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

Due to their weak final state interactions, the $\phi$ meson and $\Omega$ 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 $\Omega$ in Au+Au collisions at $\sqrt{s_{\rm NN}} = 200$ GeV and Pb+Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ 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 $\eta/s$ and the specific bulk viscosity $\zeta/s$ of the QGP. We perform a model-to-data comparison with Bayesian inference and simultaneously obtain $\eta/s=(2.08^{+1.10}_{-1.09})/4\pi$ and $\zeta/s= 0.06^{+0.04}_{-0.04}$ at $90\%$ C.L. for the baryon-free QGP at crossover temperature of about $160$ MeV. Our work provides a novel approach to simultaneously determine the $\eta/s$ and $\zeta/s$ of the QGP at hadronization.