Observed values of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for the single-Higgs and double-Higgs analyses combination, with all other coupling modifiers fixed to unity.

Observed values of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for the double-Higgs analyses, with all other coupling modifiers fixed to unity.

Observed values of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for the single-Higgs analyses, with all other coupling modifiers fixed to unity.

Observed values of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for the single-Higgs and double-Higgs combination for the generic model (free floating $\kappa_t$, $\kappa_b$, $\kappa_V$ and $\kappa_\tau$). The observed best-fit value of $\kappa_\lambda$ for the generic model is shifted slightly relative to the other models because of its correlation with the best-fit values of the $\kappa_b$, $\kappa_t$ and $\kappa_\tau$ parameters, which are slightly below, but compatible with unity.

Expected values of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for the single-Higgs and double-Higgs analyses combination derived from the combined single-Higgs and double-Higgs analyses, with all other coupling modifiers fixed to unity.

Expected values of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for the double-Higgs analyses.

Expected values of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for the single-Higgs analyses, with all other coupling modifiers fixed to unity.

Expected values of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for the single-Higgs and double-Higgs analyses for the generic model (free floating $\kappa_t$, $\kappa_b$, $\kappa_V$ and $\kappa_\tau$).

Observed constraints in the $\kappa_\lambda$–$\kappa_t$ plane from single-Higgs and double-Higgs combination. The solid lines show the 68% CL contours. The observed constraint for the single- and double-Higgs combination for $\kappa_t$ values below unity is slightly less stringent than that for the single-Higgs fit alone due to the slightly higher best-fit value for this coupling modifier.

Observed constraints in the $\kappa_\lambda$–$\kappa_t$ plane from single-Higgs and double-Higgs combination. The dashed lines show the 95% CL contours. The observed constraint for the single- and double-Higgs combination for $\kappa_t$ values below unity is slightly less stringent than that for the single-Higgs fit alone due to the slightly higher best-fit value for this coupling modifier.

Observed constraints in the $\kappa_\lambda$–$\kappa_t$ plane from double-Higgs analysis. The solid lines show the 68% CL contours. The double-Higgs contours are shown for values of $\kappa_t$ smaller than 1.2.

Observed constraints in the $\kappa_\lambda$–$\kappa_t$ plane from double-Higgs analysis. The dashed lines show the 95% CL contours. The double-Higgs contours are shown for values of $\kappa_t$ smaller than 1.2.

Observed constraints in the $\kappa_\lambda$–$\kappa_t$ plane from single-Higgs analysis. The solid lines show the 68% CL contours.

Observed constraints in the $\kappa_\lambda$–$\kappa_t$ plane from single-Higgs analysis. The dashed lines show the 95% CL contours.

Expected constraints in the $\kappa_\lambda$–$\kappa_t$ plane from single-Higgs and double-Higgs combination. The solid lines show the 68% CL contours. The double-Higgs contours are shown for values of $\kappa_t$ smaller than 1.2.

Expected constraints in the $\kappa_\lambda$–$\kappa_t$ plane from single-Higgs and double-Higgs combination. The dashed lines show the 95% CL contours. The double-Higgs contours are shown for values of $\kappa_t$ smaller than 1.2.

Expected constraints in the $\kappa_\lambda$–$\kappa_t$ plane from double-Higgs analyses. The solid lines show the 68% CL contours. The double-Higgs contours are shown for values of $\kappa_t$ smaller than 1.2.

Expected constraints in the $\kappa_\lambda$–$\kappa_t$ plane from double-Higgs analyses. The dashed lines show the 95% CL contours. The double-Higgs contours are shown for values of $\kappa_t$ smaller than 1.2.

Expected constraints in the $\kappa_\lambda$–$\kappa_t$ plane from single-Higgs analyses. The solid lines show the 68% CL contours.

Expected constraints in the $\kappa_\lambda$–$\kappa_t$ plane from single-Higgs analyses. The dashed lines show the 95% CL contours.

Observed and expected 95% CL upper limits on the sum of the ggF HH and VBF HH production cross-section from the bbbb, bb$\tau\tau$ and bb$\gamma\gamma$ decay channels, and their statistical combination. The value $m_H$=125.09 GeV is assumed when deriving the predicted SM cross section. The expected limit and the corresponding error bands are derived assuming the absence of the HH process with all nuisance parameters profiled to the observed data. The SM prediction together with its theoretical uncertainty is also shown (red vertical band).

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for the HH to bbbb analysis. All other coupling modifiers are fixed to their SM value.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for the HH to bb$\tau\tau$ analysis. All other coupling modifiers are fixed to their SM value.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for the HH to bb$\gamma\gamma$ analysis. All other coupling modifiers are fixed to their SM value.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for the double-Higgs combination. All other coupling modifiers are fixed to their SM value.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for HH to bbbb analysis. All other coupling modifiers are fixed to their SM value.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for HH to bb$\tau\tau$ analysis. All other coupling modifiers are fixed to their SM value.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for HH to bb$\gamma\gamma$ analysis. All other coupling modifiers are fixed to their SM value.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for double-Higgs combination. All other coupling modifiers are fixed to their SM value.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for the HH to bbbb analysis. All other coupling modifiers are fixed to their SM value.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for the HH to bb$\tau\tau$ analysis. All other coupling modifiers are fixed to their SM value.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for the HH to bb$\gamma\gamma$ analysis. All other coupling modifiers are fixed to their SM value.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for the double-Higgs combination. All other coupling modifiers are fixed to their SM value.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for the HH to bbbb analysis. All other coupling modifiers are fixed to their SM value.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for the HH to bb$\tau\tau$ analysis. All other coupling modifiers are fixed to their SM value.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for the HH to bb$\gamma\gamma$ analysis. All other coupling modifiers are fixed to their SM value.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for the double-Higgs combination. All other coupling modifiers are fixed to their SM value.

Observed constraints in the $\kappa_{2V}$–$\kappa_{V}$ plane from double-Higgs combination. The solid lines show the 68% (95%) CL contours.

Observed constraints in the $\kappa_{2V}$–$\kappa_{V}$ plane from double-Higgs combination. The dashed lines show the 68% (95%) CL contours.

Expected constraints in the $\kappa_{2V}$-$\kappa_{V}$ plane from double-Higgs combination. The solid lines show the 68% CL contours.

Expected constraints in the $\kappa_{2V}$-$\kappa_{V}$ plane from double-Higgs combination. The dashed lines show the 95% CL contours.

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.

This dataset corresponds to Figure 2, the v2 ratio value estimated between epd (\Psi_1) and tpc (\Psi_2) in the paper

This dataset corresponds to Figure 2, the v2 ratio value estimated between epd (\Psi_1) and epd (\Psi_2) in the paper

This dataset corresponds to Figure 3, the \Delta\gamma_{112}multiply N_{part} value estimated by tpc (\Psi_2) in the paper

This dataset corresponds to Figure 3, the \Delta\gamma_{112}multiply N_{part} value estimated by epd (\Psi_2) in the paper

This dataset corresponds to Figure 3, the \Delta\gamma_{1111}multiply N_{part} value estimated by epd (\Psi_1) in the paper

This dataset corresponds to Figure 3, the ratio between \Delta\gamma_{1111} (by epd \Psi_1) and \Delta\gamma(112) (by tpc \Psi_2) in the paper

This dataset corresponds to Figure 3, the ratio between \Delta\gamma_{1111} (by epd \Psi_1) and \Delta\gamma(112) (by epd \Psi_2) in the paper

This dataset corresponds to Figure 4, the \Delta\gamma_{112}multiply N_{part} and scaled by v_2 estimated by tpc (\Psi_2) in the paper

This dataset corresponds to Figure 4, the \Delta\gamma_{112}multiply N_{part} and scaled by v_2 estimated by epd (\Psi_2) in the paper

This dataset corresponds to Figure 4, the \Delta\gamma_{1111}multiply N_{part} and scaled by v_2 estimated by epd (\Psi_1) in the paper

This dataset corresponds to Figure 4, the ratio between \Delta\gamma_{1111} scaled by v_{211} (by epd \Psi_1) and \Delta\gamma(112) scaled by v_2 (by tpc \Psi_2) in the paper

This dataset corresponds to Figure 4, the ratio between \Delta\gamma_{1111} scaled by v_{211} (by epd \Psi_1) and \Delta\gamma(112) scaled by v_2 (by epd \Psi_2) in the paper

fig2_left_top_isobarpaper_star_blue_case2_ruru_nonzeros.

fig2_left_top_isobarpaper_star_grey_data_ruru_nonzeros.

fig2_left_top_isobarpaper_star_red_case3_ruru_nonzeros.

fig2_right_isobarpaper_star_grey_data_nonzero.

fig2_right_low_isobarpaper_star_red_case3_nonzero.

fig2_right_top_isobarpaper_star_blue_case2_nonzero.

fig3_olow_isobarpaper_star_blue_mean_multiplicity_ratio.

fig3_otop_isobarpaper_star_blue_open_mean_multiplicity_zrzr.

fig3_otop_isobarpaper_star_blue_solid_mean_multiplicity_ruru.

fig4_left_low_isobarpaper_star_blue_v2_tpc_ratio. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig4_left_low_isobarpaper_star_green_v2_tpc_eta_gt1_ratio.

fig4_left_low_isobarpaper_star_purple_v2_subEv_ratio.

fig4_left_low_isobarpaper_star_red_v2_epd_ratio. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig4_left_low_isobarpaper_star_yellow_v2_EP_ratio.

fig4_left_top_isobarpaper_star_blue_open_v2_2_zrzr.

fig4_left_top_isobarpaper_star_blue_solid_v2_2_ruru.

fig4_left_top_isobarpaper_star_green_open_v2_tpc_eta_gt1_zrzr.

fig4_left_top_isobarpaper_star_green_solid_v2_tpc_eta_gt1_ruru.

fig4_left_top_isobarpaper_star_purple_open_v2_subEv_zrzr.

fig4_left_top_isobarpaper_star_purple_solid_v2_subEv_ruru.

fig4_left_top_isobarpaper_star_red_open_v2_tpcepd_zrzr.

fig4_left_top_isobarpaper_star_red_solid_v2_tpcepd_ruru.

fig4_left_top_isobarpaper_star_yellow_open_v2_EP_zrzr.

fig4_left_top_isobarpaper_star_yellow_solid_v2_EP_ruru.

fig4_right_low_isobarpaper_star_green_v2_4_ratio. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig4_right_low_isobarpaper_star_green_v2_zdc_ratio. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig4_right_top_isobarpaper_star_green_open_v2_4_zrzr. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values". "Imaginary number of v_2{4} is presented as negative value”

fig4_right_top_isobarpaper_star_green_solid_v2_4_ruru. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values". "Imaginary number of v_2{4} is presented as negative value”

fig4_right_top_isobarpaper_star_grey_open_v2_zdc_zrzr.

fig4_right_top_isobarpaper_star_grey_solid_v2_zdc_ruru.

fig5_olow_isobarpaper_star_green_group-2. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig5_olow_isobarpaper_star_purple_group-4.

fig5_olow_isobarpaper_star_yellow_group-3. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig5_otop_isobarpaper_star_blue_group-1. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig5_otop_isobarpaper_star_green_group-2.

fig5_otop_isobarpaper_star_red_group-3. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig6_olow_isobarpaper_star_blue_solid_v2_ratio.

fig6_otop_isobarpaper_star_blue_open_v2_zrzr.

fig6_otop_isobarpaper_star_blue_solid_v2_ruru.

fig7_otop_isobarpaper_star_blue_open_Ddelta_zrzr.

fig7_otop_isobarpaper_star_blue_solid_Ddelta_ratio.

fig7_otop_isobarpaper_star_blue_solid_Ddelta_ruru.

fig8_olow_isobarpaper_star_blue_solid_Dgamma_ratio. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig8_otop_isobarpaper_star_blue_open_Dgamma_zrzr.

fig8_otop_isobarpaper_star_blue_solid_Dgamma_ruru.

fig9_olow_isobarpaper_star_blue_solid_kappa_ratio. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig9_otop_isobarpaper_star_blue_open_kappa_zrzr. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig9_otop_isobarpaper_star_blue_solid_kappa_ruru.

fig10_left_low_isobarpaper_star_blue_v2_tpc_ratio. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig10_left_low_isobarpaper_star_green_v3_tpc_ratio. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig10_left_low_isobarpaper_star_red_v2_epd_ratio. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig10_left_low_isobarpaper_star_yellow_v3_epd_ratio. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig10_left_mid_isobarpaper_star_green_open_v3_tpc_zrzr. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig10_left_mid_isobarpaper_star_green_solid_v3_tpc_ruru. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig10_left_mid_isobarpaper_star_yellow_open_v3_epd_zrzr.

fig10_left_mid_isobarpaper_star_yellow_solid_v3_epd_ruru. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig10_left_top_isobarpaper_star_blue_open_v2_tpc_zrzr.

fig10_left_top_isobarpaper_star_blue_solid_v2_tpc_ruru.

fig10_left_top_isobarpaper_star_red_open_v2_epd_zrzr.

fig10_left_top_isobarpaper_star_red_solid_v2_epd_ruru.

fig10_right_low_isobarpaper_star_blue_v3_subEv_ratio. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig10_right_low_isobarpaper_star_green_v3_tpc_ratio. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig10_right_low_isobarpaper_star_purple_v3_tpc_eta_gt1_ratio. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig10_right_low_isobarpaper_star_yellow_v3_epd_ratio. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig10_right_top_isobarpaper_star_blue_open_v3_subEv_zrzr.

fig10_right_top_isobarpaper_star_blue_solid_v3_subEv_ruru. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig10_right_top_isobarpaper_star_green_open_v3_tpc_zrzr. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig10_right_top_isobarpaper_star_green_solid_v3_tpc_ruru. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig10_right_top_isobarpaper_star_purple_open_v3_tpc_eta_gt1_zrzr.

fig10_right_top_isobarpaper_star_purple_solid_v3_tpc_eta_gt1_ruru. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig10_right_top_isobarpaper_star_yellow_open_v3_epd_zrzr.

fig10_right_top_isobarpaper_star_yellow_solid_v3_epd_ruru. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig11_low_isobarpaper_star_black_g2_tpc_ratio.

fig11_low_isobarpaper_star_blue_g3_tpc_ratio.

fig11_low_isobarpaper_star_red_Ddelta_ratio.

fig11_mid_isobarpaper_star_blue_open_g3_tpc_zrzr. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig11_mid_isobarpaper_star_blue_solid_g3_tpc_ruru. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig11_top_isobarpaper_star_black_open_g2_tpc_zrzr. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig11_top_isobarpaper_star_black_solid_g2_tpc_ruru. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig12_low_isobarpaper_star_black_g2_subEv_ratio. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig12_low_isobarpaper_star_blue_g3_subEv_ratio.

fig12_low_isobarpaper_star_red_Ddelta_ratio.

fig12_mid_isobarpaper_star_blue_open_g3_subEv_zrzr. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig12_mid_isobarpaper_star_blue_solid_g3_subEv_ruru. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig12_top_isobarpaper_star_black_open_g2_subEv_zrzr.

fig12_top_isobarpaper_star_black_solid_g2_subEv_ruru. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig13_low_isobarpaper_star_black_g2_epd_ratio.

fig13_low_isobarpaper_star_blue_g3_epd_ratio.

fig13_low_isobarpaper_star_red_Ddelta_ratio.

fig13_mid_isobarpaper_star_blue_open_g3_epd_zrzr. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig13_mid_isobarpaper_star_blue_solid_g3_epd_ruru.

fig13_top_isobarpaper_star_black_open_g2_epd_zrzr. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig13_top_isobarpaper_star_black_solid_g2_epd_ruru. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig14_low_isobarpaper_star_black_solid_k2_ratio.

fig14_low_isobarpaper_star_blue_solid_k3_ratio.

fig14_mid_isobarpaper_star_blue_open_k3_zrzr. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig14_mid_isobarpaper_star_blue_solid_k3_ruru.

fig14_top_isobarpaper_star_black_open_k2_zrzr.

fig14_top_isobarpaper_star_black_solid_k2_ruru. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig15_left_lowerleftpanel_isobarpaper_star_blue_circle_tpc_ss_zrzr_40-50. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig15_left_lowerleftpanel_isobarpaper_star_blue_square_tpc_os_zrzr_40-50.

fig15_left_lowerleftpanel_isobarpaper_star_red_circle_tpc_ss_ruru_40-50. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig15_left_lowerleftpanel_isobarpaper_star_red_square_tpc_os_ruru_40-50.

fig15_left_lowerrightpanel_isobarpaper_star_blue_circle_epd_ss_zrzr_40-50. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig15_left_lowerrightpanel_isobarpaper_star_blue_square_epd_os_zrzr_40-50. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig15_left_lowerrightpanel_isobarpaper_star_red_circle_epd_ss_ruru_40-50. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig15_left_lowerrightpanel_isobarpaper_star_red_square_epd_os_ruru_40-50. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig15_left_midleftpanel_isobarpaper_star_blue_circle_tpc_ss_zrzr_30-40.

fig15_left_midleftpanel_isobarpaper_star_blue_square_tpc_os_zrzr_30-40.

fig15_left_midleftpanel_isobarpaper_star_red_circle_tpc_ss_ruru_30-40. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig15_left_midleftpanel_isobarpaper_star_red_square_tpc_os_ruru_30-40. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig15_left_midrightpanel_isobarpaper_star_blue_circle_epd_ss_zrzr_30-40. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig15_left_midrightpanel_isobarpaper_star_blue_square_epd_os_zrzr_30-40. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig15_left_midrightpanel_isobarpaper_star_red_circle_epd_ss_ruru_30-40. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig15_left_midrightpanel_isobarpaper_star_red_square_epd_os_ruru_30-40. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig15_left_topleftpanel_isobarpaper_star_blue_circle_tpc_ss_zrzr_20-30.

fig15_left_topleftpanel_isobarpaper_star_blue_square_tpc_os_zrzr_20-30.

fig15_left_topleftpanel_isobarpaper_star_red_circle_tpc_ss_ruru_20-30.

fig15_left_topleftpanel_isobarpaper_star_red_square_tpc_os_ruru_20-30.

fig15_left_toprightpanel_isobarpaper_star_blue_circle_epd_ss_zrzr_20-30. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig15_left_toprightpanel_isobarpaper_star_blue_square_epd_os_zrzr_20-30. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig15_left_toprightpanel_isobarpaper_star_red_circle_epd_ss_ruru_20-30.

fig15_left_toprightpanel_isobarpaper_star_red_square_epd_os_ruru_20-30.

fig15_right_lowerleftpanel_isobarpaper_star_blue_circle_tpc_Deltagamma_zrzr_40-50. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig15_right_lowerleftpanel_isobarpaper_star_red_circle_tpc_Deltagamma_ruru_40-50. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig15_right_lowerrightpanel_isobarpaper_star_blue_circle_epd_Deltagamma_zrzr_40-50. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig15_right_lowerrightpanel_isobarpaper_star_red_circle_epd_Deltagamma_ruru_40-50.

fig15_right_midleftpanel_isobarpaper_star_blue_circle_tpc_Deltagamma_zrzr_30-40. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig15_right_midleftpanel_isobarpaper_star_red_circle_tpc_Deltagamma_ruru_30-40.

fig15_right_midrightpanel_isobarpaper_star_blue_circle_epd_Deltagamma_zrzr_30-40. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig15_right_midrightpanel_isobarpaper_star_red_circle_epd_Deltagamma_ruru_30-40.

fig15_right_topleftpanel_isobarpaper_star_blue_circle_tpc_Deltagamma_zrzr_20-30.

fig15_right_topleftpanel_isobarpaper_star_red_circle_tpc_Deltagamma_ruru_20-30.

fig15_right_toprightpanel_isobarpaper_star_blue_circle_epd_Deltagamma_zrzr_20-30. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig15_right_toprightpanel_isobarpaper_star_red_circle_epd_Deltagamma_ruru_20-30. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig16_a_blue_zrzr.

fig16_a_red_ruru.

fig16_b.

fig17_a_blue_zrzr. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig17_a_red_ruru.

fig17_b. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig18_a_blue_ruru_ZDCdg.

fig18_a_red_ruru_TPCdg.

fig18_b_blue_ruru_ZDCv2.

fig18_b_red_ruru_TPCv2.

fig18_c_blue_ruru_A. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig18_c_red_ruru_a.

fig18_d_red_ruru. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig18_e_blue_zrzr_ZDCdg.

fig18_e_red_zrzr_TPCdg.

fig18_f_blue_zrzr_ZDCv2.

fig18_f_red_zrzr_TPCv2.

fig18_g_blue_zrzr_A. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig18_g_red_zrzr_a. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig18_h_red_zrzr. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig19_a_blue_zrzr. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig19_a_red_ruru. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig19_b_blue_zrzr.

fig19_b_red_ruru. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig21_doubleratio.

fig22_doubleratio_ruru. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig22_doubleratio_zrzr.

fig22_fcme_ruru. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig22_fcme_zrzr.

fig23_ratio_v22.

fig23_ratio_v24. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig23_ratio_v2z. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig23_v22_ru.

fig23_v22_zr.

fig23_v24_ru. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values". "Imaginary number of v_2{4} is presented as negative value”

fig23_v24_zr. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values". "Imaginary number of v_2{4} is presented as negative value”

fig23_v2z_ru.

fig23_v2z_zr.

fig24_a_isobarpaper_star_ruru_q2_0-20.

fig24_a_isobarpaper_star_ruru_q2_20-40.

fig24_a_isobarpaper_star_ruru_q2_40-60.

fig24_a_isobarpaper_star_ruru_q2_60-100.

fig24_b_isobarpaper_ruru.

fig24_c_isobarpaper_ruru.

fig24_d_isobarpaper_star_zrzr_q2_0-20.

fig24_d_isobarpaper_star_zrzr_q2_20-40.

fig24_d_isobarpaper_star_zrzr_q2_40-60.

fig24_d_isobarpaper_star_zrzr_q2_60-100.

fig24_e_isobarpaper_zrzr.

fig24_f_isobarpaper_zrzr.

fig25_a_isobarpaper_star_blue_open_zrzr_0-10.

fig25_a_isobarpaper_star_blue_solid_ruru_0-10.

fig25_b_isobarpaper_star_red_open_zrzr_10-30.

fig25_b_isobarpaper_star_red_solid_ruru_10-30.

fig25_c_isobarpaper_star_green_open_zrzr_30-50.

fig25_c_isobarpaper_star_green_solid_ruru_30-50.

fig25_d_isobarpaper_star_orange_open_zrzr_20-50.

fig25_d_isobarpaper_star_orange_solid_ruru_20-50.

fig25_e_isobarpaper_star_open_zrzr.

fig25_e_isobarpaper_star_solid_ruru.

fig25_f_isobarpaper_star_solid_ratio. "For points without systematic uncertainties, using the method for estimating systematic uncertainties as described in the paper yields 0 values"

fig26_isobarpaper_star_black_deltagamma_by_v2_1. "({/Symbol Dg}_{112}/v_{2})_{EP,TPC}" Group-1

fig26_isobarpaper_star_black_deltagamma_by_v2_2. "({/Symbol Dg}_{112}/v_{2})_{3PC,TPC}" Group-2

fig26_isobarpaper_star_black_deltagamma_by_v2_3. "({/Symbol Dg}_{112}/v_{2})_{3PC,TPC}" Group-3

fig26_isobarpaper_star_black_deltagamma_by_v2_4. "({/Symbol Dg}_{112}/v_{2})_{SE,TPC}" Group-2

fig26_isobarpaper_star_black_deltagamma_by_v2_5. "({/Symbol Dg}_{112}/v_{2})_{SE,TPC}" Group-3

fig26_isobarpaper_star_black_deltagamma_by_v2_6. "({/Symbol Dg}_{112}/v_{2})_{SE,TPC}" Group-4

fig26_isobarpaper_star_black_deltagamma_by_v2_7. "({/Symbol Dg}_{112}/v_{2})_{SP,EPD}" Group-2

fig26_isobarpaper_star_blue_R. "{/Symbol s}@^{-1}_{R_{/Symbol Y}_2}" Group-5

fig26_isobarpaper_star_darkgreen_k_9. "{/Symbol k}_{112}" Group-1

fig26_isobarpaper_star_darkgreen_k_10. "k_{2}" Group-2

fig26_isobarpaper_star_grey_deltagamma_by_v3. "({/Symbol Dg}_{123}/v_{3})_{3PC,TPC}" Group-2

fig26_isobarpaper_star_lightgreen_k. "k_{3}" Group-2

fig27_isobarpaper_star_black_deltagamma_by_v2_1. "({/Symbol Dg}_{112}/v_{2})_{EP,TPC}" Group-1

fig27_isobarpaper_star_black_deltagamma_by_v2_2. "({/Symbol Dg}_{112}/v_{2})_{3PC,TPC}" Group-2

fig27_isobarpaper_star_black_deltagamma_by_v2_3. "({/Symbol Dg}_{112}/v_{2})_{3PC,TPC}" Group-3

fig27_isobarpaper_star_black_deltagamma_by_v2_4. "({/Symbol Dg}_{112}/v_{2})_{SE,TPC}" Group-2

fig27_isobarpaper_star_black_deltagamma_by_v2_5. "({/Symbol Dg}_{112}/v_{2})_{SE,TPC}" Group-3

fig27_isobarpaper_star_black_deltagamma_by_v2_6. "({/Symbol Dg}_{112}/v_{2})_{SE,TPC}" Group-4

fig27_isobarpaper_star_black_deltagamma_by_v2_7. "({/Symbol Dg}_{112}/v_{2})_{SP,EPD}" Group-2

fig27_isobarpaper_star_blue_R.txt. "{/Symbol s}@^{-1}_{R_{/Symbol Y}_2}" Group-5

fig27_isobarpaper_star_darkgreen_k_9. "{/Symbol k}_{112}" Group-1

fig27_isobarpaper_star_darkgreen_k_10. "k_{2}" Group-2

fig27_isobarpaper_star_grey_deltagamma_by_v3. "({/Symbol Dg}_{123}/v_{3})_{3PC,TPC}" Group-2

fig27_isobarpaper_star_lightgreen_k. "k_{3}" Group-2

fig27_isobarpaper_star_purple_r_n_13. "r(m_{inv})" Group-3

fig27_isobarpaper_star_purple_r_n_14. "1/N@_{trk}^{offline}"

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.

Centrality dependence of single cumulants C1, of net-lambda multiplicity distributions at Au + Au collision 62.4 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of single cumulants C1, of net-lambda multiplicity distributions at Au + Au collision 200 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of single cumulants C2, of net-lambda multiplicity distributions at Au + Au collision 19.6 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of single cumulants C2, of net-lambda multiplicity distributions at Au + Au collision 27 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of single cumulants C2, of net-lambda multiplicity distributions at Au + Au collision 39 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of single cumulants C2, of net-lambda multiplicity distributions at Au + Au collision 62.4 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of single cumulants C2, of net-lambda multiplicity distributions at Au + Au collision 200 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of single cumulants C3, of net-lambda multiplicity distributions at Au + Au collision 19.6 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of single cumulants C3, of net-lambda multiplicity distributions at Au + Au collision 27 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of single cumulants C3, of net-lambda multiplicity distributions at Au + Au collision 39 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of single cumulants C3, of net-lambda multiplicity distributions at Au + Au collision 62.4 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of single cumulants C3, of net-lambda multiplicity distributions at Au + Au collision 200 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of net-lambda cumulant ratio C2/C1, as a function of net-lambda multiplicity distributions at Au + Au collision 19.6 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of net-lambda cumulant ratio C2/C1, as a function of net-lambda multiplicity distributions at Au + Au collision 27 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of net-lambda cumulant ratio C2/C1, as a function of net-lambda multiplicity distributions at Au + Au collision 39 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of net-lambda cumulant ratio C2/C1, as a function of net-lambda multiplicity distributions at Au + Au collision 62.4 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of net-lambda cumulant ratio C2/C1, as a function of net-lambda multiplicity distributions at Au + Au collision 200 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of net-lambda cumulant ratio C3/C2, as a function of net-lambda multiplicity distributions at Au + Au collision 19.6 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of net-lambda cumulant ratio C3/C2, as a function of net-lambda multiplicity distributions at Au + Au collision 27 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of net-lambda cumulant ratio C3/C2, as a function of net-lambda multiplicity distributions at Au + Au collision 39 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of net-lambda cumulant ratio C3/C2, as a function of net-lambda multiplicity distributions at Au + Au collision 62.4 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of net-lambda cumulant ratio C3/C2, as a function of net-lambda multiplicity distributions at Au + Au collision 200 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Beam-energy dependence of net-lambda cumulant ratios C2/C1 in most central (0-5%) and peripheral (50-60%). Values are shown with NBD, Poisson and UrQMD predictions.

Beam-energy dependence of net-lambda cumulant ratios C3/C2 in most central (0-5%) and peripheral (50-60%). Values are shown with NBD, Poisson and UrQMD predictions.

Beam-energy dependence of net-lambda, net-proton and net-kaon cumulant ratios C2/C1 in most central (0-5%) collision.

Beam-energy dependence of net-lambda, net-proton and net-kaon cumulant ratios C3/C2 in most central (0-5%) collision.

Beam-energy dependence of net-lambda cumulant ratios C2/C1 in most central (0-5%) collision, along with results from HRG.

Beam-energy dependence of net-lambda cumulant ratios C3/C2 in most central (0-5%) collision, along with results from HRG.

Rapidity dependence of net-lambda cumulant ratios C2/C1 in most central (0-5%) collision, along with results from NBD.

Rapidity dependence of net-lambda cumulant ratios C3/C2 in most central (0-5%) collision, along with results from NBD.

Rapidity dependence of normalized C2 in most central (0-5%) collision at Au+Au 19.6 GeV.

Rapidity dependence of normalized C2 in most central (0-5%) collision at Au+Au 200 GeV.

The $p_{T}$ spectra of $\pi^{-}$ measured at midrapidity (|y|<0.1) in Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV. Spectra are plotted for nine centrality classes, with some spectra multiplied by a scale factor to improve clarity, as indicatedin the legend

The $p_{T}$ spectra of $K^{+}$ measured at midrapidity (|y|<0.1) in Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV. Spectra are plotted for nine centrality classes, with some spectra multiplied by a scale factor to improve clarity, as indicatedin the legend

The $p_{T}$ spectra of $K^{-}$ measured at midrapidity (|y|<0.1) in Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV. Spectra are plotted for nine centrality classes, with some spectra multiplied by a scale factor to improve clarity, as indicatedin the legend

Average $p_{T}$ of $\pi^{+}$ as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

Average $p_{T}$ of $\pi^{-}$ as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

Average $p_{T}$ of $K^{+}$ as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

Average $p_{T}$ of $K^{-}$ as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$= 14.5 GeV.

Average $p_{T}$ of p as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

Average $p_{T}$ of p-bar as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

dN/dy of $\pi^{+}$ scaled by 0.5*$N_{part}$ as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

dN/dy of $\pi^{-}$ scaled by 0.5*$N_{part}$ as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

dN/dy of $K^{+}$ scaled by 0.5*$N_{part}$ as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

dN/dy of $K^{-}$ scaled by 0.5*$N_{part}$ as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

dN/dy of proton scaled by 0.5*$N_{part}$ as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

dN/dy of p-bar scaled by 0.5*$N_{part}$ as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

Kinetic freeze-out temperature as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

Velocity as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

The event plane resolution calculated for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV as a function of centrality.

Inclusive charged particle elliptic flow v2 at mid-pseudorapidity (|y| <1.0) as a function of $p_{T}$ for 10-20% centrality in Au + Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

Inclusive charged particle elliptic flow v2 at mid-pseudorapidity (|y| <1.0) as a function of $p_{T}$ for 20-30% centrality in Au + Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

Inclusive charged particle elliptic flow v2 at mid-pseudorapidity (|y| <1.0) as a function of $p_{T}$ for 30-40% centrality in Au + Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

Inclusive charged particle elliptic flow v2 at mid-pseudorapidity (|y| <1.0) as a function of transverse momentum $p_{T}$ for six centrality classes, obtained using the $\eta$-sub event plane method in Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

Inclusive charged particle elliptic flow v2 at mid-pseudorapidity (|y| <1.0) as a function of $p_{T}$-integrated v2($\eta$) for six centrality classes, obtained using the $\eta$-sub event plane method in Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

The ratio inclusive charged particle elliptic flow v2 over root-mean-square participant eccentricity $Epart_{2}$ at mid-pseudorapidity as a function of $p_{T}$ for 10–20%, 30–40%, and 50–60% collision centralities in Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

Summary of centrality bins, average number of participants $N_{part}$, number of binary collisions $N_{coll}$, reaction plane eccentricity eRP, participant eccentricity epart, root-mean-square of the participant eccentricity epart{2}, and transverse area $S_{part}$ from MC Glauber simulations at $\sqrt{s_{NN}}$ = 14.5 GeV.

The inclusive charged particle elliptic flow v2($\eta$-sub) versus pseudorapidity $\eta$ at mid-pseudorapidity for $\sqrt{s_{NN}}$ = 14.5 GeV.

Rapidity-odd charged particles directed flow v1 as a function of $p_{T}$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV for 0–10%, 10–40% and 40–80% centrality intervals.

Rapidity-odd charged particles directed flow v1 as a function of $p_{T}$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 11.5 GeV for 0–10%, 10–40% and 40–80% centrality intervals.

Rapidity-odd charged particles directed flow v1 as a function of $p_{T}$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV GeV for 0–10%, 10–40% and 40–80% centrality intervals.

Rapidity-odd charged particles directed flow v1 as a function of $p_{T}$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 GeV for 0–10%, 10–40% and 40–80% centrality intervals.

Rapidity-odd charged particles directed flow v1 as a function of $p_{T}$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 27.0 GeV for 0–10%, 10–40% and 40–80% centrality intervals.

Rapidity-odd charged particles directed flow v1 as a function of $p_{T}$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 39.0 GeV for 0–10%, 10–40% and 40–80% centrality intervals.

Rapidity-odd charged particles directed flow v1 as a function of pseudorapidity $\eta$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV for 0–10%, 10–40% and 40–80% centrality intervals.

Rapidity-odd charged particles directed flow v1 as a function of pseudorapidity $\eta$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 11.5 GeV for 0–10%, 10–40% and 40–80% centrality intervals.

Rapidity-odd charged particles directed flow v1 as a function of pseudorapidity $\eta$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV for 0–10%, 10–40% and 40–80% centrality intervals.

Rapidity-odd charged particles directed flow v1 as a function of pseudorapidity $\eta$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 GeV for 0–10%, 10–40% and 40–80% centrality intervals.

Rapidity-odd charged particles directed flow v1 as a function of pseudorapidity $\eta$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 27.0 GeV for 0–10%, 10–40% and 40–80% centrality intervals.

Rapidity-odd charged particles directed flow v1 as a function of pseudorapidity $\eta$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 39.0 GeV for 0–10%, 10–40% and 40–80% centrality intervals.

Rapidity-odd charged particles directed flow v1 as a function of pseudorapidity $\eta$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 – 39 GeV for 30-60% centrality intervals.

Covariance matrix (statistical and systematic uncertainties combined) with the muon $p_{T}>35$ GeV. The units are in $10^{-4}$.

Measurements of the parameter D for two values of midrapidity range.

Measurements of D from the HIJING event generator for two values of midrapidity range.

Measurements of D in P P collisions from the PYTHIA event generator for two values of midrapidity range.

Measurements of MEAN(NCH)*NU(+-DYN) as a function of the Delta(ETARAP) range for three centrality ranges.

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Results for G1/F1 for the proton and neutron.

Results for G1/F1 for the proton and neutron.

Results for G1/F1 for the proton and neutron.

Results for G1/F1 for the proton and neutron.

Results for G1/F1 for the proton and neutron.

Results for G1/F1 for the proton and neutron.

Results for G1/F1 for the proton and neutron.

Results for G1/F1 for the proton and neutron.

Integral over X of G1 using a NLO pQCD fit.

The asymmetry for polarized photoproduction of inclusive identified pions from a polarized deuteron target. The errors are statistical only.

Detailed A1(P) for the DIS (W**2 > 4 GeV) region. Additional normalization uncertainty 3.7%.

Averaged A1(DEUT) for the DIS (W**2 > 4 GeV) region. Additional normalization uncertainty 4.9%.

Detailed A1(DEUT) for the DIS (W**2 > 4 GeV) region. Additional normalization uncertainty 4.9%.

Detailed A1(DEUT) for the DIS (W**2 > 4 GeV) region. Additional normalization uncertainty 4.9%.

Detailed A1(DEUT) for the DIS (W**2 > 4 GeV) region. Additional normalization uncertainty 4.9%.

Averaged A1(N) for the DIS (W**2 > 4 GeV) region. Additional normalization uncertainty 4.9%.

Detailed A1(N) for the DIS (W**2 > 4 GeV) region. Additional normalization uncertainty 4.9%.

Detailed A1(N) for the DIS (W**2 > 4 GeV) region. Additional normalization uncertainty 4.9%.

Detailed A1(N) for the DIS (W**2 > 4 GeV) region. Additional normalization uncertainty 4.9%.

Averaged G1(P) for the DIS (W**2 > 4 GeV**2) region. Additional normalisation uncertainty 3.7%.

G1(P) interpolated to fixed Q**2 values for the DIS (W**2 > 4 GeV**2) region assuming G1/F1 indepenedent of Q**2. Additional normalisation uncertainty 3.7%.

Detailed results of G1(P)/F1(P) for the DIS (W**2 > 4 GeV**2) region. Additional normalisation uncertainty 3.7%.

Detailed results of G1(P)/F1(P) for the DIS (W**2 > 4 GeV**2) region. Additional normalisation uncertainty 3.7%.

Detailed results of G1(P)/F1(P) for the DIS (W**2 > 4 GeV**2) region. Additional normalisation uncertainty 3.7%.

Averaged G1(DEUT) for the DIS (W**2 > 4 GeV**2) region. Additional normalisation uncertainty 4.9%.

G1(DEUT) interpolated to fixed Q**2 values for the DIS (W**2 > 4 GeV**2) region assuming G1/F1 indepenedent of Q**2. Additional normalisation uncertainty 4.9%.

Detailed results of G1(DEUT)/F1(DEUT) for the DIS (W**2 > 4 GeV**2) region. Additional normalisation uncertainty 4.9%.

Detailed results of G1(DEUT)/F1(DEUT) for the DIS (W**2 > 4 GeV**2) region. Additional normalisation uncertainty 4.9%.

Detailed results of G1(DEUT)/F1(DEUT) for the DIS (W**2 > 4 GeV**2) region. Additional normalisation uncertainty 4.9%.

Averaged G1(N) for the DIS (W**2 > 4 GeV**2) region. Additional normalisation uncertainty 4.9%.

G1(N) interpolated to fixed Q**2 values for the DIS (W**2 > 4 GeV**2) region assuming G1/F1 indepenedent of Q**2. Additional normalisation uncertainty 4.9%.

Detailed results of G1(N)/F1(N) for the DIS (W**2 > 4 GeV**2) region. Additional normalisation uncertainty 4.9%.

Detailed results of G1(N)/F1(N) for the DIS (W**2 > 4 GeV**2) region. Additional normalisation uncertainty 4.9%.

Detailed results of G1(N)/F1(N) for the DIS (W**2 > 4 GeV**2) region. Additional normalisation uncertainty 4.9%.

A2(P) measured at 29.1 GeV in the DIS (W**2 > 4 GeV**2) region. Additional normalisation uncertainty 3.7%.

A2(DEUT) measured at 29.1 GeV in the DIS (W**2 > 4 GeV**2) region. Additional normalisation uncertainty 4.9%.

A2(N) measured at 29.1 GeV in the DIS (W**2 > 4 GeV**2) region. Additional normalisation uncertainty 4.9%.

G2(P) measured at 29.1 GeV in the DIS (W**2 > 4 GeV**2) region. Additional normalisation uncertainty 3.7%.

G2(DEUT) measured at 29.1 GeV in the DIS (W**2 > 4 GeV**2) region. Additional normalisation uncertainty 4.9%.

G2(N) measured at 29.1 GeV in the DIS (W**2 > 4 GeV**2) region. Additional normalisation uncertainty 4.9%.

Data from the 5.5 degree spectrometer evolved to a mean Q**2 of 5 GeV**2 using the MSBAR parameterization. The second systematic error is due to the evolution.

Data from both spectrometers combined.

Data from both spectrometers combined. The second systematic error is due to the evolution.

Integral of G1 from the average of both spectrometers, evolved to Q**2 = 5 GeV**2 and extrapolated to full x range. The second systematic error is due to the evolution.