Physics of Collectivity and EOS from the RHIC Beam Energy Scan Program

Abstract

In this article we will review recent measurements of directed flow $v_1$ and elliptic flow $v_2$ in Au+Au collisions from the STAR Beam Energy Scan (BES) program. We systematically analyze the $v_1$ distributions for identified hadrons ($π^\pm$, $K^\pm$, $p/\bar{p}$) and $Λ$ hyperon as functions of rapidity ($y$), with particular focus on the mid-central collisions. The energy dependence of the $v_1$ slope is extracted across the BES range ($\sqrt{s_{NN}}$ = 3 -- 200 GeV). The atomic mass number ($A$) dependence of light and hyper nuclei $v_1$ to test the validity of the coalescence production mechanism. The constituent quark number (NCQ) scaling is systematically investigated based on $v_2$ measurements of identified particles and strange hadrons. We find that the NCQ scaling approximately holds in Au+Au collisions when $\sqrt{s_{NN}} \geq$ 4.5 GeV, but completely breaks down at $\sqrt{s_{NN}}$ = 3.0 and 3.2 GeV. The gradual restoration of NCQ scaling from 3.2 to 4.5 GeV suggests a possible transition in the dominant degrees of freedom from hadrons to partons. The physics of collectivity, equation of the system and relevance to the QCD phase diagram will be discussed within the framework of both hydrodynamic and hadronic transport model calculations.

Figures (8)

• Figure 1: Collision energy dependence of directed flow slope $dv_1/dy$ for $\pi$, $K$, proton, $\Lambda$, $\phi$, and $\Xi$ in 10%–40% Au+Au collisions(adapted from STAR:2021yiu). Colored bands are the calculations from transport models JAM and UrQMD.
• Figure 2: Test for coalescence sum rule of directed flow for (a) produced quarks and (b) net-baryon in 10%–40% Au+Au collisions(adapted from STAR:2017okv).
• Figure 3: Mass dependence of light nuclei and hypernuclei $dv_1/dy|_{y=0}$ at $\sqrt{s_{\rm NN}}=3$ GeV 5%-40% centrality Au + Au collisions(adapted from RN510). The calculations of transport models (JAM and UrQMD) plus coalescence are shown bars.
• Figure 4: $v_2$ as a function of $p_{\rm T}$ for $\pi$ and $p$ (panel a), and for $\phi$ and $\Omega$ (panel b) in minimum-bias Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV (adapted from STAR:2015gge).
• Figure 5: The number-of-constituent-quark ($n_q$) scaled $v_2$ as a function of $(m_T - m_0)/n_q$ in 10%--40% Au+Au collisions for $D^0$, $\Xi^-$, $\Lambda$, and $K_S^0$ (adapted from STAR:2017kkh). Here, $m_T = \sqrt{p_{\rm T}^2 + m_0^2}$ is the transverse mass.