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The 95\% CL observed (solid line) and expected (dashed line) upper limits on $\sigma B$ for a spin-1 resonance decaying to $H\gamma$ as a function of the resonance mass. The inner and outer bands give the $\pm 1$ and $\pm 2$ standard deviations of expected limits. The local deviations of the observed upper limits from the expected ones on $\sigma B$ are a result of small deviations in the data from the best-fitting background-only model.

The 95\% CL observed (solid line) and expected (dashed line) upper limits on $\sigma B$ for a spin-1 resonance decaying to $W\gamma$ as a function of the resonance mass. The inner and outer bands give the $\pm 1$ and $\pm 2$ standard deviations of expected limits. The local deviations of the observed upper limits from the expected ones on $\sigma B$ are a result of small deviations in the data from the best-fitting background-only model.

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: : The mass distributions of large-$R$ jets originating from $Z$, $W$, and $H$ bosons resulting from decays of a resonance with a mass (a) $m_{X}$ = 1~\TeV{} and (b) $m_{X}$ = 4~\TeV{} in samples of simulated events. Only the hadronic $Z$, $W$ and $H\rightarrow b\bar{b}$ decays are considered in these figures. Only the spin-0 model is shown for the $Z\gamma$ decay as the jet mass distribution is not sensitive to the signal spin hypothesis.

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: : Flowcharts of the categorization of the events in (a) $Z\gamma$ and (b) $W\gamma$ searches. In the $H\gamma$ search only the BTAG selection is applied, analogous to that applied in the $Z\gamma$ search.

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: Distributions of the reconstructed mass \mgj{} in the $W\gamma$ (a) D2, (b) VMASS, and (c) ELSE categories. The models obtained in the background-only fits are shown by the solid lines. Hypothetical signal distributions with $\sigma B$ at the level excluded multiplied by factors of 20~(for 1~\TeV{}), 10~(for 2~\TeV{}), 5~(for 4~\TeV{}), and 1~(for 6~\TeV{}) for the given signal model and resonance mass are overlaid. The $\sigma B$ lines are calculated with the scale factors applied. The bottom panels give the significance for each bin. The significance calculation assumes that the background estimate in a given bin is Poisson distributed. The calculation follows the recommendation of Ref.~\cite{binned_significance}. The impact on the background fit of the statistical uncertainties in parameters $p_i$ is shown as a light band around the solid line. This effect is incorporated into the significance calculation. : Caption not extracted

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: Efficiencies relative to the baseline selection for signal events to pass the category selection for (a) the $Z\gamma$ (in the spin 0 production hypothesis), (b) the $W\gamma$, and (c) the $H\gamma$ resonances as a function of the resonance mass $m_{X}$. The lines represent polynomial fits to the simulated data points. In the $Z\gamma$ search the categorization efficiencies have only a small dependence on the production and spin hypotheses. Statistical uncertainties are smaller than the marker size. : Caption not extracted

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Distribution of the reconstructed mass \mgj{} in the $H\gamma$ search BTAG category. The models obtained in the background-only fits are shown by the solid lines. Hypothetical signal distributions with $\sigma B$ at the level excluded multiplied by factors of 20~(for 1~\TeV{}) and 10~(for 2~\TeV{}) for the given signal model and resonance mass are overlaid. The $\sigma B$ lines are calculated with the scale factors applied. The bottom panel gives the significance for each bin. The significance calculation assumes that the background estimate in a given bin is Poisson distributed. The calculation follows the recommendation of Ref.~\cite{binned_significance}. The impact on the background fit of the statistical uncertainties in parameters $p_i$ is shown as a light band around the solid line. This effect is incorporated into the significance calculation.

: The 95\% CL observed (solid line) and expected (dashed line) upper limits on $\sigma B$ for a resonance with (a) spin-0, produced by gluon--gluon fusion, (b) spin-2, produced by gluon--gluon fusion, and (c) spin-2, produced by quark--antiquark annihilation, decaying to $Z\gamma$ as a function of the resonance mass. The inner and outer bands give the $\pm 1$ and $\pm 2$ standard deviations of expected limits. The local deviations of the observed upper limits from the expected ones on $\sigma B$ are a result of small deviations in the data from the best-fitting background-only model. : Caption not extracted

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Efficiencies for signal events to pass the baseline selection as a function of the resonance mass $m_{X}$ for different signal models, production modes, and spin hypotheses. The uncertainty bars shown are statistical only. The lines represent polynomial fits to the simulated data points. The line corresponding to the $H\gamma$ resonance baseline selection efficiency is discontinued above $m_{X}$ of 3 \TeV{} since the search for $H\gamma$ does not cover this resonance mass region.

: : Distributions of the reconstructed mass \mgj{} in the $Z\gamma$ search (a) BTAG, (b) D2, (c) VMASS, and (d) ELSE categories. The models obtained in the background-only fits are shown by the solid lines. Hypothetical signal distributions with $\sigma B$ at the level excluded multiplied by factors of 20~(for 1~\TeV{}), 10~(for 2~\TeV{}), 5~(for 4~\TeV{}), and 1~(for 6~\TeV{}) for the given signal model and resonance mass are overlaid. The $\sigma B$ lines are calculated with the scale factors applied. The bottom panels give the significance for each bin. The significance calculation assumes that the background estimate in a given bin is Poisson distributed and follows the recommendation of Ref.~\cite{binned_significance}. The impact on the background fit of the statistical uncertainties in parameters $p_i$ is shown as a light band around the solid line. This effect is incorporated into the significance calculation.