Azimuthal anisotropy in Cu+Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV

The azimuthal anisotropic flow of identified and unidentified charged particles has been systematically studied in Cu+Au collisions at $\sqrt{s_{{}_{\mathit{NN}}}}=200$ GeV for harmonics $n=1–4$ in the pseudorapidity range $\left|\eta \right|<1$. The directed flow in Cu+Au collisions is compared with the rapidity-odd and, for the first time, the rapidity-even components of charged particle directed flow in Au+Au collisions at $\sqrt{s_{{}_{\mathit{NN}}}}=200$ GeV. The slope of the directed flow pseudorapidity dependence in Cu+Au collisions is found to be similar to that in Au+Au collisions, with the intercept shifted toward positive pseudorapidity values, i.e., the Cu-going direction. The mean transverse momentum projected onto the spectator plane $\langle p_x\rangle$ in Cu+Au collision also exhibits approximately linear dependence on pseudorapidity with the intercept at about $\eta \approx -0.4$ (shifted from zero in the Au-going direction), closer to the rapidity of the Cu+Au system center of mass. The observed dependencies find a natural explanation in a picture of the directed flow originating partly due the “tilted source” and partly due to the asymmetry in the initial density distribution. A charge dependence of $\langle p_x\rangle$ was also observed in Cu+Au collisions, consistent with an effect of the initial electric field created by charge difference of the spectator protons in two colliding nuclei. The rapidity-even component of directed flow in Au+Au collisions is close to that in Pb+Pb collisions at $\sqrt{s_{{}_{\mathit{NN}}}}=2.76$ TeV, indicating a similar magnitude of dipolelike fluctuations in the initial-state density distribution. Higher harmonic flow in Cu+Au collisions exhibits similar trends to those observed in Au+Au and Pb+Pb collisions and is qualitatively reproduced by a viscous hydrodynamic model and a multiphase transport model. For all harmonics with $n\ge 2$ we observe an approximate scaling of $v_n$ with the number of constituent quarks; this scaling works as well in Cu+Au collisions as it does in Au+Au collisions.

Figure 1

Cartoon illustrating different contributions to the directed flow and their effect on the (pseudo)rapidity dependence of mean $v_1$. Panel (a) shows the effect of the “tilted source,” while panels (b) and (c) include additional effects of asymmetric density distribution and asymmetry in number of participating nucleons. In panels (b) and (c), the dashed lines represent the effect of the “tilted source” only and the solid lines represent the two effects combined.

Figure 2

Cartoon of Cu+Au collision indicating different event planes used in the analysis. Note that ${\mathrm{\Psi }}_2$ and ${\mathrm{\Psi }}_2+\pi$ define the same plane.

Figure 3

Event plane resolutions as a function of centrality in Cu+Au collisions $\mathrm{at}\sqrt{s_{{}_{\mathit{NN}}}}=200$ GeV.

Figure 4

Directed flow of charged particles measured with respect to the target (ZDCE) and projectile (ZDCW) spectator planes and the mean transverse momentum projected onto the spectator planes, as a function of $\eta$ for $0.15<p_T<5\mathrm{GeV}/c$ in 10–40% centrality for Cu+Au (a),(b) and Au+Au (c),(d) collisions at $\sqrt{s_{{}_{\mathit{NN}}}}=200$ GeV. Open boxes show the systematic uncertainties. Note that the directed flow obtained with the target spectator plane ($v_1\left\{{\mathrm{\Psi }}_{\mathrm{SP}}^t\right\}$) is shown with opposite sign.

Figure 5

Charged particle “conventional” (left) and “fluctuation” (right) components of directed flow $v_1$ and momentum shift $\langle p_x\rangle /\langle p_T\rangle$ as a function of $\eta$ in 10–40% centrality for Cu+Au and Au+Au collisions $\mathrm{at}\sqrt{s_{{}_{\mathit{NN}}}}=200$ GeV, and Pb+Pb collisions $\mathrm{at}\sqrt{s_{{}_{\mathit{NN}}}}=2.76$ TeV [24]. Thick solid and dashed lines show the hydrodynamic model calculations with $\eta /s=0.08$ and 0.16, respectively, for Cu+Au collisions [49]. Thin lines in the left panel show a linear fit to the data. Open boxes represent systematic uncertainties.

Figure 6

Slopes and intercepts of $\langle p_x\rangle /\langle p_T\rangle \left(\eta \right)$ and $v_1\left(\eta \right)$ as a function of centrality in Cu+Au and Au+Au collisions $\mathrm{at}\sqrt{s_{{}_{\mathit{NN}}}}=200$ GeV. The solid line shows the center-of-mass rapidity in Cu+Au collisions calculated by Cu and Au participants in a Glauber model. Open boxes represent systematic uncertainties.

Figure 7

Centrality dependence of the even (fluctuation) components of $v_1$ and $\langle p_x\rangle /\langle p_T\rangle$ in Cu+Au and Au+Au collisions $\mathrm{at}\sqrt{s_{{}_{\mathit{NN}}}}=200$ GeV and Pb+Pb collisions $\mathrm{at}\sqrt{s_{{}_{\mathit{NN}}}}=2.76$ TeV [24]. Open boxes represent systematic uncertainties.

Figure 8

The conventional (a)–(e) and fluctuation (f)–(j) components of directed flow, $v_1^{\mathrm{conv}\left(\mathrm{odd}\right)}$ and $v_1^{\mathrm{fluc}\left(\mathrm{even}\right)}$, of charged particles as a function of $p_T$ for different collision centralities in Cu+Au and Au+Au collisions. Open boxes represent systematic uncertainties. The broken line in panel (b) shows the viscous hydrodynamic calculation for Cu+Au collisions [49].

Figure 9

Directed flow of charged particles as a function of $p_T$ (a) and $\eta$ (b) in the 10–40% centrality bin measured with the ZDC-SMD event planes and three-point correlator in Cu+Au collisions. The $p_T$ dependence was measured in $\left|\eta \right|<1$ and the $\eta$ dependence was integrated over $0.15<p_T<5\mathrm{GeV}/c$. Open boxes represent systematic uncertainties.

Figure 10

Directed flow of ${\pi }^{+}+{\pi }^{-}$, $K^{+}+K^{-}$, and $p+\overline{p}$ as a function of $p_T$ for $\left|\eta \right|<1$ in the 10–40% centrality bin. The $p_T$-uncorrelated systematic uncertainties are shown with lines around $v_1=0$ for each particle species. $p_T$-correlated systematic uncertainty is shown only for pions with a shaded band.

Figure 11

Positively and negatively charged particles $\langle p_x\rangle$ and the difference $\mathrm{\Delta }\langle p_x\rangle$ as a function of centrality in Au+Au and Cu+Au collisions. Open and shaded boxes show systematic uncertainties.

Figure 12

Directed flow of ${\pi }^{+}$, ${\pi }^{-}$, $K^{+}$, $K^{-}$, $p$, and $\overline{p}$ measured in $\left|\eta \right|<1$ as a function of $p_T$ for the 10–40% centrality bin in Cu+Au collisions (top panels), where only the statistical uncertainties are shown. The differences in the directed flow between positively and negatively charged particles are shown in bottom panels, where the open boxes show the systematic uncertainties.

Figure 13

Higher harmonic flow coefficients $v_n\left\{{\mathrm{\Psi }}_n\right\}$ of charged particles in Cu+Au collisions as a function of $p_T$ for six centrality bins. Colored boxes around the data points show $p_T$-uncorrelated systematic uncertainties and solid thin lines around $v_n=0$ show $p_T$-correlated systematic uncertainties. Results from the PHENIX experiment [53] are compared. Only statistical uncertainty is shown for $v_2\left\{{\mathrm{\Psi }}_2^{\mathrm{BBC}}\right\}$.

Figure 14

Higher harmonic flow coefficients $v_n$ of charged particles for two selected $p_T$ bins as a function of the number of participants calculated with a Monte Carlo Glauber simulation for Cu+Au and Au+Au collisions, comparing with results in Au+Au from the PHENIX experiment [5]. Open and shaded bands represent systematic uncertainties.

Figure 15

The second and third harmonic flow coefficients of charged particles as a function of $p_T$ measured with the event plane (EP) method and scalar product method, comparing to the viscous hydrodynamic calculations [49]. Panels (a) and (c) are for 0–5% centrality, panels (b) and (d) for 20–30% centrality.

Figure 16

Higher harmonic flow coefficients $v_n$ of charged particles as a function of $p_T$ comparing to the AMPT model [59], where solid lines are for default AMPT setup and dashed lines are for the string melting version with ${\sigma }_{\mathrm{parton}}=1.5$ mb.

Figure 17

The second and third harmonic flow coefficients of ${\pi }^{+}+{\pi }^{-}$, $K^{+}+K^{-}$, and $p+\overline{p}$ as a function of $p_T$ for four centrality bins. Solid lines represent $p_T$-uncorrelated systematic uncertainties for each species. Shaded bands represent $p_T$-correlated systematic uncertainties for pions.

Figure 18

Higher harmonic flow coefficients $v_n$ of ${\pi }^{+}+{\pi }^{-}$, $K^{+}+K^{-}$, and $p+\overline{p}$ as a function of $p_T$ in the 0–40% centrality bin. Solid lines represent $p_T$-uncorrelated systematic uncertainties for each species. Shaded bands represent $p_T$-correlated systematic uncertainties for pions.

Figure 19

NCQ scaling of $v_2$, $v_3$, and $v_4$ of ${\pi }^{+}+{\pi }^{-}$, $K^{+}+K^{-}$, and $p+\overline{p}$ as a function of $p_T/n_q$ in the 0–40% centrality bin. Solid lines represent $p_T$-uncorrelated systematic uncertainties for each species. Shaded bands represent $p_T$-correlated systematic uncertainties for pions.

Figure 20

NCQ scalings of $v_2$, $v_3$, and $v_4$ of ${\pi }^{+}+{\pi }^{-}$, $K^{+}+K^{-}$, and $p+\overline{p}$ as a function of $(m_T-m_0)/n_q$ in the 0–40% centrality bin. Solid lines represent $p_T$-uncorrelated systematic uncertainties for each species. Shaded bands represent $p_T$-correlated systematic uncertainties for pions.