High transverse-momentum spectra ($p_{T} > 2.5$ GeV/c) of charged pions, protons, and antiprotons for the rapidity regions $|y| < 0.5$ (solid symbols) and $0.5 < |y| < 1.0$ (open symbols) for $d+Au$ collisions and various event centrality classes at $\sqrt{s_{NN}}=200$ GeV.

High transverse-momentum spectra ($p_{T} > 2.5$ GeV/c) of charged pions, protons, and antiprotons for the rapidity regions $|y| < 0.5$ (solid symbols) and $0.5 < |y| < 1.0$ (open symbols) for $d+Au$ collisions and various event centrality classes at $\sqrt{s_{NN}}=200$ GeV.

High transverse-momentum spectra ($p_{T} > 2.5$ GeV/c) of charged pions, protons, and antiprotons for the rapidity regions $|y| < 0.5$ (solid symbols) and $0.5 < |y| < 1.0$ (open symbols) for $d+Au$ collisions and various event centrality classes at $\sqrt{s_{NN}}=200$ GeV.

High transverse-momentum spectra ($p_{T} > 2.5$ GeV/c) of charged pions, protons, and antiprotons for the rapidity regions $|y| < 0.5$ (solid symbols) and $0.5 < |y| < 1.0$ (open symbols) for $d+Au$ collisions and various event centrality classes at $\sqrt{s_{NN}}=200$ GeV.

High transverse-momentum spectra ($p_{T} > 2.5$ GeV/c) of charged pions, protons, and antiprotons for the rapidity regions $|y| < 0.5$ (solid symbols) and $0.5 < |y| < 1.0$ (open symbols) for $d+Au$ collisions and various event centrality classes at $\sqrt{s_{NN}}=200$ GeV.

High transverse-momentum rapidity asymmetry factor ($Y_{\scriptsize{\mbox{Asym}}}$) for $\pi^{+}+\pi^{-}$ and $p+\bar{p}$ for $|y| < 0.5$ and $0.5 < |y| < 1.0$ for minimum bias $d+Au$ collisions at $\sqrt{s_{NN}}=200$ GeV. For comparison the inclusive charged hadron results from STAR [5] are also shown by the curves.

Centrality dependence of high transverse-momentum rapidity asymmetry factor ($Y_{\scriptsize{\mbox{Asym}}}$) for $\pi^{+}+\pi^{-}$ and $p+\bar{p}$ for $|y| < 0.5$ (left panels) and $0.5 < |y| < 1.0$ (right panels) for $d+Au$ collisions at $\sqrt{s_{NN}}=200$ GeV.

Centrality dependence of high transverse-momentum rapidity asymmetry factor ($Y_{\scriptsize{\mbox{Asym}}}$) for $\pi^{+}+\pi^{-}$ and $p+\bar{p}$ for $|y| < 0.5$ (left panels) and $0.5 < |y| < 1.0$ (right panels) for $d+Au$ collisions at $\sqrt{s_{NN}}=200$ GeV.

Variation of nuclear modification factor ($R_{CP}$) for $\pi^{+}+\pi^{-}$ and $p+\bar{p}$ with rapidity for $p_{T} > 2.5$ GeV/c for $d+Au$ collisions at $\sqrt{s_{NN}}=200$ GeV. Also shown for comparison are the $R_{CP}$ values for inclusive charged hadrons as a function of pseudorapidity [5]. The errors shown as boxes are the systematic errors. The error due to number of binary collisions is $\sim 14\%$ and is not shown in the figure.

Variation of $\pi^{-} / \pi^{+}$ and $\bar{p} / p$ with rapidity for $2.5 < p_{T} < 10$ GeV/c for peripheral ($40-100\%$) and n-tag events for $d+Au$ collisions at $\sqrt{s_{NN}}=200$ GeV. Also shown for comparison are the $\bar{p} / p$ for minimum bias $p+p$ collisions. The boxes are the systematic errors. The ratios for n-tag events are shifted by 0.05 units in rapidity and those for $p+p$ collisions by -0.05 units in rapidity for clarity of presentation.

Variation of $\pi^{-} / \pi^{+}$ and $\bar{p} / p$ with rapidity for $2.5 < p_{T} < 10$ GeV/c for peripheral ($40-100\%$) and n-tag events for $d+Au$ collisions at $\sqrt{s_{NN}}=200$ GeV. Also shown for comparison are the $\bar{p} / p$ for minimum bias $p+p$ collisions. The boxes are the systematic errors. The ratios for n-tag events are shifted by 0.05 units in rapidity and those for $p+p$ collisions by -0.05 units in rapidity for clarity of presentation.

Variation of double ratio $(\pi^{-} / \pi^{+})_{\scriptsize{\mbox{n-tag}}}/(\pi^{-} / \pi^{+})_{40-100\%}$ and $(\bar{p} / p)_{\scriptsize{\mbox{n-tag}}}/(\bar{p} / p)_{40-100\%}$ with rapidity for $2.5 < p_{T} < 10$ GeV/c for $d+Au$ collisions at $\sqrt{s_{NN}}=200$ GeV. The boxes are the systematic errors.

The upper panel shows $v_{2}$ vs centrality using the conventional method, where the circles and triangles represent $v_{2}$ with and without $p_{t}$ weighting, respectively. The statistical error is smaller than the symbol size. The lower panel shows the statistical error on $v_{2}$ with $p_{t}$ weighting divided by the same without weighting.

The upper panel shows $v_{2}$ vs centrality using the conventional method, where the circles and triangles represent $v_{2}$ with and without $p_{t}$ weighting, respectively. The statistical error is smaller than the symbol size. The lower panel shows the statistical error on $v_{2}$ with $p_{t}$ weighting divided by the same without weighting.

The upper panel presents $v_{2}$ vs centrality from the scalar product method (triangles) and the conventional random subevent method (circles). All statistical errors are smaller than the symbol size. The statistical error for the scalar product method divided by that for the conventional method is shown in the lower panel.

The upper panel presents $v_{2}$ vs centrality from the scalar product method (triangles) and the conventional random subevent method (circles). All statistical errors are smaller than the symbol size. The statistical error for the scalar product method divided by that for the conventional method is shown in the lower panel.

Elliptic flow as determined from the fits to the $q$ distributions in different centrality bins. The circles are from the standard method with random subevents. For the squares, all the centralities were fit separately. For the triangles, centrality bins 2-8 were fit with the same value of the nonflow parameter.

Measured elliptic flow vs centrality for $Au+Au$ at $\sqrt{s_{NN}}=130$ GeV. The circles show the conventional $v_{2}$ with estimated systematic uncertainty due to nonflow [37], the stars show the fourth-order cumulant $v_{2}$ from the generating function, the crosses show the conventional $v_{2}$ from quarter events, and the squares show the fourth-order cumulant $v_{2}$ from the four-subevent method.

Reconstructed $v_{2}$ vs pseudorapidity from the conventional method (circles), from the second-order cumulant method (triangles), and from the fourth-order cumulant method (stars), in eight centrality bins. The upper left panel shows the most peripheral events, and the lower right the most central.

Reconstructed $v_{2}$ vs pseudorapidity from the conventional method (circles), from the second-order cumulant method (triangles), and from the fourth-order cumulant method (stars), in eight centrality bins. The upper left panel shows the most peripheral events, and the lower right the most central.

Reconstructed $v_{2}$ vs pseudorapidity from the conventional method (circles), from the second-order cumulant method (triangles), and from the fourth-order cumulant method (stars), in eight centrality bins. The upper left panel shows the most peripheral events, and the lower right the most central.

Reconstructed $v_{2}$ vs pseudorapidity from the conventional method (circles), from the second-order cumulant method (triangles), and from the fourth-order cumulant method (stars), in eight centrality bins. The upper left panel shows the most peripheral events, and the lower right the most central.

Reconstructed $v_{2}$ vs pseudorapidity from the conventional method (circles), from the second-order cumulant method (triangles), and from the fourth-order cumulant method (stars), in eight centrality bins. The upper left panel shows the most peripheral events, and the lower right the most central.

Reconstructed $v_{2}$ vs pseudorapidity from the conventional method (circles), from the second-order cumulant method (triangles), and from the fourth-order cumulant method (stars), in eight centrality bins. The upper left panel shows the most peripheral events, and the lower right the most central.

Reconstructed $v_{2}$ vs pseudorapidity from the conventional method (circles), from the second-order cumulant method (triangles), and from the fourth-order cumulant method (stars), in eight centrality bins. The upper left panel shows the most peripheral events, and the lower right the most central.

Reconstructed $v_{2}$ vs pseudorapidity from the conventional method (circles), from the second-order cumulant method (triangles), and from the fourth-order cumulant method (stars), in eight centrality bins. The upper left panel shows the most peripheral events, and the lower right the most central.

Reconstructed $v_{2}$ vs $p_{t}$ from the conventional method (circles), from the second-order cumulant method (triangles), and from the fourth-order cumulant method (stars), in eight centrality bins. The upper left panel shows the most peripheral events, and the lower right the most central.

Reconstructed $v_{2}$ vs $p_{t}$ from the conventional method (circles), from the second-order cumulant method (triangles), and from the fourth-order cumulant method (stars), in eight centrality bins. The upper left panel shows the most peripheral events, and the lower right the most central.

Reconstructed $v_{2}$ vs $p_{t}$ from the conventional method (circles), from the second-order cumulant method (triangles), and from the fourth-order cumulant method (stars), in eight centrality bins. The upper left panel shows the most peripheral events, and the lower right the most central.

Reconstructed $v_{2}$ vs $p_{t}$ from the conventional method (circles), from the second-order cumulant method (triangles), and from the fourth-order cumulant method (stars), in eight centrality bins. The upper left panel shows the most peripheral events, and the lower right the most central.

Reconstructed $v_{2}$ vs $p_{t}$ from the conventional method (circles), from the second-order cumulant method (triangles), and from the fourth-order cumulant method (stars), in eight centrality bins. The upper left panel shows the most peripheral events, and the lower right the most central.

Reconstructed $v_{2}$ vs $p_{t}$ from the conventional method (circles), from the second-order cumulant method (triangles), and from the fourth-order cumulant method (stars), in eight centrality bins. The upper left panel shows the most peripheral events, and the lower right the most central.

Reconstructed $v_{2}$ vs $p_{t}$ from the conventional method (circles), from the second-order cumulant method (triangles), and from the fourth-order cumulant method (stars), in eight centrality bins. The upper left panel shows the most peripheral events, and the lower right the most central.

Reconstructed $v_{2}$ vs $p_{t}$ from the conventional method (circles), from the second-order cumulant method (triangles), and from the fourth-order cumulant method (stars), in eight centrality bins. The upper left panel shows the most peripheral events, and the lower right the most central.

Elliptic flow vs pseudorapidity from the conventional method (circles), from the second-order cumulant method (triangles), from quarter events (crosses), and from the fourth-order cumulant method (stars), averaged over all centralities from bin 2-7, as defined in Figs. 14 and 15.

Elliptic flow vs transverse momentum from the conventional method (circles), from the second-order cumulant method (triangles), from quarter events (crosses), and from the fourth-order cumulant method (stars), averaged over all centralities from bin 2-7, as defined in Figs. 14 and 15.

The ratio of $v_{2}$ from the fourth-order cumulant divided by $v_{2}$, from the conventional method as a function of $p_{t}$, averaged over all centralities from bin 2-7, as defined in Figs. 14 and 15.

The ratio of $v_{2}$ from quarter events divided by the conventional $v_{2}$ as a function of $p_{t}$. In both cases, event planes were constructed from low-$p_{t}$ (< 0.5 GeV/c) particles. The data are averaged over all centralities from bin 2-7, as defined in Figs. 14 and 15.

$v_{2}/\varepsilon$ as a function of charged particle density in $Au+Au$ collisions. Data are from E877 at the AGS (squares), NA49 at the SPS (circles), and STAR at RHIC (stars). The AGS and SPS data have been obtained by conventional flow analysis. The STAR measurements are at $\sqrt{s_{NN}}=130$ GeV, and correspond to the final corrected elliptic flow based on fourth-order cumulants, and we assume $dN/dy=1.15dN/d\eta$. The horizontal shaded bands indicate the hydrodynamic limits for different beam energies [44].