phase-space in the electron-muon channel.

The statistical correlation matrix of all the normalised differential cross-sections measured in the fiducial phase-space in the electron-muon channel.

Fiducial region definition.

The correlation matrix for the njet measurement. The last bin is inclusive.

The fiducial integrated signal strength and cross section The uncertainty breakdown is given in terms of statistical (stat), experimental (exp), theoretical uncertainties on the background (bkg) and on the signal (sig), and the luminosity uncertainty (lumi). The fiducial cross section and its full uncertainty in each bin are also given.

Impact of different categories of systematic uncertainties on the fiducial and inclusive measurements. The quoted values are obtained by repeating the fit, fixing a set of nuisance parameters of the sources corresponding to the considered category, and subtracting in quadrature the resulting uncertainty from the total uncertainty of the nominal fit. The total uncertainty is different from the sum in quadrature of the different components due to correlations between nuisance parameters built by the fit.

Fiducial region definition