In a recent preprint
Song, Bass, Heinz, Hirano, and Shen present systematic comparisons of RHIC data on elliptic flow in Au+Au collisions with a hybrid model of the reaction dynamics. They conclude that the kinematic shear viscosity ν = 4πη/s in the quark-gluon plasma phase of the reaction does not exceed 2.5 on average, compared with the lower KSS bound of 1.
The authors of the preprint combine (2+1)-dimensional second order relativistic viscous hydrodynamics for the quark-gluon plasma phase with relativistic Boltzmann dynamics for the hadronic phase of the reaction. They find excellent agreement with the STAR data over the entire centrality range; however, the value of the deduced shear viscosity depends on the assumed initial transverse density profile of the QCD matter. For the standard wounded-nucleon Glauber model, the comparison yields ν ≈ 1, while the KLN model requires ν ≈ 2.5. The conclusion ν ≤ 2.5 derives from the expectation that these two models represent the extremes of the distribution of possible density profiles.
In a related, but separate study,
Song, Bass, and Heinz show that relativistic viscous hydrodynamics with a Cooper-Frye freeze-out prescription does not provide an accurate effective description of the final hadronic phase. When comparing with full microscopic hadronic Boltzmann simulations, they find that the results using hydrodynamics for a part of the hadron phase depend on the temperature where the switch between the two macroscopic and microscopic descriptions occurs. In other words, the switching temperature needs to be chosen as close to Tc as possible.
The next interesting question is whether different commonly used Boltzmann models of the hadronic phase (e.g. UrQMD, JAM, ART) give equivalent values for the shear viscosity of the quark-gluon plasma phase. It would also be interesting to explore whether unknown resonances with masses above 2 GeV have are relevant for a correct description of the dynamics of the hadronic phase.