$\xi$ distributions for different jet $p_T$ bins.

$\xi$ distributions for different jet $p_T$ bins.

The $j_T/p_{T}^{\rm jet}$ distributions for different jet $p_T$ bins.

The $j_T/p_{T}^{\rm jet}$ distributions for different jet $p_T$ bins.

$r$ distributions for different jet $p_T$ bins.

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.

$a_2(1320)$ differential cross section in the m=-2 projection split into different reflectivity components, $\frac{d\sigma^+_{-2}}{dt}$ and $\frac{d\sigma^-_{-2}}{dt}$, in bins of four-momentum transfer. The first uncertainty is statistical, the second systematic.

$a_2(1320)$ differential cross section in the m=0 projection split into different reflectivity components, $\frac{d\sigma^+_{0}}{dt}$ and $\frac{d\sigma^-_{0}}{dt}$, in bins of four-momentum transfer. The first uncertainty is statistical, the second systematic.

$a_2(1320)$ differential cross section in the m=+1 projection split into different reflectivity components, $\frac{d\sigma^+_{+1}}{dt}$ and $\frac{d\sigma^-_{+1}}{dt}$, in bins of four-momentum transfer. The first uncertainty is statistical, the second systematic.

$a_2(1320)$ differential cross section in the m=+2 projection split into different reflectivity components, $\frac{d\sigma^+_{+2}}{dt}$ and $\frac{d\sigma^-_{+2}}{dt}$, in bins of four-momentum transfer. The first uncertainty is statistical, the second systematic.

$A_{LL}$ as a function of parton-level invariant mass for dijets with the East barrel-endcap.

$A_{LL}$ as a function of parton-level invariant mass for dijets with the West barrel-endcap.

$A_{LL}$ as a function of parton-level invariant mass for dijets with the endcap-endcap.

Distributions of the $\mathrm{NN^{SvsB}}$ output for data and the expected background after the likelihood fit in the $SR_{cQu --}$ signal region. The post-fit background expectations are shown as filled histograms, the combined pre-fit background expectations are shown as dashed lines. The signal distribution using the Wilson coefficient values $c_{tu}^{(1)}=0.04$, $c_{Qu}^{(1)}=0.1$, $c_{Qu}^{(8)}=0.1$ is shown with a dotted line, normalized to the same number of events as the background.

Summary of the observed and predicted number of events in the five 2$\ell$ control regions. The background prediction is shown after the combined likelihood fit to data under the signal-plus-background hypothesis across all control regions and signal regions. The uncertainties in the total yields are smaller than the sum in quadrature of the uncertainties in the individual contributions due to anti-correlations resulting from the likelihood fit. Int Conv refers to events with photon conversions in the inner detector, while Mat Conv refers to events with photon conversions in the detector material. QMisID refers to events with charge-misidentified lepton.

Summary of the observed and predicted number of events in the four 3$\ell$ control regions. The background prediction is shown after the combined likelihood fit to data under the signal-plus-background hypothesis across all control regions and signal regions. The uncertainties in the total yields are smaller than the sum in quadrature of the uncertainties in the individual contributions due to anti-correlations resulting from the likelihood fit. Int Conv refers to events with photon conversions in the inner detector, while Mat Conv refers to events with photon conversions in the detector material. QMisID refers to events with charge-misidentified lepton.

Comparison of the observed limits on the three WCs to the limit obtained by the ATLAS Run~1 analysis of events with $b$-tagged jets and a same-sign lepton pair [JHEP10(2015)150]. The cross-section limits from that analysis are converted to the limits on the WCs by using the fitted EFT parametrization. The bounds on the WCs are shown at the 68$\%$ CL (solid) and/or 95$\%$ CL (dashed) levels. For the ATLAS Run~1 analysis only the bounds at 95$\%$ CL are available. The vertical bar represents the SM prediction. The new-physics scale is set to $\Lambda = 1 \, \text{TeV}$.

Observed lower limits at 95$\%$ confidence level on the scale of new physics $\Lambda$ for Wilson coefficient values of 0.01, 1 and $4\pi^2$. The limits are compared with the limits obtained by the ATLAS Run~1 analysis of events with $b$-tagged jets and a same-sign lepton pair.

Observed and expected limits at 95$\%$ confidence level on the cross-section of $\sigma(pp \rightarrow tt)$.

2D likelihood scans of the Wilson coefficients $c_{tu}^{(1)}$ versus $c_{Qu}^{(1)}$. The new-physics scale is set to $\Lambda = 1 \, \text{TeV}$. In the table the $2\Delta$NLL values are shown which correspond to the minimized negative log likelihood for a given Wilson coefficient pair.

2D likelihood scans of the Wilson coefficients $c_{tu}^{(1)}$ versus $c_{Qu}^{(8)}$. The new-physics scale is set to $\Lambda = 1 \, \text{TeV}$. In the table the $2\Delta$NLL values are shown which correspond to the minimized negative log likelihood for a given Wilson coefficient pair.

2D likelihood scans of the Wilson coefficients $c_{Qu}^{(1)}$ versus $c_{Qu}^{(8)}$. The new-physics scale is set to $\Lambda = 1 \, \text{TeV}$. In the table the $2\Delta$NLL values are shown which correspond to the minimized negative log likelihood for a given Wilson coefficient pair.

1D-likelihood scan for $c_{tu}^{(1)}$. The observed and expected limits at 68\% and 95\% confidence level (CL) can be read off by finding the intersection of the likelihood scan curve with the 1$\sigma$ and 2$\sigma$ lines. The new-physics scale is set to $\Lambda = 1 \, \text{TeV}$. In the table the $2\Delta$NLL values are shown which correspond to the minimized negative log likelihood for a given Wilson coefficient value.

1D-likelihood scan for $c_{Qu}^{(1)}$. The observed and expected limits at 68\% and 95\% confidence level (CL) can be read off by finding the intersection of the likelihood scan curve with the 1$\sigma$ and 2$\sigma$ lines. The new-physics scale is set to $\Lambda = 1 \, \text{TeV}$. In the table the $2\Delta$NLL values are shown which correspond to the minimized negative log likelihood for a given Wilson coefficient value.

1D-likelihood scan for $c_{Qu}^{(8)}$. The observed and expected limits at 68\% and 95\% confidence level (CL) can be read off by finding the intersection of the likelihood scan curve with the 1$\sigma$ and 2$\sigma$ lines. The new-physics scale is set to $\Lambda = 1 \, \text{TeV}$. In the table the $2\Delta$NLL values are shown which correspond to the minimized negative log likelihood for a given Wilson coefficient value.

JPSI v2 in Au+Au collisions as a function of pT (GeV/c) for 10%--40% centrality with pT binned by [0, 2], [2, 5], and [5, 10] GeV/c.

Self-Normalized $J/\psi$ yields in the same arms before and after dimuon subtraction and the comparison with PYTHIA 8 simulations

Self-normalized $\psi(2S)$ to $J/\psi$ yields ratio as a function of Self-normalized $N_{ch}$ in the same arms

Self-normalized $\psi(2S)$ to $J/\psi$ yields ratio as a function of Self-normalized $N_{ch}$ in opposite arms

'200 GeV, Centrality: 80-100%'

'54.4 GeV, Centrality: 40-60%'

'54.4 GeV, Centrality: 60-80%'

'54.4 GeV, Centrality: 80-100%'

'200 GeV, Centrality: 80-100%'

'$0.4 < M_{ee} < 0.76 GeV/c^{2}$, Centrality: 40-60%'

'$0.4 < M_{ee} < 0.76 GeV/c^{2}$, Centrality: 60-80%'

'$0.4 < M_{ee} < 0.76 GeV/c^{2}$, Centrality: 80-100%'

'$0.76 < M_{ee} < 1.2 GeV/c^{2}$, Centrality: 40-60%'

'$0.76 < M_{ee} < 1.2 GeV/c^{2}$, Centrality: 60-80%'

'$0.76 < M_{ee} < 1.2 GeV/c^{2}$, Centrality: 80-100%'

'$1.2 < M_{ee} < 2.6 GeV/c^{2}$, Centrality: 40-60%'

'$1.2 < M_{ee} < 2.6 GeV/c^{2}$, Centrality: 60-80%'

'$1.2 < M_{ee} < 2.6 GeV/c^{2}$, Centrality: 80-100%'

'54.4 GeV, Centrality: 40-60%'

'54.4 GeV, Centrality: 60-80%'

'54.4 GeV, Centrality: 80-100%'

'200 GeV, Centrality: 80-100%'

'Centrality: 40-60%'

'Centrality: 60-80%'

'Centrality: 80-100%'

'54.4 GeV, Centrality: 40-60%'

'54.4 GeV, Centrality: 60-80%'

'54.4 GeV, Centrality: 80-100%'

'200 GeV, Centrality: 80-100%'

'$-2<cos(4\Delta\phi)>$ as a function of $p_{T}$ @ 200 GeV, Centrality: 80-100%'

'$-2<cos(4\Delta\phi)>$ as a function of $p_{T}$ @ 200 GeV, UPC'

Mean transverse momentum $\langle p_{T} \rangle$ for $\Lambda$ and $K^{0}_{S}$ at mid-rapidity as a function of $N_{\text{part}}$ at 3 GeV.

Hadron 4$\pi$ yields per mean number of participants yield as a function of $N_{\text{part}}$.

Mid-rapidity yield ratios of $\Lambda/p$, $\Xi/\Lambda$, and $K^0_{S}/\Lambda$ at 3 GeV.

The transverse-momentum spectra of $\Lambda$ for different rapidities.

The transverse-momentum spectra of $\Lambda$ for different rapidities.

The transverse-momentum spectra of $\Lambda$ for different rapidities.

The transverse-momentum spectra of $\Lambda$ for different rapidities.

The transverse-momentum spectra of $\Lambda$ for different rapidities.

The transverse-momentum spectra of $\Lambda$ for different rapidities.

The transverse-momentum spectra of $K^{0}_{S}$ for different rapidities.

The transverse-momentum spectra of $K^{0}_{S}$ for different rapidities.

The transverse-momentum spectra of $K^{0}_{S}$ for different rapidities.

The transverse-momentum spectra of $K^{0}_{S}$ for different rapidities.

The transverse-momentum spectra of $K^{0}_{S}$ for different rapidities.

The transverse-momentum spectra of $K^{0}_{S}$ for different rapidities.

Hadron mass dependence of mean transverse momentum $\langle p_{T} \rangle$.