Systematic study of symmetric cumulants at $\sqrt{s_{NN}}=200$ GeV in Au+Au collisions using a transport approach

Measurement of four-particle symmetric cumulants has been considered to be a good tool to study the correlations between amplitudes of different orders of anisotropic flow harmonics in heavy-ion collisions. These new observables have not yet been measured at the Relativistic Heavy Ion Collider. Using a multiphase transport (AMPT) model, a set of predictions for the centrality dependence of the normalized four-particle symmetric cumulants in Au+Au collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$ is given. In addition, the effects of shear viscosity and hadronic rescattering on the magnitude of symmetric cumulants are discussed using the AMPT model at $\sqrt{s_{NN}}=200\mathrm{GeV}$. It is shown that $\text{sc}(2,3)$ is found to be more sensitive to hadronic rescattering, whereas $\text{sc}(2,4)$ is more sensitive to the shear viscosity. Rapidity dependence of symmetric cumulants is also shown. A relation between symmetric cumulant and event-plane correlation is investigated using the AMPT model.

Figure 1

Transverse momentum spectra of charged hadron in Au+Au collision at $\sqrt{s_{NN}}=200\mathrm{GeV}$ for (a) $0\text{–}5\%$ (most central) (b) $20–30\%$ (mid-central) and (c) $40–60\%$ (peripheral) centrality. Black solid circles are data [13] and open markers are AMPT model calculation.

Figure 2

Transverse momentum dependence of $v_2, v_3$, and $v_4$ in Au+Au collision at $\sqrt{s_{NN}}=200\mathrm{GeV}$ for $0–10\%, 10–20\%, 20–30\%, 30–40\%, 40–50\%$, and $50–60\%$ centrality. Black solid circles are data [14] and open markers are AMPT model calculations.

Figure 3

Centrality dependence of (a) $\text{sc}(2,3)$ and (b) $\text{sc}(2,4)$ in Au+Au collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$ from the AMPT-SM model (blue) with ${\sigma }_{\mathrm{pp}}=3\mathrm{mb}$ and the AMPT-Def model (red).

Figure 4

Centrality dependence of (a) $\text{sc}(2,3)$ and (b) $\text{sc}(2,4)$ in Au+Au collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$ from the AMPT-SM model for ${\eta }_s/s=0.35$ (black), 0.18 (red), and 0.08 (blue).

Figure 5

Centrality dependence of (a) $\text{sc}(2,3)$ and (b) $\text{sc}(2,4)$ in Au+Au collision at $\sqrt{s_{NN}}=200\mathrm{GeV}$ from the AMPT-SM model (${\sigma }_{\mathrm{pp}}=3\mathrm{mb}$) for hadron cascade time = 0.6 fm/$c$ (blue) and 30 fm/$c$ (red).

Figure 6

Centrality dependence of (a) $\text{sc}(2,3)$ and (b) $\text{sc}(2,4)$ in Au+Au collision at $\sqrt{s_{NN}}=200\mathrm{GeV}$ from the AMPT-SM model (${\sigma }_{\mathrm{pp}}=3\mathrm{mb}$) with $\left|\eta \right|<1.0$ (red), $1<\left|\eta \right|<3$ (black), and $3<\left|\eta \right|<5$ (blue).

Figure 7

$\text{sc}(2,4)$ as a function of centrality from AMPT-SM (${\sigma }_{\mathrm{pp}}=10\mathrm{mb}$) and AMPT-Def models in Au+Au collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$. Black (red) symbols represent calculations using Eq. (3) [Eq. (8)].