Collisions of nuclei at large energies create fireballs of hot hadronic matter and quark gluon plasma. The properties of these extreme forms of nuclear matter can be studied by the experiments at the Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC). In this work we refine tools to study the matter in nuclear collisions and we infer the shear viscosity of hot hadronic matter from data. Hadronic observables in the final stage of the heavy-ion collisions can be described well by hydrodynamics or blastwave parameterizations. We construct a blastwave model with self-consistent viscous corrections by calculating the viscous stress tensor from the parameterized flow field in the Navier-Stokes approximation. We improve similar models developed earlier by using a more realistic flow field and by calculating the time derivative terms by solving the ideal hydrodynamic equations analytically. Such a viscous blastwave can describe important features of the fireball without running numerically expensive hydrodynamics. We can validate the blastwave by comparison with established hydrodynamic calculations. We can quantify the uncertainty and bias from the simplifications of hypersurface and flow field by systematically comparing to hydrodynamic calculations with resonance decays and bulk stress included. As a first application, we focus on the freeze-out temperature Tvfo and the specific shear viscosity η/s of hot hadronic matter at that temperature. We use statistical Bayesian analysis tools to extract η/s at T = Tvfo from experimental data. Our approach is complementary to existing extractions from viscous hydrodynamics. The latter is sensitive to an averaged shear viscosity during that time evolution while our analysis is only sensitive to the shear viscosity at kinetic freeze-out. We can use the comparison to hydrodynamics to remove some systematic bias in the extraction results of T and η/s. We can also use the viscous blastwave to provide realistic input for quark recombination models. These calculations had previously assumed breaking of thermal equilibrium in a naive way which is now replaced by viscous corrections to equilibrium.
We get the quark spectra at T ≈ Tvc from the blastwave and then use recombination to get spectra and elliptic flow vv2 of identified hadrons at intermediate transverse momentum vpr (2GeV/c < 6GeV/c).
We find a moderate breaking of the constituent quark number scaling (QNS) law consistent with experimental data from RHIC and LHC. Thus, we demonstrate that the QNS law is not a necessary feature of quark recombinatio
