Beam energy dependence of the squeeze-out effect on the directed and elliptic flow in Au + Au collisions in the high baryon density region

We present a detailed analysis of the beam energy dependence of the mechanisms for the generation of directed and elliptic flows in Au + Au collisions focusing on the role of hadronic rescattering and spectator shadowing within a microscopic transport model jam with different equations of state. A systematic study of the beam energy dependence is performed for Au + Au collisions at $\sqrt{s_{\mathit{NN}}}=2.3-62.4$ GeV. The transition of the dynamical origin of the directed flow is observed. We find that the initial Glauber-type nucleon-nucleon collisions generate negative $v_1$ for nucleons at midrapidity due to the presence of spectator matter, and this negative nucleon $v_1$ is turned to be positive by the meson-baryon interactions at the beam energy region of $\sqrt{s_{NN}}<30$ GeV. In contrast, above 30 GeV there is no spectator shadowing at midrapidity, and initial nucleon-nucleon collisions do not generate directed flow, but subsequent rescatterings among produced particles generate negative $v_1$ for nucleons. It is demonstrated that negative pion-directed flows are mostly generated by the interaction with the spectator matter. It is also shown that the squeeze-out effect is largely suppressed in the case of softening, which leads to the enhancement of elliptic flow around $\sqrt{s_{NN}}=5-7$ GeV. The elliptic flow at midrapidity above 10 GeV is not influenced by the squeeze-out due to spectator matter, while its effect is seen at the forward rapidity range of $y/y_{\mathrm{c}.\mathrm{m}.}>0.5$, which decreases as beam energy increases.

Figure 1

(a) Transverse momentum spectrum at midrapidity ($\left|y\right|<0.12$) and (b) rapidity distributions of identified particles; proton, pion, kaon in midcentral (10–40%) Au + Au collision at $\sqrt{s_{NN}}=5$ GeV from jam are compared to different EoS; cascade with mean-field potential and cascade with attractive orbit mode.

Figure 2

Directed flows as a function of rapidity in midcentral (10–40%) Au + Au collision at $\sqrt{s_{NN}}=5$ GeV from jam cascade (circles), jam with mean-field potential (squires), and jam cascade with attractive orbit (crosses). The left and right panels show the results for identified particles $p$, ${\pi }^{+}$, $K^{+}$ and antiparticles ${\pi }^{-}$, $K^{-}$, respectively.

Figure 3

Directed flows of protons as a function of rapidity in midcentral (10–40%) Au + Au collisions at $\sqrt{s_{NN}}=2.7,3.3,3.8$, and 4.3 GeV from jam cascade (dotted lines), jam mean-field mode (jam/MF) (dashed lines), jam with a first-order phase transition (jam/1OPT) (solid lines) are compared to the data from the E895 Collaboration [68].

Figure 4

Elliptic flows of charged hadrons as a function of rapidity in midcentral (10–40%) Au + Au collisions at $\sqrt{s_{NN}}=7.7,11.5,19.6,$ and 27 GeV from jam cascade (dotted lines), jam with a fisrt-order phase transition (solid lines) are compared to the STAR data [69].

Figure 5

Rapidity dependence of directed flow for protons, pions, $\mathrm{\Lambda }\mathrm{s}$, and kaons in midcentral (10–40%) Au + Au collisions at $\sqrt{s_{NN}}=7.7,11.5,19.6$, and 27 GeV calculated with the jam cascade (dotted lines) and the jam with a first-order phase transition (solid lines) are compared to STAR data [33, 70].

Figure 6

Directed flows as a function of rapidity in midcentral (10–40%) Au + Au collision at $\sqrt{s_{NN}}=5$ GeV from jam mean-field mode (jam/MF) (triangles), jam/MF without weak decay (squires), jam/MF without spectator (circles), jam/MF with only baryon-baryon collisions (diamonds), and jam/MF with only baryon-baryon collisions and without spectator (crosses). The left and right panels show the results for identified particles $p$, ${\pi }^{+}$, $K^{+}$ and antiparticles ${\pi }^{-}$, $K^{-}$, respectively.

Figure 7

Same as Fig. 6, but for $v_2$.

Figure 8

Same as Fig. 7, but for the centrality dependence of the $\eta$ integrated $v_2$ at $\left|\eta \right|<0.2$.

Figure 9

Same as Fig. 8 but for charged particles.

Figure 10

Rapidity dependence of $v_2$ for nucleons (upper) and pions (lower) in midcentral Au + Au at $\sqrt{s_{NN}}=5$ GeV are compared to the jam cascade and jam attractive orbit mode with and without spectator interaction.

Figure 11

Rapidity dependence of $v_2$ for nucleons (upper) and pions (lower) in midcentral Au + Au at $\sqrt{s_{NN}}=5$ GeV are compared to the jam cascade and jam first-order phase transition mode with and without spectator interaction.

Figure 12

Beam energy dependence of the slope of directed flow in midcentral (10–40%) Au + Au collision from jam mean-field mode (MF) (crosses), and MF without spectator (circles). Slope $d{v}_1/dy$ is obtained by the cubic fit at the range of $\left|y\right|<0.8$. The top and bottom panels show the results for protons and positive pions, respectively.

Figure 13

Same as Fig. 12, but for beam energy dependence of elliptic flows $v_2$ at midrapidity $\left|y\right|<0.2$.

Figure 14

Rapidity dependence of directed flow for nucleons (left panel) and pions (right panel) are compared in midcentral Au + Au collisions ($4.6<b<9.6$ fm) at $\sqrt{s_{NN}}=6.4$, 7.7, 11.5, 19.6, 27, 39 and 62.4 GeV from jam cascade simulations. In the calculations, acceptance cut $0.4\le p_T\le 2\mathrm{GeV}/c$ for nucleons, $0.2\le p_T\le 1.6\mathrm{GeV}/c$ for pions are imposed.

Figure 15

Beam dependence of the slope of nucleon directed flow in midcentral (10–40%) Au + Au collision from jam cascade (squires), cascade without spectator (triangles), cascade with only baryon-baryon collisions (circles), and cascade with only baryon-baryon collisions and without spectator (crosses).

Figure 16

Rapidity dependence of $v_2$ for nucleons (left panel) and pions (right panel) are compared in midcentral Au + Au collisions ($4.6<b<9.6$ fm) at $\sqrt{s_{NN}}=6.4$, 7.7, 11.5, 19.6, 27, 39 and 62.4 GeV from jam cascade simulations. In the calculations, acceptance cut $0.4\le p_T\le 2\mathrm{GeV}/c$ for nucleons, $0.2\le p_T\le 1.6\mathrm{GeV}/c$ for pions are imposed.

Figure 17

Beam energy dependence of $v_2$ for nucleons in midcentral Au + Au collisions ($4.6<b<9.4$ fm) from jam first-order phase transition and mean-field simulations with and without spectator interactions. Data are take from Ref. [84].