Reference multiplicity distributions obtained from Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV data (black markers), Glauber model (red histogram), and unfolding approach to separate single and pileup contributions. Vertical lines represent statistical uncertainties. Single, pileup, and single+pileup collisions are shown in solid blue markers, dashed green, and dashed pink lines, respectively. The 0–5% central events and 5–60% mid-central to peripheral events are indicated by black arrows. The ratio of the single+pileup to the measured multiplicity distribution is shown in the lower panel.

Reference multiplicity distributions obtained from Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV data (black markers), Glauber model (red histogram), and unfolding approach to separate single and pileup contributions. Vertical lines represent statistical uncertainties. Single, pileup, and single+pileup collisions are shown in solid blue markers, dashed green, and dashed pink lines, respectively. The 0–5% central events and 5–60% mid-central to peripheral events are indicated by black arrows. The ratio of the single+pileup to the measured multiplicity distribution is shown in the lower panel.

Proton cumulants as a function of reference multiplicity (black circles) from $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions. Centrality-binned results with and without centrality bin width corrections are represented by red circles and blue squares, respectively. Vertical dashed lines indicate the centrality classes, from right to left: 0–5%, 5–10%, 10–20%. Data points in this figure are only corrected for detector efficiency but not for the pileup effect, which will be discussed in a later section.

Proton cumulants as a function of reference multiplicity (black circles) from $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions. Centrality-binned results with and without centrality bin width corrections are represented by red circles and blue squares, respectively. Vertical dashed lines indicate the centrality classes, from right to left: 0–5%, 5–10%, 10–20%. Data points in this figure are only corrected for detector efficiency but not for the pileup effect, which will be discussed in a later section.

Proton cumulants as a function of reference multiplicity (black circles) from $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions. Centrality-binned results with and without centrality bin width corrections are represented by red circles and blue squares, respectively. Vertical dashed lines indicate the centrality classes, from right to left: 0–5%, 5–10%, 10–20%. Data points in this figure are only corrected for detector efficiency but not for the pileup effect, which will be discussed in a later section.

Proton cumulants as a function of reference multiplicity from $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions. Pileup corrected and uncorrected cumulants as a function of reference multiplicity are represented by black circles and blue open squares, respectively. Red circles and blue-filled squares represent the results of centrality binned data.

Proton cumulants as a function of reference multiplicity from $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions. Pileup corrected and uncorrected cumulants as a function of reference multiplicity are represented by black circles and blue open squares, respectively. Red circles and blue-filled squares represent the results of centrality binned data.

Ratios of proton cumulants as a function of reference multiplicity from $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions. Pileup corrected and uncorrected cumulants are represented by black circles and blue open squares, respectively. Red circles and blue-filled squares represent the results of centrality binned data.

Ratios of proton cumulants as a function of reference multiplicity from $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions. Pileup corrected and uncorrected cumulants are represented by black circles and blue open squares, respectively. Red circles and blue-filled squares represent the results of centrality binned data.

UrQMD results of the proton cumulant ratios up to sixth order in Au+Au collisions at $\sqrt{s_{\rm NN}}$= 3 GeV. The black circles are without VF correction while blue squares and red triangles are results with VFC which used $N_{\rm part}$ distributions from UrQMD and Glauber models, respectively. The blue crosses are calculations using UrQMD events with b $\leq$ 3 fm. The above results are applied CBWC except for the one (blue crosses) using b $\leq$3 fm events.

UrQMD results of the proton cumulant ratios up to sixth order in Au+Au collisions at $\sqrt{s_{\rm NN}}$= 3 GeV. The black circles are without VF correction while blue squares and red triangles are results with VFC which used $N_{\rm part}$ distributions from UrQMD and Glauber models, respectively. The blue crosses are calculations using UrQMD events with b $\leq$ 3 fm. The above results are applied CBWC except for the one (blue crosses) using b $\leq$3 fm events.

Proton cumulants up to sixth order in $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions. Data without volume fluctuation correction is shown as grey open squares while data with volume fluctuation correction using $N_{\rm part}$ distributions from Glauber and UrQMD models are shown as black circles and black open triangles, respectively. The corresponding centrality binned cumulants are shown in blue squares, red circles, and orange triangles, respectively. Similarly to Fig. 6, the vertical dashed lines indicate the centrality classes.

Proton cumulants up to sixth order in $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions. Data without volume fluctuation correction is shown as grey open squares while data with volume fluctuation correction using $N_{\rm part}$ distributions from Glauber and UrQMD models are shown as black circles and black open triangles, respectively. The corresponding centrality binned cumulants are shown in blue squares, red circles, and orange triangles, respectively. Similarly to Fig. 6, the vertical dashed lines indicate the centrality classes.

Proton cumulant ratios up to sixth order in $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions. Data without volume fluctuation correction are shown as grey open squares while data with volume fluctuation correction using $N_{\rm part}$ distributions from Glauber and UrQMD models are shown as black circles and black open triangles, respectively. The corresponding centrality binned cumulants are shown in blue squares, red circles, and orange triangles, respectively. Similarly to Fig. 6, the vertical dashed lines indicate the centrality classes.

Proton cumulant ratios up to sixth order in $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions. Data without volume fluctuation correction are shown as grey open squares while data with volume fluctuation correction using $N_{\rm part}$ distributions from Glauber and UrQMD models are shown as black circles and black open triangles, respectively. The corresponding centrality binned cumulants are shown in blue squares, red circles, and orange triangles, respectively. Similarly to Fig. 6, the vertical dashed lines indicate the centrality classes.

UrQMD results of proton cumulant ratios up to sixth order in Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV. The vertical dashed lines indicate the centrality classes.

Experimental results on centrality dependence of cumulants (left panels) and cumulant ratios (right panels) up to sixth order of the proton multiplicity distributions in Au+Au collisions at $N_{\rm part}$ = 3 GeV. The open squares are data without VF correction while red circles and blue triangles are results with VF correction with $N_{\rm part}$ distributions from Glauber and UrQMD models, respectively.

Experimental results on centrality dependence of cumulants (left panels) and cumulant ratios (right panels) up to sixth order of the proton multiplicity distributions in Au+Au collisions at $N_{\rm part}$ = 3 GeV. The open squares are data without VF correction while red circles and blue triangles are results with VF correction with $N_{\rm part}$ distributions from Glauber and UrQMD models, respectively.

Same as Fig. 14 but for correlation function (left panels) and their normalized ratios (right panels).

Same as Fig. 14 but for correlation function (left panels) and their normalized ratios (right panels).

Cumulants and cumulant ratios of proton multiplicity distributions for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV. The transverse momentum window is $p_{\rm T}$ from $0.4<p_{\rm T}<2.0$ GeV/$c$ and the rapidity window is $−0.5<y<0$. Statistical and systematic uncertainties are represented by black and gray bars, respectively. UrQMD predictions are depicted by gold bands.

Cumulants and cumulant ratios of proton multiplicity distributions for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV. The transverse momentum window is $p_{\rm T}$ from $0.4<p_{\rm T}<2.0$ GeV/$c$ and the rapidity window is $−0.5<y<0$. Statistical and systematic uncertainties are represented by black and gray bars, respectively. UrQMD predictions are depicted by gold bands.

Same as Fig. 16 but for correlation functions and correlation function ratios of proton multiplicity distributions for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV.

Same as Fig. 16 but for correlation functions and correlation function ratios of proton multiplicity distributions for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV.

The transverse-momentum and rapidity dependence of cumulant ratios of proton multiplicity distributions for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV. In the left column, the $p_{\rm T}$ analysis window is $0.4<p_{\rm T}<2.0$ GeV/$c$ while the rapidity window is varied in the range $y_{\rm min}<y<0$. In the right column, the rapidit$y$ analysis window is $−0.5<y<0$ while the $p_{\rm T}$ is varied in the range $0.4<p_{\rm T}<p_{\rm T}^{\rm max}$ GeV/$c$. The most central (0–5%) and peripheral (50–60%) events are depicted by black squares and blue triangles, respectively. Statistical and systematic uncertainties are represented by black and gray bars, respectively. UrQMD simulations for the top 0–5% and 50–60% are shown by gold and blue bands, respectively.

The transverse-momentum and rapidity dependence of cumulant ratios of proton multiplicity distributions for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV. In the left column, the $p_{\rm T}$ analysis window is $0.4<p_{\rm T}<2.0$ GeV/$c$ while the rapidity window is varied in the range $y_{\rm min}<y<0$. In the right column, the rapidit$y$ analysis window is $−0.5<y<0$ while the $p_{\rm T}$ is varied in the range $0.4<p_{\rm T}<p_{\rm T}^{\rm max}$ GeV/$c$. The most central (0–5%) and peripheral (50–60%) events are depicted by black squares and blue triangles, respectively. Statistical and systematic uncertainties are represented by black and gray bars, respectively. UrQMD simulations for the top 0–5% and 50–60% are shown by gold and blue bands, respectively.

The transverse-momentum and rapidity dependence of cumulant ratios of proton multiplicity distributions for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV. In the left column, the $p_{\rm T}$ analysis window is $0.4<p_{\rm T}<2.0$ GeV/$c$ while the rapidity window is varied in the range $y_{\rm min}<y<0$. In the right column, the rapidit$y$ analysis window is $−0.5<y<0$ while the $p_{\rm T}$ is varied in the range $0.4<p_{\rm T}<p_{\rm T}^{\rm max}$ GeV/$c$. The most central (0–5%) and peripheral (50–60%) events are depicted by black squares and blue triangles, respectively. Statistical and systematic uncertainties are represented by black and gray bars, respectively. UrQMD simulations for the top 0–5% and 50–60% are shown by gold and blue bands, respectively.

The transverse-momentum and rapidity dependence of cumulant ratios of proton multiplicity distributions for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV. In the left column, the $p_{\rm T}$ analysis window is $0.4<p_{\rm T}<2.0$ GeV/$c$ while the rapidity window is varied in the range $y_{\rm min}<y<0$. In the right column, the rapidit$y$ analysis window is $−0.5<y<0$ while the $p_{\rm T}$ is varied in the range $0.4<p_{\rm T}<p_{\rm T}^{\rm max}$ GeV/$c$. The most central (0–5%) and peripheral (50–60%) events are depicted by black squares and blue triangles, respectively. Statistical and systematic uncertainties are represented by black and gray bars, respectively. UrQMD simulations for the top 0–5% and 50–60% are shown by gold and blue bands, respectively.

As in Fig. 18 but for transverse-momentum and rapidity dependence of correlation function ratios of proton multiplicity distributions for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV.

As in Fig. 18 but for transverse-momentum and rapidity dependence of correlation function ratios of proton multiplicity distributions for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV.

As in Fig. 18 but for transverse-momentum and rapidity dependence of correlation function ratios of proton multiplicity distributions for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV.

As in Fig. 18 but for transverse-momentum and rapidity dependence of correlation function ratios of proton multiplicity distributions for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV.

Collision energy dependence of the cumulant ratios: $C_2/C_1=\sigma/M$, $C_3/C_2=S\sigma$, and $C_4/C_2=\kappa\sigma^2$, for protons (open squares) and net protons (red circles) from top 0–5% (top panels) and 50–60% (bottom panels) Au+Au collisions at RHIC. The points for protons are shifted horizontally for clarity. The new result for protons from $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions is shown as a filled square. UrQMD results with $|y|<0.5$ for protons are shown as gold bands while those for net protons are shown as green dashed lines or green bands. At 3GeV, the model results for protons (−0.5) are shown as blue crosses. UrQMD results of proton and net-proton $C_4/C_2$, see right panels, are almost totally overlapped. The open cross is the result of the model with a fixed impact parameter $b < 3$ fm. The hydrodynamic calculations, for 5% central Au+Au collisions, for protons from $|y|<0.5$ are shown as dashed red linea and the result of the 3 GeV protons from $−0.5<y<0$ is shown as an open red star.

Collision energy dependence of the cumulant ratios: $C_2/C_1=\sigma/M$, $C_3/C_2=S\sigma$, and $C_4/C_2=\kappa\sigma^2$, for protons (open squares) and net protons (red circles) from top 0–5% (top panels) and 50–60% (bottom panels) Au+Au collisions at RHIC. The points for protons are shifted horizontally for clarity. The new result for protons from $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions is shown as a filled square. UrQMD results with $|y|<0.5$ for protons are shown as gold bands while those for net protons are shown as green dashed lines or green bands. At 3GeV, the model results for protons (−0.5) are shown as blue crosses. UrQMD results of proton and net-proton $C_4/C_2$, see right panels, are almost totally overlapped. The open cross is the result of the model with a fixed impact parameter $b < 3$ fm. The hydrodynamic calculations, for 5% central Au+Au collisions, for protons from $|y|<0.5$ are shown as dashed red linea and the result of the 3 GeV protons from $−0.5<y<0$ is shown as an open red star.

Collision energy dependence of the cumulant ratios: $C_2/C_1=\sigma/M$, $C_3/C_2=S\sigma$, and $C_4/C_2=\kappa\sigma^2$, for protons (open squares) and net protons (red circles) from top 0–5% (top panels) and 50–60% (bottom panels) Au+Au collisions at RHIC. The points for protons are shifted horizontally for clarity. The new result for protons from $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions is shown as a filled square. UrQMD results with $|y|<0.5$ for protons are shown as gold bands while those for net protons are shown as green dashed lines or green bands. At 3GeV, the model results for protons (−0.5) are shown as blue crosses. UrQMD results of proton and net-proton $C_4/C_2$, see right panels, are almost totally overlapped. The open cross is the result of the model with a fixed impact parameter $b < 3$ fm. The hydrodynamic calculations, for 5% central Au+Au collisions, for protons from $|y|<0.5$ are shown as dashed red linea and the result of the 3 GeV protons from $−0.5<y<0$ is shown as an open red star.

Collision energy dependence of the cumulant ratios: $C_2/C_1=\sigma/M$, $C_3/C_2=S\sigma$, and $C_4/C_2=\kappa\sigma^2$, for protons (open squares) and net protons (red circles) from top 0–5% (top panels) and 50–60% (bottom panels) Au+Au collisions at RHIC. The points for protons are shifted horizontally for clarity. The new result for protons from $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions is shown as a filled square. UrQMD results with $|y|<0.5$ for protons are shown as gold bands while those for net protons are shown as green dashed lines or green bands. At 3GeV, the model results for protons (−0.5) are shown as blue crosses. UrQMD results of proton and net-proton $C_4/C_2$, see right panels, are almost totally overlapped. The open cross is the result of the model with a fixed impact parameter $b < 3$ fm. The hydrodynamic calculations, for 5% central Au+Au collisions, for protons from $|y|<0.5$ are shown as dashed red linea and the result of the 3 GeV protons from $−0.5<y<0$ is shown as an open red star.

Collision energy dependence of the cumulant ratios: $C_2/C_1=\sigma/M$, $C_3/C_2=S\sigma$, and $C_4/C_2=\kappa\sigma^2$, for protons (open squares) and net protons (red circles) from top 0–5% (top panels) and 50–60% (bottom panels) Au+Au collisions at RHIC. The points for protons are shifted horizontally for clarity. The new result for protons from $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions is shown as a filled square. UrQMD results with $|y|<0.5$ for protons are shown as gold bands while those for net protons are shown as green dashed lines or green bands. At 3GeV, the model results for protons (−0.5) are shown as blue crosses. UrQMD results of proton and net-proton $C_4/C_2$, see right panels, are almost totally overlapped. The open cross is the result of the model with a fixed impact parameter $b < 3$ fm. The hydrodynamic calculations, for 5% central Au+Au collisions, for protons from $|y|<0.5$ are shown as dashed red linea and the result of the 3 GeV protons from $−0.5<y<0$ is shown as an open red star.

Collision energy dependence of the cumulant ratios: $C_2/C_1=\sigma/M$, $C_3/C_2=S\sigma$, and $C_4/C_2=\kappa\sigma^2$, for protons (open squares) and net protons (red circles) from top 0–5% (top panels) and 50–60% (bottom panels) Au+Au collisions at RHIC. The points for protons are shifted horizontally for clarity. The new result for protons from $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions is shown as a filled square. UrQMD results with $|y|<0.5$ for protons are shown as gold bands while those for net protons are shown as green dashed lines or green bands. At 3GeV, the model results for protons (−0.5) are shown as blue crosses. UrQMD results of proton and net-proton $C_4/C_2$, see right panels, are almost totally overlapped. The open cross is the result of the model with a fixed impact parameter $b < 3$ fm. The hydrodynamic calculations, for 5% central Au+Au collisions, for protons from $|y|<0.5$ are shown as dashed red linea and the result of the 3 GeV protons from $−0.5<y<0$ is shown as an open red star.

'Identified transverse momentum spectra of $\pi^{-}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV'

'Identified transverse momentum spectra of $K^{-}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV'

'Identified transverse momentum spectra of $\bar{p}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV'

'Average transverse momentum as a function of $\langle$N$_{part}$$\rangle$ for $\pi^{+}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'Average transverse momentum as a function of $\langle$N$_{part}$$\rangle$ for $K^{+}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'Average transverse momentum as a function of $\langle$N$_{part}$$\rangle$ for p at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'dN/dy scaled by 0.5 × $\langle$N$_{part}$$\rangle$ as a function of $\langle$N$_{part}$$\rangle$ for $\pi^{+}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'dN/dy scaled by 0.5 × $\langle$N$_{part}$$\rangle$ as a function of $\langle$N$_{part}$$\rangle$ for $K^{+}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'dN/dy scaled by 0.5 × $\langle$N$_{part}$$\rangle$ as a function of $\langle$N$_{part}$$\rangle$ for p at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'dN/dy scaled by 0.5 × $\langle$N$_{part}$$\rangle$ as a function of $\langle$N$_{part}$$\rangle$ for $\bar{p}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'$\pi^{−}$/$\pi^{+}$ ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'$K^{−}$/$K^{+}$ ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'$\bar{p}$/p ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'$K^{+}$/$\pi^{+}$ ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'$K^{-}$/$\pi^{-}$ ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'p/$\pi^{+}$ ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'$\bar{p}$/$\pi^{-}$ ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

Net-proton cumulant ratios C4/C2, C5/C1, C6/C2 (0-40$\%$ and 50-60$\%$ centrality) and C3/C1 (0-40$\%$ centrality) in Au+Au collisions from $\sqrt{s_{NN}}$ = 3 - 200 GeV. At $\sqrt{s_{NN}}$ = 3 GeV, measurement is done for protons instead of net-protons, and with halfrapdity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5).

Net-proton cumulant ratios C4/C2, C5/C1, C6/C2 (0-40$\%$ and 50-60$\%$ centrality) and C3/C1 (0-40$\%$ centrality) from UrQMD model in Au+Au collisions from $\sqrt{s_{NN}}$ = 3 -200 GeV. At $\sqrt{s_{NN}}$ = 3 GeV, UrQMD calculation is done for protons instead of net-protons, and with halfrapdity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5).

Fifth-to-first (KS5/KS1) and sixth-to-second (KS6/KS2) order K-statistic ratios of net-proton distributions in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV for 0-40$\%$ and 50-60$\%$ centrality.

Net-proton cumulant ratio C6/C2 and corresponding K-statistic ratio (0-40$\%$) in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV as a function of sample size. Uncertainties are only statistical.

Cumulant ratios C4/C2, C5/C1, C6/C2 and C3/C1 of net-proton distributions measured with half rapdity coverage (-0.5 $<$ y $<$ 0) in 0-40$\%$ central Au+Au collisions for collider energies from $\sqrt{s_{NN}}$ = 7.7 - 54.4 GeV.

Cumulant ratios C5/C1 of net-proton distributions measured in 40-50$\%$, 60-70$\%$, and 70-80$\%$ Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. This is supplemental data and was not part of the original paper.

Inclusive Y(2S) $R_{AA}$ as a function of centrality in Au+Au collisions at 200 GeV. The bin corresponding to $N_{part}$ = 162 is for 0-60% centrality. Global uncertainty of 20.5% not shown.

Upper limit of inclusive Y(3S) $R_{AA}$ with 95% confidence level in 0-60% Au+Au collisions at 200 GeV

Upper limit of inclusive Y(3S) $R_{AA}$ with 95% confidence level in 0-60% Au+Au collisions at 200 GeV

Inclusive Y(1S) $R_{AA}$ as a function of $p_{T}$ in Au+Au collisions at 200 GeV. Global uncertainty of 6.8% not shown.

Inclusive Y(1S) $R_{AA}$ as a function of $p_{T}$ in 0-60% Au+Au collisions at 200 GeV. Global uncertainty of 6.8% not shown.

Inclusive Y(2S) R_{AA} as a function of p_{T} in Au+Au collisions at 200 GeV. Global uncertainty of 6.8% not shown.

Inclusive Y(2S) $R_{AA}$ as a function of $p_{T}$ in 0-60% Au+Au collisions at 200 GeV. Global uncertainty of 6.8% not shown.

Inclusive Y(1S) yield as a function of centrality in Au+Au collisions at 200 GeV. The bin corresponding to $N_{part}$ = 162 is for 0-60% centrality.

Inclusive Y(2S) yield as a function of centrality in Au+Au collisions at 200 GeV. The bin corresponding to $N_{part}$ = 162 is for 0-60% centrality.

Upper limit of inclusive Y(3S) yield with 95% confidence level in 0-60% Au+Au collisions at 200 GeV

Inclusive Y(1S) yield as a function of $p_{T}$ in 0-60% Au+Au collisions at 200 GeV.

Inclusive Y(2S) yield as a function of p_{T} in 0-60% Au+Au collisions at 200 GeV.

Y(2S)/Y(1S) ratio as a function of centrality in Au+Au collisions at 200 GeV. The bin corresponding to $N_{part}$ = 162 is for 0-60% centrality.

Upper limit of Y(3S)/Y(1S) ratio with 95% confidence level in 0-60% Au+Au collisions at 200 GeV

Y(2S)/Y(1S) ratio as a function of $p_{T}$ in 0-60% Au+Au collisions at 200 GeV.

$v_{2}(p_{T})$ for $K_{S}^{0}$ (Centrality:0-80%)

$v_{3}(p_{T})$ for $K_{S}^{0}$ (Centrality:0-10%)

$v_{3}(p_{T})$ for $K_{S}^{0}$ (Centrality:10-40%)

$v_{3}(p_{T})$ for $K_{S}^{0}$ (Centrality:40-80%)

$v_{3}(p_{T})$ for $K_{S}^{0}$ (Centrality:0-80%)

$v_{2}(p_{T})$ for $\Lambda$ (Centrality:0-10%)

$v_{2}(p_{T})$ for $\Lambda$ (Centrality:10-40%)

$v_{2}(p_{T})$ for $\Lambda$ (Centrality:40-80%)

$v_{2}(p_{T})$ for $\Lambda$ (Centrality:0-80%)

$v_{3}(p_{T})$ for $\Lambda$ (Centrality:0-10%)

$v_{3}(p_{T})$ for $\Lambda$ (Centrality:10-40%)

$v_{3}(p_{T})$ for $\Lambda$ (Centrality:40-80%)

$v_{3}(p_{T})$ for $\Lambda$ (Centrality:0-80%)

$v_{2}(p_{T})$ for $\bar{\Lambda}$ (Centrality:0-10%)

$v_{2}(p_{T})$ for $\bar{\Lambda}$ (Centrality:10-40%)

$v_{2}(p_{T})$ for $\bar{\Lambda}$ (Centrality:40-80%)

$v_{2}(p_{T})$ for $\bar{\Lambda}$ (Centrality:0-80%)

$v_{3}(p_{T})$ for $\bar{\Lambda}$ (Centrality:0-10%)

$v_{3}(p_{T})$ for $\bar{\Lambda}$ (Centrality:10-40%)

$v_{3}(p_{T})$ for $\bar{\Lambda}$ (Centrality:40-80%)

$v_{3}(p_{T})$ for $\bar{\Lambda}$ (Centrality:0-80%)

$v_{2}(p_{T})$ for $\phi$ (Centrality:0-10%)

$v_{2}(p_{T})$ for $\phi$ (Centrality:10-40%)

$v_{2}(p_{T})$ for $\phi$ (Centrality:40-80%)

$v_{2}(p_{T})$ for $\phi$ (Centrality:0-80%)

$v_{3}(p_{T})$ for $\phi$ (Centrality:0-10%)

$v_{3}(p_{T})$ for $\phi$ (Centrality:10-40%)

$v_{3}(p_{T})$ for $\phi$ (Centrality:0-80%)

$v_{2}(p_{T})$ for $\Xi^{-}$ (Centrality:0-10%)

$v_{2}(p_{T})$ for $\Xi^{-}$ (Centrality:10-40%)

$v_{2}(p_{T})$ for $\Xi^{-}$ (Centrality:40-80%)

$v_{2}(p_{T})$ for $\Xi^{-}$ (Centrality:0-80%)

$v_{3}(p_{T})$ for $\Xi^{-}$ (Centrality:0-10%)

$v_{3}(p_{T})$ for $\Xi^{-}$ (Centrality:10-40%)

$v_{3}(p_{T})$ for $\Xi^{-}$ (Centrality:0-80%)

$v_{2}(p_{T})$ for $\bar{\Xi^{+}}$ (Centrality:0-10%)

$v_{2}(p_{T})$ for $\bar{\Xi^{+}}$ (Centrality:10-40%)

$v_{2}(p_{T})$ for $\bar{\Xi^{+}}$ (Centrality:40-80%)

$v_{2}(p_{T})$ for $\bar{\Xi^{+}}$ (Centrality:0-80%)

$v_{3}(p_{T})$ for $\bar{\Xi^{+}}$ (Centrality:0-10%)

$v_{3}(p_{T})$ for $\bar{\Xi^{+}}$ (Centrality:10-40%)

$v_{3}(p_{T})$ for $\bar{\Xi^{+}}$ (Centrality:0-80%)

$v_{2}(p_{T})$ for $\Omega^{-}$ (Centrality:0-10%)

$v_{2}(p_{T})$ for $\Omega^{-}$ (Centrality:10-40%)

$v_{2}(p_{T})$ for $\Omega^{-}$ (Centrality:40-80%)

$v_{2}(p_{T})$ for $\Omega^{-}$ (Centrality:0-80%)

$v_{3}(p_{T})$ for $\Omega^{-}$ (Centrality:0-10%)

$v_{3}(p_{T})$ for $\Omega^{-}$ (Centrality:10-40%)

$v_{3}(p_{T})$ for $\Omega^{-}$ (Centrality:0-80%)

$v_{2}(p_{T})$ for $\bar{\Omega^{+}}$ (Centrality:0-10%)

$v_{2}(p_{T})$ for $\bar{\Omega^{+}}$ (Centrality:10-40%)

$v_{2}(p_{T})$ for $\bar{\Omega^{+}}$ (Centrality:40-80%)

$v_{2}(p_{T})$ for $\bar{\Omega^{+}}$ (Centrality:0-80%)

$v_{3}(p_{T})$ for $\bar{\Omega^{+}}$ (Centrality:0-10%)

$v_{3}(p_{T})$ for $\bar{\Omega^{+}}$ (Centrality:10-40%)

$v_{3}(p_{T})$ for $\bar{\Omega^{+}}$ (Centrality:0-80%)

$v_{2}$ of $\phi$ to $\bar{p}$ ratio

Difference of $v_{2}$ between particle and anti-particle

Difference of $v_{3}$ between particle and anti-particle

Example of combinatorial background subtracted invariant mass distributions and the extracted yields as a function of $\cos \theta^*$ for $\phi$ and $K^{*0}$ mesons. \textbf{a)} example of $\phi \rightarrow K^+ + K^-$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{b)} example of $K^{*0} (\overline{K^{*0}}) \rightarrow K^{-} \pi^{+} (K^{+} \pi^{-})$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{c)} extracted yields of $\phi$ as a function of $\cos \theta^*$; \textbf{d)} extracted yields of $K^{*0}$ as a function of $\cos \theta^*$.

Example of combinatorial background subtracted invariant mass distributions and the extracted yields as a function of $\cos \theta^*$ for $\phi$ and $K^{*0}$ mesons. \textbf{a)} example of $\phi \rightarrow K^+ + K^-$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{b)} example of $K^{*0} (\overline{K^{*0}}) \rightarrow K^{-} \pi^{+} (K^{+} \pi^{-})$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{c)} extracted yields of $\phi$ as a function of $\cos \theta^*$; \textbf{d)} extracted yields of $K^{*0}$ as a function of $\cos \theta^*$.

Example of combinatorial background subtracted invariant mass distributions and the extracted yields as a function of $\cos \theta^*$ for $\phi$ and $K^{*0}$ mesons. \textbf{a)} example of $\phi \rightarrow K^+ + K^-$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{b)} example of $K^{*0} (\overline{K^{*0}}) \rightarrow K^{-} \pi^{+} (K^{+} \pi^{-})$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{c)} extracted yields of $\phi$ as a function of $\cos \theta^*$; \textbf{d)} extracted yields of $K^{*0}$ as a function of $\cos \theta^*$.

Efficiency corrected $\phi$-meson yields as a function of cos$\theta$* and corresponding fits with Eq.1 in the method section.

Efficiency and acceptance corrected $K^{*0}$-meson yields as a function of cos$\theta$* and corresponding fits with Eq.4 in the method section.

$\phi$-meson $\rho_{00}$ obtained from 1st- and 2nd-order event planes. The red stars (gray squares) show the $\phi$-meson $\rho_{00}$ as a function of beam energy, obtained with the 2nd-order (1st-order) EP.

$\phi$-meson $\rho_{00}$ with respect to different quantization axes. $\phi$-meson $\rho_{00}$ as a function of beam energy, for the out-of-plane direction (stars) and the in-plane direction (diamonds). Curves are fits based on theoretical calculations with a $\phi$-meson field. The corresponding $G_s^{(y)}$ values obtained from the fits are shown in the legend.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

Global spin alignment measurement of $\phi$ and $K^{*0}$ vector mesons in Au+Au collisions at 0-20\% centrality. The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for $K^{*0}$-meson, obtained with the 2nd-order EP.

Global spin alignment measurement of $\phi$ and $K^{*0}$ vector mesons in Au+Au collisions at 0-20\% centrality. The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for $K^{*0}$-meson, obtained with the 2nd-order EP.

The $p_{T}$ dependencies of $v_{1}$ within $-0.4<y<-0.1$ for $t$ in 10-40% mid-central Au+Au collisions at 3 GeV.

The rapidity and $p_{T}$ dependencies of $v_{1}$ for $^{3}$He in 10-40% mid-central Au+Au collisions at 3 GeV.

The $p_{T}$ dependencies of $v_{1}$ within $-0.1<y<0$ for $^4$He in 10-40% mid-central Au+Au collisions at 3 GeV.

The $p_{T}$ dependencies of $v_{1}$ within $-0.4<y<-0.1$ for $^{4}$He in 10-40% mid-central Au+Au collisions at 3 GeV.

The rapidity and $p_{T}$ dependencies of $v_{2}$ for $p$ in 10-40% mid-central Au+Au collisions at 3 GeV.

The rapidity and $p_{T}$ dependencies of $v_{2}$ for $d$ in 10-40% mid-central Au+Au collisions at 3 GeV.

The $p_{T}$ dependencies of $v_{2}$ within $-0.1<y<0$ for $t$ in 10-40% mid-central Au+Au collisions at 3 GeV.

The $p_{T}$ dependencies of $v_{2}$ within $-0.4<y<-0.1$ for $t$ in 10-40% mid-central Au+Au collisions at 3 GeV.

The rapidity and $p_{T}$ dependencies of $v_{2}$ for $^{3}$He in 10-40% mid-central Au+Au collisions at 3 GeV.

The $p_{T}$ dependencies of $v_{2}$ within $-0.1<y<0$ for $^4$He in 10-40% mid-central Au+Au collisions at 3 GeV.

The $p_{T}$ dependencies of $v_{2}$ within $-0.4<y<-0.1$ for $^{4}$He in 10-40% mid-central Au+Au collisions at 3 GeV.

The rapidity dependencies of $v_{1}$ for $p$, $d$, and $^{3}$He in 10-40% mid-central Au+Au collisions at 3 GeV.

The rapidity dependencies of $v_{1}$ for $t$ and $^{4}$He in 10-40% mid-central Au+Au collisions at 3 GeV.

The rapidity dependencies of $v_{1}$ from JAM plus coalescence calculations in 10-40% mid-central Au+Au collisions at 3 GeV.

The rapidity dependencies of $v_{2}$ for $p$, $d$, and $^{3}$He in 10-40% mid-central Au+Au collisions at 3 GeV.

The rapidity dependencies of $v_{2}$ for $t$ and $^{4}$He in 10-40% mid-central Au+Au collisions at 3 GeV.

The rapidity dependencies of $v_{2}$ from JAM plus coalescence calculations in 10-40% mid-central Au+Au collisions at 3 GeV.

Light nucleus scaled $v_{1}$ slopes as a function os collision energy in 10-40 mid-cantral Au+Au collisions.

Light nucleus scaled $v_{1}$ slopes from JAM plus coalescence in 10-40 mid-cantral Au+Au collisions at 3 GeV.

Centrality dependence of the proton cumulant ratios for Au+Au collisions at $\sqrt{s_{NN}}$ = 3.0 GeV. Protons are from $-0.5 < y < 0$ and $0.4 < p_{T} < 2.0$ GeV/$c$. Systematic uncertainties are represented by gray bars. Statistical uncertainties are smaller than marker size. CBWC is applied to all cumulant ratios. While open squares represent the data without the VFC correction, blue triangles and red circles are the results with VFC using the $\langle N_{\rm{part}} \rangle$ distributions from the UrQMD and Glauber models, respectively. UrQMD model results are represented as gold dashed line.

Centrality dependence of the proton cumulant ratios for Au+Au collisions at $\sqrt{s_{NN}}$ = 3.0 GeV. Protons are from $-0.5 < y < 0$ and $0.4 < p_{T} < 2.0$ GeV/$c$. Systematic uncertainties are represented by gray bars. Statistical uncertainties are smaller than marker size. CBWC is applied to all cumulant ratios. While open squares represent the data without the VFC correction, blue triangles and red circles are the results with VFC using the $\langle N_{\rm{part}} \rangle$ distributions from the UrQMD and Glauber models, respectively. UrQMD model results are represented as gold dashed line.

Rapidity and transverse momentum dependence of the proton cumulant ratios for 0–5% central collisions. Black-squares, red-dots and blue-triangles stand for data without and with the VFC using Glauber and UrQMD, respectively.

Rapidity and transverse momentum dependence of the proton cumulant ratios for 0–5% central collisions. Black-squares, red-dots and blue-triangles stand for data without and with the VFC using Glauber and UrQMD, respectively.

Rapidity and transverse momentum dependence of the proton cumulant ratios for 0–5% central collisions. Black-squares, red-dots and blue-triangles stand for data without and with the VFC using Glauber and UrQMD, respectively.

Rapidity and transverse momentum dependence of the proton cumulant ratios for 0–5% central collisions. Black-squares, red-dots and blue-triangles stand for data without and with the VFC using Glauber and UrQMD, respectively.

Collision energy dependence of the ratios of cumulants, $C_4/C_2$, for proton (squares) and net-proton (red circles) from top 0-5% Au+Au collisions at RHIC. The points for protons are shifted horizontally for clarity. The new result for proton from $\sqrt{s_{NN}}$ = 3.0 GeV collisions is shown as a filled square. HADES data of $\sqrt{s_{NN}}$ = 2.4 GeV 0-10% collisions is also shown. The vertical black and gray bars are the statistical and systematic uncertainties, respectively. In addition, results from the HRG model, based on both Canonical Ensemble (CE) and Grand-Canonical Ensemble (GCE), and transport model UrQMD are presented.

Fraction of bottom hadron decayed electrons in 0-80% Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV.

Fraction of bottom hadron decayed electrons in 0-20% and 20-40% Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV.

Fraction of bottom hadron decayed electrons in 40-80% Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV.

Nuclear modification factor $R_{\rm AA}$ of inclusive heavy flavor decayed electrons in 0-80% Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV. The 8% global uncertainty from the $p$+$p$ reference and a 8% gloabl uncertainty from $N_{\rm coll.}$ are not included in the table values.

Nuclear modification factor $R_{\rm AA}$ of bottom- and charm-decay electrons in 0-80% Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV. The 8% global uncertainty from the $p$+$p$ reference and a 8% gloabl uncertainty from $N_{\rm coll.}$ are not included in the table values.

Nuclear modification factor $R_{\rm AA}$ ratio of bottom- to charm-decay electrons in 0-80% Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV.

Null hypothesis for the nuclear modification factor $R_{\rm AA}$ ratio of bottom- to charm-decay electrons in 0-80% Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV.

Nuclear modification factor $R_{\rm CP}$ ratio of bottom- and charm-decay electrons in 0-80% Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV.

Null hypotheses for the nuclear modification factor $R_{\rm CP}$ ratio of bottom- and charm-decay electrons in 0-80% Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV.

The correlation functions (corrected for nonuniform detector efficiency in $\phi$; not corrected for the absolute detection efficiency) vs. azimuthal angle difference between forward ($2.6<\eta<4.0$) $\pi^{0}$s in $p$+$p$ collisions at $\sqrt{s_{\mathrm{_{NN}}}}=200$ GeV at high $p_{T}$ ($p^{trig}_{T}$=2.5-3 GeV/c, $p^{asso}_{T}$=2-2.5 GeV/c)

The correlation functions (corrected for nonuniform detector efficiency in $\phi$; not corrected for the absolute detection efficiency) vs. azimuthal angle difference between forward ($2.6<\eta<4.0$) $\pi^{0}$s in $p$+Al collisions at $\sqrt{s_{\mathrm{_{NN}}}}=200$ GeV at high $p_{T}$ ($p^{trig}_{T}$=2.5-3 GeV/c, $p^{asso}_{T}$=2-2.5 GeV/c)

The correlation functions (corrected for nonuniform detector efficiency in $\phi$; not corrected for the absolute detection efficiency) vs. azimuthal angle difference between forward ($2.6<\eta<4.0$) $\pi^{0}$s in $p$+$Au collisions at $\sqrt{s_{\mathrm{_{NN}}}}=200$ GeV at high $p_{T}$ ($p^{trig}_{T}$=2.5-3 GeV/c, $p^{asso}_{T}$=2-2.5 GeV/c)

Relative area of MinBias $pAu/pp$ of back-to-back di-$\pi^0$ correlations at forward pseudorapidities ($2.6<\eta<4.0$) from data

Relative area of MinBias $pAl/pp$ of back-to-back di-$\pi^0$ correlations at forward pseudorapidities ($2.6<\eta<4.0$) from data

Relative area of $pAu/pp$ at b=0 of back-to-back di-$\pi^0$ correlations at forward pseudorapidities ($2.6<\eta<4.0$) from prediction

Relative width of MinBias $pAu/pp$ of back-to-back di-$\pi^0$ correlations at forward pseudorapidities ($2.6<\eta<4.0$) from data

Relative width of MinBias $pAl/pp$ of back-to-back di-$\pi^0$ correlations at forward pseudorapidities ($2.6<\eta<4.0$) from data

Relative pedestal of MinBias $pAu/pp$ of back-to-back di-$\pi^0$ correlations at forward pseudorapidities ($2.6<\eta<4.0$) from data

Relative pedestal of MinBias $pAl/pp$ of back-to-back di-$\pi^0$ correlations at forward pseudorapidities ($2.6<\eta<4.0$) from data

Relative area of MinBias $pp/pp$ of back-to-back di-$\pi^0$ correlations at forward pseudorapidities ($2.6<\eta<4.0$), the ratio is unity, error is zero

Relative area of MinBias $pA/pp$ of back-to-back di-$\pi^0$ correlations at forward pseudorapidities ($2.6<\eta<4.0$) from data