"Appendix 1.4" 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.本文报道了质心系能量√s_{NN}=200 GeV的金-金（Au+Au）碰撞中，以前向快度（forward rapidities）区域的事件平面（event planes）Ψ_m为参考，对快度中点（midrapidity）区鉴别粒子（π^±、K^±及p+$ar{p}$）的各向异性流系数（anisotropic flow coefficients）v_2{Ψ_2}、v_3{Ψ_3}、v_4{Ψ_4}与v_4{Ψ_2}的测量结果，该结果以碰撞中心度（collision centrality）及粒子横向动量（particle transverse momenta）p_T为分布变量。v_n系数呈现出与碰撞产生物质的流体动力学膨胀（hydrodynamical expansion）一致的特征模式。对于每一次谐波n（harmonic n），修正价夸克数（valence quark number）N_q标度方法（即以v_n{Ψ_m}/(N_q)^{n/2}对${ m KE}_T/N_q$作图）被观测到在宽范围的横向动能（transverse kinetic energies）${ m KE}_T$区间内，可将所有被测粒子种类的数据归一为一条统一曲线。同时利用爆轰波模型（blast-wave model）拟合观测到的v_n{Ψ_m}(p_T)系数及已发表的粒子谱，可确定冻出（freeze-out）时刻的径向流各向异性（radial flow anisotropies）ρ_n{Ψ_m}与空间偏心率（spatial eccentricities）s_n{Ψ_m}。上述结果总体上小于初始态参与者平面（participant-plane, PP）几何偏心率（geometric eccentricities）ε_n{Ψ_m^{PP}}，这一现象也在基于事件平面的量子干涉测量（quantum interferometry）得到的末态偏心率中被观测到。