Evidence of Coalescence Sum Rule in Elliptic Flow of Identified Particles in High-energy Heavy-ion Collisions

The major goal of high-energy heavy-ion collisions is to study the properties of the deconfined quark gluon plasma (QGP), such as partonic collectivity. The collective motion of constituent quarks can be derived from the anisotropic flow measurements of identified hadrons within the coalescence framework. Based on published results of elliptic flow ($v_2$), we shall test the coalescence sum rule using $K^{\pm}$, $p$, ${\bar p}$, $\Lambda$ and ${\bar \Lambda}$, and further extract $v_2$ values for produced $u$($d$, $\bar u$, $\bar d$), $s$ and $\bar s$ quarks, as well as transported $u(d)$ quarks in 10-40\% Au+Au collisions at $\sqrt{s_{\rm NN}}=$ 7.7, 11.5, 14.5, 19.6, 27, 39 and 62.4 GeV. We also attempt to link the $v_2$ difference between $\pi^-$ and $\pi^+$ to the different numbers of $u$ and $d$ quarks in the initial gold ions, and to relate the $v_2$ measurements of multi-strange hadrons to the formation times of $\phi$, $\Omega^\pm$ and $\Xi^+$.