The $p_{T}$ distributions at $|y|<0.5$ for minimum bias $p$+$p$ and peripheral Au+Au collisions. See text for an explanation of the functions used to fit the data. The errors shown are statistical only and smaller than the symbols.

$\rho^{0}/\pi$ ratios as a function of c.m. system energy. The ratios are from measurements in $e^{+} e^{−}$ collisions at $10.45$ GeV, $29$ GeV and $91$ GeV c.m. system energy, $p$+$p$ at $6.8$ GeV, $19.7$ GeV, $27.5$ GeV, and $52.5$ GeV, Kp at $7.82$ GeV and $\pi^{-}$p at $19.6$ GeV. The errors on the ratios at $\sqrt{s_{NN}}= 200$ GeV are the quadratic sum of the statistical and systematic errors. The ratios at $\sqrt{s_{NN}}= 200$ GeV are offset from one another for clarity.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$h^{−}$ pseudorapidity distribution from $5\%$ most central Au+Au collisions for $p_{T} > 100$ MeV/$c$ (filled circles) and all $p_{T}$ (open squares). The correlated systematic error on the overall normalization is estimated to be $6\%$ for $p_{T} > 0.1$ GeV/$c$ and $7\%$ for $p_{T} > 0$.

$\Lambda$ and $\bar\Lambda$ rapidity density as a function of negative hadron multiplicity at mid-rapidity. The open symbols in the figure are data points from an independent analysis of minimum bias data set using event-mixing techniques. Errors shown are statistical only. Systematic errors on hyperon yields $10\%$, on negative hadron yields $6\%$. $\Lambda$ and $\bar\Lambda$ measured for $|y|<0.5$, negative hadrons for $|\eta|<0.1$. Dashed lines correspond to $\Lambda = 0.054 h^{-}$, $\bar\Lambda = 0.040 h^{-}$.

Fit parameters from Boltzmann and exponential fits of the $m_{T}$ spectra for $\Lambda$ and $\bar\Lambda$ at mid-rapidity ($|y|<0.5$). Only statistical errors are presented. The systematic errors on $dN/dy$ and $T$ are approximately $10\%$. The Boltzmann form is adopted in Figure 2.

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

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

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

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

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

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

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

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

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

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

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

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

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

FIG. 1. (Color online) Perspective views of $2 \mathrm{D}$ charge-independent angular correlations $\Delta \rho / \sqrt{\rho_{\mathrm{ref}}}$ on $\left(\eta_{\Delta}, \phi_{\Delta}\right)$ for Au-Au collisions at $\sqrt{s_{N N}}=200$ and $62 \mathrm{GeV}$ (top and bottom rows, respectively). Centrality increases left to right from most peripheral to most central. Corrected total cross-section fractions are (left to right) $84 \%-93 \%, 55 \%-64 \%, 18 \%-28 \%,$ and $0 \%-5 \%$ for the $200-\mathrm{GeV}$ data and $84 \%-95 \%, 56 \%-65 \%$ $18 \%-28 \%,$ and $0 \%-5 \%$ for the $62 \mathrm{GeV}$ data (see Tables III and IV).

FIG. 1. (Color online) Perspective views of $2 \mathrm{D}$ charge-independent angular correlations $\Delta \rho / \sqrt{\rho_{\mathrm{ref}}}$ on $\left(\eta_{\Delta}, \phi_{\Delta}\right)$ for Au-Au collisions at $\sqrt{s_{N N}}=200$ and $62 \mathrm{GeV}$ (top and bottom rows, respectively). Centrality increases left to right from most peripheral to most central. Corrected total cross-section fractions are (left to right) $84 \%-93 \%, 55 \%-64 \%, 18 \%-28 \%,$ and $0 \%-5 \%$ for the $200-\mathrm{GeV}$ data and $84 \%-95 \%, 56 \%-65 \%$ $18 \%-28 \%,$ and $0 \%-5 \%$ for the $62 \mathrm{GeV}$ data (see Tables III and IV).

FIG. 1. (Color online) Perspective views of $2 \mathrm{D}$ charge-independent angular correlations $\Delta \rho / \sqrt{\rho_{\mathrm{ref}}}$ on $\left(\eta_{\Delta}, \phi_{\Delta}\right)$ for Au-Au collisions at $\sqrt{s_{N N}}=200$ and $62 \mathrm{GeV}$ (top and bottom rows, respectively). Centrality increases left to right from most peripheral to most central. Corrected total cross-section fractions are (left to right) $84 \%-93 \%, 55 \%-64 \%, 18 \%-28 \%,$ and $0 \%-5 \%$ for the $200-\mathrm{GeV}$ data and $84 \%-95 \%, 56 \%-65 \%$ $18 \%-28 \%,$ and $0 \%-5 \%$ for the $62 \mathrm{GeV}$ data (see Tables III and IV).

FIG. 1. (Color online) Perspective views of $2 \mathrm{D}$ charge-independent angular correlations $\Delta \rho / \sqrt{\rho_{\mathrm{ref}}}$ on $\left(\eta_{\Delta}, \phi_{\Delta}\right)$ for Au-Au collisions at $\sqrt{s_{N N}}=200$ and $62 \mathrm{GeV}$ (top and bottom rows, respectively). Centrality increases left to right from most peripheral to most central. Corrected total cross-section fractions are (left to right) $84 \%-93 \%, 55 \%-64 \%, 18 \%-28 \%,$ and $0 \%-5 \%$ for the $200-\mathrm{GeV}$ data and $84 \%-95 \%, 56 \%-65 \%$ $18 \%-28 \%,$ and $0 \%-5 \%$ for the $62 \mathrm{GeV}$ data (see Tables III and IV).

FIG. 1. (Color online) Perspective views of $2 \mathrm{D}$ charge-independent angular correlations $\Delta \rho / \sqrt{\rho_{\mathrm{ref}}}$ on $\left(\eta_{\Delta}, \phi_{\Delta}\right)$ for Au-Au collisions at $\sqrt{s_{N N}}=200$ and $62 \mathrm{GeV}$ (top and bottom rows, respectively). Centrality increases left to right from most peripheral to most central. Corrected total cross-section fractions are (left to right) $84 \%-93 \%, 55 \%-64 \%, 18 \%-28 \%,$ and $0 \%-5 \%$ for the $200-\mathrm{GeV}$ data and $84 \%-95 \%, 56 \%-65 \%$ $18 \%-28 \%,$ and $0 \%-5 \%$ for the $62 \mathrm{GeV}$ data (see Tables III and IV).

FIG. 2. (Color online) Fit decomposition of the $46 \%-56 \%$ centrality data for 62 -GeV Au-Au collisions. The top panels show from left to right the corrected data, model fit, fit residuals (data - model), and same-side 2D Gaussian. The bottom panels similarly show the away-side azimuth dipole, the nonjet azimuth quadrupole, the 1D $\eta_{\Delta}$ Gaussian, and the 2D exponential. This centrality is just below the sharp transition at $v_{\text {trans }}=3$. Fit residuals (c) are scaled up eightfold relative to the data.

FIG. 3. Fit parameters for $\left(\eta_{\Delta}, \phi_{\Delta}\right)$ correlation data from Au-Au collisions at $\sqrt{s_{N N}}=62$ (open symbols) and 200 GeV (solid symbols) versus centrality measure $\nu$ computed at fixed energy $(200 \mathrm{GeV})$. The SS $2 \mathrm{D}$ Gaussian amplitudes, $\eta_{\Delta}$ widths, and $\phi_{\Delta}$ widths are shown in the left, center, and right panels, respectively of the top row. The bottom row shows from left to right the amplitudes for the dipole, quadrupole, and SS peak width aspect ratio $\sigma_{\eta_{\Delta}} / \sigma_{\phi_{\Delta}} .$ Fitting errors are indicated by error bars where larger than the symbols. Solid lines connect the points for clarity. The dotted and dashed curves indicate Glauber linear superposition estimates for 62 - and 200 -GeV peak amplitudes respectively, as discussed in the text. The quadrupole data are consistent with Ref. [60]. The hatched regions indicate the full range of systematic uncertainties listed in Appendix F. The vertical dark bands indicate estimated $v$ equivalents for $N-N$ collisions and $b=0$ Au-Au collisions.

FIG. 3. Fit parameters for $\left(\eta_{\Delta}, \phi_{\Delta}\right)$ correlation data from Au-Au collisions at $\sqrt{s_{N N}}=62$ (open symbols) and 200 GeV (solid symbols) versus centrality measure $\nu$ computed at fixed energy $(200 \mathrm{GeV})$. The SS $2 \mathrm{D}$ Gaussian amplitudes, $\eta_{\Delta}$ widths, and $\phi_{\Delta}$ widths are shown in the left, center, and right panels, respectively of the top row. The bottom row shows from left to right the amplitudes for the dipole, quadrupole, and SS peak width aspect ratio $\sigma_{\eta_{\Delta}} / \sigma_{\phi_{\Delta}} .$ Fitting errors are indicated by error bars where larger than the symbols. Solid lines connect the points for clarity. The dotted and dashed curves indicate Glauber linear superposition estimates for 62 - and 200 -GeV peak amplitudes respectively, as discussed in the text. The quadrupole data are consistent with Ref. [60]. The hatched regions indicate the full range of systematic uncertainties listed in Appendix F. The vertical dark bands indicate estimated $v$ equivalents for $N-N$ collisions and $b=0$ Au-Au collisions.

FIG. 3. Fit parameters for $\left(\eta_{\Delta}, \phi_{\Delta}\right)$ correlation data from Au-Au collisions at $\sqrt{s_{N N}}=62$ (open symbols) and 200 GeV (solid symbols) versus centrality measure $\nu$ computed at fixed energy $(200 \mathrm{GeV})$. The SS $2 \mathrm{D}$ Gaussian amplitudes, $\eta_{\Delta}$ widths, and $\phi_{\Delta}$ widths are shown in the left, center, and right panels, respectively of the top row. The bottom row shows from left to right the amplitudes for the dipole, quadrupole, and SS peak width aspect ratio $\sigma_{\eta_{\Delta}} / \sigma_{\phi_{\Delta}} .$ Fitting errors are indicated by error bars where larger than the symbols. Solid lines connect the points for clarity. The dotted and dashed curves indicate Glauber linear superposition estimates for 62 - and 200 -GeV peak amplitudes respectively, as discussed in the text. The quadrupole data are consistent with Ref. [60]. The hatched regions indicate the full range of systematic uncertainties listed in Appendix F. The vertical dark bands indicate estimated $v$ equivalents for $N-N$ collisions and $b=0$ Au-Au collisions.

FIG. 3. Fit parameters for $\left(\eta_{\Delta}, \phi_{\Delta}\right)$ correlation data from Au-Au collisions at $\sqrt{s_{N N}}=62$ (open symbols) and 200 GeV (solid symbols) versus centrality measure $\nu$ computed at fixed energy $(200 \mathrm{GeV})$. The SS $2 \mathrm{D}$ Gaussian amplitudes, $\eta_{\Delta}$ widths, and $\phi_{\Delta}$ widths are shown in the left, center, and right panels, respectively of the top row. The bottom row shows from left to right the amplitudes for the dipole, quadrupole, and SS peak width aspect ratio $\sigma_{\eta_{\Delta}} / \sigma_{\phi_{\Delta}} .$ Fitting errors are indicated by error bars where larger than the symbols. Solid lines connect the points for clarity. The dotted and dashed curves indicate Glauber linear superposition estimates for 62 - and 200 -GeV peak amplitudes respectively, as discussed in the text. The quadrupole data are consistent with Ref. [60]. The hatched regions indicate the full range of systematic uncertainties listed in Appendix F. The vertical dark bands indicate estimated $v$ equivalents for $N-N$ collisions and $b=0$ Au-Au collisions.

FIG. 3. Fit parameters for $\left(\eta_{\Delta}, \phi_{\Delta}\right)$ correlation data from Au-Au collisions at $\sqrt{s_{N N}}=62$ (open symbols) and 200 GeV (solid symbols) versus centrality measure $\nu$ computed at fixed energy $(200 \mathrm{GeV})$. The SS $2 \mathrm{D}$ Gaussian amplitudes, $\eta_{\Delta}$ widths, and $\phi_{\Delta}$ widths are shown in the left, center, and right panels, respectively of the top row. The bottom row shows from left to right the amplitudes for the dipole, quadrupole, and SS peak width aspect ratio $\sigma_{\eta_{\Delta}} / \sigma_{\phi_{\Delta}} .$ Fitting errors are indicated by error bars where larger than the symbols. Solid lines connect the points for clarity. The dotted and dashed curves indicate Glauber linear superposition estimates for 62 - and 200 -GeV peak amplitudes respectively, as discussed in the text. The quadrupole data are consistent with Ref. [60]. The hatched regions indicate the full range of systematic uncertainties listed in Appendix F. The vertical dark bands indicate estimated $v$ equivalents for $N-N$ collisions and $b=0$ Au-Au collisions.

FIG. 3. Fit parameters for $\left(\eta_{\Delta}, \phi_{\Delta}\right)$ correlation data from Au-Au collisions at $\sqrt{s_{N N}}=62$ (open symbols) and 200 GeV (solid symbols) versus centrality measure $\nu$ computed at fixed energy $(200 \mathrm{GeV})$. The SS $2 \mathrm{D}$ Gaussian amplitudes, $\eta_{\Delta}$ widths, and $\phi_{\Delta}$ widths are shown in the left, center, and right panels, respectively of the top row. The bottom row shows from left to right the amplitudes for the dipole, quadrupole, and SS peak width aspect ratio $\sigma_{\eta_{\Delta}} / \sigma_{\phi_{\Delta}} .$ Fitting errors are indicated by error bars where larger than the symbols. Solid lines connect the points for clarity. The dotted and dashed curves indicate Glauber linear superposition estimates for 62 - and 200 -GeV peak amplitudes respectively, as discussed in the text. The quadrupole data are consistent with Ref. [60]. The hatched regions indicate the full range of systematic uncertainties listed in Appendix F. The vertical dark bands indicate estimated $v$ equivalents for $N-N$ collisions and $b=0$ Au-Au collisions.

FIG. 4. (Color online) (a) 2D data histogram from $0 \%-5 \%$ central 200 GeV Au-Au collisions $[(0,0)$ bin suppressed]. (b) Additional model component fitted to the $2 \mathrm{D}$ histogram and consisting of an AS azimuth dipole modulated by function $F\left(\eta_{\Delta}\right)$ described in the text. (c) Fit residuals including the new model component. (d) Data histogram in the first panel minus the additional model component and fitted offset. Remaining structure is described accurately by an AS dipole and SS 2D Gaussian.

FIG. 9. (a) Amplitude of SS 2D peak (jet-correlated pairs per final-state hadron) for data (solid points), GLS extrapolation from $p$ - $p$ data (dashed curve) and from the HIJING Monte Carlo (open points, dotted curve). (b) Single-particle production extrapolated from $p-p$ data (dashed curve, GLS), and from more-central Au-Au data (solid line) and HIJING (dash-dotted line, open points). (c) Single-particle hard-component production per $N-N$ binary collision from $p-p$ data, from more-central Au-Au data and from HIJING (open points). (d) Jet-correlated pair production (SS 2D peak) per $N-N$ binary collision extrapolated from $p-p$ data (GLS), and from Au-Au data (solid points) and HIJING (open points).

FIG. 9. (a) Amplitude of SS 2D peak (jet-correlated pairs per final-state hadron) for data (solid points), GLS extrapolation from $p$ - $p$ data (dashed curve) and from the HIJING Monte Carlo (open points, dotted curve). (b) Single-particle production extrapolated from $p-p$ data (dashed curve, GLS), and from more-central Au-Au data (solid line) and HIJING (dash-dotted line, open points). (c) Single-particle hard-component production per $N-N$ binary collision from $p-p$ data, from more-central Au-Au data and from HIJING (open points). (d) Jet-correlated pair production (SS 2D peak) per $N-N$ binary collision extrapolated from $p-p$ data (GLS), and from Au-Au data (solid points) and HIJING (open points).

FIG. 9. (a) Amplitude of SS 2D peak (jet-correlated pairs per final-state hadron) for data (solid points), GLS extrapolation from $p$ - $p$ data (dashed curve) and from the HIJING Monte Carlo (open points, dotted curve). (b) Single-particle production extrapolated from $p-p$ data (dashed curve, GLS), and from more-central Au-Au data (solid line) and HIJING (dash-dotted line, open points). (c) Single-particle hard-component production per $N-N$ binary collision from $p-p$ data, from more-central Au-Au data and from HIJING (open points). (d) Jet-correlated pair production (SS 2D peak) per $N-N$ binary collision extrapolated from $p-p$ data (GLS), and from Au-Au data (solid points) and HIJING (open points).

FIG. 9. (a) Amplitude of SS 2D peak (jet-correlated pairs per final-state hadron) for data (solid points), GLS extrapolation from $p$ - $p$ data (dashed curve) and from the HIJING Monte Carlo (open points, dotted curve). (b) Single-particle production extrapolated from $p-p$ data (dashed curve, GLS), and from more-central Au-Au data (solid line) and HIJING (dash-dotted line, open points). (c) Single-particle hard-component production per $N-N$ binary collision from $p-p$ data, from more-central Au-Au data and from HIJING (open points). (d) Jet-correlated pair production (SS 2D peak) per $N-N$ binary collision extrapolated from $p-p$ data (GLS), and from Au-Au data (solid points) and HIJING (open points).

FIG. 11. (Color online) (Left) Uncorrected angular correlations from 62-GeV $37 \%-46 \%$ central Au-Au collisions showing pileup distortions, especially evident as the W-shaped nonuniformity of the AS ridge on $\eta_{\Delta}$. (Right) The same data with pileup correction applied.

FIG. 4. Ridge yield Eq. (9) in $|\Delta \eta|<1.7$ and $2 \mathrm{GeV/c}<p^{assoc}_{t}$ < $p^{trig}_{t}$ as a function of $p_{t}^{t r i g}$. Solid lines are the systematic uncertainty due to $v_{2}$.

FIG. 5. Projection of $d N /\left.d \Delta \phi\right|_{a, b}$ for $0.7<|\Delta \eta|<1.4$ [Eq. (3)] in two trigger $p_{t}$ windows for $2<p_{t}^{\text {assoc }}<4 \mathrm{GeV} / \mathrm{c} .$ No background subtraction has been applied; note the suppressed zero on the vertical scale. The shaded band shows the fit of the function $k_{1}+k_{2}$. $\cos (2 \Delta \phi)$ to the recoil region $2<|\Delta \phi|<\pi$ for $4<p_{t}^{\text {trig }}<6 \mathrm{GeV} / c$. The width of the band indicates the fitting error. The solid curve represents the background estimate using the ZYAM normalization for $4<p_{t}^{\text {trig }}<6 \mathrm{GeV} / c .$ Systematic uncertainties are indicated by the light shaded band.

FIG. 6. (Color online) Differential $p_{t}$ spectrum for associated particles in central $\mathrm{Au}+$ Au collisions, with $4<p_{t}^{\text {trig }}<6$ and $6<p_{t}^{\text {trig }}<10 \mathrm{GeV} / c$ . The dash-dotted line is the inclusive hadron spectrum from central $\mathrm{Au}+$ Au collisions $[1] .$ Left panel: ridge spectrum; shaded bands show systematic uncertainty. Right panel: jet-like spectrum, also compared to $d+$ Au reference measurements. The lines in both panels show exponential fits to the data (see Table III). Data are offset horizontally for clarity.

FIG. 6. (Color online) Differential $p_{t}$ spectrum for associated particles in central $\mathrm{Au}+$ Au collisions, with $4<p_{t}^{\text {trig }}<6$ and $6<p_{t}^{\text {trig }}<10 \mathrm{GeV} / c$ . The dash-dotted line is the inclusive hadron spectrum from central $\mathrm{Au}+$ Au collisions $[1] .$ Left panel: ridge spectrum; shaded bands show systematic uncertainty. Right panel: jet-like spectrum, also compared to $d+$ Au reference measurements. The lines in both panels show exponential fits to the data (see Table III). Data are offset horizontally for clarity.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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