FIG. 2: a) left side: The correlation data for the ratio of the histograms of same-event-pairs to mixed-event-pairs for unlike-sign charged pairs, shown in a two-dimensional (2-D) perspective plot $\Delta\phi$ - $\Delta\eta$. The plot was normalized to a mean of 1. b) right side: The similar correlation data for like-sign charge pairs.

FIG. 3: a) left side: Folded correlation data for unlike-sign charge pairs on $\Delta\phi$ and $\Delta\eta$ based on demonstrated symmetries in the data. This increases the statistics in a typical bin by a factor of four. Henceforth we will be dealing with folded data only. b) right side: Similar folded data for like-sign charge pairs.

FIG. 3: a) left side: Folded correlation data for unlike-sign charge pairs on $\Delta\phi$ and $\Delta\eta$ based on demonstrated symmetries in the data. This increases the statistics in a typical bin by a factor of four. Henceforth we will be dealing with folded data only. b) right side: Similar folded data for like-sign charge pairs.

FIG. 4: “(Color online)”a) left side: The 2 dimensional (2-D) approximately gaussian signal shape equation (4) from the fit to the normalized and folded unlike-sign charge pairs signal data. b) right side: The unlike-sign charge pairs signal data corresponding to the adjoining signal function on the left side.

FIG. 4: “(Color online)”a) left side: The 2 dimensional (2-D) approximately gaussian signal shape equation (4) from the fit to the normalized and folded unlike-sign charge pairs signal data. b) right side: The unlike-sign charge pairs signal data corresponding to the adjoining signal function on the left side.

FIG. 5 :“(Color online)”a) left side: A perspective plot of the fit to the 2-D like-sign charge pairs signal shape of equation (5). b) right side: Like-sign charge pairs signal data corresponding to the adjacent signal fit on the left side.

FIG. 5: “(Color online)”a) left side: A perspective plot of the fit to the 2-D like-sign charge pairs signal shape of equation (5). b) right side: Like-sign charge pairs signal data corresponding to the adjacent signal fit on the left side.

FIG. 6: “(Color online)”a) left side: The charge dependent (CD) signal shape is a 2 dimensional (2-D) approximate gaussian which is symmetrical. The average gaussian width is 27.5$^{\circ}$ $\pm$ 3.2$^{\circ}$ (0.48 $\pm$ 0.056 rad) both in $\Delta\phi$ and $\Delta\eta$. Thus we are observing a greater probability for unlike-sign charge pairs of particles than for like-sign charge pairs emitted randomly on 2-D $\eta\phi$ directions. b) right side: The CD signal data corresponding to the adjacent signal fit on the left.

FIG. 6: “(Color online)”a) left side: The charge dependent (CD) signal shape is a 2 dimensional (2-D) approximate gaussian which is symmetrical. The average gaussian width is 27.5$^{\circ}$ $\pm$ 3.2$^{\circ}$ (0.48 $\pm$ 0.056 rad) both in $\Delta\phi$ and $\Delta\eta$. Thus we are observing a greater probability for unlike-sign charge pairs of particles than for like-sign charge pairs emitted randomly on 2-D $\eta\phi$ directions. b) right side: The CD signal data corresponding to the adjacent signal fit on the left.

FIG. 7: “(Color online)”a) left side: The fit to the charge independent (CI) signal shape which is the sum of the fits of like-sign plus unlike-sign charge pairs signals. The 2-D gaussian equivalent RMS signal has a $\Delta\phi$ width of about 32$^{\circ}$ (0.52 rad), and $\Delta\eta$ width of about 66$^{\circ}$ (1.15 rad) which is about double the $\Delta\phi$ width. b) right side: The CI signal data corresponding to the adjacent fit on the left.

FIG. 7: “(Color online)”a) left side: The fit to the charge independent (CI) signal shape which is the sum of the fits of like-sign plus unlike-sign charge pairs signals. The 2-D gaussian equivalent RMS signal has a $\Delta\phi$ width of about 32$^{\circ}$ (0.52 rad), and $\Delta\eta$ width of about 66$^{\circ}$ (1.15 rad) which is about double the $\Delta\phi$ width. b) right side: The CI signal data corresponding to the adjacent fit on the left.

FIG. 8: a) left side: The charge independent (CI) signal data with the lower range of elliptic flow amplitude and the best $\chi^2$ (the same as Figure 7b) plotted as a 2-D perspective plot on $\Delta\phi$ vs. $\Delta\eta$. b) right side: The charge independent (CI) signal data with our maximum elliptic flow amplitude used in our analysis ($\chi^2$ was worse by 1$\sigma$).

FIG. 8: a) left side: The charge independent (CI) signal data with the lower range of elliptic flow amplitude and the best $\chi^2$ (the same as Figure 7b) plotted as a 2-D perspective plot on $\Delta\phi$ vs. $\Delta\eta$. b) right side: The charge independent (CI) signal data with our maximum elliptic flow amplitude used in our analysis ($\chi^2$ was worse by 1$\sigma$).

The $v_{dyn}$ and the three terms of $v_{dyn}$ vs $\sqrt{\langle N_{ch}\rangle \langle N_{\gamma}\rangle }$ for mixed events. $Corr_{\gamma\,-ch}^{real}$ is plotted.

The $v_{dyn}$ and the three terms of $v_{dyn}$ vs $\sqrt{\langle N_{ch}\rangle \langle N_{\gamma}\rangle }$ for mixed events. $Corr_{\gamma\,-ch}^{mixed}$ is plotted.

The $v_{dyn}$ and the three terms of $v_{dyn}$ vs $\sqrt{\langle N_{ch}\rangle \langle N_{\gamma}\rangle }$ for mixed events. $\omega_{\gamma}^{real}$ is plotted.

The $v_{dyn}$ and the three terms of $v_{dyn}$ vs $\sqrt{\langle N_{ch}\rangle \langle N_{\gamma}\rangle }$ for mixed events. $\omega_{\gamma}^{mixed}$ is plotted.

The $v_{dyn}$ and the three terms of $v_{dyn}$ vs $\sqrt{\langle N_{ch}\rangle \langle N_{\gamma}\rangle }$ for mixed events. $v_{dyn}^{real}$ is plotted.

The $v_{dyn}$ and the three terms of $v_{dyn}$ vs $\sqrt{\langle N_{ch}\rangle \langle N_{\gamma}\rangle }$ for mixed events. $v_{dyn}^{mixed}$ is plotted.

The values of the observable $v_{dyn}^{ch-\gamma}$ for the same side.

The values of the observable $v_{dyn}^{ch-\gamma}$ for the same side.

The values of the observable $v_{dyn}^{ch-\gamma}$ for the away-side.

The values of the observable $v_{dyn}^{ch-\gamma}$ for the away-side.

The correlation between positive and negative charged particles measured by the FTPC and photons measured by the PMD using $v_{dyn}$ for real events.

$r_{m,1}$ vs multiplicity for first order of m.

$r_{m,1}$ vs multiplicity for first order of m.

$r_{m,1}$ vs multiplicity for second order of m.

$r_{m,1}$ vs multiplicity for second order of m.

$r_{m,1}$ vs multiplicity for third order of m.

$r_{m,1}$ vs multiplicity for third order of m.

The moments $r_{m,1}$(m=1-3) for real and mixed events as a function of order m in a fixed multiplicity bin of 47$\langle \sqrt{\langle N_{ch}\rangle \langle N_{\gamma}\rangle }\langle 54$.

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.

$v_{2}(p_{T})$ 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

Invariant yield of inclusive J/PSI(1S) times branching ratio to the dimuon decay in 40-60% Au+Au collisions at 200 GeV

Invariant yield of inclusive J/PSI(1S) times branching ratio to the dimuon decay in 60-80% Au+Au collisions at 200 GeV

Invariant yield of inclusive J/PSI(1S) times branching ratio to the dielectron decay in 0-60% Au+Au collisions at 200 GeV

Invariant yield of inclusive J/PSI(1S) times branching ratio to the dielectron decay in 0-20% Au+Au collisions at 200 GeV

Invariant yield of inclusive J/PSI(1S) times branching ratio to the dielectron decay in 20-40% Au+Au collisions at 200 GeV

Invariant yield of inclusive J/PSI(1S) times branching ratio to the dielectron decay in 40-60% Au+Au collisions at 200 GeV

Invariant yield of inclusive J/PSI(1S) times branching ratio in p+p collisions at 200 GeV. A 10% global uncertainty is not shown.

Inclusive J/PSI(1S) RAA vs. pT measured via the dimuon channel in 0-80% Au+Au collisions at 200 GeV. A global uncertainty of 12.2% is not shown.

Inclusive J/PSI(1S) RAA vs. pT measured via the dimuon channel in 0-20% Au+Au collisions at 200 GeV. A global uncertainty of 10.7% is not shown.

Inclusive J/PSI(1S) RAA vs. pT measured via the dimuon channel in 20-40% Au+Au collisions at 200 GeV. A global uncertainty of 14.5% is not shown.

Inclusive J/PSI(1S) RAA vs. pT measured via the dimuon channel in 40-60% Au+Au collisions at 200 GeV. A global uncertainty of 24.1% is not shown.

Inclusive J/PSI(1S) RAA vs. pT measured via the dimuon channel in 60-80% Au+Au collisions at 200 GeV. A global uncertainty of 38.6% is not shown.

Inclusive J/PSI(1S) RAA vs. pT measured via the dielectron channel in 0-60% Au+Au collisions at 200 GeV. A global uncertainty of 12.1% is not shown.

Inclusive J/PSI(1S) RAA vs. pT measured via the dielectron channel in 0-20% Au+Au collisions at 200 GeV. A global uncertainty of 10.7% is not shown.

Inclusive J/PSI(1S) RAA vs. pT measured via the dielectron channel in 20-40% Au+Au collisions at 200 GeV. A global uncertainty of 14.5% is not shown.

Inclusive J/PSI(1S) RAA vs. pT measured via the dielectron channel in 40-60% Au+Au collisions at 200 GeV. A global uncertainty of 24.1% is not shown.

Inclusive J/PSI(1S) RAA vs. centrality measured via the dimuon channel for pT > 0 GeV/c. The pp uncertainty of 14.3% is not shown.

Relative error on Ncoll as a function of centrality for measurement of J/PSI(1S) RAA with pT > 0 GeV/c via the dimuon channel.

Inclusive J/PSI(1S) RAA vs. centrality measured via the dimuon channel for pT > 5 GeV/c. The pp uncertainty of 15.0% is not shown.

Relative error on Ncoll as a function of centrality for measurement of J/PSI(1S) RAA with pT > 5 GeV/c via the dimuon channel.

Inclusive J/PSI(1S) RAA vs. centrality measured via the dielectron channel for pT > 5 GeV/c. The pp uncertainty of 15.0% is not shown.

Relative error on Ncoll as a function of centrality for measurement of J/PSI(1S) RAA with pT > 0 GeV/c via the dielectron channel.

The centrality dependence of e+e− invariant mass spectra within the STAR acceptance from Au+Au collisions and U+U collisions for pair pT < 0.15 GeV/c. The vertical bars on data points depict the statistical uncertainties, while the systematic uncertainties are shown as gray boxes. The hadronic cocktail yields from U+U collisions are ∼5%–12% higher than those from Au+Au collisions in given centrality bins; thus only cocktails for Au+Au collisions are shown here as solid lines, with shaded bands representing the systematic uncertainties for clarity.

The centrality dependence of e+e− invariant mass spectra within the STAR acceptance from Au+Au collisions and U+U collisions for pair pT < 0.15 GeV/c. The vertical bars on data points depict the statistical uncertainties, while the systematic uncertainties are shown as gray boxes. The hadronic cocktail yields from U+U collisions are ∼5%–12% higher than those from Au+Au collisions in given centrality bins; thus only cocktails for Au+Au collisions are shown here as solid lines, with shaded bands representing the systematic uncertainties for clarity.

The centrality dependence of e+e− invariant mass spectra within the STAR acceptance from Au+Au collisions and U+U collisions for pair pT < 0.15 GeV/c. The vertical bars on data points depict the statistical uncertainties, while the systematic uncertainties are shown as gray boxes. The hadronic cocktail yields from U+U collisions are ∼5%–12% higher than those from Au+Au collisions in given centrality bins; thus only cocktails for Au+Au collisions are shown here as solid lines, with shaded bands representing the systematic uncertainties for clarity.

The corresponding ratios of data over cocktail for Figure 1.

The corresponding ratios of data over cocktail for Figure 1.

The corresponding ratios of data over cocktail for Figure 1.

The corresponding ratios of data over cocktail for Figure 1.

The corresponding ratios of data over cocktail for Figure 1.

The corresponding ratios of data over cocktail for Figure 1.

The e+e− pair pT distributions within the STAR acceptance for different mass regions in 60%–80% Au+Au and U+U collisions compared to cocktails. The systematic uncertainties of the data are shown as gray boxes. The gray bands depict the systematic uncertainties of the cocktails.

The e+e− pair pT distributions within the STAR acceptance for different mass regions in 60%–80% Au+Au and U+U collisions compared to cocktails. The systematic uncertainties of the data are shown as gray boxes. The gray bands depict the systematic uncertainties of the cocktails.

The e+e− pair pT distributions within the STAR acceptance for different mass regions in 60%–80% Au+Au and U+U collisions compared to cocktails. The systematic uncertainties of the data are shown as gray boxes. The gray bands depict the systematic uncertainties of the cocktails.

The e+e− pair pT distributions within the STAR acceptance for different mass regions in 60%–80% Au+Au and U+U collisions compared to cocktails. The systematic uncertainties of the data are shown as gray boxes. The gray bands depict the systematic uncertainties of the cocktails.

The e+e− pair pT distributions within the STAR acceptance for different mass regions in 60%–80% Au+Au and U+U collisions compared to cocktails. The systematic uncertainties of the data are shown as gray boxes. The gray bands depict the systematic uncertainties of the cocktails.

The e+e− pair pT distributions within the STAR acceptance for different mass regions in 60%–80% Au+Au and U+U collisions compared to cocktails. The systematic uncertainties of the data are shown as gray boxes. The gray bands depict the systematic uncertainties of the cocktails.

The low-pT (pT < 0.15 GeV/c) e+e− excess mass spectra (data − cocktail) within the STAR acceptance in 60%–80% for Au + Au and U + U collisions, compared with a broadened rho meson model calculation [8]. The contributions of rho and phi from the photonuclear process are shown, as are the contributions of photon-photon process from two models [33,34]. The model calculations are for Au + Au collisions in the corresponding centrality bins.

The low-pT (pT < 0.15 GeV/c) e+e− excess mass spectra (data − cocktail) within the STAR acceptance in 60%–80% for Au + Au and U + U collisions, compared with a broadened rho meson model calculation [8]. The contributions of rho and phi from the photonuclear process are shown, as are the contributions of photon-photon process from two models [33,34]. The model calculations are for Au + Au collisions in the corresponding centrality bins.

The low-pT (pT < 0.15 GeV/c) e+e− excess mass spectra (data − cocktail) within the STAR acceptance in 40%–60% for Au + Au and U + U collisions, compared with a broadened rho meson model calculation [8]. The contributions of rho and phi from the photonuclear process are shown, as are the contributions of photon-photon process from two models [33,34]. The model calculations are for Au + Au collisions in the corresponding centrality bins.

The low-pT (pT < 0.15 GeV/c) e+e− excess mass spectra (data − cocktail) within the STAR acceptance in 40%–60% for Au + Au and U + U collisions, compared with a broadened rho meson model calculation [8]. The contributions of rho and phi from the photonuclear process are shown, as are the contributions of photon-photon process from two models [33,34]. The model calculations are for Au + Au collisions in the corresponding centrality bins.

The centrality dependence of integrated excess yields in the mass regions of 0.4–0.76, 0.76–1.2, and 1.2–2.6 GeV=c2 in Au + Au and U + U collisions. The centrality dependence of hadronic cocktail yields in the mass region of 0.76–1.2 GeV/c2 in both collisions is also shown for comparison. The systematic uncertainties are shown as gray boxes.

The centrality dependence of integrated excess yields in the mass regions of 0.4–0.76, 0.76–1.2, and 1.2–2.6 GeV=c2 in Au + Au and U + U collisions. The centrality dependence of hadronic cocktail yields in the mass region of 0.76–1.2 GeV/c2 in both collisions is also shown for comparison. The systematic uncertainties are shown as gray boxes.

The centrality dependence of integrated excess yields in the mass regions of 0.4–0.76, 0.76–1.2, and 1.2–2.6 GeV=c2 in Au + Au and U + U collisions. The centrality dependence of hadronic cocktail yields in the mass region of 0.76–1.2 GeV/c2 in both collisions is also shown for comparison. The systematic uncertainties are shown as gray boxes.

The centrality dependence of integrated excess yields in the mass regions of 0.4–0.76, 0.76–1.2, and 1.2–2.6 GeV=c2 in Au + Au and U + U collisions. The centrality dependence of hadronic cocktail yields in the mass region of 0.76–1.2 GeV/c2 in both collisions is also shown for comparison. The systematic uncertainties are shown as gray boxes.

The centrality dependence of integrated excess yields in the mass regions of 0.4–0.76, 0.76–1.2, and 1.2–2.6 GeV=c2 in Au + Au and U + U collisions. The centrality dependence of hadronic cocktail yields in the mass region of 0.76–1.2 GeV/c2 in both collisions is also shown for comparison. The systematic uncertainties are shown as gray boxes.

The centrality dependence of integrated excess yields in the mass regions of 0.4–0.76, 0.76–1.2, and 1.2–2.6 GeV/c2 in Au + Au and U + U collisions. The centrality dependence of hadronic cocktail yields in the mass region of 0.76–1.2 GeV/c2 in both collisions is also shown for comparison. The systematic uncertainties are shown as gray boxes.

The p2T distributions of excess yields within the STAR acceptance in the mass regions of 0.4–0.76 GeV/c2 in 60%–80% Au + Au and U + U collisions. The systematic uncertainties are shown as gray boxes. The solid and dotted lines are exponential fits to the data in Au + Au and U + U collisions, respectively. The dot-dashed and dot-dot- dashed lines represent the p2T distributions for the photon-photon process from two models [33,34] within the STAR acceptance in 60%–80% Au + Au collisions. The dashed lines illustrate the corresponding p2T distributions for e+e− pairs from the model [33] traversing 1 fm in a constant magnetic field of 10^14 T perpendicular to the beam line.

The p2T distributions of excess yields within the STAR acceptance in the mass regions of 0.4–0.76 GeV/c2 in 60%–80% Au + Au and U + U collisions. The systematic uncertainties are shown as gray boxes. The solid and dotted lines are exponential fits to the data in Au + Au and U + U collisions, respectively. The dot-dashed and dot-dot- dashed lines represent the p2T distributions for the photon-photon process from two models [33,34] within the STAR acceptance in 60%–80% Au + Au collisions. The dashed lines illustrate the corresponding p2T distributions for e+e− pairs from the model [33] traversing 1 fm in a constant magnetic field of 10^14 T perpendicular to the beam line.

The p2T distributions of excess yields within the STAR acceptance in the mass regions of 0.76–1.2 GeV/c2 in 60%–80% Au + Au and U + U collisions. The systematic uncertainties are shown as gray boxes. The solid and dotted lines are exponential fits to the data in Au + Au and U + U collisions, respectively. The dot-dashed and dot-dot- dashed lines represent the p2T distributions for the photon-photon process from two models [33,34] within the STAR acceptance in 60%–80% Au + Au collisions. The dashed lines illustrate the corresponding p2T distributions for e+e− pairs from the model [33] traversing 1 fm in a constant magnetic field of 10^14 T perpendicular to the beam line.

The p2T distributions of excess yields within the STAR acceptance in the mass regions of 0.76–1.2 GeV/c2 in 60%–80% Au + Au and U + U collisions. The systematic uncertainties are shown as gray boxes. The solid and dotted lines are exponential fits to the data in Au + Au and U + U collisions, respectively. The dot-dashed and dot-dot- dashed lines represent the p2T distributions for the photon-photon process from two models [33,34] within the STAR acceptance in 60%–80% Au + Au collisions. The dashed lines illustrate the corresponding p2T distributions for e+e− pairs from the model [33] traversing 1 fm in a constant magnetic field of 10^14 T perpendicular to the beam line.

The p2T distributions of excess yields within the STAR acceptance in the mass regions of 1.2–2.6 GeV/c2 in 60%–80% Au + Au and U + U collisions. The systematic uncertainties are shown as gray boxes. The solid and dotted lines are exponential fits to the data in Au + Au and U + U collisions, respectively. The dot-dashed and dot-dot- dashed lines represent the p2T distributions for the photon-photon process from two models [33,34] within the STAR acceptance in 60%–80% Au + Au collisions. The dashed lines illustrate the corresponding p2T distributions for e+e− pairs from the model [33] traversing 1 fm in a constant magnetic field of 10^14 T perpendicular to the beam line.

The p2T distributions of excess yields within the STAR acceptance in the mass regions of 1.2–2.6 GeV/c2 in 60%–80% Au + Au and U + U collisions. The systematic uncertainties are shown as gray boxes. The solid and dotted lines are exponential fits to the data in Au + Au and U + U collisions, respectively. The dot-dashed and dot-dot- dashed lines represent the p2T distributions for the photon-photon process from two models [33,34] within the STAR acceptance in 60%–80% Au + Au collisions. The dashed lines illustrate the corresponding p2T distributions for e+e− pairs from the model [33] traversing 1 fm in a constant magnetic field of 10^14 T perpendicular to the beam line.

The corresponding sqrt(p2T) of excess yields. The vertical bars on data points are the combined statistical and systematic uncertainties.

The corresponding sqrt(p2T) of excess yields. The vertical bars on data points are the combined statistical and systematic uncertainties.

Detector-level average charged particle multiplicity densities for TransMax and TransMin as functions of the leading jet pT. Points are measured data. Histograms are calculated values assuming TransMax and TransMin are derived from the same parent distribution.

Transverse charged particle densities at various center-of-mass collision energies. Uncertainties smaller than the marker sizes.