Systematic study of azimuthal anisotropy in Cu + Cu and Au + Au collisions at $\sqrt{s_{\mathit{NN}}}=62.4$ and 200 GeV

We have studied the dependence of azimuthal anisotropy $v_2$ for inclusive and identified charged hadrons in $\mathrm{Au}+\mathrm{Au}$ and $\mathrm{Cu}+\mathrm{Cu}$ collisions on collision energy, species, and centrality. The values of $v_2$ as a function of transverse momentum $p_T$ and centrality in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{\mathit{NN}}}}=200$ and 62.4 GeV are the same within uncertainties. However, in $\mathrm{Cu}+\mathrm{Cu}$ collisions we observe a decrease in $v_2$ values as the collision energy is reduced from 200 to 62.4 GeV. The decrease is larger in the more peripheral collisions. By examining both $\mathrm{Au}+\mathrm{Au}$ and $\mathrm{Cu}+\mathrm{Cu}$ collisions we find that $v_2$ depends both on eccentricity and the number of participants, $N_{\mathrm{part}}$. We observe that $v_2$ divided by eccentricity ($\varepsilon$) monotonically increases with $N_{\mathrm{part}}$ and scales as $N_{\mathrm{part}}^{1/3}$. The $\mathrm{Cu}+\mathrm{Cu}$ data at 62.4 GeV falls below the other scaled $v_2$ data. For identified hadrons, $v_2$ divided by the number of constituent quarks $n_q$ is independent of hadron species as a function of transverse kinetic energy $K{E}_T=m_T-m$ between $0.1<K{E}_T/n_q<1$ GeV. Combining all of the above scaling and normalizations, we observe a near-universal scaling, with the exception of the $\mathrm{Cu}+\mathrm{Cu}$ data at 62.4 GeV, of $v_2/(n_q·\varepsilon ·N_{\mathrm{part}}^{1/3})$ vs $K{E}_T/n_q$ for all measured particles.

Figure 1

Installed and active detectors for the RUN-4 configuration of the PHENIX experiment. Shown are the two central spectrometer arms viewed in a cut through the collision vertex.

Figure 2

(a) Track/hit matching distribution of $d\varphi /\sigma$ at PC3 without $E/p$ cut for indicated $p_T$ bins; (b) same quantity, but after applying an $E/p>0.2$ cut.

Figure 3

Distributions of $t-t_{\pi \mathrm{expected}}$, the difference between the measured TOF in the TOF (upper) and EMC (lower) and the time calculated assuming each candidate track is a pion. Resolutions are ${\sigma }_T\sim 120$ ps for TOF and ${\sigma }_T\sim 400$ ps for EMCal in $\mathrm{Au}+\mathrm{Au}$ at 200-GeV data.

Figure 4

Second-order event-plane resolution vs centrality in $\mathrm{Au}+\mathrm{Au}$ and $\mathrm{Cu}+\mathrm{Cu}$ at 200 and 62.4 GeV. The event plane is measured by BBC.

Figure 5

(a) $v_2$ vs centrality with three different reaction planes (BBC South, North, South-North combined) for $\mathrm{Au}+\mathrm{Au}$ 200 GeV. (b) The ratio of $v_2$ with BBC South or North reaction plane to $v_2$ with South-North combined.

Figure 6

$v_2$ for inclusive charged hadrons in $\mathrm{Au}+\mathrm{Au}$ at $\sqrt{s_{{}_{\mathit{NN}}}}=200$ GeV for the centralities indicated. The error bars show statistical uncertainties and the bands show systematic uncertainties. In many cases, the systematic uncertainties are smaller than the symbols.

Figure 7

$v_2$ for inclusive charged hadrons in $\mathrm{Au}+\mathrm{Au}$ at $\sqrt{s_{{}_{\mathit{NN}}}}=62.4$ and 200 GeV for the centralities indicated. The error bars show statistical uncertainties and the bands show systematic uncertainties. In many cases, the systematic uncertainties are smaller than the symbols.

Figure 8

$v_2$ for inclusive charged hadrons in $\mathrm{Cu}+\mathrm{Cu}$ at $\sqrt{s_{{}_{\mathit{NN}}}}=62.4$ GeV compared with 200 GeV [7] for the centralities indicated. The error bars show statistical uncertainties and the bands show systematic uncertainties. In many cases, the systematic uncertainties are smaller than the symbols.

Figure 9

Comparison of integrated $v_2$ at $\sqrt{s_{{}_{\mathit{NN}}}}=62.4$ and 200 GeV in $\mathrm{Au}+\mathrm{Au}$. Solid symbols indicate $\sqrt{s_{{}_{\mathit{NN}}}}=200$ GeV and open symbols indicate $\sqrt{s_{{}_{\mathit{NN}}}}=62.4$ GeV. Ranges of $p_T$ integrated are 0.2–1.0 (circles), 1.0–2.0 (squares), and 2.0–4.0 (triangles) $\mathrm{GeV}/c$. The bars indicate the statistical uncertainties and the boxes indicate the systematic uncertainties. In many cases, the systematic uncertainties are smaller than the symbols.

Figure 10

Comparison of integrated $v_2$ at $\sqrt{s_{{}_{\mathit{NN}}}}=62.4$ and 200 GeV in $\mathrm{Cu}+\mathrm{Cu}$. Open symbols indicate $\sqrt{s_{{}_{\mathit{NN}}}}=62.4$ GeV and solid symbols indicate $\sqrt{s_{{}_{\mathit{NN}}}}=200$ GeV. Ranges of $p_T$ integrated are 0.2–1.0 (circles), 1.0–2.0 (squares), and 2.0–4.0 (triangles) $\mathrm{GeV}/c$. The bars indicate the statistical uncertainties and the boxes indicate the systematic uncertainties. In many cases, the systematic uncertainties are smaller than the symbols.

Figure 11

The top three panels show the comparison of integrated $v_2$ as a function of $N_{\mathrm{part}}$ and the bottom three panels show the comparison of the normalized $v_2/\varepsilon$ vs $N_{\mathrm{part}}$ in both $\mathrm{Au}+\mathrm{Au}$ and $\mathrm{Cu}+\mathrm{Cu}$ at 200 and 62.4 GeV. The ranges of $p_T$ integration are 0.2–1.0, 1.0–2.0, and 2.0–4.0 $\mathrm{GeV}/c$ from left to right and top to bottom panels, respectively. Both statistical and systematic uncertainties are included in the error bars.

Figure 12

Comparison of $v_2$ ($p_T$) at 200 GeV for two example systems with different collision size ($\mathrm{Au}+\mathrm{Au}$ or $\mathrm{Cu}+\mathrm{Cu}$) but approximately the same $\varepsilon$. Black symbols indicate $\mathrm{Au}+\mathrm{Au}$ and red symbols indicate $\mathrm{Cu}+\mathrm{Cu}$. The average number of participants $N_{\mathrm{part}}$ is 166.6 for 20%–30%, 114.2 for 30%–40%, and 45.5 for 50%–60% at $\mathrm{Au}+\mathrm{Au}$ collisions, and $N_{\mathrm{part}}$ is 73.6 for 10%–20%, 53.0 for 20%–30%, and 25.4 for 40%–50% at $\mathrm{Cu}+\mathrm{Cu}$ collisions.

Figure 13

Comparison of integrated $v_2/(\varepsilon ·N_{\mathrm{part}}^{1/3}$) as a function of $N_{\mathrm{part}}$ for two collision energies and two collision systems, $\mathrm{Au}+\mathrm{Au}$ at 200 GeV, $\mathrm{Au}+\mathrm{Au}$ at 62.4 GeV, $\mathrm{Cu}+\mathrm{Cu}$ at 200 GeV, and $\mathrm{Cu}+\mathrm{Cu}$ at 62.4 GeV. Ranges of $p_T$ integration are 0.2–1.0, 1.0–2.0, and 2.0–4.0 $\mathrm{GeV}/c$ from left to right panels, respectively. All uncertainties from the measured $v_2, \varepsilon$, and $N_{\mathrm{part}}$ are included in the error bars.

Figure 14

$v_2$ vs $p_T$ for $\pi /K/p$ emitted from $\mathrm{Au}+\mathrm{Au}$ at 62.4 and 200 GeV and $\mathrm{Cu}+\mathrm{Cu}$ at 200-GeV collisions for the centralities indicated. The lines for each point indicate the statistical uncertainties, and the boxes are systematic uncertainties. In many cases, the systematic uncertainties are smaller than the symbols.

Figure 15

Comparison of $v_2$ between $\sqrt{s_{{}_{\mathit{NN}}}}=62.4$ and 200 GeV for $\pi /K/p$ emitted from 0%–10%, 10%–20%, and 20%–30% central $\mathrm{Au}+\mathrm{Au}$ collisions. Both results for all species agree within the errors. The lines indicate the statistical uncertainties at each point and the boxes indicate the systematic uncertainties. In many cases, the systematic uncertainties are smaller than the symbols.

Figure 16

Comparison of the $v_2$ of particles and antiparticles for a minimum bias sample 0%–92% at 200 GeV and 10%–40% central at 62.4 GeV in $\mathrm{Au}+\mathrm{Au}$ collisions. The lines for each point indicate the statistical uncertainties, and the boxes are systematic uncertainties. In many cases, the systematic uncertainties are smaller than the symbols.

Figure 17

The ratio $v_2/n_q$ vs $p_T/n_q$ for $\pi /K/p$ emitted from $\mathrm{Au}+\mathrm{Au}$ at 62.4- and 200-GeV collisions and $\mathrm{Cu}+\mathrm{Cu}$ at 200-GeV collisions for the centralities indicated. The lines for each point indicate the statistical uncertainties, and the boxes are systematic uncertainties. In many cases, the systematic uncertainties are smaller than the symbols.

Figure 18

The ratio $v_2/n_q$ vs $K{E}_T/n_q$ for $\pi /K/p$ emitted from $\mathrm{Au}+\mathrm{Au}$ at 62.4- and 200-GeV collisions and $\mathrm{Cu}+\mathrm{Cu}$ at 200-GeV collisions for the centralities indicated. The lines for each point indicate the statistical uncertainties and the boxes are systematic uncertainties. In many cases, the systematic uncertainties are smaller than the symbols.

Figure 19

The ratio of $v_2/n_q$ vs $K{E}_T/n_q$ to the fit for $\pi /K/p$ emitted from $\mathrm{Au}+\mathrm{Au}$ at 62.4- and 200-GeV collisions and $\mathrm{Cu}+\mathrm{Cu}$ at 200-GeV collisions for the centralities indicated. The lines for each point indicate the statistical uncertainties.

Figure 20

The left panel shows $v_2$ vs $p_T$; the right panel is the ratio $v_2/n_q$ vs $p_T/n_q$ for the indicated hadrons emitted from 10%–40% central $\mathrm{Au}+\mathrm{Au}$ collisions in $\mathrm{Au}+\mathrm{Au}$ at 62.4 GeV. The error bars include both systematic and statistical uncertainties.

Figure 21

The ratio $v_2/n_q$ vs $K{E}_T/n_q$ for the indicated hadrons emitted from 10%–40% central $\mathrm{Au}+\mathrm{Au}$ collisions at 62.4 GeV. The error bars include both systematic and statistical uncertainties.

Figure 22

The left panel shows $v_2$ vs $p_T$ and the right panel shows $v_2$/($\varepsilon · N_{\mathrm{part}}^{1/3} · n_q$) vs $K{E}_T/n_q$ for $\pi /K/p$ in $\mathrm{Au}+\mathrm{Au}$ at 200 GeV, in $\mathrm{Au}+\mathrm{Au}$ at 62.4 GeV, and in $\mathrm{Cu}+\mathrm{Cu}$ at 200 GeV for five centrality bins over 0%–50% in 10% steps for each system. There are 45 data sets in each panel.