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Compact Muon Solenoid
LHC, CERN

CMS-HIG-19-015 ; CERN-EP-2021-038
Measurements of Higgs boson production cross sections and couplings in the diphoton decay channel at $\sqrt{s} = $ 13 TeV
JHEP 07 (2021) 027
Abstract: Measurements of Higgs boson production cross sections and couplings in events where the Higgs boson decays into a pair of photons are reported. Events are selected from a sample of proton-proton collisions at $\sqrt{s} = $ 13 TeV collected by the CMS detector at the LHC from 2016 to 2018, corresponding to an integrated luminosity of 137 fb$^{-1}$. Analysis categories enriched in Higgs boson events produced via gluon fusion, vector boson fusion, vector boson associated production, and production associated with top quarks are constructed. The total Higgs boson signal strength, relative to the standard model (SM) prediction, is measured to be 1.12 $\pm$ 0.09. Other properties of the Higgs boson are measured, including SM signal strength modifiers, production cross sections, and its couplings to other particles. These include the most precise measurements of gluon fusion and vector boson fusion Higgs boson production in several different kinematic regions, the first measurement of Higgs boson production in association with a top quark pair in five regions of the Higgs boson transverse momentum, and an upper limit on the rate of Higgs boson production in association with a single top quark. All results are found to be in agreement with the SM expectations.
Figures & Tables Summary Additional Figures & Tables References CMS Publications
Figures

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Figure 1:
Diagram showing the full set of STXS stage-1.2 bins, adapted from Ref. [10], defined for events with $ {{| y_\mathrm{H} |}} < $ 2.5. The solid boxes represent each STXS stage-1.2 bin. The units of ${{p_{\mathrm {T}}} ^\mathrm{H}}$, ${m_{\text {jj}}}$, ${{p_{\mathrm {T}}} ^{\mathrm{H} \text {jj}}}$, and ${{p_{\mathrm {T}}} ^{{\mathrm{V}}}}$ are in GeV. The shaded regions indicate the STXS bins that are divided at stage 1.2, but are not measured independently in this analysis.

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Figure 2:
Comparison of the dielectron invariant mass spectra in data (black points) and simulation (blue histogram), after applying energy scale corrections to data and energy smearing to the simulation, for ${\mathrm{Z} \to \mathrm{ee}}$ events with electrons reconstructed as photons. The statistical and systematic uncertainty on the simulation is shown by the pink band. The comparison is shown for events where both electrons are reconstructed in the ECAL barrel (left), and both in the ECAL endcaps (right). The lower panels show the ratio of the data to the MC simulation in black points, with the uncertainty on the ratio represented by the pink band. The full data set collected in 2016-2018 and the corresponding simulation are shown.

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Figure 2-a:
Comparison of the dielectron invariant mass spectra in data (black points) and simulation (blue histogram), after applying energy scale corrections to data and energy smearing to the simulation, for ${\mathrm{Z} \to \mathrm{ee}}$ events with electrons reconstructed as photons. The statistical and systematic uncertainty on the simulation is shown by the pink band. The comparison is shown for events where both electrons are reconstructed in the ECAL barrel. The lower panel shows the ratio of the data to the MC simulation in black points, with the uncertainty on the ratio represented by the pink band. The full data set collected in 2016-2018 and the corresponding simulation are shown.

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Figure 2-b:
Comparison of the dielectron invariant mass spectra in data (black points) and simulation (blue histogram), after applying energy scale corrections to data and energy smearing to the simulation, for ${\mathrm{Z} \to \mathrm{ee}}$ events with electrons reconstructed as photons. The statistical and systematic uncertainty on the simulation is shown by the pink band. The comparison is shown for events where both electrons are reconstructed in the ECAL endcaps. The lower panel shows the ratio of the data to the MC simulation in black points, with the uncertainty on the ratio represented by the pink band. The full data set collected in 2016-2018 and the corresponding simulation are shown.

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Figure 3:
The left plot shows the distribution of the photon identification BDT score of the lowest scoring photon in diphoton pairs with 100 $ < {m_{\gamma \gamma}} < $ 180 GeV, for data events passing the preselection (black points), and for simulated background events (red band). Histograms are also shown for different components of the simulated background. The blue histogram corresponds to simulated Higgs boson signal events. The right plot shows the same distribution for ${\mathrm{Z} \to \mathrm{ee}}$ events in data and simulation, where the electrons are reconstructed as photons. The statistical and systematic uncertainty in simulation is also shown (pink band). Photons with an identification BDT score in the grey shaded region (below $-$0.9) are not considered in the analysis. The full data set collected in 2016-2018 and the corresponding simulation are shown.

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Figure 3-a:
Distribution of the photon identification BDT score of the lowest scoring photon in diphoton pairs with 100 $ < {m_{\gamma \gamma}} < $ 180 GeV, for data events passing the preselection (black points), and for simulated background events (red band). Histograms are also shown for different components of the simulated background. The blue histogram corresponds to simulated Higgs boson signal events. Photons with an identification BDT score in the grey shaded region (below $-$0.9) are not considered in the analysis. The full data set collected in 2016-2018 and the corresponding simulation are shown.

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Figure 3-b:
Distribution of the photon identification BDT score of the lowest scoring photon in diphoton pairs with 100 $ < {m_{\gamma \gamma}} < $ 180 GeV for ${\mathrm{Z} \to \mathrm{ee}}$ events in data and simulation, where the electrons are reconstructed as photons. The statistical and systematic uncertainty in simulation is also shown (pink band). "Photons" with an identification BDT score in the grey shaded region (below $-$0.9) are not considered in the analysis. The full data set collected in 2016-2018 and the corresponding simulation are shown.

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Figure 4:
The left plot shows the validation of the ${\mathrm{H} \to \gamma \gamma}$ vertex identification algorithm on ${\mathrm{Z} \to \mu^{+} \mu^{-}}$ events, where the muon tracks are omitted when performing the event reconstruction. This allows the fraction of events with the correctly assigned vertex estimated with simulation to be compared with data, as a function of the ${p_{\mathrm {T}}}$ of the dimuon system, serving as a validation of the vertex identification BDT. Simulated events are weighted to match the distributions of pileup and distribution of vertices along the beam axis in data. The right plot demonstrates that the average vertex probability to be within 1 cm of the true vertex agrees with the true vertex efficiency in simulated events. The full data set collected in 2016-2018 and the corresponding simulation are shown.

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Figure 4-a:
Validation of the ${\mathrm{H} \to \gamma \gamma}$ vertex identification algorithm on ${\mathrm{Z} \to \mu^{+} \mu^{-}}$ events, where the muon tracks are omitted when performing the event reconstruction. This allows the fraction of events with the correctly assigned vertex estimated with simulation to be compared with data, as a function of the ${p_{\mathrm {T}}}$ of the dimuon system, serving as a validation of the vertex identification BDT. Simulated events are weighted to match the distributions of pileup and distribution of vertices along the beam axis in data. The full data set collected in 2016-2018 and the corresponding simulation are shown.

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Figure 4-b:
The plot demonstrates that the average vertex probability to be within 1 cm of the true vertex agrees with the true vertex efficiency in simulated events. The full data set collected in 2016-2018 and the corresponding simulation are shown.

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Figure 5:
The most probable STXS class from the ggH BDT in ${\mathrm{Z} \to \mathrm{ee}}$ events where the electrons are reconstructed as photons is shown. The points show the predicted class for data, whilst the histogram shows predicted score for simulated Drell-Yan events, including statistical and systematic uncertainties (pink band). The full data set collected in 2016-2018 and the corresponding simulation are shown.

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Figure 6:
The left plot shows the distribution of the diphoton BDT score in events with ${m_{\gamma \gamma}}$ in the range 100-120 or 130-180 GeV, for data events passing the preselection (black points), and for simulated background events (red band). Histograms are also shown for different components of the simulated background in red. The blue histogram corresponds to simulated Higgs boson signal events ($\times $100). The right plot shows the same distribution in ${\mathrm{Z} \to \mathrm{ee}}$ events where the electrons are reconstructed as photons. The points show the score for data, the histogram shows the score for simulated Drell-Yan events, including statistical and systematic uncertainties (pink band). The regions shaded grey contain diphoton BDT scores below the lowest threshold used to define an analysis category. The full data set collected in 2016-2018 and the corresponding simulation are shown.

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Figure 6-a:
Distribution of the diphoton BDT score in events with ${m_{\gamma \gamma}}$ in the range 100-120 or 130-180 GeV, for data events passing the preselection (black points), and for simulated background events (red band). Histograms are also shown for different components of the simulated background in red. The blue histogram corresponds to simulated Higgs boson signal events ($\times $100). The regions shaded grey contain diphoton BDT scores below the lowest threshold used to define an analysis category. The full data set collected in 2016-2018 and the corresponding simulation are shown.

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Figure 6-b:
Distribution of the diphoton BDT score in events with ${m_{\gamma \gamma}}$ in the range 100-120 or 130-180 GeV, in ${\mathrm{Z} \to \mathrm{ee}}$ events where the electrons are reconstructed as photons. The points show the score for data, the histogram shows the score for simulated Drell-Yan events, including statistical and systematic uncertainties (pink band). The regions shaded grey contain diphoton BDT scores below the lowest threshold used to define an analysis category. The full data set collected in 2016-2018 and the corresponding simulation are shown.

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Figure 7:
The left plot shows the distribution of the dijet BDT output VBF probability in events with ${m_{\gamma \gamma}}$ in the range 100-120 or 130-180 GeV, for data events passing the dijet preselection (black points), and for simulated background events (red band). Histograms are also shown for different components of the simulated background in red. The orange histogram corresponds to simulated VBF signal events, with the ggH events shown in blue (both $\times $100). The right plot shows the same distribution in ${\mathrm{Z} \to \mathrm{ee}}$ events where the electrons are reconstructed as photons. The points show the score for data, the histogram shows the score for simulated Drell-Yan events, including statistical and systematic uncertainties (pink band). The regions shaded grey contain VBF probability values below the lowest threshold used to define an analysis category. The full data set collected in 2016-2018 and the corresponding simulation are shown.

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Figure 7-a:
Distribution of the dijet BDT output VBF probability in events with ${m_{\gamma \gamma}}$ in the range 100-120 or 130-180 GeV, for data events passing the dijet preselection (black points), and for simulated background events (red band). Histograms are also shown for different components of the simulated background in red. The orange histogram corresponds to simulated VBF signal events, with the ggH events shown in blue (both $\times $100). The regions shaded grey contain VBF probability values below the lowest threshold used to define an analysis category. The full data set collected in 2016-2018 and the corresponding simulation are shown.

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Figure 7-b:
Distribution of the dijet BDT output VBF probability in events with ${m_{\gamma \gamma}}$ in the range 100-120 or 130-180 GeV, in ${\mathrm{Z} \to \mathrm{ee}}$ events where the electrons are reconstructed as photons. The points show the score for data, the histogram shows the score for simulated Drell-Yan events, including statistical and systematic uncertainties (pink band). The regions shaded grey contain VBF probability values below the lowest threshold used to define an analysis category. The full data set collected in 2016-2018 and the corresponding simulation are shown.

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Figure 8:
The left plot shows the distribution of the VH hadronic BDT output score in events with ${m_{\gamma \gamma}}$ in the range 100-120 or 130-180 GeV, for data events passing the preselection (black points), and for simulated background events (red band). Histograms are also shown for different components of the simulated background in red. The sum of all background distributions is scaled to the data. The orange histogram corresponds to simulated VH hadronic signal events. The right plot shows the same distribution in $ {\mathrm{Z} \to \mathrm{ee}} $+jets events where the electrons are reconstructed as photons. The points show the score for data, the histogram shows the score for simulated Drell-Yan events, including statistical and systematic uncertainties (pink band). The regions shaded grey contain VH hadronic BDT scores below the lowest threshold used to define an analysis category. The full data set collected in 2016-2018 and the corresponding simulation are shown.

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Figure 8-a:
Distribution of the VH hadronic BDT output score in events with ${m_{\gamma \gamma}}$ in the range 100-120 or 130-180 GeV, for data events passing the preselection (black points), and for simulated background events (red band). Histograms are also shown for different components of the simulated background in red. The sum of all background distributions is scaled to the data. The orange histogram corresponds to simulated VH hadronic signal events. The regions shaded grey contain VH hadronic BDT scores below the lowest threshold used to define an analysis category. The full data set collected in 2016-2018 and the corresponding simulation are shown.

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Figure 8-b:
Distribution of the VH hadronic BDT output score in events with ${m_{\gamma \gamma}}$ in the range 100-120 or 130-180 GeV, in $ {\mathrm{Z} \to \mathrm{ee}} $+jets events where the electrons are reconstructed as photons. The points show the score for data, the histogram shows the score for simulated Drell-Yan events, including statistical and systematic uncertainties (pink band). The regions shaded grey contain VH hadronic BDT scores below the lowest threshold used to define an analysis category. The full data set collected in 2016-2018 and the corresponding simulation are shown.

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Figure 9:
Output scores for the three VH leptonic BDTs. The VH MET BDT is shown in the upper left, with the ZH leptonic BDT in the upper right, and the WH leptonic BDT below. In each case, the signal and background simulation are shown as histograms with the data as black points. Events are taken from the $ {m_{\gamma \gamma}} $ sidebands, satisfying either 100 $ < {m_{\gamma \gamma}} < $ 120 GeV or 130 $ < {m_{\gamma \gamma}} < $ 180 GeV. The statistical uncertainty in the data points is denoted as vertical bars and that on the background simulation by the pink band. The simulated signal and background distributions are normalised to the luminosity of the data. To increase its visibility, the signal is scaled by a factor of 500 for the VH MET BDT, with a factor of 50 applied for both ZH leptonic and WH leptonic BDTs. The regions shaded grey are not considered in the analysis. The full data set collected in 2016-2018 and the corresponding simulation are shown.

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Figure 9-a:
Distribution of the output score for the VH MET BDT. The signal and background simulation are shown as histograms with the data as black points. Events are taken from the $ {m_{\gamma \gamma}} $ sidebands, satisfying either 100 $ < {m_{\gamma \gamma}} < $ 120 GeV or 130 $ < {m_{\gamma \gamma}} < $ 180 GeV. The statistical uncertainty in the data points is denoted as vertical bars and that on the background simulation by the pink band. The simulated signal and background distributions are normalised to the luminosity of the data. To increase its visibility, the signal is scaled by a factor of 500. The regions shaded grey are not considered in the analysis. The full data set collected in 2016-2018 and the corresponding simulation are shown.

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Figure 9-b:
Distribution of the output score for the ZH leptonic BDT. The signal and background simulation are shown as histograms with the data as black points. Events are taken from the $ {m_{\gamma \gamma}} $ sidebands, satisfying either 100 $ < {m_{\gamma \gamma}} < $ 120 GeV or 130 $ < {m_{\gamma \gamma}} < $ 180 GeV. The statistical uncertainty in the data points is denoted as vertical bars and that on the background simulation by the pink band. The simulated signal and background distributions are normalised to the luminosity of the data. To increase its visibility, the signal is scaled by a factor of 50. The regions shaded grey are not considered in the analysis. The full data set collected in 2016-2018 and the corresponding simulation are shown.

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Figure 9-c:
Distribution of the output score for the WH leptonic BDT. The signal and background simulation are shown as histograms with the data as black points. Events are taken from the $ {m_{\gamma \gamma}} $ sidebands, satisfying either 100 $ < {m_{\gamma \gamma}} < $ 120 GeV or 130 $ < {m_{\gamma \gamma}} < $ 180 GeV. The statistical uncertainty in the data points is denoted as vertical bars and that on the background simulation by the pink band. The simulated signal and background distributions are normalised to the luminosity of the data. To increase its visibility, the signal is scaled by a factor of 50. The regions shaded grey are not considered in the analysis. The full data set collected in 2016-2018 and the corresponding simulation are shown.

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Figure 10:
Distributions of tHq BDT-bkg score (left) and the top DNN (right), which are used together to define the tHq leptonic analysis category. Events are taken from the $ {m_{\gamma \gamma}} $ sidebands, satisfying either 100 $ < {m_{\gamma \gamma}} < $ 120 GeV or 130 $ < {m_{\gamma \gamma}} < $ 180 GeV. The statistical uncertainty in the background estimation is represented by the pink band. The regions shaded grey contain BDT-bkg and top DNN scores below and above the respective thresholds for the tHq analysis category. The full data set collected in 2016-2018 and the corresponding simulation are shown.

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Figure 10-a:
Distribution of the tHq BDT-bkg score, which is used to define the tHq leptonic analysis category. Events are taken from the $ {m_{\gamma \gamma}} $ sidebands, satisfying either 100 $ < {m_{\gamma \gamma}} < $ 120 GeV or 130 $ < {m_{\gamma \gamma}} < $ 180 GeV. The statistical uncertainty in the background estimation is represented by the pink band. The region shaded grey contains scores below the threshold for the tHq analysis category. The full data set collected in 2016-2018 and the corresponding simulation are shown.

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Figure 10-b:
Distribution of the top DNN, which is used to define the tHq leptonic analysis category. Events are taken from the $ {m_{\gamma \gamma}} $ sidebands, satisfying either 100 $ < {m_{\gamma \gamma}} < $ 120 GeV or 130 $ < {m_{\gamma \gamma}} < $ 180 GeV. The statistical uncertainty in the background estimation is represented by the pink band. The region shaded grey contains scores above the threshold for the tHq analysis category. The full data set collected in 2016-2018 and the corresponding simulation are shown.

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Figure 11:
Distributions of BDT-bkg output used in the analysis categories targeting ttH production, for the leptonic (left) and the hadronic (right) channels. The upper two plots show events taken from the $ {m_{\gamma \gamma}} $ sidebands, satisfying either 100 $ < {m_{\gamma \gamma}} < $ 120 GeV or 130 $ < {m_{\gamma \gamma}} < $ 180 GeV. The lower two contain events from the ttZ control regions, described in the text. The grey region contains BDT-bkg scores below the lowest threshold for the ttH analysis categories. Total background uncertainties (statistical $\oplus $ systematic) are represented by the black (pink) shaded bands.

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Figure 11-a:
Distribution of BDT-bkg output used in the analysis categories targeting ttH production, for the leptonic channel. The plot shows events taken from the $ {m_{\gamma \gamma}} $ sidebands, satisfying either 100 $ < {m_{\gamma \gamma}} < $ 120 GeV or 130 $ < {m_{\gamma \gamma}} < $ 180 GeV. The grey region contains BDT-bkg scores below the lowest threshold for the ttH analysis categories. Total background uncertainties (statistical $\oplus $ systematic) are represented by the black (pink) shaded bands.

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Figure 11-b:
Distribution of BDT-bkg output used in the analysis categories targeting ttH production, for the hadronic channel. The plot shows events taken from the $ {m_{\gamma \gamma}} $ sidebands, satisfying either 100 $ < {m_{\gamma \gamma}} < $ 120 GeV or 130 $ < {m_{\gamma \gamma}} < $ 180 GeV. The grey region contains BDT-bkg scores below the lowest threshold for the ttH analysis categories. Total background uncertainties (statistical $\oplus $ systematic) are represented by the black (pink) shaded bands.

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Figure 11-c:
Distribution of BDT-bkg output used in the analysis categories targeting ttH production, for the leptonic channel. The plot contains events from the ttZ control regions, described in the text. The grey region contains BDT-bkg scores below the lowest threshold for the ttH analysis categories. Total background uncertainties (statistical $\oplus $ systematic) are represented by the black (pink) shaded bands.

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Figure 11-d:
Distribution of BDT-bkg output used in the analysis categories targeting ttH production, for the hadronic channel. The plot contains events from the ttZ control regions, described in the text. The grey region contains BDT-bkg scores below the lowest threshold for the ttH analysis categories. Total background uncertainties (statistical $\oplus $ systematic) are represented by the black (pink) shaded bands.

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Figure 12:
The shape of the parametric signal model for each year of simulated data, and for the sum of all years together, is shown. The open squares represent weighted simulation events and the blue line the corresponding model. Also shown is the ${\sigma _{\text {eff}}}$ value (half the width of the narrowest interval containing 68.3% of the ${m_{\gamma \gamma}}$ distribution) in the grey shaded area. The contribution of the signal model from each year of data taking is illustrated with the dotted lines. The models are shown for an analysis category targeting ggH 0J high ${{p_{\mathrm {T}}} ^\mathrm{H}}$ production (left), and for the weighted sum of all analysis categories (right). Here each analysis category is weighted by S/(S+B), where S and B are the numbers of expected signal and background events, respectively, in a $ \pm $1$ {\sigma _{\text {eff}}} $ ${m_{\gamma \gamma}}$ window centred on ${m_\mathrm{H}}$.

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Figure 12-a:
The shape of the parametric signal model for each year of simulated data, and for the sum of all years together, is shown. The open squares represent weighted simulation events and the blue line the corresponding model. Also shown is the ${\sigma _{\text {eff}}}$ value (half the width of the narrowest interval containing 68.3% of the ${m_{\gamma \gamma}}$ distribution) in the grey shaded area. The contribution of the signal model from each year of data taking is illustrated with the dotted lines. The models are shown for an analysis category targeting ggH 0J high ${{p_{\mathrm {T}}} ^\mathrm{H}}$ production.

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Figure 12-b:
The shape of the parametric signal model for each year of simulated data, and for the sum of all years together, is shown. The open squares represent weighted simulation events and the blue line the corresponding model. Also shown is the ${\sigma _{\text {eff}}}$ value (half the width of the narrowest interval containing 68.3% of the ${m_{\gamma \gamma}}$ distribution) in the grey shaded area. The contribution of the signal model from each year of data taking is illustrated with the dotted lines. The models are shown for the weighted sum of all analysis categories. Here each analysis category is weighted by S/(S+B), where S and B are the numbers of expected signal and background events, respectively, in a $ \pm $1$ {\sigma _{\text {eff}}} $ ${m_{\gamma \gamma}}$ window centred on ${m_\mathrm{H}}$.

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Figure 13:
The composition of the analysis categories in terms of a merged set of STXS bins is shown. The granularity of the STXS bin merging corresponds to the finest granularity used for the cross section measurements in this analysis. Analysis categories targeting a common STXS region are summed, where the signal compositions of the individual categories are weighted in the sum by the expected ratio of signal to signal-plus-background events. The colour scale corresponds to the fractional yield in each analysis category group (rows) accounted for by each STXS process (columns). Each row therefore sums to 100%. Entries with values less than 0.5% are not shown. Simulated events for each year in the period 2016-2018 are combined with appropriate weights corresponding to their relative integrated luminosity in data. The column labelled as "qqH rest" includes contributions from the qqH 0J, qqH 1J, qqH $ {m_{\text {jj}}} < $ 60 GeV and qqH 120 $ < {m_{\gamma \gamma}} < $ 350 GeV STXS bins.

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Figure 14:
Data points (black) and signal-plus-background model fit for the sum of all analysis categories is shown. Each analysis category is weighted by S/(S+B), where S and B are the numbers of expected signal and background events, respectively, in a $ \pm $1$ {\sigma _{\text {eff}}} $ ${m_{\gamma \gamma}}$ window centred on ${m_\mathrm{H}}$. The one (green) standard deviation and two (yellow) standard deviation bands show the uncertainties in the background component of the fit. The solid red line shows the total signal-plus-background contribution, whereas the dashed red line shows the background component only. The lower panel shows the residuals after subtraction of this background component.

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Figure 15:
The best fit signal-plus-background model with data points (black) in the fit to signal strength modifiers of the four principal production modes. The model is shown separately for groups of analysis categories targeting the ggH (upper left), VBF (upper right), VH (lower left) and top quark associated (lower right) production modes. Here, the analysis categories in each group are summed after weighting by S/(S+B), where S and B are the numbers of expected signal and background events in a $ \pm $1$ {\sigma _{\text {eff}}} $ ${m_{\gamma \gamma}}$ window centred on ${m_\mathrm{H}}$. The one standard deviation (green) and two standard deviation (yellow) bands show the uncertainties in the background component of the fit. The solid red line shows the total signal-plus-background contribution, whereas the dashed red line represents the background component only. The lower panel in each plot shows the residuals after subtraction of this background component.

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Figure 15-a:
The best fit signal-plus-background model with data points (black) in the fit to signal strength modifiers of the four principal production modes. The model is shown for groups of analysis categories targeting the ggH production modes. Here, the analysis categories in each group are summed after weighting by S/(S+B), where S and B are the numbers of expected signal and background events in a $ \pm $1$ {\sigma _{\text {eff}}} $ ${m_{\gamma \gamma}}$ window centred on ${m_\mathrm{H}}$. The one standard deviation (green) and two standard deviation (yellow) bands show the uncertainties in the background component of the fit. The solid red line shows the total signal-plus-background contribution, whereas the dashed red line represents the background component only. The lower panel shows the residuals after subtraction of this background component.

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Figure 15-b:
The best fit signal-plus-background model with data points (black) in the fit to signal strength modifiers of the four principal production modes. The model is shown for groups of analysis categories targeting the VBF production modes. Here, the analysis categories in each group are summed after weighting by S/(S+B), where S and B are the numbers of expected signal and background events in a $ \pm $1$ {\sigma _{\text {eff}}} $ ${m_{\gamma \gamma}}$ window centred on ${m_\mathrm{H}}$. The one standard deviation (green) and two standard deviation (yellow) bands show the uncertainties in the background component of the fit. The solid red line shows the total signal-plus-background contribution, whereas the dashed red line represents the background component only. The lower panel shows the residuals after subtraction of this background component.

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Figure 15-c:
The best fit signal-plus-background model with data points (black) in the fit to signal strength modifiers of the four principal production modes. The model is shown for groups of analysis categories targeting the VH production modes. Here, the analysis categories in each group are summed after weighting by S/(S+B), where S and B are the numbers of expected signal and background events in a $ \pm $1$ {\sigma _{\text {eff}}} $ ${m_{\gamma \gamma}}$ window centred on ${m_\mathrm{H}}$. The one standard deviation (green) and two standard deviation (yellow) bands show the uncertainties in the background component of the fit. The solid red line shows the total signal-plus-background contribution, whereas the dashed red line represents the background component only. The lower panel shows the residuals after subtraction of this background component.

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Figure 15-d:
The best fit signal-plus-background model with data points (black) in the fit to signal strength modifiers of the four principal production modes. The model is shown for groups of analysis categories targeting the top quark associated production modes. Here, the analysis categories in each group are summed after weighting by S/(S+B), where S and B are the numbers of expected signal and background events in a $ \pm $1$ {\sigma _{\text {eff}}} $ ${m_{\gamma \gamma}}$ window centred on ${m_\mathrm{H}}$. The one standard deviation (green) and two standard deviation (yellow) bands show the uncertainties in the background component of the fit. The solid red line shows the total signal-plus-background contribution, whereas the dashed red line represents the background component only. The lower panel shows the residuals after subtraction of this background component.

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Figure 16:
Observed results of the fit to signal strength modifiers of the four principal production modes. The contributions to the total uncertainty in each parameter from the theoretical systematic, experimental systematic, and statistical components are shown. The colour scheme is chosen to match the diagram presented in Fig. 1. The compatibility of this fit with respect to the SM prediction, expressed as a $p$-value, is approximately 50%. Also shown in black is the result of the fit to the inclusive signal strength modifier, which has a $p$-value of 17%.

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Figure 17:
A summary of the impact of the main sources of systematic uncertainty in the fit to signal strength modifiers of the four principal production modes. The observed (expected) impacts are shown by the solid (empty) bars. The colour scheme is chosen to match the diagram presented in Fig. 1.

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Figure 18:
Observed results of the maximal merging scheme STXS fit. The best fit cross sections are plotted together with the respective 68% CL intervals. The systematic components of the uncertainty in each parameter are shown by the coloured boxes. The hatched grey boxes demonstrate the theoretical uncertainties in the SM predictions. The lower panel shows the ratio of the fitted values to the SM predictions. Here the tH cross section ratio has a different scale, due to its high best fit value and uncertainty. The cross sections are constrained to be non-negative, as indicated by the hashed pattern below zero. The parameters whose best fit values are at zero are known to have 68% CL intervals which slightly under-cover; this is checked to be a small effect using pseudo-experiments. The colour scheme is chosen to match the diagram presented in Fig. 1. The compatibility of this fit with respect to the SM prediction, expressed as a $p$-value, is approximately 31%.

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Figure 19:
Observed correlations between the 17 parameters considered in the maximal merging STXS fit. The size of the correlations is indicated by the colour scale.

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Figure 20:
Observed results of the minimal merging scheme STXS fit. The best fit cross sections are plotted together with the respective 68% CL intervals. The systematic components of the uncertainty in each parameter are shown by the coloured boxes. The hatched grey boxes demonstrate the theoretical uncertainties in the SM predictions. The lower panel shows the ratio of the fitted values to the SM predictions. Here the tH cross section ratio has a different scale, due to its high best fit value and uncertainty. The cross sections are constrained to be non-negative, as indicated by the hashed pattern below zero. The parameters whose best fit values are at zero are known to have 68% CL intervals which slightly under-cover; this is checked to be a small effect using pseudo-experiments. The colour scheme is chosen to match the diagram presented in Fig. 1. The orange lines dashed with blue for the VBF-like parameters represent contributions from both the ggH and the qqH STXS bins. The compatibility of this fit with respect to the SM prediction, expressed as a $p$-value, is approximately 70%.

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Figure 21:
Observed correlations between the 27 parameters considered in the minimal merging STXS fit. The size of the correlations is indicated by the colour scale.

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Figure 22:
Observed two-dimensional likelihood scans performed in the $\kappa $-framework: $ {\kappa _{\mathrm{V}}} $-vs-$ {\kappa _\text {F}} $ in the resolved $\kappa $ model (upper) and $ {\kappa _\gamma} $-vs-$ {\kappa _\mathrm{g}} $ in the unresolved $\kappa $ model (lower). The 68 and 95% CL regions are given by the solid and dashed contours, respectively. The best fit and SM points are shown by the black cross and red diamond, respectively. The colour scale indicates the value of the test statistic.

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Figure 22-a:
Observed two-dimensional $ {\kappa _{\mathrm{V}}} $-vs-$ {\kappa _\text {F}} $ likelihood scan performed in the in the resolved $\kappa $ model. The 68 and 95% CL regions are given by the solid and dashed contours, respectively. The best fit and SM points are shown by the black cross and red diamond, respectively. The colour scale indicates the value of the test statistic.

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Figure 22-b:
Observed two-dimensional $ {\kappa _\gamma} $-vs-$ {\kappa _\mathrm{g}} $ likelihood scan performed in the in the unresolved $\kappa $ model. The 68 and 95% CL regions are given by the solid and dashed contours, respectively. The best fit and SM points are shown by the black cross and red diamond, respectively. The colour scale indicates the value of the test statistic.
Tables

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Table 1:
Schema of the photon preselection requirements. The requirements depend both on whether a photon is in the barrel or endcap, and on its $ {R_\mathrm {9}}$ value.

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Table 2:
Definition of the ggH STXS bins. The product of the cross section and branching fraction ($\mathcal {B}$), evaluated at $ \sqrt {s}= $ 13 TeV and $ {m_\mathrm{H}} = $ 125 GeV, is given for each bin in the last column. The fraction of the total production mode cross section from each STXS bin is also shown. Events originating from ggZH production, in which the Z decays hadronically, are grouped with ggH in the STXS measurements and are shown as a separate column in the table. The bbH production mode, whose $\sigma _{\text {SM}}\mathcal {B}= $ 1.054 fb, is grouped together with the ggH 0J high ${{p_{\mathrm {T}}} ^\mathrm{H}}$ bin. Unless stated otherwise, the STXS bins are defined for $ {{| y_\mathrm{H} |}} < $ 2.5. Events with $ {{| y_\mathrm{H} |}} > $ 2.5 are mostly outside of the experimental acceptance and therefore have a negligible contribution to all analysis categories.

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Table 3:
The expected number of signal events for $ {m_\mathrm{H}} = $ 125 GeV in analysis categories targeting ggH production, excluding those targeting the VBF-like phase space, shown for an integrated luminosity of 137 fb$^{-1}$. The fraction of the total number of events arising from each production mode in each analysis category is provided, as is the fraction of events originating from the targeted STXS bin or bins. Entries with values less than 0.05% are not shown. Here qqH includes contributions from both VBF and hadronic VH production, whilst "Top" includes ttH and tH together. The $ {\sigma _{\text {eff}}} $, defined as the smallest interval containing 68.3% of the ${m_{\gamma \gamma}}$ distribution, is listed for each analysis category. The final column shows the expected ratio of signal to signal-plus-background, S/(S+B), where S and B are the numbers of expected signal and background events in a $ \pm $1$ {\sigma _{\text {eff}}} $ window centred on $ {m_\mathrm{H}} $.

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Table 4:
Definition of the qqH STXS bins. The product of the cross section and branching fraction ($\mathcal {B}$), evaluated at $ \sqrt {s}= $ 13 TeV and $ {m_\mathrm{H}} = $ 125 GeV, is given for each bin in the last column. The fraction of the total production mode cross section from each STXS bin is also shown. Unless stated otherwise, the STXS bins are defined for $ {{| y_\mathrm{H} |}} < $ 2.5. Events with $ {{| y_\mathrm{H} |}} > $ 2.5 are mostly outside of the experimental acceptance and therefore have a negligible contribution to all analysis categories.

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Table 5:
The expected number of signal events for $ {m_\mathrm{H}} = $ 125 GeV in analysis categories targeting VBF-like phase space and VH production in which the vector boson decays hadronically, shown for an integrated luminosity of 137 fb$^{-1}$. The fraction of the total number of events arising from each production mode in each analysis category is provided, as is the fraction of events originating from the targeted STXS bin or bins. Entries with values less than 0.05% are not shown. Here ggH includes contributions from the ggZ (qqH and bbH production modes, whilst "Top" represents both ttH and tH production together. The $ {\sigma _{\text {eff}}} $, defined as the smallest interval containing 68.3% of the ${m_{\gamma \gamma}}$ distribution, is listed for each analysis category. The final column shows the expected ratio of signal to signal-plus-background, S/(S+B), where S and B are the numbers of expected signal and background events in a $ \pm $1$ {\sigma _{\text {eff}}} $ window centred on $ {m_\mathrm{H}} $.

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Table 6:
Definition of the VH leptonic STXS bins. The product of the cross section and branching fraction ($\mathcal {B}$), evaluated at $ \sqrt {s}= $ 13 TeV and $ {m_\mathrm{H}} = $ 125 GeV, is given for each bin in the last column. The fraction of the total production mode cross section from each STXS bin is also shown. Unless stated otherwise, the STXS bins are defined for $ {{| y_\mathrm{H} |}} < $ 2.5. Events with $ {{| y_\mathrm{H} |}} > $ 2.5 are mostly outside of the experimental acceptance and therefore have a negligible contribution to all analysis categories. Only leptonic decays of the W and Z bosons are included in these definitions.

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Table 7:
The expected number of signal events for $ {m_\mathrm{H}} = $ 125 GeV in analysis categories targeting Higgs boson production in association with a leptonically decaying W or Z boson, shown for an integrated luminosity of 137 fb$^{-1}$. The fraction of the total number of events arising from each production mode in each analysis category is provided, as is the fraction of events originating from the targeted STXS bin or bins. Entries with values less than 0.05% are not shown. Here ggH includes contributions from the ggZ (qqH and bbH production modes, qqH incorporates both VBF and VH production with hadronic vector boson decays, and "Top" represents both ttH and tH production together. The $ {\sigma _{\text {eff}}} $, defined as the smallest interval containing 68.3% of the ${m_{\gamma \gamma}}$ distribution, is listed for each analysis category. The final column shows the expected ratio of signal to signal-plus-background, S/(S+B), where S and B are the numbers of expected signal and background events in a $ \pm $1$ {\sigma _{\text {eff}}} $ window centred on $ {m_\mathrm{H}} $.

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Table 8:
Definition of the ttH, tH, and bbH STXS bins. The product of the cross section and branching fraction ($\mathcal {B}$), evaluated at $ \sqrt {s}= $ 13 TeV and $ {m_\mathrm{H}} = $ 125 GeV, is given for each bin in the last column. The fraction of the total production mode cross section from each STXS bin is also shown. Unless stated otherwise, the STXS bins are defined for $ {{| y_\mathrm{H} |}} < $ 2.5. Events with $ {{| y_\mathrm{H} |}} > $ 2.5 are mostly outside of the experimental acceptance and therefore have a negligible contribution to all analysis categories.

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Table 9:
The expected number of signal events for $ {m_\mathrm{H}} = $ 125 GeV in analysis categories targeting Higgs boson production in association with top quark, shown for an integrated luminosity of 137 fb$^{-1}$. The fraction of the total number of events arising from each production mode in each analysis category is provided, as is the fraction of events originating from the targeted STXS bin or bins. Entries with values less than 0.05% are not shown. Here ggH includes contributions from the ggZ (qqH and bbH production modes, whilst qqH incorporates both VBF and hadronic VH production. The $ {\sigma _{\text {eff}}} $, defined as the smallest interval containing 68.3% of the ${m_{\gamma \gamma}}$ distribution, is listed for each analysis category. The final column shows the expected ratio of signal to signal-plus-background, S/(S+B), where S and B are the numbers of expected signal and background events in a $ \pm $1$ {\sigma _{\text {eff}}} $ window centred on $ {m_\mathrm{H}} $.

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Table 10:
Description of the different categorisation regions, listed in descending order of priority in the first column. The second column shows each targeted STXS bin, or merged group of bins, together with the number of associated analysis categories. The last row contains the bins for which no analysis categories are constructed.

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Table 11:
A summary of the maximal and minimal parameter merging scenarios. The STXS bins that contribute to each parameter are listed. Furthermore, the bins that are constrained to their respective SM predictions in the fits are listed in the final row.

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Table 12:
Results of the maximal merging scheme STXS fit. The best fit cross sections are shown together with the respective 68% CL intervals. The uncertainty is decomposed into the systematic and statistical components. The expected uncertainties on the fitted parameters are given in brackets. Also listed are the SM predictions for the cross sections and the theoretical uncertainty in those predictions.

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Table 13:
Results of the minimal merging scheme STXS fit. The best fit cross sections are shown together with the respective 68% CL intervals. The uncertainty is decomposed into the systematic and statistical components. The expected uncertainties on the fitted parameters are given in brackets. Also listed are the SM predictions for the cross sections and the theoretical uncertainty in those predictions.
Summary
Measurements of Higgs boson properties with the Higgs boson decaying into a pair of photons are reported. Events with two photons are selected from a sample of proton-proton collisions at a centre-of-mass energy $\sqrt{s}= $ 13 TeV collected with the CMS detector at the LHC from 2016 to 2018, corresponding to an integrated luminosity of 137 fb$^{-1}$. Analysis categories enriched in events produced via gluon fusion, vector boson fusion, vector boson associated production, production associated with two top quarks, and production associated with one top quark are constructed.

A range of production and coupling properties of the Higgs boson are measured. The total Higgs boson signal strength, relative to the standard model (SM) prediction, is measured to be 1.12 $\pm$ 0.09. A simultaneous measurement of the signal strengths of the four principal Higgs boson production mechanisms is performed and found to be compatible with the SM prediction with a $p$-value of 50%. Two different measurements are performed within the simplified template cross section framework, in which 17 and 27 independent kinematic regions are measured simultaneously, with corresponding $p$-values with respect to the SM of 31 and 70%, respectively. Many of these kinematic regions are measured for the first time, including a simultaneous measurement of Higgs boson production in association with two top quarks in five different regions of the Higgs boson transverse momentum ${p_{\mathrm{T}}^{\mathrm{H}}}$. Furthermore, several additional measurements are the most precise made in a single channel to date. These include cross sections of vector boson fusion in different kinematic regions, gluon fusion in association with jets, and the region of gluon fusion production with ${p_{\mathrm{T}}^{\mathrm{H}}} > $ 200 GeV, which is particularly sensitive to physics beyond the SM. The gluon fusion cross section with ${p_{\mathrm{T}}^{\mathrm{H}}} > $ 200 GeV is found to be consistent with the SM, with a measured value of 0.9$_{-0.3}^{+0.4}$ relative to the SM prediction. An upper limit on the rate of Higgs boson production in association with a single top quark is also presented. The observed (expected) limit at 95% confidence level is found to be 14 (8) times the SM prediction. All other results, such as measurements of the Higgs boson's couplings to vector bosons and to fermions, are also in agreement with the SM expectations.
Additional Figures

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Additional Figure 1:
Schematic to show the maximal merging scheme. The parameters of interest are defined by the solid boxes.

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Additional Figure 2:
Schematic to show the minimal merging scheme. The parameters of interest are defined by the solid boxes. The orange and blue boxes correspond to the VBF-like parameters which include contributions from both the ggH and qqH STXS bins.

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Additional Figure 3:
Observed correlations between the signal strength modifiers of the four principal production modes. The size of the correlations is indicated by the colour scale.

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Additional Figure 4:
Observed results of the STXS stage 0 fit. The best fit cross sections are plotted along with the respective 68% confidence intervals. The systematic components of the uncertainty in each parameter are shown by the coloured boxes. The hatched grey boxes demonstrate the theoretical uncertainties in the SM predictions. The lower panel shows the ratio of the fitted values to the SM predictions. Here the tH cross section ratio has a different scale, due to its high best fit value and uncertainty. The cross sections are constrained to be non-negative, as indicated by the hashed pattern below zero. The colour scheme is chosen to match the diagram presented in Fig. 1. The compatibility of this fit with respect to the SM prediction, expressed as a $p$-value, is approximately 61%.

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Additional Figure 5:
Observed correlations between the parameters in the STXS stage 0 fit. The size of the correlations is indicated by the colour scale.

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Additional Figure 6:
Observed two-dimensional likelihood scans for pairs of parameters in the maximal merging STXS fit with the largest correlations: ggH VBF-like vs qqH VBF-like (upper) and tH vs ttH (lower). The 68 and 95% CL regions are given by the solid and dashed contours, respectively. The best fit and SM points are shown by the black cross and red diamond, respectively. The parameters are plotted as a ratio with respect to their SM prediction.

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Additional Figure 6-a:
Observed two-dimensional likelihood scans for pairs of parameters in the maximal merging STXS fit with the largest correlations: ggH VBF-like vs qqH VBF-like (upper) and tH vs ttH (lower). The 68 and 95% CL regions are given by the solid and dashed contours, respectively. The best fit and SM points are shown by the black cross and red diamond, respectively. The parameters are plotted as a ratio with respect to their SM prediction.

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Additional Figure 6-b:
Observed two-dimensional likelihood scans for pairs of parameters in the maximal merging STXS fit with the largest correlations: ggH VBF-like vs qqH VBF-like (upper) and tH vs ttH (lower). The 68 and 95% CL regions are given by the solid and dashed contours, respectively. The best fit and SM points are shown by the black cross and red diamond, respectively. The parameters are plotted as a ratio with respect to their SM prediction.

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Additional Figure 7:
One-dimensional likelihood scans in $ {\kappa _\text {F}} $, in the resolved $\kappa $ model where the value of $ \kappa $ is profiled in the fit. The expected and observed scans are shown in red and black, respectively.

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Additional Figure 8:
Visualisations of a candidate single top-associated production event in data. The event is selected in the tHq leptonic analysis category and is characterised by two photon candidates with a diphoton invariant mass of 125.52 GeV, shown by the green blocks. The top quark decays into a W boson and a b quark. The long red line depicts the muon from the decay of the W boson and the red cone depicts the b-tagged jet originating from the b quark. The jet produced from the additional quark is shown as the orange cone.

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Additional Figure 8-a:
Visualisations of a candidate single top-associated production event in data. The event is selected in the tHq leptonic analysis category and is characterised by two photon candidates with a diphoton invariant mass of 125.52 GeV, shown by the green blocks. The top quark decays into a W boson and a b quark. The long red line depicts the muon from the decay of the W boson and the red cone depicts the b-tagged jet originating from the b quark. The jet produced from the additional quark is shown as the orange cone.

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Additional Figure 8-b:
Visualisations of a candidate single top-associated production event in data. The event is selected in the tHq leptonic analysis category and is characterised by two photon candidates with a diphoton invariant mass of 125.52 GeV, shown by the green blocks. The top quark decays into a W boson and a b quark. The long red line depicts the muon from the decay of the W boson and the red cone depicts the b-tagged jet originating from the b quark. The jet produced from the additional quark is shown as the orange cone.
Additional Tables

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Additional Table 1:
Results of the STXS stage 0 fit. The best fit cross sections are shown together with the respective 68% CL intervals. The uncertainty is decomposed into the systematic and statistical components. The expected uncertainties on the fitted parameters, computed assuming the SM predicted cross section values, are given in brackets. Also listed are the SM predictions for the cross sections and the theoretical uncertainty in those predictions.
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