Suppl. Fig. 7. The reconstructed shower angle for all single photon events. The individual signal and background event type categories added together form the unconstrained prediction.

Suppl. Fig. 7. The constrained covariance matrix for the reconstructed shower angle for all single-photon events. The matrix shows uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Data statistical uncertainties are not included. An example of how to add Pearson data statistical uncertainties can be found in the example code repository.

Suppl. Fig. 7. The unconstrained covariance matrix for reconstructed shower angle for all single-photon events. The matrix shows uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Data statistical uncertainties are not included. An example of how to add Pearson data statistical uncertainties can be found in the example code repository.

Fig. 3. The reconstructed number of protons, with a proton KE energy threshold of 35 MeV, for all single-photon events. The individual signal and background event type categories added together form the unconstrained prediction.

Fig. 4, Suppl. Fig. 8. The reconstructed shower energy for zero proton events binned from 0 to 600 MeV. The individual signal and background event type categories added together form the unconstrained prediction.

Fig. 4. The constrained covariance matrix for the reconstructed shower energy for zero proton events binned from 0 to 600 MeV. The matrix shows uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Data statistical uncertainties are not included. An example of how to add Pearson data statistical uncertainties can be found in the example code repository.

Fig. 4. The unconstrained covariance matrix for reconstructed shower energy for zero proton events binned from 0 to 600 MeV. The matrix shows uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Data statistical uncertainties are not included. An example of how to add Pearson data statistical uncertainties can be found in the example code repository.

Fig. 6. The reconstructed shower energy for zero proton events binned from 150 to 1250 MeV, with LEE prediction. The individual signal and background event type categories added together form the unconstrained prediction. The "LEE" category is the unfolded MiniBooNE LEE model prediction scaled under the neutrino-target nucleon interaction assumption.

Fig. 6. The constrained covariance matrix for the reconstructed shower energy for zero proton events binned from 150 to 1250 MeV. Both with and without the LEE model added. The matrix shows uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Data statistical uncertainties are not included. An example of how to add Pearson data statistical uncertainties can be found in the example code repository.

Fig. 6. The unconstrained covariance matrix for reconstructed shower energy for zero proton events binned from 150 to 1250 MeV. Both with and without the LEE model added. The matrix shows uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Data statistical uncertainties are not included. An example of how to add Pearson data statistical uncertainties can be found in the example code repository.

Suppl. Fig. 10. The reconstructed shower backwards projected distance for zero proton events. The individual signal and background event type categories added together form the unconstrained prediction.

Suppl. Fig. 9. The reconstructed shower angle for zero proton events. Includes LEE model prediction. The individual signal and background event type categories added together form the unconstrained prediction. The "LEE" category is the unfolded MiniBooNE LEE model prediction scaled under the neutrino-target nucleon interaction assumption.

Suppl. Fig. 9. The constrained covariance matrix for the reconstructed shower angle for zero proton events. The matrix shows uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Data statistical uncertainties are not included. An example of how to add Pearson data statistical uncertainties can be found in the example code repository.

Suppl. Fig. 9. The unconstrained covariance matrix for reconstructed shower angle for zero proton events. The matrix shows uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Data statistical uncertainties are not included. An example of how to add Pearson data statistical uncertainties can be found in the example code repository.

1$\gamma$Xp shower energy and angle selection efficiencies for true 1$\gamma$Xp events. NaN values indicate a "divide by zero" case where zero events were present in the bin before any selection was applied. Energy and Angle values represent bin lower edges.

1$\gamma$0p shower energy and angle selection efficiencies for true single-photon events with no other true particles of any energy. NaN values indicate a "divide by zero" case where zero events were present in the bin before any selection was applied. Energy and Angle values represent bin lower edges.

Covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Pearson data statistical uncertainties have been included, and include small correlations due to events which can be selected by both WC and Pandora. The first four bins are the WC $1\gamma Np$, WC $1\gamma 0p$, Pandora $1\gamma 1p$, and Pandora $1\gamma 0p$ channels, and the next four sets of 16 bins are the NC $\pi^0 Np$, NC $\pi^0 0p$, $\nu_\mu$CC $Np$, and $\nu_\mu$CC $0p$ channels. This corresponds to Fig. 1 of the paper and Fig. 6 of the Supplemental Material.

Constrained WC $1\gamma Np$ energy distribution. There are 6 bins from 0 to 600 MeV of reconstructed shower energy, with an additional overflow bin. Constrained systematic uncertainties on the predictions are illustrated, and a more detailed covariance matrix is included in the Constrained Energy Distributions Covariance Matrix tab. This corresponds to Fig. 2 of the paper.

Constrained WC $1\gamma 0p$ energy distribution. There are 14 bins from 0 to 700 MeV of reconstructed shower energy, with an additional overflow bin. Constrained systematic uncertainties on the predictions are illustrated, and a more detailed covariance matrix is included in the Constrained Energy Distributions Covariance Matrix tab. This corresponds to Fig. 2 of the paper.

Constrained Pandora $1\gamma 1p$ energy distribution. There are 6 bins from 0 to 600 MeV of reconstructed shower energy, with an additional overflow bin. Constrained systematic uncertainties on the predictions are illustrated, and a more detailed covariance matrix is included in the Constrained Energy Distributions Covariance Matrix tab. This corresponds to Fig. 2 of the paper.

Constrained Pandora $1\gamma 0p$ energy distribution. There are 14 bins from 0 to 700 MeV of reconstructed shower energy, with an additional overflow bin. Constrained systematic uncertainties on the predictions are illustrated, and a more detailed covariance matrix is included in the Constrained Energy Distributions Covariance Matrix tab. This corresponds to Fig. 2 of the paper.

Constrained covariance matrix showing constrained uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Pearson data statistical uncertainties have been included, and include small correlations due to events which can be selected by both WC and Pandora. The first seven bins are the WC $1\gamma Np$ reconstructed shower energy from 0-600 MeV with an overflow bin, the next 15 bins are the WC $1\gamma 0p$ reconstructed shower energy from 0-700 MeV with an overflow bin, the next seven bins are the Pandora $1\gamma 1p$ reconstructed shower energy from 0-600 MeV with an overflow bin, and the last 15 bins are the Pandora $1\gamma 0p$ reconstructed shower energy from 0-700 MeV with an overflow bin. This corresponds to Fig. 2 of the paper.

2D efficiency matrix showing the efficiency of the WC $1\gamma Np$ selection with respect to all true NC Delta Radiative Decay events which interact in the fiducial volume. The efficiency is shown as a function of true photon energy and angle. There are 10 bins from -1 to 1 in true photon $\cos \theta$ and 15 bins from 0 to 1500 MeV in true photon energy. NaN values indicate a "divide by zero" case where zero events were present in the bin before any selection was applied. This corresponds to Fig. 9 of the Supplemental Material.

2D efficiency matrix showing the efficiency of the WC $1\gamma 0p$ selection with respect to all true NC Delta Radiative Decay events which interact in the fiducial volume. The efficiency is shown as a function of true photon energy and angle. There are 10 bins from -1 to 1 in true photon $\cos \theta$ and 30 bins from 0 to 1500 MeV in true photon energy. NaN values indicate a "divide by zero" case where zero events were present in the bin before any selection was applied. This corresponds to Fig. 9 of the Supplemental Material.

2D efficiency matrix showing the efficiency of the Pandora $1\gamma 1p$ selection with respect to all true NC Delta Radiative Decay events which interact in the fiducial volume. The efficiency is shown as a function of true photon energy and angle. There are 10 bins from -1 to 1 in true photon $\cos \theta$ and 15 bins from 0 to 1500 MeV in true photon energy, with lower bin edges indicated in the table. NaN values indicate a "divide by zero" case where zero events were present in the bin before any selection was applied. This corresponds to Fig. 9 of the Supplemental Material.

2D efficiency matrix showing the efficiency of the Pandora $1\gamma 0p$ selection with respect to all true NC Delta Radiative Decay events which interact in the fiducial volume. The efficiency is shown as a function of true photon energy and angle. There are 10 bins from -1 to 1 in true photon $\cos \theta$ and 30 bins from 0 to 1500 MeV in true photon energy, with lower bin edges indicated in the table. NaN values indicate a "divide by zero" case where zero events were present in the bin before any selection was applied. This corresponds to Fig. 9 of the Supplemental Material.

2D efficiency matrix showing the efficiency of the WC $1\gamma 0p$ selection with respect to all true zero-primary-final-state-proton NC Delta Radiative Decay events which interact in the fiducial volume. The efficiency is shown as a function of true photon energy and angle. There are 10 bins from -1 to 1 in true photon $\cos \theta$ and 30 bins from 0 to 1500 MeV in true photon energy, with lower bin edges indicated in the table. NaN values indicate a "divide by zero" case where zero events were present in the bin before any selection was applied.

2D efficiency matrix showing the efficiency of the Pandora $1\gamma 0p$ selection with respect to all true zero-primary-final-state-proton NC Delta Radiative Decay events which interact in the fiducial volume. The efficiency is shown as a function of true photon energy and angle. There are 10 bins from -1 to 1 in true photon $\cos \theta$ and 30 bins from 0 to 1500 MeV in true photon energy, with lower bin edges indicated in the table. NaN values indicate a "divide by zero" case where zero events were present in the bin before any selection was applied.

Fig. 3 bottom figure - Distributions of MC simulation compared with data for reconstructed shower energy in the 1$e$0$p$0$\pi$ signal channel, along with the LEE Signal Model 2. The signal and background event categories are summed to form the unconstrained prediction (excluding LEE). Signal events correspond to $\nu_e$ CC events. Background events include $\nu$ with $\pi^0$ events, $\nu$ other events, and cosmic ray events. In Fig. 3, the LEE component is plotted on top of the constrained prediction (excluding LEE) for illustrative purposes. In all statistical tests (results summarized in Table I), the prediction under an LEE hypothesis corresponds to a constrained prediction including LEE. The statistical uncertainties of data use a combined Neyman-Pearson (CNP) version (Eq.(19) in https://doi.org/10.1016/j.nima.2020.163677).

Fig. 4 top figure - Distributions of MC simulation compared with data for reconstructed shower cos($\theta$) in the 1$e$N$p$0$\pi$ signal channel, along with the LEE Signal Model 2. The signal and background event categories are summed to form the unconstrained prediction (excluding LEE). Signal events correspond to $\nu_e$ CC events. Background events include $\nu$ with $\pi^0$ events, $\nu$ other events, and cosmic ray events. In Fig. 4, the LEE component is plotted on top of the constrained prediction (excluding LEE) for illustrative purposes. In all statistical tests (results summarized in Table I), the prediction under an LEE hypothesis corresponds to a constrained prediction including LEE. The statistical uncertainties of data use a combined Neyman-Pearson (CNP) version (Eq.(19) in https://doi.org/10.1016/j.nima.2020.163677).

Fig. 4 bottom figure - Distributions of MC simulation compared with data for reconstructed shower cos($\theta$) in the 1$e$0$p$0$\pi$ signal channel, along with the LEE Signal Model 2. The signal and background event categories are summed to form the unconstrained prediction (excluding LEE). Signal events correspond to $\nu_e$ CC events. Background events include $\nu$ with $\pi^0$ events, $\nu$ other events, and cosmic ray events. In Fig. 4, the LEE component is plotted on top of the constrained prediction (excluding LEE) for illustrative purposes. In all statistical tests (results summarized in Table I), the prediction under an LEE hypothesis corresponds to a constrained prediction including LEE. The statistical uncertainties of data use a combined Neyman-Pearson (CNP) version (Eq.(19) in https://doi.org/10.1016/j.nima.2020.163677).

Fig. 1 top figure - Reconstructed neutrino energy distributions of the 1$\mu$N$p$0$\pi$ control sample (sideband). The signal and background event categories are summed to form the unconstrained prediction. Signal events correspond to $\nu_\mu$ CC events. Background events include $\nu_e$ CC events, NC without $\pi^0$ events, NC with $\pi^0$ events, and cosmic ray events. The statistical uncertainties of data use a combined Neyman-Pearson (CNP) version (Eq.(19) in https://doi.org/10.1016/j.nima.2020.163677).

Fig. 1 middle figure - Reconstructed neutrino energy distributions of the 1$\mu$0$p$0$\pi$ control sample (sideband). The signal and background event categories are summed to form the unconstrained prediction. Signal events correspond to $\nu_\mu$ CC events. Background events include $\nu_e$ CC events, NC without $\pi^0$ events, NC with $\pi^0$ events, and cosmic ray events. The statistical uncertainties of data use a combined Neyman-Pearson (CNP) version (Eq.(19) in https://doi.org/10.1016/j.nima.2020.163677).

Fig. 1 bottom figure - Reconstructed neutrino energy distributions of the NC$\pi^{0}$ control sample (sideband). The signal and background event categories are summed to form the unconstrained prediction. Signal events correspond to NC with $\pi^0$ events. Background events include $\nu_\mu$ CC events, $\nu_e$ CC events, NC without $\pi^0$ events, and cosmic ray events. Only bins up to 1 GeV in this sideband are released and are used in the constraint procedure due to low statistics above this energy. The statistical uncertainties of data use a combined Neyman-Pearson (CNP) version (Eq.(19) in https://doi.org/10.1016/j.nima.2020.163677).

The covariance matrix includes both signal channels and sideband channels, with the LEE component either excluded or included in the signal channels. All channels are binned in reconstructed neutrino energy. Fig. 2 in Supplemental Material shows the corresponding correlation matrix. The constraint procedure uses the correlations with sideband channels to update the prediction and its uncertainty in the signal region. The matrix accounts for uncertainties and correlations between bins due to flux, cross-section, hadron reinteraction, detector systematics, MC statistics, and cosmic ray statistics. Data statistical uncertainties are not included.

The covariance matrix includes both signal channels and sideband channels, with the LEE component either excluded or included in the signal channels. Signal channels are binned shower energy and sideband channels are binned in reconstructed neutrino energy. The constraint procedure uses the correlations with sideband channels to update the prediction and its uncertainty in the signal region. The matrix accounts for uncertainties and correlations between bins due to flux, cross-section, hadron reinteraction, detector systematics, MC statistics, and cosmic ray statistics. Data statistical uncertainties are not included.

The covariance matrix includes both signal channels and sideband channels, with the LEE component either excluded or included in the signal channels. Signal channels are binned shower cos($\theta$) and sideband channels are binned in reconstructed neutrino energy. The constraint procedure uses the correlations with sideband channels to update the prediction and its uncertainty in the signal region. The matrix accounts for uncertainties and correlations between bins due to flux, cross-section, hadron reinteraction, detector systematics, MC statistics, and cosmic ray statistics. Data statistical uncertainties are not included.

The covariance matrices of the sideband channels, binned in reconstructed neutrino energy. The systematic covariance matrix accounts for uncertainties and correlations between bins due to flux, cross-section, hadron reinteraction, detector systematics, MC statistics, and cosmic ray statistics. The total covariance matrix additionally includes data statistical uncertainties (CNP version). The $\chi^2$ values shown in Fig. 1 are calculated using this total covariance matrix, together with the data and MC predictions from the released sideband distribtions.

The unconstrained covariance matrices of the signal channels, binned in reconstructed neutrino energy, with the LEE component either excluded or included. The systematic covariance matrix accounts for uncertainties and correlations between bins due to flux, cross-section, hadron reinteraction, detector systematics, MC statistics, and cosmic ray statistics. The total covariance matrix additionally includes data statistical uncertainties (CNP version). The unconstrained systematic uncertainty in neutrino energy, shown in Supplemental Material Fig. 19, is derived from this systematic covariance matrix (excluding LEE).

The constrained covariance matrices of the signal channels, binned in reconstructed neutrino energy, with the LEE component either excluded or included. The constrained systematic uncertainty in neutrino energy, shown in Supplemental Material Fig. 19, is derived from the systematic covariance matrix (excluding LEE). The $\chi^2$ values shown in Fig. 2 and Table I are calculated using these total covariance matrices, together with the data and constrained predictions from the released signal distributions under the $H_0$ hypothesis (LEE excluded) and $H_1$ hypothesis (LEE included).

The unconstrained covariance matrices of the signal channels, binned in reconstructed shower energy, with the LEE component either excluded or included. The systematic covariance matrix accounts for uncertainties and correlations between bins due to flux, cross-section, hadron reinteraction, detector systematics, MC statistics, and cosmic ray statistics. The total covariance matrix additionally includes data statistical uncertainties (CNP version). The unconstrained systematic uncertainty in shower energy, shown in Supplemental Material Fig. 20, is derived from this systematic covariance matrix (excluding LEE).

The constrained covariance matrices of the signal channels, binned in reconstructed shower energy, with the LEE component either excluded or included. The constrained systematic uncertainty in shower energy, shown in Supplemental Material Fig. 20, is derived from the systematic covariance matrix (excluding LEE). The $\chi^2$ values shown in Fig. 3 and Table I are calculated using these total covariance matrices, together with the data and constrained predictions from the released signal distributions under the $H_0$ hypothesis (LEE excluded) and $H_1$ hypothesis (LEE included).

The unconstrained covariance matrices of the signal channels, binned in reconstructed shower cos($\theta$), with the LEE component either excluded or included. The systematic covariance matrix accounts for uncertainties and correlations between bins due to flux, cross-section, hadron reinteraction, detector systematics, MC statistics, and cosmic ray statistics. The total covariance matrix additionally includes data statistical uncertainties (CNP version). The unconstrained systematic uncertainty in shower cos($\theta$), shown in Supplemental Material Fig. 21, is derived from this systematic covariance matrix (excluding LEE).

The constrained covariance matrices of the signal channels, binned in reconstructed shower cos($\theta$), with the LEE component either excluded or included. The constrained systematic uncertainty in shower cos($\theta$), shown in Supplemental Material Fig. 21, is derived from the systematic covariance matrix (excluding LEE). The $\chi^2$ values shown in Fig. 4 and Table I are calculated using these total covariance matrices, together with the data and constrained predictions from the released signal distributions under the $H_0$ hypothesis (LEE excluded) and $H_1$ hypothesis (LEE included).

Observed and expected 95% CL upper limits on the visible $\tau\nu$ production cross section, $\sigma_{\rm vis} = \sigma(pp \to \tau\nu +X) \cdot \mathcal{A} \cdot \varepsilon$, for $m_{\rm T}$ thresholds ranging from 200 to 2950 GeV. See HepData abstract for details on how to use this data for reinterpretation.

Observed 95% CL upper limits on the cross-section times branching ratio as a function of the W′ mass in several NUGIM models defined by the value of the parameter cot$\theta$.

Expected 95% CL upper limits on the cross-section times branching ratio as a function of the W′ mass in several NUGIM models defined by the value of the parameter cot$\theta$.

Acceptance for $W^{\prime}_{\rm SSM}$ as a function of the $W^{\prime}_{\rm SSM}$ mass, shown after successively applying selection at generator-level. The acceptance times efficiency is calculated with respect to all $W^{\prime}_{\rm SSM} \to \tau\nu$ events with a generated $\tau\nu$ mass above 25 GeV. The "selected tau" criteria include the requirement of a $\tau_{\rm had-vis}$ with $p_{\rm T}$ > 30 GeV and $|\eta|$ < 2.4.

Acceptance times efficiency for $W^{\prime}_{\rm SSM}$ as a function of the $W^{\prime}_{\rm SSM}$ mass, shown after successively applying selection at reconstruction-level. The acceptance times efficiency is calculated with respect to all $W^{\prime}_{\rm SSM} \to \tau\nu$ events with a generated $\tau\nu$ mass above 25 GeV. "Preselection" includes all criteria prior to those shown.

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.

Signal selection efficiency ($\epsilon$) times acceptance ($A$) as a function of $H^{\pm}$. The estimated $\epsilon\times A$ arises from the lepton selection and triggering (∼30%) as well as jet selection and flavour tagging (∼10% or lower). The decrease of $\epsilon\times A$ for $m_{H^{\pm}}$ = 120 GeV and higher is expected from the kinematic constraint on the $H^{\pm}$ decay products due to the top-quark mass.

Comparison between data and background prediction before the fit (Pre-Fit) for the mass of the FCNC top-quark candidate in SR1. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The four FCNC LH signals are also shown separately, normalized to five times the cross-section corresponding to the most stringent observed branching ratio limits. The first (last) bin in all distributions includes the underflow (overflow). The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction before the fit (Pre-Fit) for the mass of the SM top-quark candidate in SR2. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The four FCNC LH signals are also shown separately, normalized to five times the cross-section corresponding to the most stringent observed branching ratio limits. The first (last) bin in all distributions includes the underflow (overflow). The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction before the fit (Pre-Fit) for the transverse momentum of the Z boson candidate in SR2. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The four FCNC LH signals are also shown separately, normalized to five times the cross-section corresponding to the most stringent observed branching ratio limits. The first (last) bin in all distributions includes the underflow (overflow). The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction after the fit to data (Post-Fit) for the FCNC tZu LH coupling extraction. The distribution is for the $D_{1}$ discriminant in the mass sideband CR1. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The FCNC tZu LH signals are also separately shown, normalized to 500 times the best fit of the signal yield. The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction after the fit to data (Post-Fit) for the FCNC tZu LH coupling extraction. The distribution is for the $D_{2}^{u}$ discriminant in the mass sideband CR2. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The FCNC tZu LH signals are also separately shown, normalized to 500 times the best fit of the signal yield. The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction after the fit to data (Post-Fit) for the FCNC tZu LH coupling extraction. The distribution is for the $D_{1}$ discriminant in SR1. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The FCNC tZu LH signals are also separately shown, normalized to 50 times the best fit of the signal yield. The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction after the fit to data (Post-Fit) for the FCNC tZu LH coupling extraction. The distribution is for the $D_{2}^{u}$ discriminant in SR2. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The FCNC tZu LH signals are also separately shown, normalized to 50 times the best fit of the signal yield. The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction after the fit to data (Post-Fit) for the FCNC tZc LH coupling extraction. The distribution is for the $D_{1}$ discriminant in the mass sideband CR1. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The FCNC tZc LH signals are also separately shown, normalized to 500 times the best fit of the signal yield. The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction after the fit to data (Post-Fit) for the FCNC tZc LH coupling extraction. The distribution is for the $D_{2}^{c}$ discriminant in the mass sideband CR2. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The FCNC tZc LH signals are also separately shown, normalized to 500 times the best fit of the signal yield. The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction after the fit to data (Post-Fit) for the FCNC tZc LH coupling extraction. The distribution is for the $D_{1}$ discriminant in SR1. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The FCNC tZc LH signals are also separately shown, normalized to 50 times the best fit of the signal yield. The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction after the fit to data (Post-Fit) for the FCNC tZc LH coupling extraction. The distribution is for the $D_{2}^{c}$ discriminant in SR2. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The FCNC tZc LH signals are also separately shown, normalized to 50 times the best fit of the signal yield. The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction after the fit to data (Post-Fit) for the FCNC tZu LH coupling extraction. The distribution is for the leading lepton $p_{T}$ in the $t\bar{t}$ CR. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The FCNC tZu LH signals are also shown separately, normalized to $10^{3}$ times the best fit of the signal yield. The last bin includes the overflow. The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction after the fit to data (Post-Fit) for the FCNC tZu LH coupling extraction. The distribution is for the third lepton $p_{T}$ in the $t\bar{t}$ CR. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The FCNC tZu LH signals are also shown separately, normalized to $10^{3}$ times the best fit of the signal yield. The last bin includes the overflow. The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction after the fit to data (Post-Fit) for the FCNC tZu LH coupling extraction. The distribution is for the leading lepton $p_{T}$ in the $t\bar{t}Z$ CR. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The FCNC tZu LH signals are also shown separately, normalized to $10^{3}$ times the best fit of the signal yield. The last bin includes the overflow. The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction after the fit to data (Post-Fit) for the FCNC tZu LH coupling extraction. The distribution is for the $D_{1}$ discriminant in the $t\bar{t}Z$ CR. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The FCNC tZu LH signals are also shown separately, normalized to $10^{3}$ times the best fit of the signal yield. The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Expected and observed combined limits at 95% CL on the production cross-section of vector-like T in an $(X,T)$ doublet (50% $T\rightarrow Zt$, 50% $T\rightarrow Ht$).

Expected and observed combined limits at 95% CL on the production cross-section of vector-like T in a $T$ singlet (50% $T\rightarrow Wb$, 25% $T\rightarrow Zt$, 25% $T\rightarrow Ht$).

Expected and observed combined limits at 95% CL on the production cross-section of vector-like B for 100% $B\rightarrow Zb$.

Expected and observed combined limits at 95% CL on the production cross-section of vector-like B in a $(B,Y)$ doublet (50% $B\rightarrow Zb$, 50% $B\rightarrow Hb$).

Expected and observed combined limits at 95% CL on the production cross-section of vector-like B in a B singlet (50% $B\rightarrow Wt$, 25% $B\rightarrow Zb$, 25% $B\rightarrow Hb$).

Distribution of the final discriminant after the combined background-only fit in the 2$\ell$ 2$b$ double-tag 1 signal region. The signal contribution is the expected distribution for a singlet TT with a mass of 1.2 TeV. The last bin contains overflow.

Distribution of the final discriminant after the combined background-only fit in the 2$\ell$ 2$b$ top-tag signal region. The signal contribution is the expected distribution for a singlet TT with a mass of 1.2 TeV. The last bin contains overflow.

Distribution of the final discriminant after the combined background-only fit in the 2$\ell$ 1$b$ $V$-tag signal region. The signal contribution is the expected distribution for a singlet TT with a mass of 1.2 TeV. The last bin contains overflow.

Distribution of the final discriminant after the combined background-only fit in the 2$\ell$ 1$b$ no-tag signal region. The signal contribution is the expected distribution for a singlet TT with a mass of 1.2 TeV. The last bin contains overflow.

Distribution of the final discriminant after the combined background-only fit in the 3$\ell$ $VV$ control region. The signal contribution is the expected distribution for a singlet TT with a mass of 1.2 TeV. The last bin contains overflow.

Distribution of the final discriminant after the combined background-only fit in the 3$\ell$ $H$-tag signal region. The signal contribution is the expected distribution for a singlet TT with a mass of 1.2 TeV. The last bin contains overflow.

Distribution of the final discriminant after the combined background-only fit in the 3$\ell$ top-tag signal region. The signal contribution is the expected distribution for a singlet TT with a mass of 1.2 TeV. The last bin contains overflow.

Distribution of the final discriminant after the combined background-only fit in the 2$\ell$ 1$b$ control region. The signal contribution is the expected distribution for a singlet TT with a mass of 1.2 TeV. The last bin contains overflow.

Distribution of the final discriminant after the combined background-only fit in the 2$\ell$ 2$b$ control region. The signal contribution is the expected distribution for a singlet TT with a mass of 1.2 TeV. The last bin contains overflow.