Third harmonic flow of charged particles in Au $+$ Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV

We report measurements of the third harmonic coefficient of the azimuthal anisotropy, $v_3$, known as triangular flow. The analysis is for charged particles in Au+Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV, based on data from the STAR experiment at the BNL Relativistic Heavy Ion Collider. Two-particle correlations as a function of their pseudorapidity separation are fit with narrow and wide Gaussians. Measurements of triangular flow are extracted from the wide Gaussian, from two-particle cumulants with a pseudorapidity gap, and also from event plane analysis methods with a large pseudorapidity gap between the particles and the event plane. These results are reported as a function of transverse momentum and centrality. A large dependence on the pseudorapidity gap is found. Results are compared with other experiments and model calculations.

Figure 1

$v_3^2\left\{2\right\}$ vs. transverse momentum and pseudorapidity separation for charged hadron pairs in 200 GeV Au+Au minimum bias collisions. The $p_T$ is for one of the particles, integrated over the $p_T$ values of the other particle in the range $0.15<p_T<2.0$ $\mathrm{GeV}/c$.

Figure 2

$v_3^2\left\{2\right\}$ vs. the pseudorapidity separation of the particles in pairs for charged hadrons with $0.15<p_T<2.0$ $\mathrm{GeV}/c$ within two centrality intervals in 200 GeV Au+Au collisions. Data are fit with narrow and wide Gaussians. Like sign (LS), unlike sign (US), and charge independent (CI) cases are shown with only statistical errors. The dashed curves under the peaks are the wide Gaussian fits.

Figure 3

The width in units of $\Delta \eta$ and amplitude of the charge independent wide Gaussian as a function of transverse momentum for most central ($0\%$–$5\%$) and midcentral ($30\%$–$40\%$) Au+Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV. The plotted errors are statistical.

Figure 4

The width in units of $\Delta \eta$ and amplitude of the wide Gaussian as a function of centrality for charge independent (CI) and like sign (LS) particles with $0.15<p_T<2.0$ $\mathrm{GeV}/c$ for Au+Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV. The errors on the data points are statistical. The upper edge of the systematic error band for the like sign particles shows the width of the wide Gaussian required to also fit the data from the FTPC.

Figure 5

The third harmonic coefficient as a function of pseudorapidity for different centralities for Au+Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV, with track selection in the TPC of $0.15<p_T<2.0$ $\mathrm{GeV}/c$. Results are shown for the event plane constructed either in the TPC or in the FTPCs. The horizontal lines are fits to the FTPC results.

Figure 6

The top panels show third harmonic coefficient as a function of $p_T$ for the wide Gaussian method and for the event plane in the TPC, for two centralities for Au+Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV, for tracks in the TPC with $-1.0<\eta <1.0$. The wide Gaussian was weighted with either the number of particle pairs or by unity. The bottom panels show the ratio of $v_3$ from the wide Gaussian method to $v_3$ from the TPC subevent method.

Figure 7

The third harmonic coefficient as a function of $p_T$, for different centralities for Au+Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV, for tracks in the TPC with $-1.0<\eta <1.0$. The event planes are constructed either in the TPC or in the FTPCs.

Figure 8

The third harmonic coefficient as a function of centrality from different methods of analysis for Au+Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV, integrated for $0.15<p_T<2.0$ $\mathrm{GeV}/c$ and $-1.0<\eta <1.0$. The curves connect the points and the bands show the systematic uncertainties. The systematic errors of the wide Gaussian method are similar to those for the TPC event plane method.

Figure 9

The square of the third harmonic coefficient as a function of pseudorapidity separation for Au+Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV for tracks with $0.15<p_T<2.0$ $\mathrm{GeV}/c$. Shown are unlike sign (US), charge independent (CI), and like sign (LS) results at $0\%$–$5\%$ centrality (open symbols) and $30\%$–$40\%$ centrality (closed symbols). Most of the points at low $\left|\Delta \eta \right|$ are not plotted because they correspond to the narrow Gaussian and go off the top of the scale. Also shown, by larger symbols, are the squares of the mean $v_3$ values (connected by purple dotted and dot-dashed lines) at the same two centralities from three analysis methods: The point at $\left|\Delta \eta \right|=$ 0.63 is from the subevent method using the TPC with $\left|\eta \right|<1$. The point at 1.33 is from the 2-particle cumulant method with $\left|\Delta \eta \right|>1$. The point at 3.21 is from correlations with the FTPC event plane. The dashed (green) curves without points are from a minimum bias Glasma calculation [36] for $\sqrt{s_{\mathit{NN}}}=200$ GeV with $0.15<p_T<2.0$ $\mathrm{GeV}/c$ done for the STAR acceptance with overall normalization set to the data at $\left|\Delta \eta \right|=1$.

Figure 10

(a) The fourth power of the third harmonic coefficient from four-particle cumulants is plotted as a function of centrality for Au+Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV, with track selections $0.15<p_T<2.0$ $\mathrm{GeV}/c$ and $-1.0<\eta <1.0$. The ALICE results [37] are for Pb$+$Pb collisions at $\sqrt{s_{\mathit{NN}}}=2.76$ TeV, with track selections $0.2<p_T<5.0$ $\mathrm{GeV}/c$ and $-0.8<\eta <0.8$. (b) The points in the top figure are divided by the fourth power of the third harmonic flow from the $\eta$ subevent method, showing the deviation from 2.

Figure 11

The third harmonic coefficient is plotted as a function of transverse momentum, for different centralities. The STAR $v_3\left\{\mathrm{TPC}\right\}$ results are from Fig. 7. Also shown are PHENIX results, ATLAS results starting at $10\%$ centrality, and ALICE results for $30\%$–$40\%$ centrality.

Figure 12

$v_2$ (top) and $v_3$ (bottom) for Au+Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV in $0\%$–$5\%$ (left), $20\%$–$30\%$ (middle), and $30\%$–$40\%$ (right) centrality as a function of transverse momentum at midrapidity, compared with ideal [14] (b), (e) and viscous hydro [14] (all), AMPT transport [15] (a), (c), (d), (f), NeXSPheRIO [42] (b), (c), (e), (f), and parton hardon string dynamics [53] (f) models. The STAR $v_2$ values (top) are from Ref. [49].