"Figure 2.2.0" 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$sqrt{s_{NN}}=200 ext{GeV}$的金-金（Au+Au）碰撞中，中间快度区（midrapidity）已鉴别粒子（$pi^pm$、$K^pm$以及$p+ar{p}$）的各向异性流系数（anisotropic flow coefficients）$v_2{Psi_2}$、$v_3{Psi_3}$、$v_4{Psi_4}$与$v_4{Psi_2}$的测量结果。上述系数基于前向快度区的事件平面（event plane）$Psi_m$构建，其取值随碰撞中心度与粒子横向动量$p_T$变化。 $v_n$系数展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。 对于每阶谐波$n$，修正价夸克数（valence quark number）$N_q$标度律（即绘制$v_n{Psi_m}/(N_q)^{n/2}$随横向动能（transverse kinetic energy, ${ m KE}_T$）$/N_q$的变化曲线）可将所有被测粒子种类在宽范围横向动能${ m KE}_T$下的数据统一为一条单曲线。 通过同时采用爆炸波模型（blast-wave model）拟合测得的$v_n{Psi_m}(p_T)$系数与已发表的粒子谱，可提取出冻出（freeze-out）阶段的径向流各向异性$ ho_n{Psi_m}$与空间偏心率$s_n{Psi_m}$。 这些物理量普遍小于初始态参与者平面（participant-plane, PP）几何偏心率$varepsilon_n{Psi_m^{ m PP}}$，这一结论也在基于事件平面的量子干涉测量（quantum interferometry）得到的末态偏心率结果中得到验证。