Baryon-density dependence of viscosities of the quark-gluon plasma at hadronization

The $\varphi$ meson and $\mathrm{\Omega }$ baryon provide unique probes of the properties of the quark-gluon plasma (QGP) at hadronization in relativistic heavy-ion collisions. Using the quark recombination model with the quark phase-space information parameterized in a viscous blast wave, we perform Bayesian inference of the shear and bulk viscosities of the QGP at hadronization with a temperature of $T\approx 160$ MeV by analyzing the $\varphi$ and $\mathrm{\Omega }$ data in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathrm{NN}}}=19.6–200$ GeV and $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV, corresponding to a baryon chemical potential variation from ${\mu }_B\approx 0$ (at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV) to 200 MeV (at $\sqrt{s_{\mathrm{NN}}}=19.6$ GeV). We find that the shear viscosity to enthalpy ratio $\eta T/(\epsilon +P)$ of the QGP at hadronization decreases as ${\mu }_B$ increases, with $\eta T/(\epsilon +P)\approx 0.18$ at ${\mu }_B=0$ and $\eta T/(\epsilon +P)\approx 0.08$ at ${\mu }_B=200$ MeV, while the corresponding specific bulk viscosity is essentially constant with $\zeta T/(\epsilon +P)=0.02–0.04$ for ${\mu }_B<200$ MeV. Our results suggest that the QGP at hadronization ($T\approx 160$ MeV) with finite baryon density is more close to perfect fluid than that with zero baryon density.

Figure 1

Posterior distributions of $\eta T/(\epsilon +P)$ and $\zeta T/(\epsilon +P)$ for (a) $\mathrm{Au}+\mathrm{Au}$ 19.6 GeV and (b) 62.4 GeV. The numbers indicate the median values with the 68.3% credibility range.

Figure 2

Transverse-momentum spectra and elliptic flows $v_2$ of $\varphi$ mesons and $\mathrm{\Omega }$ baryons (selected centrality bins). For $\mathrm{Au}+\mathrm{Au}$ at 19.6–62.4 GeV, we use data of ${\mathrm{\Omega }}^{-}$. For $\mathrm{Au}+\mathrm{Au}$ at 200 GeV and $\mathrm{Pb}+\mathrm{Pb}$ at 2.76 TeV, we use data of ${\mathrm{\Omega }}^{-}+{\overline{\mathrm{\Omega }}}^{+}$. Solid lines are recombination calculation using the best-fit parameters. The data from STAR [81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91] and ALICE [92, 93, 94] are included for comparison.

Figure 3

Baryon chemical potential dependence of (a) shear and (b) bulk viscosities for QGP/hadronic matter at hadronization with $T\approx 160$ MeV(see text for details).