"Figure 4.3.3" of "Measurement of the higher-order anisotropic flow coefficients for identified hadrons in Au$+$Au collisions at $\sqrt{s_{_{NN}}}$ = 200 GeV"

Measurements of the anisotropic flow coefficients $v_2\{\Psi_2\}$, $v_3\{\Psi_3\}$, $v_4\{\Psi_4\}$, and $v_4\{\Psi_2\}$ for identified particles ($\pi^{\pm}$, $K^{\pm}$, and $p+\bar{p}$) at midrapidity, obtained relative to the event planes $\Psi_m$ at forward rapidities in Au$+$Au collisions at $\sqrt{s_{_{NN}}}$ = 200 GeV, are presented as a function of collision centrality and particle transverse momenta $p_T$. The $v_n$ coefficients show characteristic patterns consistent with hydrodynamical expansion of the matter produced in the collisions. For each harmonic $n$, a modified valence quark number $N_q$ scaling (plotting $v_n\{\Psi_m\}/(N_q)^{n/2}$ versus ${\rm KE}_T/N_q$) is observed to yield a single curve for all the measured particle species for a broad range of transverse kinetic energies ${\rm KE}_T$. A simultaneous blast-wave model fit to the observed $v_n\{\Psi_m\}(p_T)$ coefficients and published particle spectra identifies radial flow anisotropies $\rho_n\{\Psi_m\}$ and spatial eccentricities $s_n\{\Psi_m\}$ at freeze-out. These are generally smaller than the initial-state participant-plane (PP) geometric eccentricities $\varepsilon_n\{\Psi_m^{\rm PP}\}$, as also observed in the final eccentricity from quantum interferometry measurements with respect to the event plane.

本文呈现了质心系能量√s_{NN}=200 GeV的金金（Au+Au）碰撞中，相对于前向快度区域事件平面（event planes）Ψ_m测得的中心快度区间（midrapidity）内鉴别粒子（identified particles：π^±、K^±及p+$ar{p}$）的各向异性流系数（anisotropic flow coefficients）v₂{Ψ₂}、v₃{Ψ₃}、v₄{Ψ₄}与v₄{Ψ₂}，其结果以碰撞中心度（collision centrality）和粒子横向动量（transverse momenta p_T）为变量的函数形式给出。该v_n系数序列呈现出与碰撞产生物质的流体动力学膨胀（hydrodynamical expansion）相符的特征模式。针对每一个谐波阶数n，修正价夸克数$N_q$标度关系（即以v_n{Ψ_m}/(N_q)^{n/2}对KE_T/N_q作图）被观测到可将所有被测粒子种类在宽泛的横向动能（transverse kinetic energies KE_T）范围内的数据统一为一条单一曲线。同时采用爆轰波模型（blast-wave model）对观测到的v_n{Ψ_m}(p_T)系数与已发表的粒子谱进行联合拟合，确定了冻出（freeze-out）阶段的径向流各向异性（radial flow anisotropies）ρ_n{Ψ_m}与空间偏心率（spatial eccentricities）s_n{Ψ_m}。上述偏心率通常小于初始态参与者平面（participant-plane，PP）几何偏心率ε_n{Ψ_m^{PP}}，这一结论也与基于事件平面的量子干涉测量（quantum interferometry measurements）得到的末态偏心率观测结果一致。