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

The $\phi$ meson and $\Omega$ 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 blastwave, we perform Bayesian inference of the shear and bulk viscosities of the QGP at hadronization with a temperature of $T\sim 160$ MeV by analyzing the $\phi$ and $\Omega$ data in Au+Au collisions at $\sqrt{s_{\rm NN}}=$ 19.6-200 GeV and Pb+Pb collisions at $\sqrt{s_{\rm NN}}=$ 2.76 TeV, corresponding to a baryon chemical potential variation from $\mu_B\approx 0$ (at $\sqrt{s_{\rm NN}}= 2.76$ TeV) to $200$ MeV (at $\sqrt{s_{\rm NN}}= 19.6$ 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 $\zeta T/(\epsilon + P)=0.02\sim 0.04$ for $\mu_B<200$ MeV. Our results suggest that the QGP at hadronization ($T\sim 160$ MeV) with finite baryon density is more close to perfect fluid than that with zero baryon density.