Bulk properties of the matter produced at energies of the beam energy scan program

Recent STAR data on the bulk observables in the energy range of the beam energy scan program at the Relativistic Heavy Ion Collider are analyzed within the model of three-fluid dynamics (3FD). The simulations are performed with different equations of state (EoS's). The purely hadronic EoS fails to reproduce the data. A good, though imperfect, overall reproduction of the data is found within the deconfinement scenarios. The crossover EoS turns out to be slightly preferable. For this reproduction a fairly strong baryon stopping in the quark-gluon phase is required. The 3FD model does not need two separate freeze-outs (i.e., kinetic and chemical ones) to describe the STAR data. A unified freeze-out is applied at all energies.

Figure 1

Dynamical trajectories of the matter in the central region of colliding Au+Au nuclei ($b=2$ fm) at BES-RHIC energies. The trajectories are plotted in terms of the proper (i.e., in the local rest frame) baryon density ($n_B$) and the proper energy density minus $n_B{m}_N$ ($\varepsilon -m_N{n}_B$) where $m_N$ is the nucleon mass. Only expansion stages of the evolution are displayed. Symbols on the trajectories indicate the time rate of the evolution; time span between marks is 1 fm/$c$. Evolution of the equilibrated matter is displayed by solid lines, while the stage before the equilibration is displayed by dashed lines. The trajectories are presented for two EoS's: (a) the first-order-transition (1st-order-tr.) EoS and (b) the crossover EoS. For the 1st-order-tr. EoS the mixed phase is displayed by the shadowed region. For the crossover EoS the displayed borders correspond to values of the QGP fraction $W_{QGP}=$ 0.1, 0.5, 0.7, and 0.9. The inaccessible region is restricted by $\varepsilon (n_B,T=0)-m_N{n}_B$ from above.

Figure 2

Transverse-momentum spectra at the midrapidity of various particles produced in central ($b=2$ fm) Au+Au collisions at $\sqrt{s_{NN}}=$ 7.7–39 GeV predicted by the 3FD model with three considered EoS's. Experimental STAR data (0–5% centrality) are from Ref. [1].

Figure 3

Transverse-momentum spectra at midrapidity of various particles produced in noncentral ($b=11$ fm) Au+Au collisions at $\sqrt{s_{NN}}=39$ GeV predicted by the 3FD model with two considered deconfinement EoS's. Experimental STAR data (50–60% centrality) are from Ref. [1].

Figure 4

Mean transverse mass (minus particle mass) at midrapidity for various particles produced in central ($b=2$ fm) Au+Au collisions as functions of the collision energy. Experimental data are taken from Refs. [22, 23, 24, 25, 26] for AGS, [27, 28, 29, 30] for SPS, and [1] for BES-RHIC energies.

Figure 5

Midrapidity densities $dN/dy$ of various particles produced in Au+Au collisions at $\sqrt{s_{NN}}=$ 7.7–39 GeV as functions of the centrality (and impact parameter squared, cf. upper scale) predicted by 3FD model with two considered deconfinement EoS's. Experimental STAR data are from Ref. [1].

Figure 6

Midrapidity densities $dN/dy$ of various particles produced in central ($b=2$ fm) Au+Au collisions predicted by 3FD calculations with two considered deconfinement EoS's as functions of the center-of-mass energy. Thin lines for $p$ and $\overline{p}$ represent densities without contributions of weak decays (corresponding to NA49 data [37, 38]), while thick lines (for $p$ and $\overline{p}$) display densities including the weak-decay contributions which are relevant to the STAR data [1]. Experimental data are from compilation of Ref. [36] complemented by recent data from STAR Collaboration [1] (stars and open diamonds) and the latest update of the compilation of NA49 results [37, 38].

Figure 7

The energy dependence of ratios of the midrapidity densities $dN/dy$: (a) $K^{+}$ to ${\pi }^{+}$ and (b) $K^{-}$ to ${\pi }^{-}$. Compilation of experimental data is from Ref. [38] complemented by recent STAR data [1] and [21] for $\sqrt{s_{NN}}=62$ GeV (stars). Calculated ratios with pions including contribution from weak decays are also displayed by thin lines.

Figure 8

The energy dependence of ratios of the midrapidity densities $dN/dy$: (a) $K^{-}$ to $K^{+}$ and (b) $\overline{p}$ to $p$. Experimental STAR data are from Ref. [1].