Clustering of color sources and the shear viscosity of the QGP in heavy ion collisions at RHIC and LHC energies

We present our results on the shear viscosity to entropy ratio ( η / s ) in the framework of the clustering of the color sources of the matter produced at RHIC and LHC energies. The onset of de-confinement transition is identified by the spanning percolating cluster in 2D percolation. The relativistic kinetic theory relation for η / s is evaluated using the initial temperature ( T ) and the mean free path ( λ mfp ). The analytic expression for η / s covers a wide temperature range. At T ∼150 MeV below the hadron to QGP transition temperature of ∼168 MeV, with increasing temperatures the η / s value drop sharply and reaches a broad minimum η / s ∼0.20 at T ∼175–185 MeV. Above this temperature η / s grows slowly. The measured values of η / s are 0.204±0.020 and 0.262±0.026 at the initial temperature of 193.6±3 MeV from central Au+Au collisions at (RHIC) and 262.2±13 MeV in central Pb+Pb collisions at (LHC). These η / s values are 2.5 and 3.3 times the AdS/CFT conjectured lower bound 1/4 π but are consistent with theoretical η / s estimates for a strongly coupled QGP.