Directed flow in an extended multiphase transport model

We have studied the rapidity-odd directed flow in ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ collisions in the beam energy range from $\sqrt{s_{\mathit{NN}}}=7.7$ to 39 GeV within the framework of an extended multiphase transport model with both partonic and hadronic mean-field potentials incorporated. Effects of the partonic scatterings, mean-field potentials, hadronization, and hadronic evolution on the directed flow are investigated, and it is found that the final directed flow is mostly sensitive to the partonic scatterings and the hadronization mechanism. Our study shows that a negative slope of the proton directed flow does not necessarily need the equation of state with a first-order phase transition.

Figure 1

Directed flow $v_1$ of quarks [(a), (c)] and antiquarks [(b), (d)] versus rapidity $y$ at different times in midcentral Au+Au collisions at $\sqrt{s_{\mathit{NN}}}$ = 7.7 [(a), (b)] and 39 GeV [(c), (d)]. Note the different scales for $v_1$ at 7.7 and 39 GeV.

Figure 2

Directed flow $v_1$ of freeze-out quarks [(a), (c)] and antiquarks [(b), (d)] versus rapidity $y$ from the parton scattering cross sections of 1, 3, and 10 mb in midcentral Au+Au collisions at $\sqrt{s_{\mathit{NN}}}$ = 7.7 [(a), (b)] and 39 GeV [(c), (d)]. Note the different scales for $v_1$ at 7.7 and 39 GeV.

Figure 3

Directed flow $v_1$ of freeze-out quarks [(a), (c)] and antiquarks [(b), (d)] versus rapidity $y$ from only partonic scatterings (cascade), partonic scatterings together with the scalar potential (scalar), and partonic scatterings together with both scalar and vector potentials (scalar+vector) in midcentral Au+Au collisions at $\sqrt{s_{\mathit{NN}}}$ = 7.7 [(a), (c)] and 39 GeV [(b), (d)]. Note the different scales for $v_1$ at 7.7 and 39 GeV.

Figure 4

Directed flow $v_1$ of final partons and initial protons as well as initial antiprotons from the mix-event spatial coalescence approach in the extended AMPT model (r coal) and the dynamical coalescence approach (dyn coal) versus rapidity $y$ in midcentral Au+Au collisions at $\sqrt{s_{\mathit{NN}}}$ = 7.7 [(a), (b)] and 39 GeV [(c), (d)]. Note the different scales for $v_1$ at 7.7 and 39 GeV.

Figure 5

Directed flow $v_1$ of final partons as well as initial and final protons and antiprotons versus rapidity $y$ in midcentral Au+Au collisions at $\sqrt{s_{\mathit{NN}}}$ = 7.7, 11.5, 19.6, 27, and 39 GeV.

Figure 6

Directed flow slope $d{v}_1{/dy|}_{y=0}$ of protons, antiprotons, and net protons versus collisions energy in midcentral Au+Au collisions with $R_V=0$ (a) and $R_V=1.1$ (b). Results of star symbols are experimental data measured by the STAR Collaboration [6], and the lines are the directed flow slope from the dynamical coalescence approach.

Figure 7

Equation of state in the [number density (${\rho }^0$), temperature ($T$)] plane of the partonic phase from the NJL model with $R_V=0$, and the corresponding trajectories of the central region of the partonic phase in midcentral Au+Au collisions at $\sqrt{s_{\mathit{NN}}}$ = 7.7 and 39 GeV based on the extended AMPT model. The spinodal region with ${(\partial P/\partial {\rho }^0)}_T<0$ is also approximately marked.