HFE (electrons from semileptonic decays of heavy-flavor hadrons) invariant yields in different centrality intervals of Au+Au collisions at $\sqrt{s_{\rm NN}}=200$ GeV. The vertical bars and the boxes represent statistical and systematic uncertainties, respectively. The horizontal bars indicate the bin width.

HFE (electrons from semileptonic decays of heavy-flavor hadrons) $R_{\rm AA}$ (red circles) as a function of $p_{\rm T}$ in different centrality intervals of Au+Au collisions at $\sqrt{s_{\rm NN}}=200$ GeV, compared with STAR (yellow stars) and PHENIX (green squares) published results, and Duke ((modified Langevin transport model, blue line) and PHSD (parton-hadron-string dynamics model, orange line) model calculations. Vertical bars and boxes around data points represent combined statistical and systematic uncertainties from both Au+Au and $p$+$p$ measurements, respectively. Boxes at unity show the global uncertainties, which for this analysis include the 8% global uncertainty on $p$+$p$ reference and the $N_{\rm coll}$ uncertainties. The left box is for PHENIX and the right one for STAR.

HFE (electrons from semileptonic decays of heavy-flavor hadrons) $R_{\rm AA}$ (red circles) as a function of $N_{\rm part}$ in Au+Au collisions at $\sqrt{s_{\rm NN}}=200$ GeV, compared with PHENIX measurements (green squares), and Duke (blue line) and PHSD (orange line) model calculations. Vertical bars and boxes around data points represent statistical and systematic uncertainties from Au+Au measurements, respectively. The gray band represents the $N_{\rm coll}$ uncertainties. The boxes at unity show the global uncertainties including the total uncertainties of the $p$+$p$ reference.

Mass dependence of the mid-rapidity $v_1$ slope, $dv_1/dy$, for $\Lambda$, $^{3}_{\Lambda}$H and $^{4}_{\Lambda}$H from the $\sqrt{s_{NN}}$ = 3 GeV 5-40% mid-central Au+Au collisions. The statistical and systematic uncertainties are presented by vertical lines and square brackets, respectively. The slopes of $p$, $d$, $t$, $^3$He and $^4$He from the same collisions are shown as black circles. The blue and dashed green lines are the results of a linear fit to the measured light nuclei and hypernuclei $v_1$ slopes, respectively. For comparison, calculations of transport models plus coalescence afterburner are shown as gold and red bars from JAM model, and blue bars from UrQMD model.

Mass dependence of the mid-rapidity $v_1$ slope, $dv_1/dy$, for $\Lambda$, $^{3}_{\Lambda}$H and $^{4}_{\Lambda}$H from the $\sqrt{s_{NN}}$ = 3 GeV 5-40% mid-central Au+Au collisions. The statistical and systematic uncertainties are presented by vertical lines and square brackets, respectively. The slopes of $p$, $d$, $t$, $^3$He and $^4$He from the same collisions are shown as black circles. The blue and dashed green lines are the results of a linear fit to the measured light nuclei and hypernuclei $v_1$ slopes, respectively. For comparison, calculations of transport models plus coalescence afterburner are shown as gold and red bars from JAM model, and blue bars from UrQMD model.

Mass dependence of the mid-rapidity $v_1$ slope, $dv_1/dy$, for $\Lambda$, $^{3}_{\Lambda}$H and $^{4}_{\Lambda}$H from the $\sqrt{s_{NN}}$ = 3 GeV 5-40% mid-central Au+Au collisions. The statistical and systematic uncertainties are presented by vertical lines and square brackets, respectively. The slopes of $p$, $d$, $t$, $^3$He and $^4$He from the same collisions are shown as black circles. The blue and dashed green lines are the results of a linear fit to the measured light nuclei and hypernuclei $v_1$ slopes, respectively. For comparison, calculations of transport models plus coalescence afterburner are shown as gold and red bars from JAM model, and blue bars from UrQMD model.

Mass dependence of the mid-rapidity $v_1$ slope, $dv_1/dy$, for $\Lambda$, $^{3}_{\Lambda}$H and $^{4}_{\Lambda}$H from the $\sqrt{s_{NN}}$ = 3 GeV 5-40% mid-central Au+Au collisions. The statistical and systematic uncertainties are presented by vertical lines and square brackets, respectively. The slopes of $p$, $d$, $t$, $^3$He and $^4$He from the same collisions are shown as black circles. The blue and dashed green lines are the results of a linear fit to the measured light nuclei and hypernuclei $v_1$ slopes, respectively. For comparison, calculations of transport models plus coalescence afterburner are shown as gold and red bars from JAM model, and blue bars from UrQMD model.

Mass dependence of the mid-rapidity $v_1$ slope, $dv_1/dy$, for $\Lambda$, $^{3}_{\Lambda}$H and $^{4}_{\Lambda}$H from the $\sqrt{s_{NN}}$ = 3 GeV 5-40% mid-central Au+Au collisions. The statistical and systematic uncertainties are presented by vertical lines and square brackets, respectively. The slopes of $p$, $d$, $t$, $^3$He and $^4$He from the same collisions are shown as black circles. The blue and dashed green lines are the results of a linear fit to the measured light nuclei and hypernuclei $v_1$ slopes, respectively. For comparison, calculations of transport models plus coalescence afterburner are shown as gold and red bars from JAM model, and blue bars from UrQMD model.

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.

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.

Rapidity($y$) dependence of $v_1$ (top panels) and $v_2$ (bottom panels) of proton and $\Lambda$ baryons (left panels), pions (middle panels) and kaons (right panels) in 10-40% centrality for the $\sqrt{s_{NN}}$ = 3GeV Au+Au collisions. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points. The UrQMD and JAM results are shown as bands:golden, red and blue bands stand for JAM mean-field, UrQMD mean-field and UrQMD cascade mode, respectively. The value of the incompressibility $\kappa$ = 380 MeV is used in the mean-field option. More detailed model descriptions and data comparisons can be found in Supplemental Material.

Rapidity($y$) dependence of $v_1$ (top panels) and $v_2$ (bottom panels) of proton and $\Lambda$ baryons (left panels), pions (middle panels) and kaons (right panels) in 10-40% centrality for the $\sqrt{s_{NN}}$ = 3GeV Au+Au collisions. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points. The UrQMD and JAM results are shown as bands:golden, red and blue bands stand for JAM mean-field, UrQMD mean-field and UrQMD cascade mode, respectively. The value of the incompressibility $\kappa$ = 380 MeV is used in the mean-field option. More detailed model descriptions and data comparisons can be found in Supplemental Material.

Rapidity($y$) dependence of $v_1$ (top panels) and $v_2$ (bottom panels) of proton and $\Lambda$ baryons (left panels), pions (middle panels) and kaons (right panels) in 10-40% centrality for the $\sqrt{s_{NN}}$ = 3GeV Au+Au collisions. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points. The UrQMD and JAM results are shown as bands:golden, red and blue bands stand for JAM mean-field, UrQMD mean-field and UrQMD cascade mode, respectively. The value of the incompressibility $\kappa$ = 380 MeV is used in the mean-field option. More detailed model descriptions and data comparisons can be found in Supplemental Material.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

Collision energy dependence of (top panel) directed flow slope $dv_1/dy|_{y=0}$ for p, $\Lambda, \pi$(combined from $\pi^{\pm}$), K(combined from $K^{\pm}$ and $K_S^0$), $\phi$ and $\Xi^−$, and (bottom panel) elliptic flow $v_2$ for p, $\pi$(combined from $\pi^{\pm}$) in heavy- ion collisions. Collision centrality for all data from RHIC is 10-40%, except for 4.5 GeV where 10-30% is for $dv_1/dy|_{y=0}$ and 0-30% is for $v_2$. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points. The JAM and UrQMD results are shown as colored bands:golden, red and blue bands stand for JAM mean-field, UrQMD mean-field and UrQMD cascade mode, respectively. For clarity the x-axis value of the data points have been shifted.

Collision energy dependence of (top panel) directed flow slope $dv_1/dy|_{y=0}$ for p, $\Lambda, \pi$(combined from $\pi^{\pm}$), K(combined from $K^{\pm}$ and $K_S^0$), $\phi$ and $\Xi^−$, and (bottom panel) elliptic flow $v_2$ for p, $\pi$(combined from $\pi^{\pm}$) in heavy- ion collisions. Collision centrality for all data from RHIC is 10-40%, except for 4.5 GeV where 10-30% is for $dv_1/dy|_{y=0}$ and 0-30% is for $v_2$. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points. The JAM and UrQMD results are shown as colored bands:golden, red and blue bands stand for JAM mean-field, UrQMD mean-field and UrQMD cascade mode, respectively. For clarity the x-axis value of the data points have been shifted.

Collision energy dependence of (top panel) directed flow slope $dv_1/dy|_{y=0}$ for p, $\Lambda, \pi$(combined from $\pi^{\pm}$), K(combined from $K^{\pm}$ and $K_S^0$), $\phi$ and $\Xi^−$, and (bottom panel) elliptic flow $v_2$ for p, $\pi$(combined from $\pi^{\pm}$) in heavy- ion collisions. Collision centrality for all data from RHIC is 10-40%, except for 4.5 GeV where 10-30% is for $dv_1/dy|_{y=0}$ and 0-30% is for $v_2$. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points. The JAM and UrQMD results are shown as colored bands:golden, red and blue bands stand for JAM mean-field, UrQMD mean-field and UrQMD cascade mode, respectively. For clarity the x-axis value of the data points have been shifted.

Collision energy dependence of (top panel) directed flow slope $dv_1/dy|_{y=0}$ for p, $\Lambda, \pi$(combined from $\pi^{\pm}$), K(combined from $K^{\pm}$ and $K_S^0$), $\phi$ and $\Xi^−$, and (bottom panel) elliptic flow $v_2$ for p, $\pi$(combined from $\pi^{\pm}$) in heavy- ion collisions. Collision centrality for all data from RHIC is 10-40%, except for 4.5 GeV where 10-30% is for $dv_1/dy|_{y=0}$ and 0-30% is for $v_2$. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points. The JAM and UrQMD results are shown as colored bands:golden, red and blue bands stand for JAM mean-field, UrQMD mean-field and UrQMD cascade mode, respectively. For clarity the x-axis value of the data points have been shifted.

Collision energy dependence of (top panel) directed flow slope $dv_1/dy|_{y=0}$ for p, $\Lambda, \pi$(combined from $\pi^{\pm}$), K(combined from $K^{\pm}$ and $K_S^0$), $\phi$ and $\Xi^−$, and (bottom panel) elliptic flow $v_2$ for p, $\pi$(combined from $\pi^{\pm}$) in heavy- ion collisions. Collision centrality for all data from RHIC is 10-40%, except for 4.5 GeV where 10-30% is for $dv_1/dy|_{y=0}$ and 0-30% is for $v_2$. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points. The JAM and UrQMD results are shown as colored bands:golden, red and blue bands stand for JAM mean-field, UrQMD mean-field and UrQMD cascade mode, respectively. For clarity the x-axis value of the data points have been shifted.

Collision energy dependence of (top panel) directed flow slope $dv_1/dy|_{y=0}$ for p, $\Lambda, \pi$(combined from $\pi^{\pm}$), K(combined from $K^{\pm}$ and $K_S^0$), $\phi$ and $\Xi^−$, and (bottom panel) elliptic flow $v_2$ for p, $\pi$(combined from $\pi^{\pm}$) in heavy- ion collisions. Collision centrality for all data from RHIC is 10-40%, except for 4.5 GeV where 10-30% is for $dv_1/dy|_{y=0}$ and 0-30% is for $v_2$. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points. The JAM and UrQMD results are shown as colored bands:golden, red and blue bands stand for JAM mean-field, UrQMD mean-field and UrQMD cascade mode, respectively. For clarity the x-axis value of the data points have been shifted.

Collision energy dependence of (top panel) directed flow slope $dv_1/dy|_{y=0}$ for p, $\Lambda, \pi$(combined from $\pi^{\pm}$), K(combined from $K^{\pm}$ and $K_S^0$), $\phi$ and $\Xi^−$, and (bottom panel) elliptic flow $v_2$ for p, $\pi$(combined from $\pi^{\pm}$) in heavy- ion collisions. Collision centrality for all data from RHIC is 10-40%, except for 4.5 GeV where 10-30% is for $dv_1/dy|_{y=0}$ and 0-30% is for $v_2$. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points. The JAM and UrQMD results are shown as colored bands:golden, red and blue bands stand for JAM mean-field, UrQMD mean-field and UrQMD cascade mode, respectively. For clarity the x-axis value of the data points have been shifted.

Collision energy dependence of (top panel) directed flow slope $dv_1/dy|_{y=0}$ for p, $\Lambda, \pi$(combined from $\pi^{\pm}$), K(combined from $K^{\pm}$ and $K_S^0$), $\phi$ and $\Xi^−$, and (bottom panel) elliptic flow $v_2$ for p, $\pi$(combined from $\pi^{\pm}$) in heavy- ion collisions. Collision centrality for all data from RHIC is 10-40%, except for 4.5 GeV where 10-30% is for $dv_1/dy|_{y=0}$ and 0-30% is for $v_2$. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points. The JAM and UrQMD results are shown as colored bands:golden, red and blue bands stand for JAM mean-field, UrQMD mean-field and UrQMD cascade mode, respectively. For clarity the x-axis value of the data points have been shifted.

Collision energy dependence of (top panel) directed flow slope $dv_1/dy|_{y=0}$ for p, $\Lambda, \pi$(combined from $\pi^{\pm}$), K(combined from $K^{\pm}$ and $K_S^0$), $\phi$ and $\Xi^−$, and (bottom panel) elliptic flow $v_2$ for p, $\pi$(combined from $\pi^{\pm}$) in heavy- ion collisions. Collision centrality for all data from RHIC is 10-40%, except for 4.5 GeV where 10-30% is for $dv_1/dy|_{y=0}$ and 0-30% is for $v_2$. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points. The JAM and UrQMD results are shown as colored bands:golden, red and blue bands stand for JAM mean-field, UrQMD mean-field and UrQMD cascade mode, respectively. For clarity the x-axis value of the data points have been shifted.

Event by event net-proton multiplicity, $\Delta N_{p}$, distributions for Au+Au collisions at √sNN = 27, 54.4, and 200 GeV in 0-10% and 30-40% centralities at midrapidity (|y| < 0.5) for the transverse momentum range of 0.4 < $p_{T}$ (GeV/c) < 2.0. These distributions are normalized by the corresponding numbers of events and are not corrected for detector efficiencies. Statistical uncertainties are shown as vertical lines. The dashed lines show the Skellam distributions for each collision energy and centrality. The bottom panel shows the ratio of the data to the Skellam expectations.

Event by event net-proton multiplicity, $\Delta N_{p}$, distributions for Au+Au collisions at √sNN = 27, 54.4, and 200 GeV in 0-10% and 30-40% centralities at midrapidity (|y| < 0.5) for the transverse momentum range of 0.4 < $p_{T}$ (GeV/c) < 2.0. These distributions are normalized by the corresponding numbers of events and are not corrected for detector efficiencies. Statistical uncertainties are shown as vertical lines. The dashed lines show the Skellam distributions for each collision energy and centrality. The bottom panel shows the ratio of the data to the Skellam expectations.

Event by event net-proton multiplicity, $\Delta N_{p}$, distributions for Au+Au collisions at √sNN = 27, 54.4, and 200 GeV in 0-10% and 30-40% centralities at midrapidity (|y| < 0.5) for the transverse momentum range of 0.4 < $p_{T}$ (GeV/c) < 2.0. These distributions are normalized by the corresponding numbers of events and are not corrected for detector efficiencies. Statistical uncertainties are shown as vertical lines. The dashed lines show the Skellam distributions for each collision energy and centrality. The bottom panel shows the ratio of the data to the Skellam expectations.

Net-proton $C_{6}/C_{2}$ as a function of rapidity (left) and transverse momentum acceptance (right) from $\sqrt{s_{NN}}$ = 27 GeV (crosses), 54.4 (open squares), and 200 GeV (filled circles) Au+Au collisions. The upper and lower plots are for 0-10% and 30-40% centralities, respectively. The error bars are statistical and caps are systematic errors. Points for different beam energies are staggered horizontally to improve clarity. UrQMD transport model results are shown as shaded and hatched bands. The Skellam expectation ($C_{6}/C_{2} = 1) is shown as long-dashed lines.

Net-proton $C_{6}/C_{2}$ as a function of rapidity (left) and transverse momentum acceptance (right) from $\sqrt{s_{NN}}$ = 27 GeV (crosses), 54.4 (open squares), and 200 GeV (filled circles) Au+Au collisions. The upper and lower plots are for 0-10% and 30-40% centralities, respectively. The error bars are statistical and caps are systematic errors. Points for different beam energies are staggered horizontally to improve clarity. UrQMD transport model results are shown as shaded and hatched bands. The Skellam expectation ($C_{6}/C_{2} = 1) is shown as long-dashed lines.

Net-proton $C_{6}/C_{2}$ as a function of rapidity (left) and transverse momentum acceptance (right) from $\sqrt{s_{NN}}$ = 27 GeV (crosses), 54.4 (open squares), and 200 GeV (filled circles) Au+Au collisions. The upper and lower plots are for 0-10% and 30-40% centralities, respectively. The error bars are statistical and caps are systematic errors. Points for different beam energies are staggered horizontally to improve clarity. UrQMD transport model results are shown as shaded and hatched bands. The Skellam expectation ($C_{6}/C_{2} = 1) is shown as long-dashed lines.

Net-proton $C_{6}/C_{2}$ as a function of rapidity (left) and transverse momentum acceptance (right) from $\sqrt{s_{NN}}$ = 27 GeV (crosses), 54.4 (open squares), and 200 GeV (filled circles) Au+Au collisions. The upper and lower plots are for 0-10% and 30-40% centralities, respectively. The error bars are statistical and caps are systematic errors. Points for different beam energies are staggered horizontally to improve clarity. UrQMD transport model results are shown as shaded and hatched bands. The Skellam expectation ($C_{6}/C_{2} = 1) is shown as long-dashed lines.

Net-proton $C_{6}/C_{2}$ as a function of rapidity (left) and transverse momentum acceptance (right) from $\sqrt{s_{NN}}$ = 27 GeV (crosses), 54.4 (open squares), and 200 GeV (filled circles) Au+Au collisions. The upper and lower plots are for 0-10% and 30-40% centralities, respectively. The error bars are statistical and caps are systematic errors. Points for different beam energies are staggered horizontally to improve clarity. UrQMD transport model results are shown as shaded and hatched bands. The Skellam expectation ($C_{6}/C_{2} = 1) is shown as long-dashed lines.

Net-proton $C_{6}/C_{2}$ as a function of rapidity (left) and transverse momentum acceptance (right) from $\sqrt{s_{NN}}$ = 27 GeV (crosses), 54.4 (open squares), and 200 GeV (filled circles) Au+Au collisions. The upper and lower plots are for 0-10% and 30-40% centralities, respectively. The error bars are statistical and caps are systematic errors. Points for different beam energies are staggered horizontally to improve clarity. UrQMD transport model results are shown as shaded and hatched bands. The Skellam expectation ($C_{6}/C_{2} = 1) is shown as long-dashed lines.

Collisions centrality dependence of net-proton $C_{6}/C_{2}$ in Au+Au collisions for |$y$| < 0.5 and 0.4 < $p_{T}$ (GeV/c) < 2.0. The error bars are statistical and caps are systematic errors. Points for different beam energies are staggered horizontally to improve clarity. A shaded band shows the results from UrQMD model calculations. UrQMD calculations from the above three collision energies are consistent among them so they are merged in order to reduce statistical fluctuations. Details on these calculations can be found in the Supplemental Material at [URL will be inserted by publisher]. The lattice QCD calculations [16, 17] for T = 160 MeV and $\mu_{B}$ < 110 MeV. are shown as a blue band at $\langle N_{part}\rangle$ $\approx$ 340.

Collisions centrality dependence of net-proton $C_{6}/C_{2}$ in Au+Au collisions for |$y$| < 0.5 and 0.4 < $p_{T}$ (GeV/c) < 2.0. The error bars are statistical and caps are systematic errors. Points for different beam energies are staggered horizontally to improve clarity. A shaded band shows the results from UrQMD model calculations. UrQMD calculations from the above three collision energies are consistent among them so they are merged in order to reduce statistical fluctuations. Details on these calculations can be found in the Supplemental Material at [URL will be inserted by publisher]. The lattice QCD calculations [16, 17] for T = 160 MeV and $\mu_{B}$ < 110 MeV. are shown as a blue band at $\langle N_{part}\rangle$ $\approx$ 340.

Collisions centrality dependence of net-proton $C_{6}/C_{2}$ in Au+Au collisions for |$y$| < 0.5 and 0.4 < $p_{T}$ (GeV/c) < 2.0. The error bars are statistical and caps are systematic errors. Points for different beam energies are staggered horizontally to improve clarity. A shaded band shows the results from UrQMD model calculations. UrQMD calculations from the above three collision energies are consistent among them so they are merged in order to reduce statistical fluctuations. Details on these calculations can be found in the Supplemental Material at [URL will be inserted by publisher]. The lattice QCD calculations [16, 17] for T = 160 MeV and $\mu_{B}$ < 110 MeV. are shown as a blue band at $\langle N_{part}\rangle$ $\approx$ 340.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Cumulants and their ratios up to the sixth order corrected for non-binomial efficiencies for 200 GeV Au+Au collisions at 0-5% centrality. The CBWC is applied for 2.5% centrality bin width. Results from the conventional efficiency correction are shown as black filled circles, results from the unfolding with the binomial detector response are shown as black open circles, and results from beta-binomial detector response with $\alpha+\sigma$, $\alpha$ and $\alpha-\sigma$ are shown in green triangles, red squares and blue triangles, respectively. C5, C6, C2/C1, C5/C1 and C6/C2 are scaled by constant shown in each column.

Collision centrality dependence of net-proton C6/C2 in Au+Au collisions for $\sqrt{s_{NN}}$ = 200 GeV within |y| < 0.5 and 0.4 < pT (GeV/c) < 2.0. Results with and without the CBWC are overlaid. The results are corrected for detector efficiencies. Points for different calculation methods are staggered horizontally to improve clarity.

Collision centrality dependence of net-proton C6/C2 in Au+Au collisions for $\sqrt{s_{NN}}$ = 27, 54.4, and 200 GeV within |y| < 0.5 and 0.4 < pT (GeV/c) < 2.0. Points for different beam energies are staggered horizontally to improve clarity. Shaded and hatched bands show the results from UrQMD model calculations The lattice QCD calculations [13, 14] for T = 160 MeV and $\mu_{B}$ < 110 MeV. are shown as a blue band at $\langle N_{part}\rangle$ $\approx$ 340.

Reference charged particle multiplicity distributions using only pions and kaons ...

Reference charged particle multiplicity distributions using only pions and kaons ...

Reference charged particle multiplicity distributions using only pions and kaons ...

Reference charged particle multiplicity distributions using only pions and kaons ...

Reference charged particle multiplicity distributions using only pions and kaons ...

Reference charged particle multiplicity distributions using only pions and kaons ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$C_{n}$ of net-proton distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV as a function of $N_{part}$.

$C_{n}$ of net-proton distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV as a function of $N_{part}$.

$C_{n}$ of net-proton distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV as a function of $N_{part}$.

$C_{n}$ of net-proton distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV as a function of $N_{part}$.

$C_{n}$ of net-proton distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 GeV as a function of $N_{part}$.

$C_{n}$ of net-proton distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 GeV as a function of $N_{part}$.

$C_{n}$ of net-proton distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 GeV as a function of $N_{part}$.

$C_{n}$ of net-proton distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 GeV as a function of $N_{part}$.

$C_{n}$ of net-proton distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV as a function of $N_{part}$.

$C_{n}$ of net-proton distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV as a function of $N_{part}$.

$C_{n}$ of net-proton distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV as a function of $N_{part}$.

$C_{n}$ of net-proton distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV as a function of $N_{part}$.

$\kappa\sigma^2$ as a function of collision energy for Au+Au collisions for 0-5% centrality.

Efficiency uncorrected $C_n$ of net-proton proton and anti-proton multiplicity distribution in Au+Au collisions at $\sqrt{s_\text{NN}}$ = 7.7 - 200 GeV as function of $\left\langle N_\text{part} \right\rangle$.

Efficiencies of proton and anti-proton as a function of $p_\mathrm{T}$ in Au+Au collisions for various $\sqrt{s_\text{NN}}$ and collision centralities.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Unfolded net-proton multiplicity distributions for $\sqrt{s_{NN}$ = 200 GeV Au+Au collisions.

Unfolded net-proton multiplicity distributions for $\sqrt{s_{NN}$ = 200 GeV Au+Au collisions.

Unfolded net-proton multiplicity distributions for $\sqrt{s_{NN}$ = 200 GeV Au+Au collisions.

Unfolded net-proton multiplicity distributions for $\sqrt{s_{NN}$ = 200 GeV Au+Au collisions.

Unfolded net-proton multiplicity distributions for $\sqrt{s_{NN}$ = 200 GeV Au+Au collisions.

Unfolded net-proton multiplicity distributions for $\sqrt{s_{NN}$ = 200 GeV Au+Au collisions.

Unfolded net-proton multiplicity distributions for $\sqrt{s_{NN}$ = 200 GeV Au+Au collisions.

Cumulant ratios as a function of $N_{part}$ for net-proton distributions in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV

Cumulant ratios as a function of $N_{part}$ for net-proton distributions in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV

Collision centrality dependence of proton, anti-proton and net-proton cumulants

Cumulants and their ratios as a function of $<N_{part}>$, for the net-proton distribution

Centrality dependence of normalized correlation functions $\kappa_n/$kappa_1$ for proton and anti-proton multiplicity distribution

Rapidity acceptance dependence of cumulants of proton, anti-proton and net-proton multiplicity distributions in 0-5% central Au+Au collision ...

Rapidity acceptance dependence of normalized correlation functions up to fourth order.

Rapidity-acceptance dependence of cumulant ratios of proton, anti-proton and net-proton multiplicity distributions in 0-5% central Au+Au collisions...

pT-acceptance dependence of cumulants of proton, anti-proton and net-proton multiplicity distributions for 0-5% central Au+Au collisions ...

pT-acceptance dependence of the normalized correlation functions up to fourth order ($\kappa_n/\kappa_1$, $n$ = 2, 3, 4) for proton and anti-proton multiplicity distributions in 0-5% central Au+Au collisions ...

pT-acceptance dependence of cumulant ratios of proton, anti-proton and net-proton multiplicity distributions for 0-5% central Au+Au collisions ...

Cumulant ratios from HRG model as a function of collision energy $\sqrt{s_{NN}}$

UrQMD results on pT acceptance dependence for cumulant ratios for proton and baryon

Polynomial fit of cumulant ratios as a function of collision energy $\sqrt{s_{NN}}$

Polynomial fit of cumulant ratios as a function of collision energy $\sqrt{s_{NN}}$

Polynomial fit of cumulant ratios as a function of collision energy $\sqrt{s_{NN}}$

Collision energy dependence of $C_2/C_1$, $C_3/C_2$ and $C_4/C_2$ for net-proton multiplicity distribution in 0-5% central Au+Au collisions. The expreimental net-proton measurements are compared to corresponding values from UrQMD and HRG models within the expreimental acceptances.

Collision energy dependence of $C_2/C_1$, $C_3/C_2$ and $C_4/C_2$ for net-proton multiplicity distribution in 0-5% central Au+Au collisions. The expreimental net-proton measurements are compared to corresponding values from UrQMD and HRG models within the expreimental acceptances.

Collision energy dependence of $C_2/C_1$, $C_3/C_2$ and $C_4/C_2$ for net-proton multiplicity distribution in 0-5% central Au+Au collisions. The expreimental net-proton measurements are compared to corresponding values from UrQMD and HRG models within the expreimental acceptances.

Collision energy dependence of $C_2/C_1$, $C_3/C_2$ and $C_4/C_2$ for net-proton multiplicity distribution in 0-5% central Au+Au collisions. The expreimental net-proton measurements are compared to corresponding values from UrQMD and HRG models within the expreimental acceptances.

Collision energy dependence of $C_2/C_1$, $C_3/C_2$ and $C_4/C_2$ for net-proton multiplicity distribution in 0-5% central Au+Au collisions. The expreimental net-proton measurements are compared to corresponding values from UrQMD and HRG models within the expreimental acceptances.

Collision energy dependence of $C_2/C_1$, $C_3/C_2$ and $C_4/C_2$ for net-proton multiplicity distribution in 0-5% central Au+Au collisions. The expreimental net-proton measurements are compared to corresponding values from UrQMD and HRG models within the expreimental acceptances.

Collision energy dependence of $C_2/C_1$, $C_3/C_2$ and $C_4/C_2$ for net-proton multiplicity distribution in 0-5% central Au+Au collisions. The expreimental net-proton measurements are compared to corresponding values from UrQMD and HRG models within the expreimental acceptances.

Polarization of $\Lambda$ and $\bar\Lambda$ as a function of $\eta$ for the $20\%–60\%$ centrality bin in Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV. Open boxes and vertical lines show systematic and statistical uncertainties. Note that the data points for Λ are slightly shifted for visibility.

Polarization of $\Lambda$ and $\bar\Lambda$ as a function of observed charge asymmetry $A_{ch}$ normalized with its RMS $\sigma_{A_{ch}}$ for the $20\%–60\%$ centrality bin in Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV. Open boxes and vertical lines show systematic and statistical uncertainties. Solid and dashed lines show linear fitting functions.

Global polarization of $\Lambda$ and $\bar{\Lambda}$ using the new $\alpha_\Lambda=0.732$ updated on PDG2020 as a function of the collision energy $\sqrt{s_{_{NN}}}$ for 20-50% centrality Au+Au collisions. Thin lines show calculations from a 3+1D cascade + viscous hydrodynamic model (UrQMD+vHLLE) and bold lines show the AMPT model calculations. In the case of each model, primary $\Lambda$ with and without the feed-down effect are indicated by dashed and solid lines, respectively. Open boxes and vertical lines show systematic and statistical uncertainties, respectively. Note that the data points at 200 GeV and for $\bar{\Lambda}$ are slightly horizontally shifted for visibility.

$\Lambda$ ($\bar\Lambda$) polarization using the new $\alpha_\Lambda=0.732$ updated on PDG2020 as a function of the collision centrality in Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV. Open boxes and vertical lines show systematic and statistical uncertainties. The data points for Λ are slightly shifted for visibility.

Polarization of $\Lambda$ and $\bar\Lambda$ using the new $\alpha_\Lambda=0.732$ updated on PDG2020 as a function of $p_{T}$ for the $20\%–60\%$ centrality bin in Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV. Open boxes and vertical lines show systematic and statistical uncertainties, respectively. Hydrodynamic model calculations for Λ with two different initial conditions (IC) are compared. Note that the data points for Λ are slightly shifted for visibility.

Polarization of $\Lambda$ and $\bar\Lambda$ using the new $\alpha_\Lambda=0.732$ updated on PDG2020 as a function of $\eta$ for the $20\%–60\%$ centrality bin in Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV. Open boxes and vertical lines show systematic and statistical uncertainties. Note that the data points for Λ are slightly shifted for visibility.

Polarization of $\Lambda$ and $\bar\Lambda$ using the new $\alpha_\Lambda=0.732$ updated on PDG2020 as a function of observed charge asymmetry $A_{ch}$ normalized with its RMS $\sigma_{A_{ch}}$ for the $20\%–60\%$ centrality bin in Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV. Open boxes and vertical lines show systematic and statistical uncertainties. Solid and dashed lines show linear fitting functions.

The balance function in terms of $\Delta \eta$ for all charged particles with $0.2 < p_{T} < 2.0$ GeV/$c$ from central Au+Au collisions (0-5%) for $\sqrt{s_{NN}}=27$ GeV. The data are the measured balance functions corrected by subtracting balance functions calculated using mixed events. Also shown are balance functions calculated using shuffled events.

The balance function in terms of $\Delta \eta$ for all charged particles with $0.2 < p_{T} < 2.0$ GeV/$c$ from central Au+Au collisions (0-5%) for $\sqrt{s_{NN}}=39$ GeV. The data are the measured balance functions corrected by subtracting balance functions calculated using mixed events. Also shown are balance functions calculated using shuffled events.

The balance function in terms of $\Delta \eta$ for all charged particles with $0.2 < p_{T} < 2.0$ GeV/$c$ from central Au+Au collisions (0-5%) for $\sqrt{s_{NN}}=62.4$ GeV. The data are the measured balance functions corrected by subtracting balance functions calculated using mixed events. Also shown are balance functions calculated using shuffled events.

The balance function in terms of $\Delta \eta$ for all charged particles with $0.2 < p_{T} < 2.0$ GeV/$c$ from central Au+Au collisions (0-5%) for $\sqrt{s_{NN}}=200$ GeV. The data are the measured balance functions corrected by subtracting balance functions calculated using mixed events. Also shown are balance functions calculated using shuffled events.

Energy dependence of the balance function widths compared with the widths of the balance functions calculated using shuffled events. Also shown are the balance function widths calculated using UrQMD. The dashed line represents the width of the balance function calculated using shuffled events for a constant $dN/d\eta$ distribution. Error bars represent the statistical error and the shaded bands represent the systematic error.

Energy dependence of the balance function widths compared with the widths of the balance functions calculated using shuffled events. Also shown are the balance function widths calculated using UrQMD. The dashed line represents the width of the balance function calculated using shuffled events for a constant $dN/d\eta$ distribution. Error bars represent the statistical error and the shaded bands represent the systematic error.

Energy dependence of the balance function widths compared with the widths of the balance functions calculated using shuffled events. Also shown are the balance function widths calculated using UrQMD. The dashed line represents the width of the balance function calculated using shuffled events for a constant $dN/d\eta$ distribution. Error bars represent the statistical error and the shaded bands represent the systematic error.

Energy dependence of the balance function widths compared with the widths of the balance functions calculated using shuffled events. Also shown are the balance function widths calculated using UrQMD. The dashed line represents the width of the balance function calculated using shuffled events for a constant $dN/d\eta$ distribution. Error bars represent the statistical error and the shaded bands represent the systematic error.

Energy dependence of the balance function widths compared with the widths of the balance functions calculated using shuffled events. Also shown are the balance function widths calculated using UrQMD. The dashed line represents the width of the balance function calculated using shuffled events for a constant $dN/d\eta$ distribution. Error bars represent the statistical error and the shaded bands represent the systematic error.

Energy dependence of the balance function widths compared with the widths of the balance functions calculated using shuffled events. Also shown are the balance function widths calculated using UrQMD. The dashed line represents the width of the balance function calculated using shuffled events for a constant $dN/d\eta$ distribution. Error bars represent the statistical error and the shaded bands represent the systematic error.

Energy dependence of the balance function widths compared with the widths of the balance functions calculated using shuffled events. Also shown are the balance function widths calculated using UrQMD. The dashed line represents the width of the balance function calculated using shuffled events for a constant $dN/d\eta$ distribution. Error bars represent the statistical error and the shaded bands represent the systematic error.

Balance function widths for the most central events ($0-5\%$) compared with balance function widths calculated using shuffled events. Also shown are balance function widths calculated using UrQMD and shuffled UrQMD events. The dashed line represents the width of the balance function calculated using shuffled events for a constant $dN/d\eta$ distribution.

Acceptance-corrected balance function widths for Au+Au measured over the range $0.1 < \Delta \eta < 1.6$ compared with similar results from Pb+Pb collisions from ALICE. Only statistical errors are shown. Lines represent fits of the form $a + b(N_{part})^{0.01}$.

Acceptance-corrected balance function widths for Au+Au measured over the range $0.1 < \Delta \eta < 1.6$ compared with similar results from Pb+Pb collisions from ALICE. Only statistical errors are shown. Lines represent fits of the form $a + b(N_{part})^{0.01}$.

Acceptance-corrected balance function widths for Au+Au measured over the range $0.1 < \Delta \eta < 1.6$ compared with similar results from Pb+Pb collisions from ALICE. Only statistical errors are shown. Lines represent fits of the form $a + b(N_{part})^{0.01}$.

Acceptance-corrected balance function widths for Au+Au measured over the range $0.1 < \Delta \eta < 1.6$ compared with similar results from Pb+Pb collisions from ALICE. Only statistical errors are shown. Lines represent fits of the form $a + b(N_{part})^{0.01}$.

Acceptance-corrected balance function widths for Au+Au measured over the range $0.1 < \Delta \eta < 1.6$ compared with similar results from Pb+Pb collisions from ALICE. Only statistical errors are shown. Lines represent fits of the form $a + b(N_{part})^{0.01}$.

Acceptance-corrected balance function widths for Au+Au measured over the range $0.1 < \Delta \eta < 1.6$ compared with similar results from Pb+Pb collisions from ALICE. Only statistical errors are shown. Lines represent fits of the form $a + b(N_{part})^{0.01}$.

Acceptance-corrected balance function widths for Au+Au measured over the range $0.1 < \Delta \eta < 1.6$ compared with similar results from Pb+Pb collisions from ALICE. Only statistical errors are shown. Lines represent fits of the form $a + b(N_{part})^{0.01}$.

Acceptance-corrected balance function widths for Au+Au measured over the range $0.1 < \Delta \eta < 1.6$ compared with similar results from Pb+Pb collisions from ALICE. Only statistical errors are shown. Lines represent fits of the form $a + b(N_{part})^{0.01}$.

Acceptance-corrected balance function widths for Au+Au measured over the range $0.1 < \Delta \eta < 1.6$ normalized to the most peripheral centrality bin compared with similar results from Pb+Pb collisions from ALICE. Only statistical errors are shown. Lines represent fits of the form $a + b(N_{part})^{0.01}$.

Acceptance-corrected balance function widths for Au+Au measured over the range $0.1 < \Delta \eta < 1.6$ normalized to the most peripheral centrality bin compared with similar results from Pb+Pb collisions from ALICE. Only statistical errors are shown. Lines represent fits of the form $a + b(N_{part})^{0.01}$.

Acceptance-corrected balance function widths for Au+Au measured over the range $0.1 < \Delta \eta < 1.6$ normalized to the most peripheral centrality bin compared with similar results from Pb+Pb collisions from ALICE. Only statistical errors are shown. Lines represent fits of the form $a + b(N_{part})^{0.01}$.

Acceptance-corrected balance function widths for Au+Au measured over the range $0.1 < \Delta \eta < 1.6$ normalized to the most peripheral centrality bin compared with similar results from Pb+Pb collisions from ALICE. Only statistical errors are shown. Lines represent fits of the form $a + b(N_{part})^{0.01}$.

Acceptance-corrected balance function widths for Au+Au measured over the range $0.1 < \Delta \eta < 1.6$ normalized to the most peripheral centrality bin compared with similar results from Pb+Pb collisions from ALICE. Only statistical errors are shown. Lines represent fits of the form $a + b(N_{part})^{0.01}$.

Acceptance-corrected balance function widths for Au+Au measured over the range $0.1 < \Delta \eta < 1.6$ normalized to the most peripheral centrality bin compared with similar results from Pb+Pb collisions from ALICE. Only statistical errors are shown. Lines represent fits of the form $a + b(N_{part})^{0.01}$.

Acceptance-corrected balance function widths for Au+Au measured over the range $0.1 < \Delta \eta < 1.6$ normalized to the most peripheral centrality bin compared with similar results from Pb+Pb collisions from ALICE. Only statistical errors are shown. Lines represent fits of the form $a + b(N_{part})^{0.01}$.

Acceptance-corrected balance function widths for Au+Au measured over the range $0.1 < \Delta \eta < 1.6$ normalized to the most peripheral centrality bin compared with similar results from Pb+Pb collisions from ALICE. Only statistical errors are shown. Lines represent fits of the form $a + b(N_{part})^{0.01}$.