Anisotropic Flow of Identified Particles in Au + Au Collisions at $\sqrt{s_{NN}}$ = 3-3.9 GeV at RHIC

In these proceedings, we present transverse momentum dependence of the mid-rapidity slope of directed flow ($dv_1/dy|_{y=0}$) for $\pi^+$ and $K_S^0$ in Au + Au collisions at $\sqrt{s_{NN}}$ = 3.0, 3.2, 3.5, and 3.9 GeV. Both $\pi^+$ and $K_S^0$ show negative $v_1$ slope at low $p_T$ ($p_T<0.6$ GeV/$c$). Collision energy dependence of $v_1$ slope and $p_T$-integrated $v_2$ for $\pi^{\pm}$, $K_S^0$, and $\Lambda$ are also presented. A comparison to JAM model calculations indicates that spectator shadowing can lead to anti-flow at low $p_T$. In addition, a breaking of the Number of Constitute Quark (NCQ) scaling of elliptic flow ($v_2$) is observed at $\sqrt{s_{NN}}$ = 3.2 GeV, which implies the dominance of hadronic degrees of freedom occurs in collisions at $\sqrt{s_{NN}}$ = 3.2 GeV and below.


Introduction
The goals of Beam Energy Scan (BES) program at Relativistic Heavy Ion Collider (RHIC) are searching for the possible QCD critical point and locating the first order phase boundary [1].The energy dependence of net-proton v 1 slope [2] shows possible minimum at √ s NN ≈ 10 -20 GeV, implies that the softest point of Equation of State (EoS) may exist within this range of collision energy.The existence of partonic collectivity is observed through NCQ scaling of v 2 at higher BES energies ( √ s NN > 7.7 GeV) [3], while the break NCQ scaling of v 2 at √ s NN = 3.0 GeV [4] indicates the partonic collectivity is disappeared at this energy.In this contribution, we present the most recent measurements of directed flow (v 1 ) and elliptic flow (v 2 ) of identified particles (π ± , K ± , K 0 S , p, and Λ) at √ s NN = 3.0 -3.9 GeV in Fixed Target Au + Au collisions.

Experiment Setup
For identification of π ± , K ± , protons and anti-protons, a combination of Time Projection Chamber (TPC) [5] and Time of Flight (TOF) [6] is used.The left panel of Figure 1 illustrates the rigidity (p/q: particle momentum divided by charge) dependence of ionization energy loss (dE/dx) in the TPC.The dashed line represents the theoretical ionization energy loss curve for particle passing through the TPC.Particle identification by TOF is based on particle mass square (m 2 ) distribution, which can be obtained from particle velocity (β).Moreover, the Kalman Filter (KF) particle package [7], where the covariance matrix of reconstructed tracks is taken into account, is employed to reconstruct weak decay particles (K 0 S and Λ).An example of reconstructing the invariant mass using the KF particle package is demonstrated with the K 0 S meson in the right panel of Figure 1.

Anti-flow of Kaon
The anti-flow of kaon was first observed by E895 Collaboration at 6 A GeV [8].It was attributed to the repulsive potential associated with the strange quark in K 0 S .We have observed anti-flow behavior in kaons and pions for p T < 0.6 GeV/c in mid-central Au + Au collisions at √ s NN = 3.0, 3.2, 3.5, and 3.9 GeV using the fixed target data from STAR. Figure 2 shows transverse momentum (p T ) dependence of v 1 slope (dv 1 /dy| y=0 ) for π + and K 0 S from STAR.The hadronic transport model JAM [9] calculations are compared with experimental data at 3.9 GeV.The JAM model in hadronic cascade mode (blue band) can successfully capture the anti-flow pattern at low p T for π + and K 0 S , even without the inclusion of a kaon potential [8].However, the JAM model with baryonic mean field (red band), tends to overestimate the v 1 slope for π + and K 0 S .Additionally, the JAM mean field without spectator contribution (black band) exhibits a larger v 1 slope compared to the one with spectators.The data-model comparisons suggest that the shadowing effect [10] from the spectator may also play a significant role in generating anti-flow at low p T .

NCQ Scaling of v 2
The left and right panels of Figure 3 illustrate the number of constituent quarks (n q ) scaled elliptic flow (v 2 /n q ) as a function of transverse kinetic energy ((m T − m 0 )/n q ) for particles (π + , K + , K 0 S , p, and Λ) and the corresponding anti-particles (π − , K − , and K 0 S ), respectively for Au + Au collisions at √ s NN = 3.2 GeV.The NCQ scaling of v 2 is broken completely for particles and anti-particles at √ s NN = 3.2 GeV.The existence of partonic collectivity is observed through NCQ scaling of v 2 at higher BES energies ( √ s NN > 7.7 GeV) [3].The disappearing of NCQ scaling in v 2 at √ s NN = 3.2 GeV implies that hadronic interactions play an important role at this energy and below [4,11].

Figure 1 .
Figure 1.Left: Rigidity dependence of particle ionization energy loss in TPC.Right: Invariant mass distribution of K 0 S in Au + Au collisions at √ s NN = 3.5 GeV.

Figure 2 .
Figure 2. v 1 slope of π + (left) and K 0 S (right) as function of transverse momentum and a comparison with JAM calculation at √ s NN = 3.9 GeV.

Figure 4 .
Figure 4. v 1 slope (top) and p T -integrated v 2 (bottom) as a function of collision energy and compared with JAM calculation for Λ.Note that p T windows for π ± , K 0 S , and Λ are 0.2 < p T < 1.6 GeV/c, 0.4 < p T < 1.6 GeV/c, and 0.4 < p T < 2.0 GeV/c, respectively.And the rapidity window is −0.5 < y < 0 for p T -integrated v 2 .