Bayesian Inference of the Specific Shear and Bulk Viscosities of the Quark-Gluon Plasma at Crossover from $\phi$ and $\mathrm{\Omega }$ Observables

Due to their weak final state interactions, the $\phi$ meson and $\mathrm{\Omega }$ baryon provide unique probes of the properties of the quark-gluon plasma (QGP) formed in relativistic heavy-ion collisions. Using the quark recombination model with the quark phase-space information parameterized in a viscous blastwave, we study the transverse-momentum spectra and elliptic flows of $\phi$ and $\mathrm{\Omega }$ in Au+Au collisions at $\sqrt{s_{\mathrm{N}\mathrm{N}}}=200$ GeV and Pb+Pb collisions at $\sqrt{s_{\mathrm{N}\mathrm{N}}}=2.76$ TeV. The viscous blastwave includes non-equilibrium deformations of thermal distributions due to shear and bulk stresses and thus carries information on the specific shear viscosity $\eta \mathrm{/}s$ and the specific bulk viscosity $\zeta \mathrm{/}s$ of the QGP. We perform a model-to-data comparison with Bayesian inference and simultaneously obtain $\eta \mathrm{/}s=(2.08_{-1.09}^{+1.10})\mathrm{/}4\pi$ and $\zeta \mathrm{/}s=0.06_{-0.04}^{+0.04}$ at $90\mathrm{\%}$ C.L. for the baryon-free QGP at crossover temperature of about $160$ MeV. Our work provides a novel approach to simultaneously determine the $\eta \mathrm{/}s$ and $\zeta \mathrm{/}s$ of the QGP at hadronization.