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.

Upsilon 1S+2S+3S integrated cross section.

Upsilon 1S+2S+3S invariant cross section.

Upsilon 2S and 3S invariant cross section.

Upsilon 1S+2S+3S invariant cross section vs. rapidity.

Upsilon 1S invariant cross section.

Upsilon 2S invariant cross section.

Upsilon 3S invariant cross section.

Upsilon 1S invariant cross section vs. rapidity.

Upsilon 2S invariant cross section vs. rapidity.

Upsilon 3S invariant cross section vs. rapidity.

Upsilon x_{T} dependence

Upsilon x_{T} dependence.

Upsilon cross section ratios vs. collision energy.

Upsilon cross section ratios vs. charged particle multiplicity.

Upsilon cross section ratios vs. charged particle multiplicity.

Upsilon cross section ratios vs. charged particle multiplicity.

Upsilon cross section ratios vs. charged particle multiplicity.

Upsilon cross section ratios vs. charged particle multiplicity.

Self-normalized Upsilon ratio vs. charged particle multiplicity

Self-normalized Upsilon ratio vs. charged particle multiplicity

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

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

The transverse-mass dependence of the correlation-strength parameter $\lambda$ in 30-40% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the correlation-strength parameter $\lambda$ in 40-50% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the correlation-strength parameter $\lambda$ in 50-60% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the Lévy-scale parameter $R$ in 0-10% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the Lévy-scale parameter $R$ in 10-20% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the Lévy-scale parameter $R$ in 20-30% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the Lévy-scale parameter $R$ in 30-40% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the Lévy-scale parameter $R$ in 40-50% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the Lévy-scale parameter $R$ in 50-60% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the Lévy-index of stability parameter $\alpha$ in 0-10% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the Lévy-index of stability parameter $\alpha$ in 10-20% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the Lévy-index of stability parameter $\alpha$ in 20-30% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the Lévy-index of stability parameter $\alpha$ in 30-40% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the Lévy-index of stability parameter $\alpha$ in 40-50% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the Lévy-index of stability parameter $\alpha$ in 50-60% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the normalized correlation-strength parameter $\lambda/\lambda_{\rm max}$ for 0-10% centrality intervals. For each centrality bin the data are fitted with the Gaussian function of Eq. (15). This parameterization can describe the data and is discussed in detail in Section VI B. The fit parameters with the statistic and systematic uncertainties are shown in Fig. 7.

The transverse-mass dependence of the normalized correlation-strength parameter $\lambda/\lambda_{\rm max}$ for 10-20% centrality intervals. For each centrality bin the data are fitted with the Gaussian function of Eq. (15). This parameterization can describe the data and is discussed in detail in Section VI B. The fit parameters with the statistic and systematic uncertainties are shown in Fig. 7.

The transverse-mass dependence of the normalized correlation-strength parameter $\lambda/\lambda_{\rm max}$ for 20-30% centrality intervals. For each centrality bin the data are fitted with the Gaussian function of Eq. (15). This parameterization can describe the data and is discussed in detail in Section VI B. The fit parameters with the statistic and systematic uncertainties are shown in Fig. 7.

The transverse-mass dependence of the normalized correlation-strength parameter $\lambda/\lambda_{\rm max}$ for 30-40% centrality intervals. For each centrality bin the data are fitted with the Gaussian function of Eq. (15). This parameterization can describe the data and is discussed in detail in Section VI B. The fit parameters with the statistic and systematic uncertainties are shown in Fig. 7.

The transverse-mass dependence of the normalized correlation-strength parameter $\lambda/\lambda_{\rm max}$ for 40-50% centrality interval. For each centrality bin the data are fitted with the Gaussian function of Eq. (15). This parameterization can describe the data and is discussed in detail in Section VI B. The fit parameters with the statistic and systematic uncertainties are shown in Fig. 7.

The transverse-mass dependence of the normalized correlation-strength parameter $\lambda/\lambda_{\rm max}$ for 50-60% centrality interval. For each centrality bin the data are fitted with the Gaussian function of Eq. (15). This parameterization can describe the data and is discussed in detail in Section VI B. The fit parameters with the statistic and systematic uncertainties are shown in Fig. 7.

The transverse-mass dependence of the inverse square of the Lévy-scale parameter $R$, shown in 0-10% centrality bin. The values and uncertainties of the A and B linear fit parameters with the statistic and systematic uncertainties are shown in Fig. 8.

The transverse-mass dependence of the inverse square of the Lévy-scale parameter $R$, shown in 10-20% centrality bin. The values and uncertainties of the A and B linear fit parameters with the statistic and systematic uncertainties are shown in Fig. 8.

The transverse-mass dependence of the inverse square of the Lévy-scale parameter $R$, shown in 20-30% centrality bin. The values and uncertainties of the A and B linear fit parameters with the statistic and systematic uncertainties are shown in Fig. 8.

The transverse-mass dependence of the inverse square of the Lévy-scale parameter $R$, shown in 30-40% centrality bin. The values and uncertainties of the A and B linear fit parameters with the statistic and systematic uncertainties are shown in Fig. 8.

The transverse-mass dependence of the inverse square of the Lévy-scale parameter $R$, shown in 40-50% centrality bin. The values and uncertainties of the A and B linear fit parameters with the statistic and systematic uncertainties are shown in Fig. 8.

The transverse-mass dependence of the inverse square of the Lévy-scale parameter $R$, shown in 50-60% centrality bin. The values and uncertainties of the A and B linear fit parameters with the statistic and systematic uncertainties are shown in Fig. 8.

The transverse-mass dependence of the $\widehat{R}$ parameter, shown in 0-10% centrality bin. The values and uncertainties of the linear fit parameters $\widehat{A}$ and $\widehat{B}$ with the statistic and systematic uncertainties are shown in Fig. 9

The transverse-mass dependence of the $\widehat{R}$ parameter, shown in 10-20% centrality bin. The values and uncertainties of the linear fit parameters $\widehat{A}$ and $\widehat{B}$ with the statistic and systematic uncertainties are shown in Fig. 9

The transverse-mass dependence of the $\widehat{R}$ parameter, shown in 20-30% centrality bin. The values and uncertainties of the linear fit parameters $\widehat{A}$ and $\widehat{B}$ with the statistic and systematic uncertainties are shown in Fig. 9

The transverse-mass dependence of the $\widehat{R}$ parameter, shown in 30-40% centrality bin. The values and uncertainties of the linear fit parameters $\widehat{A}$ and $\widehat{B}$ with the statistic and systematic uncertainties are shown in Fig. 9

The transverse-mass dependence of the $\widehat{R}$ parameter, shown in 40-50% centrality bin. The values and uncertainties of the linear fit parameters $\widehat{A}$ and $\widehat{B}$ with the statistic and systematic uncertainties are shown in Fig. 9

The transverse-mass dependence of the $\widehat{R}$ parameter, shown in 50-60% centrality bin. The values and uncertainties of the linear fit parameters $\widehat{A}$ and $\widehat{B}$ with the statistic and systematic uncertainties are shown in Fig. 9

The $H$ parameter that characterize the magnitude of the $\lambda/\lambda_{max}(m_T)$ and is defined in Eq. (15)., shown as functions of $N_{part}$.

The $\sigma$ parameter that characterize the width of the $\lambda/\lambda_{max}(m_T)$ and is defined in Eq. (15)., shown as functions of $N_{part}$.

The parameter $A$ of the affine linear fit to the inverse square of the Lévy-scale parameter that are defined in Eq.(12) as function of $N_{part}$

The parameter $B$ of the affine linear fit to the inverse square of the Lévy-scale parameter that are defined in Eq.(12) as function of $N_{part}$

The parameter $\widehat{A}$ of the affine linear fit to the inverse of the $\widehat{R}$ parameter that are defined in Eq.(14) as function of $N_{part}$.

The parameter $\widehat{B}$ of the affine linear fit to the inverse of the $\widehat{R}$ parameter that are defined in Eq.(14) as function of $N_{part}$.

The centrality dependence of $\alpha_0$, the $m_T$-averaged value of $\alpha$ as a function of $N_{part}$.

The Lévy scale parameter $R$ as a function of $N^{1/3}_{part}$ at $m_T=0.326$ GeV.

The Lévy scale parameter $R$ as a function of $N^{1/3}_{part}$ at $m_T=0.438$ GeV.

The Lévy scale parameter $R$ as a function of $N^{1/3}_{part}$ at $m_T=0.553$ GeV.

The Lévy scale parameter $R$ as a function of $N^{1/3}_{part}$ at $m_T=0.670$ GeV.

The Lévy scale parameter $R$ as a function of $N^{1/3}_{part}$ at $m_T=0.787$ GeV.

Monte Carlo calcuations with no mass drop assumed in 0-10%.

Monte Carlo calcuations with no mass drop assumed in 10-20%.

Monte Carlo calcuations with no mass drop assumed in 20-30%.

Monte Carlo calcuations with no mass drop assumed in 30-40%.

Monte Carlo calcuations with no mass drop assumed in 40-50%.

Monte Carlo calcuations with no mass drop assumed in 50-60%.

Monte Carlo calcuations with the best mass drop assumed in 0-10%.

Monte Carlo calcuations with the best mass drop assumed in 10-20%.

Monte Carlo calcuations with the best mass drop assumed in 20-30%.

Monte Carlo calcuations with the best mass drop assumed in 30-40%.

Monte Carlo calcuations with the best mass drop assumed in 40-50%.

Monte Carlo calcuations with the best mass drop assumed in 50-60%.

The best values of $B^{-1}_{\eta\prime}$ spectrum of the $\eta\prime$ condensate in the six centrality classes.

The centrality dependence of the best values of the in-medium mass of the $m^{*}_{\eta\prime}$.

The CL maps of the comparison of the MC to data in 0-10% (see Fig. 11).

The CL maps of the comparison of the MC to data in 10-20% (see Fig. 11).

The CL maps of the comparison of the MC to data in 20-30% (see Fig. 11).

The CL maps of the comparison of the MC to data in 30-40% (see Fig. 11).

The CL maps of the comparison of the MC to data in 40-50% (see Fig. 11).

The CL maps of the comparison of the MC to data in 50-60% (see Fig. 11).

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.