Observables in ultrarelativistic heavy-ion collisions from two different transport approaches for the same initial conditions

For nucleus-nucleus collisions at energies currently available at the BNL Relativistic Heavy Ion Collider (RHIC), we calculate observables in two different transport approaches, i.e., the $n$-body molecular dynamical model “relativistic quantum molecular dynamics for strongly interacting matter with phase transition or crossover” (RSP) and the two-body parton hadron string dynamics (PHSD), starting out from the same distribution in the initial energy density at the quark gluon plasma (QGP) formation time. The RSP dynamics is based on the Nambu-Jona-Lasinio (NJL) Lagrangian, whereas in PHSD the partons are described by the dynamical quasiparticle model (DQPM). Despite the very different description of the parton properties and their interactions and of the hadronization in both approaches, the final transverse momentum distributions of pions turn out to be quite similar, which is less visible for the strange mesons owing to the large NJL cross sections involved. Our findings can be attributed, in part, to a partial thermalization of the quark degrees of freedom in central $\mathrm{Au}+\mathrm{Au}$ collisions for both approaches. The rapidity distribution of mesons shows a stronger sensitivity to the nature of the degrees of freedom involved and to their interaction strength in the QGP.

Figure 1

Energy density from PHSD for Au-Au collisions at $\sqrt{s_{NN}}=200$ $A$ GeV and $b=2$ fm ($\sim 0\%–5\%$ centrality) in the transverse plane (a), (c) and the longitudinal plane (b), (d) and at the QGP formation time ($t\approx t_0+0.5$ fm/$c$) (a), (b) and a later time ($t=t_0+1.0$ fm/$c$) (c), (d).

Figure 2

Cell velocities in PHSD for a Au-Au collision at $\sqrt{s_{NN}}=200$ GeV and $b=2$ fm (0%–5% centrality), in the transverse direction ($z=0.37$ fm) (a) and in the longitudinal direction ($x=0$ fm) (b).

Figure 3

Strangeness abundance from PHSD for a Au-Au collision at $\sqrt{s_{NN}}=200$ GeV and $b=2$ fm (0%–5% centrality) in the transverse plane (for $z=0.37$ fm) (a) and in the $z\text{−}y$ plane (for $x=0$ fm) (b).

Figure 4

Masses of $u$ quark (a) and $\pi$ meson (b) as a function of $(T,\mu )$ in the NJL model. Note the different orientation of the axis in the upper (a) and lower (b) plots.

Figure 5

NJL cross sections for $u\overline{d}\to u\overline{d}$ (a) and $u\overline{s}\to {\pi }^{+}{K}^0$ (b) as a function of $(T,\sqrt{s}-{\sqrt{s}}_0)$ in the NJL model, where ${\sqrt{s}}_0$ denotes the threshold center-of-mass energy.

Figure 6

Time evolution of the elliptic flow $v_2$ for the expanding fireball in PHSD and RSP for smooth Gaussian initial conditions with a spatial eccentricity of $\varepsilon =0.75$.

Figure 7

The elliptic flow over eccentricity ratio $v_2/\varepsilon$ as a function of the eccentricity for the expanding fireball in PHSD and RSP for smooth Gaussian initial conditions.

Figure 8

Conversion of energy density in the cell—where equilibrium is assumed—from one model to another, knowing their equations of state and the real particle density.

Figure 9

Equation-of-state comparison between NJL and DQPM for the particle density (a) and energy density (b). Lattice QCD data are taken from Ref. [40].

Figure 10

Probability distribution of particle momenta ($p_z,p_x$) in a cell at rest.

Figure 11

Out-of-equilibrium conversion of energy density in the cell from one model to another, knowing their equations of state and the real particle density.

Figure 12

Initial distributions of the quarks in PHSD and RSP, using the three different conversion methods explained in the text. We display the transverse momentum spectrum for $\left|y\right|<0.5$ and the rapidity distribution, for light quarks in the top panels [(a) and (b)] and for strange quarks in the bottom panels [(c) and (d)].

Figure 13

Final distributions of the mesons in PHSD and RSP, using the three difference conversion methods explained in the text. We display the transverse momentum spectrum for $\left|y\right|<0.5$ and the rapidity distribution, for pions in the top panels [(a) and (b)] and for kaons in the bottom panels [(c) and (d)]. The PHSD results are shown with and without final state hadron rescattering.

Figure 14

Elliptic flow $v_2\left(EP\right)$, as a function of transverse momentum $p_T$ (a) and of the rapidity $y$ (b) for Au-Au collisions at $\sqrt{s}=200$ $A$ GeV and $b=8.4$ fm (30%–40% centrality) for PHSD and RSP. The different results of RSP correspond to different conversion methods of the PHSD initial condition to RSP initial conditions (see text for explanation). The PHSD calculations including hadronic rescattering are shown by full lines; the PHSD results without hadronic rescattering (and without the contribution of baryons)—to be compared to the present RSP results which do not include hadronic rescattering—are displayed by dashed lines.

Figure 15

Space-time distribution $d^{2}N/dtd{r}_T$ of elastic ($q\overline{q}\to q\overline{q}$) (a) and inelastic ($q\overline{q}\to MM$) (b) collisions in RSP.

Figure 16

Probability distribution of hadronization collisions according to $\sqrt{s}$ from RSP.

Figure 17

Example of a collision probability profile as a function of the the impact parameter $b$.