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).

$A_{LL}$ 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.

90% CL WIMP SDn cross sections, including sensitivities and nuclear structure uncertainties

90% CL WIMP SDp cross sections, including sensitivities and nuclear structure uncertainties

90% CL WIMP SDp cross sections, including sensitivities and nuclear structure uncertainties

Data selection efficiency as a function of nuclear recoil energy

Data selection efficiency as a function of nuclear recoil energy

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

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