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.

'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'

Data from Figure 2, panel b, U+U, 0-0.5% Centrality, 0.2<p_{T}<3 GeV/c

Data from Figure 3, panel a, 0.2<p_{T}<3 GeV/c

Data from Figure 3, panel b, 0.2<p_{T}<3 GeV/c

Data from Figure 3, panel c, 0.2<p_{T}<3 GeV/c

Data from Figure 3, panel d, 0-5% Centrality, 0.2<p_{T}<3 GeV/c

Data from Figure 3, panel e, 0-5% Centrality, 0.2<p_{T}<3 GeV/c

Data from Figure 3, panel f, 0-5% Centrality, 0.2<p_{T}<3 GeV/c

Data from Figure 4, panel a, Au+Au, 2subevent method, 0.2<p_{T}<3 GeV/c

Data from Figure 4, panel a, U+U, 2subevent method, 0.2<p_{T}<3 GeV/c

Data from Figure 4, panel b, Au+Au, 0.2<p_{T}<3 GeV/c

Data from Figure 4, panel b, U+U, 0.2<p_{T}<3 GeV/c

Data from Figure 4, panel c, Au+Au, 0.2<p_{T}<3 GeV/c

Data from Figure 4, panel c, U+U, 0.2<p_{T}<3 GeV/c

Data from Figure 4, panel d, Au+Au, 0.2<p_{T}<3 GeV/c

Data from Figure 4, panel d, U+U, 0.2<p_{T}<3 GeV/c

Data from Figure 5, panel a, Au+Au, 2subevent method, 0.2<p_{T}<3 GeV/c

Data from Figure 5, panel a, Au+Au, standard method, 0.2<p_{T}<3 GeV/c

Data from Figure 5, panel a, Au+Au, difference, 0.2<p_{T}<3 GeV/c

Data from Figure 5, panel b, Au+Au, 2subevent method, 0.2<p_{T}<3 GeV/c

Data from Figure 5, panel b, Au+Au, standard, 0.2<p_{T}<3 GeV/c

Data from Figure 5, panel b, Au+Au, difference, 0.2<p_{T}<3 GeV/c

Data from Figure 5, panel c, Au+Au, 2subevent method, 0.2<p_{T}<3 GeV/c

Data from Figure 5, panel c, Au+Au, standard, 0.2<p_{T}<3 GeV/c

Data from Figure 5, panel c, Au+Au, difference, 0.2<p_{T}<3 GeV/c

Net-proton cumulant ratios, (a) $C_{2}/C_{1}$, (b) $C_{3}/C_{2}$, (c) $C_{4}/C_{2}$, (d) $C_{5}/C_{1}$, and (e) $C_{6}/C_{2}$ as a function of charged-particle multiplicity from $\sqrt{s}=200$ GeV $p$+$p$ collisions. Black solid lines and red bands represent the statistical and systematic uncertainties, respectively. Cyan points represent event averages for $3 < m_{\rm ch}^{\rm TPC} < 30$, and they are plotted at the corresponding value of $m_{\rm ch}^{\rm TPC}$. The uncertainties on the cyan points are smaller than the marker size. The Skellam baselines are shown as dotted lines. The results of the PYTHIA8 calculations are shown by hatched-golden bands. The golden bands at $m_{\rm ch}^{\rm TPC}\approx 6$ are the results from the PYTHIA8 calculations averaged over multiplicities.

Rapidity-acceptance dependence of the net-proton cumulant ratios, (a) $C_{4}/C_{2}$, (b) $C_{5}/C_{1}$, and (c) $C_{6}/C_{2}$ shown as a function of the charged-particle multiplicity, $m_{\rm ch}^{\rm TPC}$, from $\sqrt{s}=200$ GeV $p$+$p$ collisions. Solid squares, triangles, and circles represent the results with $|y|<0.1$, $0.3$, and $0.5$, respectively. Black solid lines and colored bands show the statistical and systematic uncertainties.The data points and their uncertainties for $|y|<0.1$ and $0.3$ are slightly shifted for clarity. The Skellam baselines are shown by dotted lines.

Net-proton cumulant ratios, (a) $C_{4}/C_{2}$, (b) $C_{5}/C_{1}$, and (c) $C_{6}/C_{2}$ as a function of charged-particle multiplicity for $p$+$p$ collisions and Au+Au collisions at 200 GeV for $|y|<0.5$ and $0.4<p_{\rm T}<2.0$ GeV/$c$. Cyan markers represent event averages for $3<m_{\rm ch}^{\rm TPC}<30$ from the $p$+$p$ collisions. Results from Au+Au collisions are shown as triangles for the 0-40%, 40-50%, 50-60%, 60-70%, and 70-80% centrality bins. Red and grey bands show the systematic uncertainties for $p$+$p$ collisions and Au+Au collisions, respectively. The $m_{\rm ch}^{\rm TPC}$ values are not corrected for the reconstruction efficiency of the TPC. The golden bands at $m_{\rm ch}^{\rm TPC}\approx 6$ represent the results from PYTHIA8 calculations averaged over multiplicity. The Skellam baselines are shown in dotted lines. The purple bands show corresponding susceptibility ratios of baryon number from lattice QCD calculations, where the multiplicity range is chosen arbitrary.

Net-proton cumulant ratios, (a) $C_{4}/C_{2}$, (b) $C_{5}/C_{1}$, and (c) $C_{6}/C_{2}$ as a function of charged-particle multiplicity for $p$+$p$ collisions and Au+Au collisions at 200 GeV for $|y|<0.5$ and $0.4<p_{\rm T}<2.0$ GeV/$c$. Cyan markers represent event averages for $3<m_{\rm ch}^{\rm TPC}<30$ from the $p$+$p$ collisions. Results from Au+Au collisions are shown as triangles for the 0-40%, 40-50%, 50-60%, 60-70%, and 70-80% centrality bins. Red and grey bands show the systematic uncertainties for $p$+$p$ collisions and Au+Au collisions, respectively. The $m_{\rm ch}^{\rm TPC}$ values are not corrected for the reconstruction efficiency of the TPC. The golden bands at $m_{\rm ch}^{\rm TPC}\approx 6$ represent the results from PYTHIA8 calculations averaged over multiplicity. The Skellam baselines are shown in dotted lines. The purple bands show corresponding susceptibility ratios of baryon number from lattice QCD calculations, where the multiplicity range is chosen arbitrary.

Invariant mass distributions of $^3\hbox{He}+\pi^-$ (A), $^3\overline{\hbox{He}}+\pi^+$ (B), $^4\hbox{He}+\pi^-$ (C) and $^4\overline{\hbox{He}}+\pi^+$ (D). The solid bands mark the signal invariant mass regions. The obtained signal count ($N_{\rm Sig}$), background count ($N_{\rm Bg}$), and signal significance are listed in each panel.

(A) (anti)hypernuclei yields versus $L/\beta\gamma$. The vertical error bars represent the statistical error only.

(A) (anti)hypernuclei yields versus $L/\beta\gamma$. The vertical error bars represent the statistical error only.

Our measured (anti)hypernuclei lifetimes compared with world data and theoretical predictions (solid triangles). Error bars and boxes represent statistical and systematic uncertainties, respectively. Vertical solid lines with shaded regions show the average lifetime of (anti)hypernuclei and their corresponding uncertainties. The vertical gray line shows the lifetime of the free $\Lambda$.

Production yield ratios of various particles with the same baryon number. Results combining all collision systems in this work are shown by filled stars. Open stars show results with only U+U and Au+Au collisions, while quadrangular stars show results with only Zr+Zr and Ru+Ru collisions. Statistical uncertainties and systematic uncertainties are shown by vertical bars and boxes, respectively. Previous measurement results and thermal model predictions are also shown for comparison. Ratio Typle Index, 0:$\frac{{}^{3}\bar{He}}{{}^{3}He}$ 1:$\frac{{}^{3}\bar{He}}{{}^{3}He}\times\frac{\bar{p}}{p}$ 2:$\frac{{}^{4}\bar{He}}{{}^{4}He}$ 3:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{{}^{3}_{\Lambda}H}$ 4:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{{}^{3}_{\Lambda}H}\times\frac{\bar{p}}{p}$ 5:$\frac{{}^{4}_{\bar{\Lambda}}\bar{H}}{{}^{4}_{\Lambda}H}$ 6:$\frac{{}^{3}_{\Lambda}H}{{}^{3}He}$ 7:$\frac{{}^{4}_{\Lambda}H}{{}^{4}He}$ 8:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{^{3}\bar{He}}$ 9:$\frac{{}^{4}_{\bar{\Lambda}}\bar{H}}{^{4}\bar{He}}$

Production yield ratios of various particles with the same baryon number. Results combining all collision systems in this work are shown by filled stars. Open stars show results with only U+U and Au+Au collisions, while quadrangular stars show results with only Zr+Zr and Ru+Ru collisions. Statistical uncertainties and systematic uncertainties are shown by vertical bars and boxes, respectively. Previous measurement results and thermal model predictions are also shown for comparison. Ratio Typle Index, 0:$\frac{{}^{3}\bar{He}}{{}^{3}He}$ 1:$\frac{{}^{3}\bar{He}}{{}^{3}He}\times\frac{\bar{p}}{p}$ 2:$\frac{{}^{4}\bar{He}}{{}^{4}He}$ 3:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{{}^{3}_{\Lambda}H}$ 4:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{{}^{3}_{\Lambda}H}\times\frac{\bar{p}}{p}$ 5:$\frac{{}^{4}_{\bar{\Lambda}}\bar{H}}{{}^{4}_{\Lambda}H}$ 6:$\frac{{}^{3}_{\Lambda}H}{{}^{3}He}$ 7:$\frac{{}^{4}_{\Lambda}H}{{}^{4}He}$ 8:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{^{3}\bar{He}}$ 9:$\frac{{}^{4}_{\bar{\Lambda}}\bar{H}}{^{4}\bar{He}}$

Production yield ratios of various particles with the same baryon number. Results combining all collision systems in this work are shown by filled stars. Open stars show results with only U+U and Au+Au collisions, while quadrangular stars show results with only Zr+Zr and Ru+Ru collisions. Statistical uncertainties and systematic uncertainties are shown by vertical bars and boxes, respectively. Previous measurement results and thermal model predictions are also shown for comparison. Ratio Typle Index, 0:$\frac{{}^{3}\bar{He}}{{}^{3}He}$ 1:$\frac{{}^{3}\bar{He}}{{}^{3}He}\times\frac{\bar{p}}{p}$ 2:$\frac{{}^{4}\bar{He}}{{}^{4}He}$ 3:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{{}^{3}_{\Lambda}H}$ 4:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{{}^{3}_{\Lambda}H}\times\frac{\bar{p}}{p}$ 5:$\frac{{}^{4}_{\bar{\Lambda}}\bar{H}}{{}^{4}_{\Lambda}H}$ 6:$\frac{{}^{3}_{\Lambda}H}{{}^{3}He}$ 7:$\frac{{}^{4}_{\Lambda}H}{{}^{4}He}$ 8:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{^{3}\bar{He}}$ 9:$\frac{{}^{4}_{\bar{\Lambda}}\bar{H}}{^{4}\bar{He}}$

Production yield ratios of various particles with the same baryon number. Results combining all collision systems in this work are shown by filled stars. Open stars show results with only U+U and Au+Au collisions, while quadrangular stars show results with only Zr+Zr and Ru+Ru collisions. Statistical uncertainties and systematic uncertainties are shown by vertical bars and boxes, respectively. Previous measurement results and thermal model predictions are also shown for comparison. Ratio Typle Index, 0:$\frac{{}^{3}\bar{He}}{{}^{3}He}$ 1:$\frac{{}^{3}\bar{He}}{{}^{3}He}\times\frac{\bar{p}}{p}$ 2:$\frac{{}^{4}\bar{He}}{{}^{4}He}$ 3:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{{}^{3}_{\Lambda}H}$ 4:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{{}^{3}_{\Lambda}H}\times\frac{\bar{p}}{p}$ 5:$\frac{{}^{4}_{\bar{\Lambda}}\bar{H}}{{}^{4}_{\Lambda}H}$ 6:$\frac{{}^{3}_{\Lambda}H}{{}^{3}He}$ 7:$\frac{{}^{4}_{\Lambda}H}{{}^{4}He}$ 8:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{^{3}\bar{He}}$ 9:$\frac{{}^{4}_{\bar{\Lambda}}\bar{H}}{^{4}\bar{He}}$

Reconstruction efficiency as a function of $L/(\beta\gamma)$ obtained from the embedding Monte Carlo technique. Hypernuclei have stricter topological cuts than antihypernuclei to suppress knock-out $^3\hbox{He}$ and $^4\hbox{He}$, resulting in lower efficiencies.

Reconstruction efficiency as a function of $L/(\beta\gamma)$ obtained from the embedding Monte Carlo technique. Hypernuclei have stricter topological cuts than antihypernuclei to suppress knock-out $^3\hbox{He}$ and $^4\hbox{He}$, resulting in lower efficiencies.

H3L, antiH3L, H4L and antiH4L candidate invariant-mass distributions in different $L/\beta\gamma$ intervals.

H3L, antiH3L, H4L and antiH4L candidate invariant-mass distributions in different $L/\beta\gamma$ intervals.

H3L, antiH3L, H4L and antiH4L candidate invariant-mass distributions in different $L/\beta\gamma$ intervals.

H3L, antiH3L, H4L and antiH4L candidate invariant-mass distributions in different $L/\beta\gamma$ intervals.

$dN/d(L/\beta\gamma)$ as a function of $L/\beta\gamma$ for $\Lambda$ and $\bar{\Lambda}$, and exponential fits to obtain their lifetimes.

Efficiency corrected $p_{T}$ spectra for $^3\hbox{He}$, $^3\overline{\hbox{He}}$, \htl, and \ahtl. The spectra are in the phase space of $|y|<0.7$ with only MB-triggered events. The spectra are not normalized by the number of events. The lines represent the BW-function fits.

Efficiency corrected $p_{T}$ spectra for $^3\hbox{He}$, $^3\overline{\hbox{He}}$, \htl, and \ahtl. The spectra are in the phase space of $|y|<0.7$ with only MB-triggered events. The spectra are not normalized by the number of events. The lines represent the BW-function fits.

'$\overline{\Lambda}$ $D_{LL}$ as a function of $p_{T}$ at $0 < \eta_{\Lambda(\overline{\Lambda})} < 1.2$'

'$\Lambda$ $D_{LL}$ as a function of $p_{T}$ at $-1.2 < \eta_{\Lambda(\overline{\Lambda})} < 0$'

'$\overline{\Lambda}$ $D_{LL}$ as a function of $p_{T}$ at $-1.2 < \eta_{\Lambda(\overline{\Lambda})} < 0$'

'$\Lambda$ $D_{LL}$ as a function of $p_{T}$ at $0 < \eta_{\Lambda(\overline{\Lambda})} < 1.2$'

'$\overline{\Lambda}$ $D_{LL}$ as a function of $p_{T}$ at $0 < \eta_{\Lambda(\overline{\Lambda})} < 1.2$'

'Two-year-combined $\Lambda$ $D_{LL}$ as a function of $p_{T}$ at $0 < \eta_{\Lambda(\overline{\Lambda})} < 1.2$'

'Two-year-combined $\overline{\Lambda}$ $D_{LL}$ as a function of $p_{T}$ at $0 < \eta_{\Lambda(\overline{\Lambda})} < 1.2$'

'Two-year-combined $\Lambda+\overline{\Lambda}$ $D_{LL}$ as a function of $p_{T}$ at $0 < \eta_{\Lambda(\overline{\Lambda})} < 1.2$'

'Two-year-combined $\Lambda$ $D_{LL}$ as a function of $p_{T}$ at $-1.2 < \eta_{\Lambda(\overline{\Lambda})} < 0$'

'Two-year-combined $\overline{\Lambda}$ $D_{LL}$ as a function of $p_{T}$ at $-1.2 < \eta_{\Lambda(\overline{\Lambda})} < 0$'

'$\Lambda$ $D_{LL}$ as a function of z at $0 < \eta_{jet} < 1.0$'

'$\overline{\Lambda}$ $D_{LL}$ as a function of z at $0 < \eta_{jet} < 1.0$'

'$\Lambda$ $D_{LL}$ as a function of z at $-1.0 < \eta_{jet} < 0$'

'$\overline{\Lambda}$ $D_{LL}$ as a function of z at $-1.0 < \eta_{jet} < 0$'

'particle jet pt as a function of $\Lambda$ z'

'particle jet pt as a function of $\overline{\Lambda}$ z'

'$\Lambda$ $D_{TT}$ as a function of $p_{T}$ at $0 < \eta_{\Lambda(\overline{\Lambda})} < 1.2$'

'$\overline{\Lambda}$ $D_{TT}$ as a function of $p_{T}$ at $0 < \eta_{\Lambda(\overline{\Lambda})} < 1.2$'

'$\Lambda$ $D_{TT}$ as a function of $p_{T}$ at $-1.2 < \eta_{\Lambda(\overline{\Lambda})} < 0$'

'$\overline{\Lambda}$ $D_{TT}$ as a function of $p_{T}$ at $-1.2 < \eta_{\Lambda(\overline{\Lambda})} < 0$'

'$\Lambda$ $D_{TT}$ as a function of $p_{T}$ at $0 < \eta_{\Lambda(\overline{\Lambda})} < 1.2$'

'$\overline{\Lambda}$ $D_{TT}$ as a function of $p_{T}$ at $0 < \eta_{\Lambda(\overline{\Lambda})} < 1.2$'

'Two-year-combined $\Lambda$ $D_{TT}$ as a function of $p_{T}$ at $0 < \eta_{\Lambda(\overline{\Lambda})} < 1.2$'

'Two-year-combined $\overline{\Lambda}$ $D_{TT}$ as a function of $p_{T}$ at $0 < \eta_{\Lambda(\overline{\Lambda})} < 1.2$'

'Two-year-combined $\Lambda$ $D_{TT}$ as a function of $p_{T}$ at $-1.2 < \eta_{\Lambda(\overline{\Lambda})} < 0$'

'Two-year-combined $\overline{\Lambda}$ $D_{TT}$ as a function of $p_{T}$ at $-1.2 < \eta_{\Lambda(\overline{\Lambda})} < 0$'

'$\Lambda$ $D_{TT}$ as a function of z at $0 < \eta_{jet} < 1.0$'

'$\overline{\Lambda}$ $D_{TT}$ as a function of z at $0 < \eta_{jet} < 1.0$'

'$\Lambda$ $D_{TT}$ as a function of z at $-1.0 < \eta_{jet} < 0$'

'$\overline{\Lambda}$ $D_{TT}$ as a function of z at $-1.0 < \eta_{jet} < 0$'

'particle jet pt as a function of $\Lambda$ z'

'particle jet pt as a function of $\overline{\Lambda}$ z'

$p_{T, jet}$ resolution for $20 < p_{T, jet}^{GEN} < 40$ GeV/c $R=0.4$ full jets. Jets are measured from all angles relative to the event plane in the 20-50% most central events.

Response matrix showing correlation between GEN and RECO $p_{T, jet}$ for matched GEN-level to RECO-level jets. Jets are measured from all angles relative to the event plane in the 20-50% most central events.

Yield measurement of near-side associated charged hadrons for 15-20 GeV/c in-plane jets from 20-50% centrality collisions.

Yield measurement of near-side associated charged hadrons for 15-20 GeV/c mid-plane jets from 20-50% centrality collisions.

Yield measurement of near-side associated charged hadrons for 15-20 GeV/c out-of-plane jets from 20-50% centrality collisions.

Yield measurement of near-side associated charged hadrons for 15-20 GeV/c JEWEL (with recoils) jets from 20-50% centrality collisions.

Yield measurement of near-side associated charged hadrons for 15-20 GeV/c JEWEL (no recoils) jets from 20-50% centrality collisions.

Yield measurement of near-side associated charged hadrons for 15-20 GeV/c in-plane ($p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Yield measurement of near-side associated charged hadrons for 15-20 GeV/c mid-plane ($p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Yield measurement of near-side associated charged hadrons for 15-20 GeV/c out-of-plane ($p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Yield measurement of near-side associated charged hadrons for 15-20 GeV/c JEWEL (with recoils, $p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Yield measurement of near-side associated charged hadrons for 15-20 GeV/c JEWEL (no recoils, $p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Yield measurement of away-side associated charged hadrons for 15-20 GeV/c in-plane jets from 20-50% centrality collisions.

Yield measurement of away-side associated charged hadrons for 15-20 GeV/c mid-plane jets from 20-50% centrality collisions.

Yield measurement of away-side associated charged hadrons for 15-20 GeV/c out-of-plane jets from 20-50% centrality collisions.

Yield measurement of away-side associated charged hadrons for 15-20 GeV/c JEWEL (with recoils) jets from 20-50% centrality collisions.

Yield measurement of away-side associated charged hadrons for 15-20 GeV/c JEWEL (no recoils) jets from 20-50% centrality collisions.

Yield measurement of away-side associated charged hadrons for 15-20 GeV/c in-plane ($p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Yield measurement of away-side associated charged hadrons for 15-20 GeV/c mid-plane ($p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Yield measurement of away-side associated charged hadrons for 15-20 GeV/c out-of-plane ($p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Yield measurement of away-side associated charged hadrons for 15-20 GeV/c JEWEL (with recoils, $p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Yield measurement of away-side associated charged hadrons for 15-20 GeV/c JEWEL (no recoils, $p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Yield measurement of near-side associated charged hadrons for 20-40 GeV/c in-plane jets from 20-50% centrality collisions.

Yield measurement of near-side associated charged hadrons for 20-40 GeV/c mid-plane jets from 20-50% centrality collisions.

Yield measurement of near-side associated charged hadrons for 20-40 GeV/c out-of-plane jets from 20-50% centrality collisions.

Yield measurement of near-side associated charged hadrons for 20-40 GeV/c JEWEL (with recoils) jets from 20-50% centrality collisions.

Yield measurement of near-side associated charged hadrons for 20-40 GeV/c JEWEL (no recoils) jets from 20-50% centrality collisions.

Yield measurement of near-side associated charged hadrons for 20-40 GeV/c in-plane ($p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Yield measurement of near-side associated charged hadrons for 20-40 GeV/c mid-plane ($p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Yield measurement of near-side associated charged hadrons for 20-40 GeV/c out-of-plane ($p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Yield measurement of near-side associated charged hadrons for 20-40 GeV/c JEWEL (with recoils, $p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Yield measurement of near-side associated charged hadrons for 20-40 GeV/c JEWEL (no recoils, $p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Yield measurement of away-side associated charged hadrons for 20-40 GeV/c in-plane jets from 20-50% centrality collisions.

Yield measurement of away-side associated charged hadrons for 20-40 GeV/c mid-plane jets from 20-50% centrality collisions.

Yield measurement of away-side associated charged hadrons for 20-40 GeV/c out-of-plane jets from 20-50% centrality collisions.

Yield measurement of away-side associated charged hadrons for 20-40 GeV/c JEWEL (with recoils) jets from 20-50% centrality collisions.

Yield measurement of away-side associated charged hadrons for 20-40 GeV/c JEWEL (no recoils) jets from 20-50% centrality collisions.

Yield measurement of away-side associated charged hadrons for 20-40 GeV/c in-plane ($p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Yield measurement of away-side associated charged hadrons for 20-40 GeV/c mid-plane ($p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Yield measurement of away-side associated charged hadrons for 20-40 GeV/c out-of-plane ($p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Yield measurement of away-side associated charged hadrons for 20-40 GeV/c JEWEL (with recoils, $p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Yield measurement of away-side associated charged hadrons for 20-40 GeV/c JEWEL (no recoils, $p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Width measurement of near-side associated charged hadrons for 15-20 GeV/c in-plane jets from 20-50% centrality collisions.

Width measurement of near-side associated charged hadrons for 15-20 GeV/c mid-plane jets from 20-50% centrality collisions.

Width measurement of near-side associated charged hadrons for 15-20 GeV/c out-of-plane jets from 20-50% centrality collisions.

Width measurement of near-side associated charged hadrons for 15-20 GeV/c JEWEL (with recoils) jets from 20-50% centrality collisions.

Width measurement of near-side associated charged hadrons for 15-20 GeV/c JEWEL (no recoils) jets from 20-50% centrality collisions.

Width measurement of near-side associated charged hadrons for 15-20 GeV/c in-plane ($p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Width measurement of near-side associated charged hadrons for 15-20 GeV/c mid-plane ($p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Width measurement of near-side associated charged hadrons for 15-20 GeV/c out-of-plane ($p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Width measurement of near-side associated charged hadrons for 15-20 GeV/c JEWEL (with recoils, $p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Width measurement of near-side associated charged hadrons for 15-20 GeV/c JEWEL (no recoils, $p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Width measurement of away-side associated charged hadrons for 15-20 GeV/c in-plane jets from 20-50% centrality collisions.

Width measurement of away-side associated charged hadrons for 15-20 GeV/c mid-plane jets from 20-50% centrality collisions.

Width measurement of away-side associated charged hadrons for 15-20 GeV/c out-of-plane jets from 20-50% centrality collisions.

Width measurement of away-side associated charged hadrons for 15-20 GeV/c JEWEL (with recoils) jets from 20-50% centrality collisions.

Width measurement of away-side associated charged hadrons for 15-20 GeV/c JEWEL (no recoils) jets from 20-50% centrality collisions.

Width measurement of away-side associated charged hadrons for 15-20 GeV/c in-plane ($p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Width measurement of away-side associated charged hadrons for 15-20 GeV/c mid-plane ($p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Width measurement of away-side associated charged hadrons for 15-20 GeV/c out-of-plane ($p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Width measurement of away-side associated charged hadrons for 15-20 GeV/c JEWEL (with recoils, $p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Width measurement of away-side associated charged hadrons for 15-20 GeV/c JEWEL (no recoils, $p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Width measurement of near-side associated charged hadrons for 20-40 GeV/c in-plane jets from 20-50% centrality collisions.

Width measurement of near-side associated charged hadrons for 20-40 GeV/c mid-plane jets from 20-50% centrality collisions.

Width measurement of near-side associated charged hadrons for 20-40 GeV/c out-of-plane jets from 20-50% centrality collisions.

Width measurement of near-side associated charged hadrons for 20-40 GeV/c JEWEL (with recoils) jets from 20-50% centrality collisions.

Width measurement of near-side associated charged hadrons for 20-40 GeV/c JEWEL (no recoils) jets from 20-50% centrality collisions.

Width measurement of near-side associated charged hadrons for 20-40 GeV/c in-plane ($p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Width measurement of near-side associated charged hadrons for 20-40 GeV/c mid-plane ($p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Width measurement of near-side associated charged hadrons for 20-40 GeV/c out-of-plane ($p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Width measurement of near-side associated charged hadrons for 20-40 GeV/c JEWEL (with recoils, $p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Width measurement of near-side associated charged hadrons for 20-40 GeV/c JEWEL (no recoils, $p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Width measurement of away-side associated charged hadrons for 20-40 GeV/c in-plane jets from 20-50% centrality collisions.

Width measurement of away-side associated charged hadrons for 20-40 GeV/c mid-plane jets from 20-50% centrality collisions.

Width measurement of away-side associated charged hadrons for 20-40 GeV/c out-of-plane jets from 20-50% centrality collisions.

Width measurement of away-side associated charged hadrons for 20-40 GeV/c JEWEL (with recoils) jets from 20-50% centrality collisions.

Width measurement of away-side associated charged hadrons for 20-40 GeV/c JEWEL (no recoils) jets from 20-50% centrality collisions.

Width measurement of away-side associated charged hadrons for 20-40 GeV/c in-plane ($p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Width measurement of away-side associated charged hadrons for 20-40 GeV/c mid-plane ($p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Width measurement of away-side associated charged hadrons for 20-40 GeV/c out-of-plane ($p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Width measurement of away-side associated charged hadrons for 20-40 GeV/c JEWEL (with recoils, $p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

Width measurement of away-side associated charged hadrons for 20-40 GeV/c JEWEL (no recoils, $p_{T, assoc}$ inclusive) jets from 20-50% centrality collisions.

mid-plane/in-plane ratio of near-side yields associated charged hadrons for 15-20 GeV/c jets from 20-50% centrality collisions.

out-of-plane/in-plane ratio of near-side yields associated charged hadrons for 15-20 GeV/c jets from 20-50% centrality collisions.

mid-plane/in-plane ($p_{T, assoc}$ inclusive) ratio of near-side yields associated charged hadrons for 15-20 GeV/c jets from 20-50% centrality collisions.

out-of-plane/in-plane ($p_{T, assoc}$ inclusive) ratio of near-side yields associated charged hadrons for 15-20 GeV/c jets from 20-50% centrality collisions.

mid-plane/in-plane ratio of away-side yields associated charged hadrons for 15-20 GeV/c jets from 20-50% centrality collisions.

out-of-plane/in-plane ratio of away-side yields associated charged hadrons for 15-20 GeV/c jets from 20-50% centrality collisions.

mid-plane/in-plane ($p_{T, assoc}$ inclusive) ratio of away-side yields associated charged hadrons for 15-20 GeV/c jets from 20-50% centrality collisions.

out-of-plane/in-plane ($p_{T, assoc}$ inclusive) ratio of away-side yields associated charged hadrons for 15-20 GeV/c jets from 20-50% centrality collisions.

mid-plane/in-plane ratio of near-side yields associated charged hadrons for 20-40 GeV/c jets from 20-50% centrality collisions.

out-of-plane/in-plane ratio of near-side yields associated charged hadrons for 20-40 GeV/c jets from 20-50% centrality collisions.

mid-plane/in-plane ($p_{T, assoc}$ inclusive) ratio of near-side yields associated charged hadrons for 20-40 GeV/c jets from 20-50% centrality collisions.

out-of-plane/in-plane ($p_{T, assoc}$ inclusive) ratio of near-side yields associated charged hadrons for 20-40 GeV/c jets from 20-50% centrality collisions.

mid-plane/in-plane ratio of away-side yields associated charged hadrons for 20-40 GeV/c jets from 20-50% centrality collisions.

out-of-plane/in-plane ratio of away-side yields associated charged hadrons for 20-40 GeV/c jets from 20-50% centrality collisions.

mid-plane/in-plane ($p_{T, assoc}$ inclusive) ratio of away-side yields associated charged hadrons for 20-40 GeV/c jets from 20-50% centrality collisions.

out-of-plane/in-plane ($p_{T, assoc}$ inclusive) ratio of away-side yields associated charged hadrons for 20-40 GeV/c jets from 20-50% centrality collisions.