Chiral symmetry restoration versus deconfinement in heavy-ion collisions at high baryon density

We study the production of strange hadrons in nucleus-nucleus collisions from 4 to $160 A$ GeV within the parton-hadron-string dynamics (PHSD) transport approach that is extended to incorporate essentials aspects of chiral symmetry restoration (CSR) in the hadronic sector (via the Schwinger mechanism) on top of the deconfinement phase transition as implemented in PHSD. Especially the $K^{+}/{\pi }^{+}$ and the $(\mathrm{\Lambda }+{\mathrm{\Sigma }}^0)/{\pi }^{-}$ ratios in central Au+Au collisions are found to provide information on the relative importance of both transitions. The modeling of chiral symmetry restoration is driven by the pion-nucleon $\mathrm{\Sigma }$ term in the computation of the quark scalar condensate $\langle \overline{q}q\rangle$ that serves as an order parameter for CSR and also scales approximately with the effective quark masses $m_s$ and $m_q$. Furthermore, the nucleon scalar density ${\rho }_s$, which also enters the computation of $\langle \overline{q}q\rangle$, is evaluated within the nonlinear $\sigma -\omega$ model which is constrained by Dirac-Brueckner calculations and low-energy heavy-ion reactions. The Schwinger mechanism (for string decay) fixes the ratio of strange to light quark production in the hadronic medium. We find that above $\sim 80 A$ GeV the reaction dynamics of heavy nuclei is dominantly driven by partonic degrees of freedom such that traces of the chiral symmetry restoration are hard to identify. Our studies support the conjecture of “quarkyonic matter” in heavy-ion collisions from about 5 to $40 A$ GeV and provide a microscopic explanation for the maximum in the $K^{+}/{\pi }^{+}$ ratio at about $30 A$ GeV, which only shows up if a transition to partonic degrees of freedom is incorporated in the reaction dynamics and is discarded in the traditional hadron-string models.

Figure 1

The ratio $m_N^{*}/m_N$ as a function of the energy density $\epsilon$ (9) at $T=0$ in the nonlinear $\sigma -\omega$ model for the parameter-set NL3 in comparison to the respective ratio for the scalar quark condensate (solid red line) from (4) (using ${\mathrm{\Sigma }}_{\pi }=45$ MeV). The effective light quark mass ratio $m_q/m_q^0$ (11) is displayed by the dot-dashed green line for comparison.

Figure 2

The strangness ratio $s/u$ in the string decay (1) as a function of the energy density $\epsilon$ (9) as evaluated within the nonlinear $\sigma -\omega$ model for the parameter sets NL3 and NL1 for $T=0$ on the basis of Eqs. (10), (11), and (4).

Figure 3

The ratio (4) for the scalar quark condensate as a function of $x$ and $z$ (for $y=0$) at different times $t$ for central Au+Au collisions at $30 A$ GeV, employing the parameter set NL3 for the computation of the baryon scalar density. The white borderline separates the space-time regions of deconfined matter and hadronic matter.

Figure 4

The rapidity distribution of pions, kaons, protons, and $(\mathrm{\Lambda }+{\mathrm{\Sigma }}^0)$'s for 5% central Au+Au collisions at $10.7 A$ GeV in comparison to the experimental data from Ref. [88]. The solid (red) lines show the results from PHSD (including CSR) while the blue solid lines show the results from HSD (including CSR) without partonic degrees of freedom. The dashed (red) line reflects the PHSD results without CSR while the dashed blue line shows results from HSD without CSR.

Figure 5

The rapidity distribution of pions, kaons, protons, and $(\mathrm{\Lambda }+{\mathrm{\Sigma }}^0)$'s for 5% central Au+Au collisions at $30 A$ GeV in comparison to the experimental data from Ref. [89]. The coding of the lines is the same as in Fig. 4.

Figure 6

The rapidity distribution of pions, kaons, protons, and $(\mathrm{\Lambda }+{\mathrm{\Sigma }}^0)$'s for 5% central Au+Au collisions at $158 A$ GeV in comparison to the experimental data from Ref. [90]. The coding of the lines is the same as in Fig. 4.

Figure 7

The ratios $K^{+}/{\pi }^{+},K^{-}/{\pi }^{-}$ (a), and $\mathrm{\Lambda }/{\pi }^{-}$ (b) at midrapidity from 5% central Au+Au collisions as a function of the invariant energy $\sqrt{s_{NN}}$ up to the top RHIC energy in comparison to the experimental data from [91]. The coding of the lines is the same as in Fig. 4.