Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T}}^{\mathrm{lead.\,lep.}}$.

Fiducial differential cross-sections as a function of $p_{\mathrm{T}}^{\mathrm{sub-lead.\,lep.}}$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T}}^{\mathrm{sub-lead.\,lep.}}$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T}}^{\mathrm{sub-lead.\,lep.}}$.

Fiducial differential cross-sections as a function of $p_{\mathrm{T},e\mu}$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T},e\mu}$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T},e\mu}$.

Fiducial differential cross-sections as a function of $|y_{e\mu}|$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $|y_{e\mu}|$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $|y_{e\mu}|$.

Fiducial differential cross-sections as a function of $m_{e\mu}$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $m_{e\mu}$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $m_{e\mu}$.

Fiducial differential cross-sections as a function of $|\Delta\phi_{e\mu}|$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $|\Delta\phi_{e\mu}|$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $|\Delta\phi_{e\mu}|$.

Fiducial differential cross-sections as a function of $\cos(\theta^{*})$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $\cos(\theta^{*})$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $\cos(\theta^{*})$.

Fiducial differential cross-sections as a function of $E_{\mathrm{T}}^{\mathrm{miss}}$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $E_{\mathrm{T}}^{\mathrm{miss}}$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $E_{\mathrm{T}}^{\mathrm{miss}}$.

Fiducial differential cross-sections as a function of $H_{\mathrm{T}}^{\mathrm{lep}+\mathrm{MET}}$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $H_{\mathrm{T}}^{\mathrm{lep}+\mathrm{MET}}$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $H_{\mathrm{T}}^{\mathrm{lep}+\mathrm{MET}}$.

Fiducial differential cross-sections as a function of $m_{\mathrm{T},e\mu}$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $m_{\mathrm{T},e\mu}$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $m_{\mathrm{T},e\mu}$.

Fiducial differential cross-sections as a function of the number of jets. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable Number of jets ($p_{\mathrm{T}} > $ 30 GeV).

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable Number of jets ($p_{\mathrm{T}} > $ 30 GeV).

Fiducial differential cross-sections as a function of $S_{\mathrm{T}}$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $S_{\mathrm{T}}$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $S_{\mathrm{T}}$.

Fiducial differential cross-sections for $p_{\mathrm{T},e\mu}$ in the region with 85 $<m_{e\mu}<$ 150, for the nNNLO MATRIX prediction and various four flavour PDF sets. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The measurement is compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1 using four different four-flavour NNLO PDF sets: NNPDF3.0, NNPDF3.1, CT18, and MSHT20.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T},e\mu}$ (85 $<m_{e\mu}<$ 150).

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T},e\mu}$ (85 $<m_{e\mu}<$ 150).

Fiducial differential cross-sections for $|y_{e\mu}|$ in the region with 85 $<m_{e\mu}<$ 150, for the nNNLO MATRIX prediction and various four flavour PDF sets. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The measurement is compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1 using four different four-flavour NNLO PDF sets: NNPDF3.0, NNPDF3.1, CT18, and MSHT20.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $|y_{e\mu}|$ (85 $<m_{e\mu}<$ 150).

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $|y_{e\mu}|$ (85 $<m_{e\mu}<$ 150).

Fiducial differential cross-sections for $p_{\mathrm{T},e\mu}$ in the region with 150 $<m_{e\mu}<$ 250, for the nNNLO MATRIX prediction and various four flavour PDF sets. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The measurement is compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1 using four different four-flavour NNLO PDF sets: NNPDF3.0, NNPDF3.1, CT18, and MSHT20.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T},e\mu}$ (150 $<m_{e\mu}<$ 250).

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T},e\mu}$ (150 $<m_{e\mu}<$ 250).

Fiducial differential cross-sections for $|y_{e\mu}|$ in the region with 150 $<m_{e\mu}<$ 250, for the nNNLO MATRIX prediction and various four flavour PDF sets. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The measurement is compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1 using four different four-flavour NNLO PDF sets: NNPDF3.0, NNPDF3.1, CT18, and MSHT20.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $|y_{e\mu}|$ (150 $<m_{e\mu}<$ 250).

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $|y_{e\mu}|$ (150 $<m_{e\mu}<$ 250).

Fiducial differential cross-sections for $p_{\mathrm{T},e\mu}$ in the region with $m_{e\mu}>$ 250, for the nNNLO MATRIX prediction and various four flavour PDF sets. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The measurement is compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1 using four different four-flavour NNLO PDF sets: NNPDF3.0, NNPDF3.1, CT18, and MSHT20.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T},e\mu}$ ($m_{e\mu}>$ 250).

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T},e\mu}$ ($m_{e\mu}>$ 250).

Fiducial differential cross-sections for $|y_{e\mu}|$ in the region with $m_{e\mu}>$ 250, for the nNNLO MATRIX prediction and various four flavour PDF sets. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The measurement is compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1 using four different four-flavour NNLO PDF sets: NNPDF3.0, NNPDF3.1, CT18, and MSHT20.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $|y_{e\mu}|$ ($m_{e\mu}>$ 250).

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $|y_{e\mu}|$ ($m_{e\mu}>$ 250).

Measured value of the charge asymmetry, $A_{C}$.

Charge asymmetry $A_C$ measured as a function of the absolute difference of the absolute lepton rapidities $||\eta_{l+}|-|\eta_{l-}||$. The measured values are shown as points, whose error bars represent the statistical uncertainty, while the solid bands indicate the size of the total uncertainty. In the bottom panel, the central value of the charge asymmetry divided by the total uncertainty of the $A_C$ measurement is shown. The measurement is compared with the NNLO+PS predictions from Powheg MiNNLO+Pythia8 with vertical lines denoting PDF uncertainties.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $A_{C}$ vs. $||\eta_{l+}|-|\eta_{l-}||$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $A_{C}$ vs. $||\eta_{l+}|-|\eta_{l-}||$.

Charge asymmetry $A_C$ measured as a function of the invariant mass of the dilepton system $m_{e\mu}$. The measured values are shown as points, whose error bars represent the statistical uncertainty, while the solid bands indicate the size of the total uncertainty. In the bottom panel, the central value of the charge asymmetry divided by the total uncertainty of the $A_C$ measurement is shown. The measurement is compared with the NNLO+PS predictions from Powheg MiNNLO+Pythia8 with vertical lines denoting PDF uncertainties.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $A_{C}$ vs. $m_{e\mu}$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $A_{C}$ vs. $m_{e\mu}$.

Measured value of the asymmetry in the CP-odd observable $O_{z}$, $A_{CP}$.

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).

Expected exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos.

Observed exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos.

Observed exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos.

Observed exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos.

Expected exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos.

Expected exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos.

Expected exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos.

Observed exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos.

Observed exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos.

Observed exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos.

Expected exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM1.

Expected exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM1.

Expected exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM1.

Observed exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM1.

Observed exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM1.

Observed exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM1.

Expected exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM2.

Expected exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM2.

Expected exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM2.

Observed exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM2.

Observed exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM2.

Observed exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM2.

Expected exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM3.

Expected exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM3.

Expected exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM3.

Observed exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM3.

Observed exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM3.

Observed exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM3.

Expected exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp1.

Expected exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp1.

Expected exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp1.

Observed exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp1.

Observed exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp1.

Observed exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp1.

Expected exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp2.

Expected exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp2.

Expected exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp2.

Observed exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp2.

Observed exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp2.

Observed exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp2.

Expected exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp3.

Expected exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp3.

Expected exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp3.

Observed exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp3.

Observed exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp3.

Observed exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp3.

Expected exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp-1c.

Expected exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp-1c.

Expected exclusion limit at 95% CL for pair production of top squarks decaying to top or charm quarks and 1 GeV neutralinos for different branching fraction assumptions.

Expected exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to top or charm quarks and 1 GeV neutralinos for different branching fraction assumptions.

Expected exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to top or charm quarks and 1 GeV neutralinos for different branching fraction assumptions.

Observed exclusion limit at 95% CL for pair production of top squarks decaying to top or charm quarks and 1 GeV neutralinos for different branching fraction assumptions.

Observed exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to top or charm quarks and 1 GeV neutralinos for different branching fraction assumptions.

Observed exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to top or charm quarks and 1 GeV neutralinos for different branching fraction assumptions.

Expected exclusion limit at 95% CL for pair production of top squarks decaying to top or charm quarks and 200 GeV neutralinos for different branching fraction assumptions.

Expected exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to top or charm quarks and 200 GeV neutralinos for different branching fraction assumptions.

Expected exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to top or charm quarks and 200 GeV neutralinos for different branching fraction assumptions.

Observed exclusion limit at 95% CL for pair production of top squarks decaying to top or charm quarks and 200 GeV neutralinos for different branching fraction assumptions.

Observed exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to top or charm quarks and 200 GeV neutralinos for different branching fraction assumptions.

Observed exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to top or charm quarks and 200 GeV neutralinos for different branching fraction assumptions.

Expected exclusion limit $(-1\sigma)$ at 95% CL for pair production of up-type scalar LQs coupled to first generation leptons and second generation quarks.

Expected exclusion limit $(+1\sigma)$ at 95% CL for pair production of up-type scalar LQs coupled to first generation leptons and second generation quarks.

Expected exclusion limit at 95% CL for pair production of up-type scalar LQs coupled to first generation leptons and second generation quarks.

Observed exclusion limit $(+1\sigma)$ at 95% CL for pair production of up-type scalar LQs coupled to first generation leptons and second generation quarks.

Observed exclusion limit $(-1\sigma)$ at 95% CL for pair production of up-type scalar LQs coupled to first generation leptons and second generation quarks.

Observed exclusion limit at 95% CL for pair production of up-type scalar LQs coupled to first generation leptons and second generation quarks.

Expected exclusion limit $(-1\sigma)$ at 95% CL for pair production of up-type scalar LQs coupled to second generation leptons and quarks.

Expected exclusion limit $(+1\sigma)$ at 95% CL for pair production of up-type scalar LQs coupled to second generation leptons and quarks.

Expected exclusion limit at 95% CL for pair production of up-type scalar LQs coupled to second generation leptons and quarks.

Observed exclusion limit $(+1\sigma)$ at 95% CL for pair production of up-type scalar LQs coupled to second generation leptons and quarks.

Observed exclusion limit $(-1\sigma)$ at 95% CL for pair production of up-type scalar LQs coupled to second generation leptons and quarks.

Observed exclusion limit at 95% CL for pair production of up-type scalar LQs coupled to second generation leptons and quarks.

Observed upper limit on the cross-section at 95% CL for pair production of top squarks decaying into charm quarks and neutralinos for the fit with the best expected CL$_\mathrm{S}$.

Observed upper limit on the cross-section for pair production of up-type scalar LQs coupled to first generation leptons and second generation quarks.

Observed upper limit on the cross-section for pair production of up-type scalar LQs coupled to second generation leptons and quarks.

Expected upper limit on the cross-section $(-1\sigma)$ for $U(1)$ vector LQ models in the minimal coupling scenario with $\beta_{23}=1$, corresponding to a branching fraction $\mathcal{B}(\mathrm{vLQ}^\mathrm{u,min}_{23}\rightarrow c\nu) = 0.5$.

Expected upper limit on the cross-section $(+1\sigma)$ for $U(1)$ vector LQ models in the minimal coupling scenario with $\beta_{23}=1$, corresponding to a branching fraction $\mathcal{B}(\mathrm{vLQ}^\mathrm{u,min}_{23}\rightarrow c\nu) = 0.5$.

Expected upper limit on the cross-section for $U(1)$ vector LQ models in the minimal coupling scenario with $\beta_{23}=1$, corresponding to a branching fraction $\mathcal{B}(\mathrm{vLQ}^\mathrm{u,min}_{23}\rightarrow c\nu) = 0.5$.

Observed upper limit on the cross-section for $U(1)$ vector LQ models in the minimal coupling scenario with $\beta_{23}=1$, corresponding to a branching fraction $\mathcal{B}(\mathrm{vLQ}^\mathrm{u,min}_{23}\rightarrow c\nu) = 0.5$.

Expected upper limit on the cross-section $(-1\sigma)$ for $U(1)$ vector LQ models in the Yang-Mills coupling scenario with $\beta_{23}=1$, corresponding to a branching fraction $\mathcal{B}(\mathrm{vLQ}^\mathrm{u,YM}_{23}\rightarrow c\nu) = 0.5$.

Expected upper limit on the cross-section $(+1\sigma)$ for $U(1)$ vector LQ models in the Yang-Mills coupling scenario with $\beta_{23}=1$, corresponding to a branching fraction $\mathcal{B}(\mathrm{vLQ}^\mathrm{u,YM}_{23}\rightarrow c\nu) = 0.5$.

Expected upper limit on the cross-section for $U(1)$ vector LQ models in the Yang-Mills coupling scenario with $\beta_{23}=1$, corresponding to a branching fraction $\mathcal{B}(\mathrm{vLQ}^\mathrm{u,YM}_{23}\rightarrow c\nu) = 0.5$.

Observed upper limit on the cross-section for $U(1)$ vector LQ models in the Yang-Mills coupling scenario with $\beta_{23}=1$, corresponding to a branching fraction $\mathcal{B}(\mathrm{vLQ}^\mathrm{u,YM}_{23}\rightarrow c\nu) = 0.5$.

Distribution of $R_{\mathrm{ISR}}$ in SR-Comp-1c showing the data and the expected backgrounds, after simultaneously fitting all the control regions. The pre-fit yields for a representative $m(\tilde{t}_1,\tilde{\chi}_1^0)=(450,430)$ GeV signal is included. Processes with top quarks and multiple vector bosons are included in "Other". The right-most bin does not include the overflow entry but the $x$-axis range is chosen to include all observed data.

Distribution of $E_\mathrm{T}^\mathrm{miss}\mathrm{ Sig.}$ in SR-HM1 showing the data and the expected backgrounds, after simultaneously fitting all the control regions. The pre-fit yields for a representative $m(\tilde{t}_1,\tilde{\chi}_1^0)=(1000,1)$ GeV signal is included. Processes with top quarks and multiple vector bosons are included in "Other". The right-most bin does not include the overflow entry but the $x$-axis range is chosen to include all observed data.

Distribution of $m_{\mathrm{T}}^{\mathrm{min}}(c)$ in SR-HM2 showing the data and the expected backgrounds, after simultaneously fitting all the control regions. The pre-fit yields for a representative $m(\tilde{t}_1,\tilde{\chi}_1^0)=(750,450)$ GeV signal is included. Processes with top quarks and multiple vector bosons are included in "Other". The right-most bin does not include the overflow entry but the $x$-axis range is chosen to include all observed data.

Distribution of $R_{\mathrm{ISR}}$ in SR-Comp1 showing the data and the expected backgrounds, after simultaneously fitting all the control regions. The pre-fit yields for a representative $m(\tilde{t}_1,\tilde{\chi}_1^0)=(600,550)$ GeV signal is included. Processes with top quarks and multiple vector bosons are included in "Other". The right-most bin does not include the overflow entry but the $x$-axis range is chosen to include all observed data.

Distribution of $R_{\mathrm{ISR}}$ in SR-Comp2 showing the data and the expected backgrounds, after simultaneously fitting all the control regions. The pre-fit yields for a representative $m(\tilde{t}_1,\tilde{\chi}_1^0)=(550,470)$ GeV signal is included. Processes with top quarks and multiple vector bosons are included in "Other". The right-most bin does not include the overflow entry but the $x$-axis range is chosen to include all observed data.

Distribution of $R_{\mathrm{ISR}}$ in SR-Comp3 showing the data and the expected backgrounds, after simultaneously fitting all the control regions. The pre-fit yields for a representative $m(\tilde{t}_1,\tilde{\chi}_1^0)=(550,375)$ GeV signal is included. Processes with top quarks and multiple vector bosons are included in "Other". The right-most bin does not include the overflow entry but the $x$-axis range is chosen to include all observed data.

Acceptance across the SUSY signal grid for SR-Comp-1c.

Acceptance across the SUSY signal grid for SR-HM1.

Acceptance across the SUSY signal grid for SR-HM2.

Acceptance across the SUSY signal grid for SR-HM3.

Acceptance across the SUSY signal grid for SR-HM-Disc.

Acceptance across the SUSY signal grid for SR-Comp1.

Acceptance across the SUSY signal grid for SR-Comp2.

Acceptance across the SUSY signal grid for SR-Comp3.

Acceptance across the $\mathrm{LQ}^\mathrm{u}_{21}$ signal grid for SR-HM1.

Acceptance across the $\mathrm{LQ}^\mathrm{u}_{21}$ signal grid for SR-HM2.

Acceptance across the $\mathrm{LQ}^\mathrm{u}_{21}$ signal grid for SR-HM3.

Acceptance across the $\mathrm{LQ}^\mathrm{u}_{21}$ signal grid for SR-HM-Disc.

Acceptance across the $\mathrm{LQ}^\mathrm{u}_{22}$ signal grid for SR-HM1.

Acceptance across the $\mathrm{LQ}^\mathrm{u}_{22}$ signal grid for SR-HM2.

Acceptance across the $\mathrm{LQ}^\mathrm{u}_{22}$ signal grid for SR-HM3.

Acceptance across the $\mathrm{LQ}^\mathrm{u}_{22}$ signal grid for SR-HM-Disc.

Acceptance for the $\mathrm{vLQ}^\mathrm{u,min}_{23}$ signal model in SR-HM1.

Acceptance for the $\mathrm{vLQ}^\mathrm{u,min}_{23}$ signal model in SR-HM2.

Acceptance for the $\mathrm{vLQ}^\mathrm{u,min}_{23}$ signal model in SR-HM3.

Acceptance for the $\mathrm{vLQ}^\mathrm{u,min}_{23}$ signal model in SR-HM-Disc.

Acceptance for the $\mathrm{vLQ}^\mathrm{u,YM}_{23}$ signal model in SR-HM1.

Acceptance for the $\mathrm{vLQ}^\mathrm{u,YM}_{23}$ signal model in SR-HM2.

Acceptance for the $\mathrm{vLQ}^\mathrm{u,YM}_{23}$ signal model in SR-HM3.

Acceptance for the $\mathrm{vLQ}^\mathrm{u,YM}_{23}$ signal model in SR-HM-Disc.

Efficiency for the $\mathrm{vLQ}^\mathrm{u,min}_{23}$ signal model in SR-HM1. Due to the limited statistical power of the signal samples, efficiencies can fluctuate and can drop to zero.

Efficiency for the $\mathrm{vLQ}^\mathrm{u,min}_{23}$ signal model in SR-HM2. Due to the limited statistical power of the signal samples, efficiencies can fluctuate and can drop to zero.

Efficiency for the $\mathrm{vLQ}^\mathrm{u,min}_{23}$ signal model in SR-HM3. Due to the limited statistical power of the signal samples, efficiencies can fluctuate and can drop to zero.

Efficiency for the $\mathrm{vLQ}^\mathrm{u,min}_{23}$ signal model in SR-HM-Disc. Due to the limited statistical power of the signal samples, efficiencies can fluctuate and can drop to zero.

Efficiency for the $\mathrm{vLQ}^\mathrm{u,YM}_{23}$ signal model in SR-HM1. Due to the limited statistical power of the signal samples, efficiencies can fluctuate and can drop to zero.

Efficiency for the $\mathrm{vLQ}^\mathrm{u,YM}_{23}$ signal model in SR-HM2. Due to the limited statistical power of the signal samples, efficiencies can fluctuate and can drop to zero.

Efficiency for the $\mathrm{vLQ}^\mathrm{u,YM}_{23}$ signal model in SR-HM3. Due to the limited statistical power of the signal samples, efficiencies can fluctuate and can drop to zero.

Efficiency for the $\mathrm{vLQ}^\mathrm{u,YM}_{23}$ signal model in SR-HM-Disc. Due to the limited statistical power of the signal samples, efficiencies can fluctuate and can drop to zero.

Acceptance times efficiency across the SUSY signal grid for SR-Comp-1c.

Acceptance times efficiency across the SUSY signal grid for SR-HM1.

Acceptance times efficiency across the SUSY signal grid for SR-HM2.

Acceptance times efficiency across the SUSY signal grid for SR-HM3.

Acceptance times efficiency across the SUSY signal grid for SR-HM-Disc.

Acceptance times efficiency across the SUSY signal grid for SR-Comp1.

Acceptance times efficiency across the SUSY signal grid for SR-Comp2.

Acceptance times efficiency across the SUSY signal grid for SR-Comp3.

Acceptance times efficiency across the $\mathrm{LQ}^\mathrm{u}_{21}$ signal grid for SR-HM1.

Acceptance times efficiency across the $\mathrm{LQ}^\mathrm{u}_{21}$ signal grid for SR-HM2.

Acceptance times efficiency across the $\mathrm{LQ}^\mathrm{u}_{21}$ signal grid for SR-HM3.

Acceptance times efficiency across the $\mathrm{LQ}^\mathrm{u}_{21}$ signal grid for SR-HM-Disc.

Acceptance times efficiency across the $\mathrm{LQ}^\mathrm{u}_{22}$ signal grid for SR-HM1.

Acceptance times efficiency across the $\mathrm{LQ}^\mathrm{u}_{22}$ signal grid for SR-HM2.

Acceptance times efficiency across the $\mathrm{LQ}^\mathrm{u}_{22}$ signal grid for SR-HM3.

Acceptance times efficiency across the $\mathrm{LQ}^\mathrm{u}_{22}$ signal grid for SR-HM-Disc.

Acceptance times efficiency for the $\mathrm{vLQ}^\mathrm{u,min}_{23}$ signal model in SR-HM1.

Acceptance times efficiency for the $\mathrm{vLQ}^\mathrm{u,min}_{23}$ signal model in SR-HM2.

Acceptance times efficiency for the $\mathrm{vLQ}^\mathrm{u,min}_{23}$ signal model in SR-HM3.

Acceptance times efficiency for the $\mathrm{vLQ}^\mathrm{u,min}_{23}$ signal model in SR-HM-Disc.

Acceptance times efficiency for the $\mathrm{vLQ}^\mathrm{u,YM}_{23}$ signal model in SR-HM1.

Acceptance times efficiency for the $\mathrm{vLQ}^\mathrm{u,YM}_{23}$ signal model in SR-HM2.

Acceptance times efficiency for the $\mathrm{vLQ}^\mathrm{u,YM}_{23}$ signal model in SR-HM3.

Acceptance times efficiency for the $\mathrm{vLQ}^\mathrm{u,YM}_{23}$ signal model in SR-HM-Disc.

Cutflow table for SR-Comp-1c using the $m(\tilde{t}_{1},\tilde{\chi}_{1}^{0}) = (450,430)$ GeV signal point as the benchmark. All jet-related variables use jets with $p_\mathrm{T}>20$ GeV. The "Preselection" requirement includes: $E_\mathrm{T}^\mathrm{miss}>250$ GeV; events containing electrons or muons are vetoed; at least two jets must be present of which at least one must be identified as a $c$-tagged jet; events with jets that have been identified as $b$-tagged are discarded; the minimum azimuthal angular ($\phi$) distance between the (up to) four leading jets and the $\vec{p}_\mathrm{T}^\mathrm{miss}$ is required to be greater than 0.4.

Cutflow table for SR-Comp1 using the $m(\tilde{t}_{1},\tilde{\chi}_{1}^{0}) = (600,550)$ GeV signal point as the benchmark. All jet-related variables use jets with $p_\mathrm{T}>20$ GeV. The "Preselection" requirement includes: $E_\mathrm{T}^\mathrm{miss}>250$ GeV; events containing electrons or muons are vetoed; at least two jets must be present of which at least one must be identified as a $c$-tagged jet; events with jets that have been identified as $b$-tagged are discarded; the minimum azimuthal angular ($\phi$) distance between the (up to) four leading jets and the $\vec{p}_\mathrm{T}^\mathrm{miss}$ is required to be greater than 0.4.

Cutflow table for SR-Comp2 using the $m(\tilde{t}_{1},\tilde{\chi}_{1}^{0}) = (550,470)$ GeV signal point as the benchmark. All jet-related variables use jets with $p_\mathrm{T}>20$ GeV. The "Preselection" requirement includes: $E_\mathrm{T}^\mathrm{miss}>250$ GeV; events containing electrons or muons are vetoed; at least two jets must be present of which at least one must be identified as a $c$-tagged jet; events with jets that have been identified as $b$-tagged are discarded; the minimum azimuthal angular ($\phi$) distance between the (up to) four leading jets and the $\vec{p}_\mathrm{T}^\mathrm{miss}$ is required to be greater than 0.4.

Cutflow table for SR-Comp3 using the $m(\tilde{t}_{1},\tilde{\chi}_{1}^{0}) = (550,375)$ GeV signal point as the benchmark. All jet-related variables use jets with $p_\mathrm{T}>20$ GeV. The "Preselection" requirement includes: $E_\mathrm{T}^\mathrm{miss}>250$ GeV; events containing electrons or muons are vetoed; at least two jets must be present of which at least one must be identified as a $c$-tagged jet; events with jets that have been identified as $b$-tagged are discarded; the minimum azimuthal angular ($\phi$) distance between the (up to) four leading jets and the $\vec{p}_\mathrm{T}^\mathrm{miss}$ is required to be greater than 0.4.

Cutflow table for SR-HM1 using the $m(\tilde{t}_{1},\tilde{\chi}_{1}^{0}) = (1000,1)$ GeV signal point as the benchmark. All jet-related variables use jets with $p_\mathrm{T}>40$ GeV, however, the $E_\mathrm{T}^\mathrm{miss}$ is calculated with jets with $p_\mathrm{T}>20$ GeV. The "Preselection" requirement includes: $E_\mathrm{T}^\mathrm{miss}>250$ GeV; events containing electrons or muons are vetoed; at least two jets must be present of which at least one must be identified as a $c$-tagged jet; events with jets that have been identified as $b$-tagged are discarded; the minimum azimuthal angular ($\phi$) distance between the (up to) four leading jets and the $\vec{p}_\mathrm{T}^\mathrm{miss}$ is required to be greater than 0.4.

Cutflow table for SR-HM2 using the $m(\tilde{t}_{1},\tilde{\chi}_{1}^{0}) = (750,450)$ GeV signal point as the benchmark. All jet-related variables use jets with $p_\mathrm{T}>40$ GeV, however, the $E_\mathrm{T}^\mathrm{miss}$ is calculated with jets with $p_\mathrm{T}>20$ GeV. The "Preselection" requirement includes: $E_\mathrm{T}^\mathrm{miss}>250$ GeV; events containing electrons or muons are vetoed; at least two jets must be present of which at least one must be identified as a $c$-tagged jet; events with jets that have been identified as $b$-tagged are discarded; the minimum azimuthal angular ($\phi$) distance between the (up to) four leading jets and the $\vec{p}_\mathrm{T}^\mathrm{miss}$ is required to be greater than 0.4.

Cutflow table for SR-HM3 using the $m(\tilde{t}_{1},\tilde{\chi}_{1}^{0}) = (750,450)$ GeV signal point as the benchmark. All jet-related variables use jets with $p_\mathrm{T}>40$ GeV, however, the $E_\mathrm{T}^\mathrm{miss}$ is calculated with jets with $p_\mathrm{T}>20$ GeV. The "Preselection" requirement includes: $E_\mathrm{T}^\mathrm{miss}>250$ GeV; events containing electrons or muons are vetoed; at least two jets must be present of which at least one must be identified as a $c$-tagged jet; events with jets that have been identified as $b$-tagged are discarded; the minimum azimuthal angular ($\phi$) distance between the (up to) four leading jets and the $\vec{p}_\mathrm{T}^\mathrm{miss}$ is required to be greater than 0.4.

Cutflow table for SR-HM-Disc using the $m(\tilde{t}_{1},\tilde{\chi}_{1}^{0}) = (750,450)$ GeV signal point as the benchmark. All jet-related variables use jets with $p_\mathrm{T}>40$ GeV, however, the $E_\mathrm{T}^\mathrm{miss}$ is calculated with jets with $p_\mathrm{T}>20$ GeV. The "Preselection" requirement includes: $E_\mathrm{T}^\mathrm{miss}>250$ GeV; events containing electrons or muons are vetoed; at least two jets must be present of which at least one must be identified as a $c$-tagged jet; events with jets that have been identified as $b$-tagged are discarded; the minimum azimuthal angular ($\phi$) distance between the (up to) four leading jets and the $\vec{p}_\mathrm{T}^\mathrm{miss}$ is required to be greater than 0.4.

Cutflow table for SR-HM1 using the $m(\mathrm{LQ}_{21}^\mathrm{u}) = 600$ GeV signal point, with a 50% branching fraction to $c\nu$, as the benchmark. All jet-related variables use jets with $p_\mathrm{T}>40$ GeV, however, the $E_\mathrm{T}^\mathrm{miss}$ is calculated with jets with $p_\mathrm{T}>20$ GeV. The "Preselection" requirement includes: $E_\mathrm{T}^\mathrm{miss}>250$ GeV; events containing electrons or muons are vetoed; at least two jets must be present of which at least one must be identified as a $c$-tagged jet; events with jets that have been identified as $b$-tagged are discarded; the minimum azimuthal angular ($\phi$) distance between the (up to) four leading jets and the $\vec{p}_\mathrm{T}^\mathrm{miss}$ is required to be greater than 0.4.

Cutflow table for SR-HM2 using the $m(\mathrm{LQ}_{21}^\mathrm{u}) = 600$ GeV signal point, with a 50% branching fraction to $c\nu$, as the benchmark. All jet-related variables use jets with $p_\mathrm{T}>40$ GeV, however, the $E_\mathrm{T}^\mathrm{miss}$ is calculated with jets with $p_\mathrm{T}>20$ GeV. The "Preselection" requirement includes: $E_\mathrm{T}^\mathrm{miss}>250$ GeV; events containing electrons or muons are vetoed; at least two jets must be present of which at least one must be identified as a $c$-tagged jet; events with jets that have been identified as $b$-tagged are discarded; the minimum azimuthal angular ($\phi$) distance between the (up to) four leading jets and the $\vec{p}_\mathrm{T}^\mathrm{miss}$ is required to be greater than 0.4.

Cutflow table for SR-HM3 using the $m(\mathrm{LQ}_{21}^\mathrm{u}) = 600$ GeV signal point, with a 50% branching fraction to $c\nu$, as the benchmark. All jet-related variables use jets with $p_\mathrm{T}>40$ GeV, however, the $E_\mathrm{T}^\mathrm{miss}$ is calculated with jets with $p_\mathrm{T}>20$ GeV. The "Preselection" requirement includes: $E_\mathrm{T}^\mathrm{miss}>250$ GeV; events containing electrons or muons are vetoed; at least two jets must be present of which at least one must be identified as a $c$-tagged jet; events with jets that have been identified as $b$-tagged are discarded; the minimum azimuthal angular ($\phi$) distance between the (up to) four leading jets and the $\vec{p}_\mathrm{T}^\mathrm{miss}$ is required to be greater than 0.4.

Cutflow table for SR-HM-Disc using the $m(\mathrm{LQ}_{21}^\mathrm{u}) = 600$ GeV signal point, with a 50% branching fraction to $c\nu$, as the benchmark. All jet-related variables use jets with $p_\mathrm{T}>40$ GeV, however, the $E_\mathrm{T}^\mathrm{miss}$ is calculated with jets with $p_\mathrm{T}>20$ GeV. The "Preselection" requirement includes: $E_\mathrm{T}^\mathrm{miss}>250$ GeV; events containing electrons or muons are vetoed; at least two jets must be present of which at least one must be identified as a $c$-tagged jet; events with jets that have been identified as $b$-tagged are discarded; the minimum azimuthal angular ($\phi$) distance between the (up to) four leading jets and the $\vec{p}_\mathrm{T}^\mathrm{miss}$ is required to be greater than 0.4.

Total invariant mass distribution $m_{4\ell}$ in Signal Region 2.

Selected events in the ($m_{4\ell}$, $\left\langle m_{\ell\ell}\right\rangle$) plane, SR1

Selected events in the ($m_{4\ell}$, $\left\langle m_{\ell\ell}\right\rangle$) plane, SR2

Expected background events in the $(m_{4\ell}, \langle m_{\ell\ell}\rangle)$ plane, SR1

Expected signal shape for $(m_{S}, m_{Z_d}) = (110~\text{GeV},30~\text{GeV}$) in the $(m_{4\ell}, \langle m_{\ell\ell}\rangle)$ plane, SR1. The signal distributions are normalized to unit volume.

Expected background events in the $(m_{4\ell}, \langle m_{\ell\ell}\rangle)$ plane, SR2. Events that satisfy $|m_{ab,cd} - m_Z| < 8~\text{GeV}$ are removed by the Z-veto requirement, however not all events lying behind the mask in the plot, corresponding to $\langle m_{\ell\ell}\rangle$ values between 83 and 99 GeV, are deleted.

Expected signal shape for $(m_{S}, m_{Z_{d}}) = (750~\text{GeV},150~\text{GeV}$) in the $(m_{4\ell}, \langle m_{\ell\ell}\rangle)$ plane, SR2. The signal distributions are normalized to unit volume. Events that satisfy $|m_{ab,cd} - m_Z| < 8~\text{GeV}$ are removed by the Z-veto requirement, however not all events lying behind the mask in the plot, corresponding to $\langle m_{\ell\ell}\rangle$ values between 83 and 99 GeV, are deleted.

Expected 95% CL limit on $\sigma \mathcal{B}(S\rightarrow Z_{d}Z_{d} \rightarrow 4\ell)$, SR1

Observed 95% CL limit on $\sigma \mathcal{B}(S\rightarrow Z_{d}Z_{d} \rightarrow 4\ell)$, SR1

Observed / Expected 95% CL limit ratio in SR1

Expected 95% CL limit on $\mathcal{B}(S\rightarrow Z_{d}Z_{d} \rightarrow 4\ell)$ with Z-veto, SR2

Observed 95% CL limit on $\sigma \mathcal{B}(S\rightarrow Z_{d}Z_{d} \rightarrow 4\ell)$ with Z-veto, SR2

Observed / Expected 95% CL limit ratio with Z-veto, SR2

Local $p_0$-values in the ($m_{S}, m_{Z_{d}}$) plane, SR1

Local $p_0$-values in the ($m_{S}, m_{Z_{d}}$) plane, SR2 with Z-veto applied

Observed data in Signal Region 1 in the $(m_{4\ell}, \langle m_{\ell\ell}\rangle)$ plane.

Observed data in Signal Region 2 in the $(m_{4\ell}, \langle m_{\ell\ell}\rangle)$ plane. Events that satisfy $|m_{ab,cd} - m_Z| < 8~\text{GeV}$ are removed by the Z-veto requirement, however not all events lying behind the mask in the plot, corresponding to <m_ll> values between 83 and 99 GeV, are deleted.

Distributions of the average dilepton mass $\left\langle m_{\ell\ell}\right\rangle = \frac{1}{2}\left(m_{ab} + m_{cd}\right)$ for Signal Region 1 in the $4e$ final state.

Distributions of the average dilepton mass $\left\langle m_{\ell\ell}\right\rangle = \frac{1}{2}\left(m_{ab} + m_{cd}\right)$ for Signal Region 1 in the $2e2\mu$ final state.

Distributions of the average dilepton mass $\left\langle m_{\ell\ell}\right\rangle = \frac{1}{2}\left(m_{ab} + m_{cd}\right)$ for Signal Region 1 in the $4\mu$ final state.

Distributions of the average dilepton mass $\left\langle m_{\ell\ell}\right\rangle = \frac{1}{2}\left(m_{ab} + m_{cd}\right)$ for Signal Region 2 in the $4e$ final state.

Distributions of the average dilepton mass $\left\langle m_{\ell\ell}\right\rangle = \frac{1}{2}\left(m_{ab} + m_{cd}\right)$ for Signal Region 2 in the $2e2\mu$ final state.

Distributions of the average dilepton mass $\left\langle m_{\ell\ell}\right\rangle = \frac{1}{2}\left(m_{ab} + m_{cd}\right)$ for Signal Region 2 in the $4\mu$ final state.

Distributions of the total invariant mass $m_{4\ell}$ for Signal Region 1 in the $4e$ final state. The SR1 requirement $m_{4\ell} < 115~\text{GeV}$ is not applied here.

Distributions of the total invariant mass $m_{4\ell}$ for Signal Region 1 in the $2e2\mu$ final state. The SR1 requirement $m_{4\ell} < 115~\text{GeV}$ is not applied here.

Distributions of the total invariant mass $m_{4\ell}$ for Signal Region 1 in the $4\mu$ final state. The SR1 requirement $m_{4\ell} < 115~\text{GeV}$ is not applied here.

Distributions of the total invariant mass $m_{4\ell}$ for Signal Region 2 in the $4e$ final state.

Distributions of the total invariant mass $m_{4\ell}$ for Signal Region 2 in the $2e2\mu$ final state.

Distributions of the total invariant mass $m_{4\ell}$ for Signal Region 2 in the $4\mu$ final state.

Post-fit distribution of the GNN score evaluated with $m_{H/A}$ = 400 GeV in the validation region in the 2LOS region with $\geq 8$ jets. These regions do not enter the fit. The post-fit background prediction is obtained using the post-fit nuisance parameters from the background-only fit in the control and signal regions.

Observed and expected 95% CL upper limits on the cross-section times branching ratio,$ \sigma(pp \rightarrow t\bar{t}H/A ) \times B(H/A \rightarrow t\bar{t})$, as a function of $m_{H/A}$, obtained using the 1L/2LOS final states.

Observed and expected 95% CL lower limits on tanβ as a function of the $m_{H/A}$ mass obtained using the 1L/2LOS final states, assuming a Type-II 2HDM in the alignment limit. Values of tanβ below the observed limit are excluded. The scenario where both the scalar $H$ and pseudo-scalar $A$ contribute with $m_H = m_A$ is shown.

Observed and expected 95% CL lower limits on tanβ as a function of the $m_{H/A}$ mass obtained using the 1L/2LOS final states, assuming a Type-II 2HDM in the alignment limit. Values of tanβ below the observed limit are excluded. The scenario with the contribution from scalar $H$ only is shown.

Observed and expected 95% CL lower limits on tanβ as a function of the $m_{H/A}$ mass obtained using the 1L/2LOS final states, assuming a Type-II 2HDM in the alignment limit. Values of tanβ below the observed limit are excluded. The scenario with the contribution from pseudo-scalar $A$ only is shown.

Expected and observed 95% CL upper limits on the cross-section times branching ratio,$ \sigma(pp \rightarrow t\bar{t}H/A ) \times B(H/A \rightarrow t\bar{t})$, as a function of $m_{H/A}$, obtained from the combination of the 1L/2LOS and 2LSS/ML final states.

Expected and observed 95% CL lower limits on tanβ as a function of the $m_{H/A}$ mass obtained using the 1L/2LOS and 2LSS/ML final states, assuming a Type-II 2HDM in the alignment limit. Values of tanβ below the observed limit are excluded. The scenario where both the scalar $H$ and pseudo-scalar $A$ contribute with $m_H = m_A$ is shown.

Expected and observed 95% CL lower limits on tanβ as a function of the $m_{H/A}$ mass obtained using the 1L/2LOS and 2LSS/ML final states, assuming a Type-II 2HDM in the alignment limit. Values of tanβ below the observed limit are excluded. The scenario with the contribution from scalar $H$ only is shown.

Expected and observed 95% CL lower limits on tanβ as a function of the $m_{H/A}$ mass obtained using the 1L/2LOS and 2LSS/ML final states, assuming a Type-II 2HDM in the alignment limit. Values of tanβ below the observed limit are excluded. The scenario with the contribution from pseudo-scalar $A$ only is shown.

Expected and Observed 95% CL upper limits on the $ \sigma(pp \rightarrow t\bar{t})\times B(S_8\rightarrow t\bar{t})$ production cross-section as a function of $m_{S_8}$, obtained from the combination of the 1L/2LOS and 2LSS/ML final states. The expected limits from the individual 1L/2LOS and 2LSS/ML analyses are also shown.

Post-fit distribution of the GNN scores evaluated with $m_{H/A}$ = 700 GeV in the 1L region with $\geq 10$ jets and four $b$-tagged jets. The fit is performed under the background-only hypothesis.

Post-fit distribution of the GNN scores evaluated with $m_{H/A}$ = 700 GeV in the 2LOS region with $\geq 8$ jets and $\geq 4$ $b$-tagged jets. The fit is performed under the background-only hypothesis.

Post-fit distribution of the GNN scores evaluated with $m_{H/A}=$1000 GeV,in the 1L region with $\geq 10$ jets four $b$-tagged jets. The fit is performed under the background-only hypothesis.

Post-fit distribution of the GNN scores evaluated with $m_{H/A}=$1000 GeV in the 2LOS region with $\geq 8$ jets and $\geq 4$ $b$-tagged jets. The fit is performed under the background-only hypothesis.

Post-fit distribution of the most important global features used in the GNN training, Sum of the pcb scores of the six jets with the highest scores ($\sum_{i\in[1,6]}\mathrm{pcb}_i$), in the region where the training is performed, i.e., the region with $\geq 9$ jets and $\geq3$ $b$-tagged jets in the 1L channel. The fit is performed under the background-only hypothesis using the GNN scores evaluated with $m_{H/A} = 400$ GeV.

Post-fit distribution of the most important global features used in the GNN training, Sum of the pcb scores of the six jets with the highest scores ($\sum_{i\in[1,6]}\mathrm{pcb}_i$), in the region where the training is performed i.e.the region with $\geq 7$ jets and $\geq3$ $b$-tagged jets in the 2LOS channel. The fit is performed under the background-only hypothesis using the GNN scores evaluated with $m_{H/A} = 400$ GeV.

Post-fit distribution of the most important global features used in the GNN training, $p_{\mathrm{T}}$ sum of all reconstructed leptons and jets ($\mathrm{H}_{\mathrm{T}}^{\mathrm{all}}$), in the region where the training is performed, i.e., the region with $\geq 9$ jets and $\geq3$ $b$-tagged jets in the 1L channel. The fit is performed under the background-only hypothesis using the GNN scores evaluated with $m_{H/A} = 400$ GeV.

Post-fit distribution of the most important global features used in the GNN training, $p_{\mathrm{T}}$ sum of all reconstructed leptons and jets ($\mathrm{H}_{\mathrm{T}}^{\mathrm{all}}$), in the region where the training is performed, i.e. the region with $\geq 7$ jets and $\geq3$ $b$-tagged jets in the 2LOS channel. The fit is performed under the background-only hypothesis using the GNN scores evaluated with $m_{H/A} = 400$ GeV.

Post-fit distribution of the most important global features used in the GNN training, Number of jets, in the region where the training is performed, i.e., the region with $\geq 9$ jets and $\geq3$ $b$-tagged jets in the 1L channel. The fit is performed under the background-only hypothesis using the GNN scores evaluated with $m_{H/A} = 400$ GeV.

Post-fit distribution of the most important global features used in the GNN training, Number of jets, in the region where the training is performed, i.e., the region with $\geq 7$ jets and $\geq3$ $b$-tagged jets in the 2LOS channel. The fit is performed under the background-only hypothesis using the GNN scores evaluated with $m_{H/A} = 400$ GeV.

The cutflow table for $N1$ and $N2$ signal samples for different mass points. The samples consist of both $ee$ and $\mu\mu$ final states in equal ratio. Each sample is normalized to a total cross-section of 0.1 pb. The abbreviations used in the table are, SC = Same Charge, SF = Same Flavor.

The cutflow table for $N3$ signal samples for different mass points. The samples consist of both $ee$ and $\mu\mu$ final states in equal ratio. Each sample is normalized to a total cross-section of 10 pb. The abbreviations used in the table are, SS = Same Charge, SF = Same Flavor.

Expected and observed upper limits on the strength of HNL mixing with electron neutrinos

Expected and observed upper limits on the strength of HNL mixing with muon neutrinos

Expected and observed upper limits on the strength of HNL mixing with tau neutrinos