Measurements of directed, elliptic, and triangular flow in Cu + Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV

Measurements of anisotropic flow Fourier coefficients ($v_n$) for inclusive charged particles and identified hadrons ${\pi }^{\pm }, K^{\pm }, p$, and $\overline{p}$ produced at midrapidity in $\mathrm{Cu}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{\mathit{NN}}}}=200$ GeV are presented. The data were collected in 2012 by the PHENIX experiment at the Relativistic Heavy-Ion Collider (RHIC). The particle azimuthal distributions with respect to different-order symmetry planes ${\mathrm{\Psi }}_n$, for $n=1$, 2, and 3 are studied as a function of transverse momentum $p_T$ over a broad range of collision centralities. Mass ordering, as expected from hydrodynamic flow, is observed for all three harmonics. The charged-particle results are compared with hydrodynamical and transport model calculations. We also compare these $\mathrm{Cu}+\mathrm{Au}$ results with those in $\mathrm{Cu}+\mathrm{Cu}$ and $\mathrm{Au}+\mathrm{Au}$ collisions at the same $\sqrt{s_{\mathit{NN}}}$ and find that the $v_2$ and $v_3$, as a function of transverse momentum, follow a common scaling with $1/\left({\varepsilon }_n{N}_{\mathrm{part}}^{1/3}\right)$.

Figure 1

The PHENIX detector configuration for RHIC Run-12 data-taking period

Figure 2

Sketch of a noncentral heavy-ion collision. See text for description of the figure.

Figure 3

(a) Event-plane resolution as a function of centrality for the SMDS detectors. (b), (c) Second- and third-order event-plane resolution. The BBC event-plane resolution is obtained from two subevents and BBCS, BBCN, CNT from three subevents as a function of centrality.

Figure 4

$v_1\left(p_T\right)$ for charged hadrons measured with respect to the Cu spectator neutrons at midrapidity in $\mathrm{Cu}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV. Error bars show the statistical uncertainties, and shaded boxes indicate the systematic uncertainties.

Figure 5

$v_2\left(p_T\right)$ for charged hadrons measured at midrapidity in $\mathrm{Cu}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV. Uncertainties are as in Fig. 4.

Figure 6

$v_3\left(p_T\right)$ for charged hadrons measured at midrapidity in $\mathrm{Cu}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV. Uncertainties are as in Fig. 4.

Figure 7

The second-order Fourier coefficients $v_2\left(p_T\right)$ for charge-combined identified hadrons ${\pi }^{\pm }, K^{\pm }, p$, and $\overline{p}$ measured at midrapidity in $\mathrm{Cu}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV for the centrality classes marked in each panel. The symbols represent the measured $v_2\left(p_T\right)$ values, the error bars show the statistical uncertainties, and the shaded boxes indicate the systematic uncertainties from PID. The full systematic uncertainties, that are mostly common to all particle species, are shown in Table 3.

Figure 8

The third-order Fourier coefficients $v_3\left(p_T\right)$ for charge-combined identified hadrons ${\pi }^{\pm }, K^{\pm }, p$, and $\overline{p}$ measured at midrapidity in $\mathrm{Cu}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV for 0%–30% centrality. The symbols represent the measured $v_3\left(p_T\right)$ values, the error bars show the statistical uncertainties, and the shaded boxes indicate the systematic uncertainties from PID. The full systematic uncertainties, which are mostly common to all particle species, are shown in Table 3.

Figure 9

The first-order Fourier coefficients $v_1\left(p_T\right)$ for charge-combined identified hadrons ${\pi }^{\pm }, K^{\pm }, p$, and $\overline{p}$ measured at midrapidity in $\mathrm{Cu}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV for 10%–50% centrality. The symbols represent the measured $v_1\left(p_T\right)$ values with respect to the Cu spectator neutrons, the error bars show the statistical uncertainties, and the shaded boxes indicate the systematic uncertainties from PID. The full systematic uncertainties, which are mostly common to all particle species, are shown in Table 2.

Figure 10

The second-order Fourier coefficients $v_2\left(p_T\right)$ for charged hadrons measured at midrapidity in $\mathrm{Cu}+\mathrm{Au}, \mathrm{Au}+\mathrm{Au}$ [12], and $\mathrm{Cu}+\mathrm{Cu}$ [12] collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV. In each panel, the $v_2\left(p_T\right)$ coefficients are compared for the same centrality class, as marked in the figure. The symbols represent the measured $v_2\left(p_T\right)$ values, the error bars show the statistical uncertainties, and the shaded boxes indicate the systematic uncertainties.

Figure 11

Scaled second-order Fourier coefficients $v_2\left(p_T\right)/{\varepsilon }_2$ for charged hadrons measured at midrapidity in $\mathrm{Cu}+\mathrm{Au}, \mathrm{Au}+\mathrm{Au}$ [12], and $\mathrm{Cu}+\mathrm{Cu}$ [12] collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV. In each panel, the $v_2\left(p_T\right)$ values measured in the centrality classes marked in the figure are scaled by the average second-order participant eccentricity ${\varepsilon }_2$ in the initial state of the collisions as determined by a Monte Carlo Glauber calculation described in the text. The symbols represent the scaled $v_2\left(p_T\right)/{\varepsilon }_2$ values, the error bars show the statistical uncertainties, and the shaded boxes indicate the systematic uncertainties.

Figure 12

Scaled second-order Fourier coefficients $v_2\left(p_T\right)/\left({\varepsilon }_2{N}_{\mathrm{part}}^{1/3}\right)$ for charged hadrons measured at midrapidity in $\mathrm{Cu}+\mathrm{Au}, \mathrm{Au}+\mathrm{Au}$ [12], and $\mathrm{Cu}+\mathrm{Cu}$ [12] collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV. In each panel, the $v_2\left(p_T\right)$ values measured in the centrality classes marked in the figure are scaled by the average second-order participant eccentricity ${\varepsilon }_2$ in the initial state of the collisions as determined by a Monte Carlo Glauber calculation described in the text, and the corresponding number of nucleon participants $N_{\mathrm{part}}^{1/3}$. The symbols represent the scaled $v_2\left(p_T\right)/\left({\varepsilon }_2{N}_{\mathrm{part}}^{1/3}\right)$ values, the error bars show the statistical uncertainties, and the shaded boxes indicate the systematic uncertainties.

Figure 13

The third-order Fourier coefficients $v_3\left(p_T\right)$ for charged hadrons measured at midrapidity in $\mathrm{Cu}+\mathrm{Au}$ and $\mathrm{Au}+\mathrm{Au}$ [22] collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV. In each panel, the $v_3\left(p_T\right)$ coefficients are compared for the same centrality class, as marked in the figure. The symbols represent the measured $v_3\left(p_T\right)$ values, the error bars show the statistical uncertainties, and the shaded boxes indicate the systematic uncertainties.

Figure 14

Scaled third-order Fourier coefficients $v_3\left(p_T\right)/{\varepsilon }_3$ for charged hadrons measured at midrapidity in $\mathrm{Cu}+\mathrm{Au}$ and $\mathrm{Au}+\mathrm{Au}$ [22] collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV. In each panel, the $v_3\left(p_T\right)$ values measured in the centrality classes marked in the figure are scaled by the average third-order participant eccentricity ${\varepsilon }_3$ in the initial state of the collisions as determined by a Monte Carlo Glauber calculation described in the text. The symbols represent the scaled $v_3\left(p_T\right)/{\varepsilon }_3$ values, and the error bars show the statistical uncertainties. The shaded boxes indicate the systematic uncertainties in the $\mathrm{Cu}+\mathrm{Au}$ measurements, and the lines around the points marked with a cross show the systematic uncertainties in the $\mathrm{Au}+\mathrm{Au}$ measurements.

Figure 15

Scaled third-order Fourier coefficients $v_3\left(p_T\right)/\left({\varepsilon }_3{N}_{\mathrm{part}}^{1/3}\right)$ for charged hadrons measured at midrapidity in $\mathrm{Cu}+\mathrm{Au}$ and $\mathrm{Au}+\mathrm{Au}$ [22] collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV. In each panel, the $v_3\left(p_T\right)$ values measured in the centrality classes marked in the figure are scaled by the average third-order participant eccentricity ${\varepsilon }_3$ in the initial state of the collisions as determined by a Monte Carlo Glauber calculation described in the text and the corresponding number of nucleon participants $N_{\mathrm{part}}^{1/3}$. The symbols represent the scaled $v_3\left(p_T\right)/\left({\varepsilon }_3{N}_{\mathrm{part}}^{1/3}\right)$ values, and the error bars show the statistical uncertainties. The shaded boxes indicate the systematic uncertainties in the $\mathrm{Cu}+\mathrm{Au}$ measurements, and the lines around the points marked with a cross show the systematic uncertainties in the $\mathrm{Au}+\mathrm{Au}$ measurements.

Figure 16

The second-order Fourier coefficients $v_2\left(p_T\right)$ for charged hadrons measured at midrapidity in $\mathrm{Cu}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV in comparison with hydrodynamics calculations for the centrality classes marked in each panel. The symbols represent the measured $v_2\left(p_T\right)$ values, the error bars show the statistical uncertainties, and the shaded boxes indicate the systematic uncertainties. The theoretical calculations, shown with the solid and dashed lines, are performed with two different values of the specific viscosity $\eta /s$ marked in the figure.

Figure 17

The third-order Fourier coefficients $v_3\left(p_T\right)$ for charged hadrons measured at midrapidity in $\mathrm{Cu}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV in comparison with hydrodynamics calculations for the centrality classes marked in each panel. The symbols represent the measured $v_3\left(p_T\right)$ values, the error bars show the statistical uncertainties, and the shaded boxes indicate the systematic uncertainties. The theoretical calculations, shown with the solid and dashed lines, are performed with two different values of the specific viscosity $\eta /s$ marked in the figure.

Figure 18

The second-order Fourier coefficients $v_2\left(p_T\right)$ for charged hadrons measured at midrapidity in $\mathrm{Cu}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV in comparison to AMPT model calculation for the centrality classes marked in each panel. The symbols represent the measured $v_2\left(p_T\right)$ values, the error bars show the statistical uncertainties, and the shaded boxes indicate the systematic uncertainties. For the theoretical calculations, which are shown with lines, only statistical uncertainties are plotted.

Figure 19

The third-order Fourier coefficients $v_3\left(p_T\right)$ for charged hadrons measured at midrapidity in $\mathrm{Cu}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV in comparison to AMPT model calculation for the centrality classes marked in each panel. The symbols represent the measured $v_3\left(p_T\right)$ values, the error bars show the statistical uncertainties, and the shaded boxes indicate the systematic uncertainties. For the theoretical calculations, which are shown with lines, only statistical uncertainties are plotted.

Figure 20

The top panels show the maximum-normalized distribution of first-order participant plane angle ${\mathrm{\Psi }}_1$ computed from the initial coordinates of participant nucleons determined with (a) black-disk, and (b) gray-disk Monte Carlo Glauber simulations. The bottom panels show AMPT $v_1$ computed with respect to the impact parameter $\vec{b}$, and ${\mathrm{\Psi }}_1$ using (c) black-disk and (d) gray-disk Monte Carlo for the initial conditions.