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.

Data selection efficiency as a function of nuclear recoil energy

Data points used in analysis in log_10(S2)-S1 space

Two graphs show the results of the scan over the horizontal and vertical displacements of the antiproton beam (see Table 3, before) and the horizontal and vertical angles (on the right). The color represents the intensity of the signal obtained on the MCP from the annihilations of the trapped antiprotons. The parameter space has been organized in this way, assuming that displacements and angles have independent effects, not for physics reasons, but because scanning over the full parameter space would have been impossible time-wise (10 steps per dimension 4 dimensions x 5 min of duration of the script ~35 days!).

Results of the beam steering optimization. Convergence plot of the highest observed number of annihilation events.

Results of the beam steering optimization. Density plots of the evaluations in the four-parameter space dimensions.

Results of the beam steering optimization. Density plots of the evaluations in the four-parameter space dimensions.

Results of the beam steering optimization. Density plots of the evaluations in the four-parameter space dimensions.

Results of the beam steering optimization. Density plots of the evaluations in the four-parameter space dimensions.

Results of the trap closing time optimization. Convergence plot of the highest observed number of annihilation events.

Results of the trap closing time optimization. Number of observed annihilation events as a function of the trap closing time. The result is different from the one in 2022 (Figure 6) because the capture electrode voltage was raised from 10 to 15 kV.

Synchronization results in the asynchronous parallel operation mode, showing the time difference between the start of different parallel scripts, in a schedule of 50 scripts. Both plots are accompanied by a single point plot adjacent on the right, representing the average δT over all 50 runs. In the same-duration script case (a), the high average can be explained by intrinsic delays included in Tamer and Monkey to avoid race conditions. In the different-duration script case (b), a linear trend is visible that comes from the increase in the duration time between different Kaslis. The bottom plot shows δT corrected for the linear trend, showing the average jitter value of -5 to 5 s.

Synchronization results in the asynchronous parallel operation mode, showing the time difference between the start of different parallel scripts, in a schedule of 50 scripts. Both plots are accompanied by a single point plot adjacent on the right, representing the average δT over all 50 runs. In the same-duration script case (a), the high average can be explained by intrinsic delays included in Tamer and Monkey to avoid race conditions. In the different-duration script case (b), a linear trend is visible that comes from the increase in the duration time between different Kaslis. The bottom plot shows δT corrected for the linear trend, showing the average jitter value of -5 to 5 s.

Synchronization results in the asynchronous parallel operation mode, showing the time difference between the start of different parallel scripts, in a schedule of 50 scripts. Both plots are accompanied by a single point plot adjacent on the right, representing the average δT over all 50 runs. In the same-duration script case (a), the high average can be explained by intrinsic delays included in Tamer and Monkey to avoid race conditions. In the different-duration script case (b), a linear trend is visible that comes from the increase in the duration time between different Kaslis. The bottom plot shows δT corrected for the linear trend, showing the average jitter value of -5 to 5 s.

Synchronization results in the synchronous parallel operation mode, showing the time difference between the start of different parallel scripts, in a schedule of 50 scripts. Both in the same-duration case (a) and in the different-duration case (b), the time difference between the start of different parallel scripts is stable around 5 ms, independently of the duration of the scripts. Both plots are accompanied by a single point plot adjacent on the right, representing the average δT over all 50 runs.

Synchronization results in the synchronous parallel operation mode, showing the time difference between the start of different parallel scripts, in a schedule of 50 scripts. Both in the same-duration case (a) and in the different-duration case (b), the time difference between the start of different parallel scripts is stable around 5 ms, independently of the duration of the scripts. Both plots are accompanied by a single point plot adjacent on the right, representing the average δT over all 50 runs.

'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 $\langle p_{T} \rangle$.

Directed flow vs pseudorapidity.

Directed flow vs pseudorapidity.

Directed flow vs pseudorapidity.

Directed flow vs pseudorapidity.

Directed flow vs pseudorapidity.

Directed flow vs pseudorapidity.

Directed flow vs pseudorapidity.

Directed flow vs pseudorapidity.

Directed flow vs pseudorapidity.

Directed flow vs pseudorapidity.

Directed flow vs pseudorapidity.

Directed flow vs pseudorapidity.

Directed flow vs pseudorapidity.

Directed flow vs pseudorapidity.

Directed flow vs pseudorapidity.

Directed flow vs pseudorapidity.

Directed flow vs pseudorapidity.

Directed flow vs pseudorapidity.

Directed flow vs pseudorapidity.

Directed flow vs pseudorapidity.

Directed flow vs pseudorapidity.

Directed flow vs pseudorapidity.

Directed flow vs pseudorapidity.

Directed flow vs pseudorapidity.

Directed flow vs pseudorapidity.

Directed flow as a function of (pseudorapidity-y_beam) for Au+Au collisions at sqrt{s_NN} = 19.6 GeV for 0-40% centrality.

Directed flow as a function of (pseudorapidity-y_beam) for Au+Au collisions at sqrt{s_NN} = 27 GeV for 0-40% centrality.

Directed flow as a function of pseudorapidity for Au+Au collisions at sqrt{s_NN} = 19.6 GeV for 10-40% centrality.

Directed flow as a function of pseudorapidity for Au+Au collisions at sqrt{s_NN} = 27 GeV for 10-40% centrality.

Isoscalar interaction coupling limit for Lagrangian 7

Isoscalar interaction coupling limit for Lagrangian 10

Isovector interaction coupling limit for Lagrangian 14

Isoscalar interaction coupling limit for Lagrangian 6

Isovector interaction coupling limit for Lagrangian 7

Isovector interaction coupling limit for Lagrangian 9

Isoscalar interaction coupling limit for Lagrangian 18

Isoscalar interaction coupling limit for Lagrangian 4

Isoscalar interaction coupling limit for Lagrangian 2

Isovector interaction coupling limit for Lagrangian 18

Isoscalar interaction coupling limit for Lagrangian 9

Isovector interaction coupling limit for Lagrangian 1

Isovector interaction coupling limit for Lagrangian 8

Isovector interaction coupling limit for Lagrangian 5

Isovector interaction coupling limit for Lagrangian 17

Isoscalar interaction coupling limit for Lagrangian 5

Isoscalar interaction coupling limit for Lagrangian 8

Isovector interaction coupling limit for Lagrangian 12

Isoscalar interaction coupling limit for Lagrangian 11

Isovector interaction coupling limit for Lagrangian 15

Isoscalar interaction coupling limit for Lagrangian 3

Isoscalar interaction coupling limit for Lagrangian 13

Isoscalar interaction coupling limit for Lagrangian 16

Isovector interaction coupling limit for Lagrangian 3

Isovector interaction coupling limit for Lagrangian 20

Isovector interaction coupling limit for Lagrangian 4

Isoscalar interaction coupling limit for Lagrangian 14

Isoscalar interaction coupling limit for Lagrangian 12

Isovector interaction coupling limit for Lagrangian 13

Isovector interaction coupling limit for Lagrangian 11

Isoscalar interaction coupling limit for Lagrangian 20

Isoscalar interaction coupling limit for Lagrangian 17

Isoscalar interaction coupling limit for Lagrangian 15

Isovector interaction coupling limit for Lagrangian 6

Isovector interaction coupling limit for Lagrangian 2

Isovector interaction coupling limit for Lagrangian 10

Isovector interaction coupling limit for Lagrangian 16