Mass, quark-number, and $\sqrt{s_{\mathit{NN}}}$ dependence of the second and fourth flow harmonics in ultrarelativistic nucleus-nucleus collisions

We present STAR measurements of the azimuthal anisotropy parameter $v_2$ for pions, kaons, protons, $\Lambda ,\overline{\Lambda },\Xi +\overline{\Xi }$, and $\Omega +\overline{\Omega }$, along with $v_4$ for pions, kaons, protons, and $\Lambda +\overline{\Lambda }$ at midrapidity for Au+Au collisions at $\sqrt{s_{\mathit{NN}}}=62.4$ and 200 GeV. The $v_2(p_T)$ values for all hadron species at 62.4 GeV are similar to those observed in 130 and 200 GeV collisions. For observed kinematic ranges, $v_2$ values at 62.4, 130, and 200 GeV are as little as 10–15% larger than those in Pb+Pb collisions at $\sqrt{s_{\mathit{NN}}}=17.3$ GeV. At intermediate transverse momentum ($p_T$ from 1.5–5 GeV/$c$), the 62.4 GeV $v_2(p_T)$ and $v_4(p_T)$ values are consistent with the quark-number scaling first observed at 200 GeV. A four-particle cumulant analysis is used to assess the nonflow contributions to pions and protons and some indications are found for a smaller nonflow contribution to protons than pions. Baryon $v_2$ is larger than antibaryon $v_2$ at 62.4 and 200 GeV, perhaps indicating either that the initial spatial net-baryon distribution is anisotropic, that the mechanism leading to transport of baryon number from beam- to midrapidity enhances $v_2$ or that antibaryon and baryon annihilation is larger in the in-plane direction.

Figure 1

Minimum-bias (0–80% of the collision cross section) $v_2(p_T)$ for identified hadrons at $\left|\eta \right|<1$ from Au+Au collisions at $\sqrt{s_{\mathit{NN}}}=62.4$ GeV. To facilitate comparisons between panels, $v_2$ values for inclusive charged hadrons are displayed in each panel. The error bars on the data points represent statistical uncertainties. Systematic uncertainties for the identified particles are shown as shaded bands around $v_2=0$.

Figure 2

The unidentified charged hadron, charged pion, $K_S^0$, charged kaon, proton, and $\Lambda +\overline{\Lambda }$ $v_2$ as a function of $p_T$ for 10–40%, 0–10%, and 40–80% of the Au+Au interaction cross section at $\sqrt{s_{\mathit{NN}}}=62.4$ GeV. Weak-decay feeddown errors are included in the error bars on the data points, whereas nonflow and tracking error uncertainties are plotted as bands around $v_2=0$, which apply to all identified particles. The errors are asymmetric and the portion of the error band above (below) zero represents the negative (positive) error.

Figure 3

The ratio of $\overline{\Lambda }$ $v_2$ to Λ $v_2$. The data are from minimum bias Au+Au collisions at $\sqrt{s_{\mathit{NN}}}=$ 62.4 and 200 GeV. The bands show the average values of the ratios within the indicated $p_T$ ranges.

Figure 4

The $p_T$ integrated ratio of $\overline{\Lambda }$ $v_2$ to Λ $v_2$ for three centrality intervals: 0–10%, 10–40%, and 40–80%. The data are from Au+Au collisions at $\sqrt{s_{\mathit{NN}}}=$ 62.4 and 200 GeV.

Figure 5

Identified particle $v_2$ from minimum bias collisions at $\sqrt{s_{\mathit{NN}}}=62.4$ GeV scaled by the number of valence quarks in the hadron ($n_q$) and plotted versus $p_T/n_q$ (a) and $(m_T-m_0)/n_q$ (b). In each case a polynomial curve is fit to all particles except pions. The ratio of $v_2/n_q$ to the fit function is shown in the bottom panels (c) and (d).

Figure 6

$v_2/n_q$ scaled by the mean eccentricity of the initial overlap region versus $(m_T-m_0)/n_q$ for 0–10%, 10–40%, and 40–80% most central Au+Au collisions at $\sqrt{s_{\mathit{NN}}}=62.4$ GeV.

Figure 7

(Top panels) Minimum bias $v_4$ for pions, charged kaons, $K_S^0$, antiprotons, and $\Lambda +\overline{\Lambda }$ at $\sqrt{s_{\mathit{NN}}}=$ 62.4 GeV. In the left panel the solid (dashed) line shows the value for $v_2^2$ for pions (kaons). In the right panel the dashed line is $v_2^2$ for $\Lambda +\overline{\Lambda }$. (Bottom panels) $v_4$ scaled by $v_2^2$ (points where $v_4$ and $v_2$ fluctuate around zero are not plotted). Gray bands correspond to the fit results described in the text and Table 2. The systematic errors on the $v_4/v_2^2$ ratio from nonflow are included in the error bars leading to asymmetric errors.

Figure 8

(Top panel) $v_2$ for pions and protons at $\sqrt{s_{\mathit{NN}}}=$ 62.4 and 17.3-GeV. The 62.4-GeV data are from TOF and $\mathit{dE}/\mathit{dx}$ measurements combined. (Middle and bottom panels) Ratios of $v_2$ for ${\pi }^{+}+{\pi }^{-},K_S^0,p+\overline{p},\Lambda +\overline{\Lambda }$ and at different center-of-mass energies scaled by the values at 62.4 GeV. The gray and yellow bands represent systematic uncertainties in the $v_2$ ratios arising from nonflow effects. The gray bands (above unity) are the uncertainties for the 200-GeV/62.4-GeV data and the yellow bands (below unity) are for the 17.3-GeV/62.4-GeV data.