### Speaker

Prof.
Rolf Scharenberg
(Purdue University)

### Description

The major challenge in heavy ion physics is to extract the equation of state and the shear viscosity to entropy ratio $\eta/s$ from the data. In the clustering of color sources (CSPM) the charged particle transverse momentum spectrum is used to measure the percolation density parameter $\xi$, which determines the initial temperature T, energy density $\epsilon$, and the $\eta/s$ ratio versus T in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV .
For 0.9 $T_{c} < T < $1.2 $T_{c}$ ($T_{c}$ = 167.7 MeV), the sound velocity $C_{s}^{2}$ from the mass less non interacting constituent version of CSPM agrees with Lattice QCD (LQCD)$C_{s}^{2}$ values . For T$ >$ 1.2$T_{c}$ there is a significant difference with the LQCD values\cite{eos}.
The measured CSPM value for $\eta/s$ = 0.20, at 1.15$T_{c}$ is consistent with a strongly coupled QGP and increases with T. The Trace Anomaly $\triangle $ is defined as $(\epsilon-3p)/T^{4}$.
Above $T_{c}$, the LQCD $\triangle $ and the reciprocal of $\eta/s$ fall off with 1/T. At $T_{c}$ , $s/\eta$ has a magnitude of $\sim$5.5 , non interacting - CSPM has a $\triangle\sim$ 5.5 and LQCD $\triangle \sim $5.5. The change in $\triangle$ and $s/\eta$ with 1/T describes the transition from a strongly to weakly coupled QGP. Above $T_{c}$, $s/\eta$ and the LQCD $\triangle$ may have the same underlying structure. The $C_{s}^{2}$ values for the QGP obtained using the $s/\eta \sim 5.5$ version of CSPM above $T_{c}$ are in excellent agreement with LQCD \cite{wupp, hotqcd}.
The CSPM predictions for Pb-Pb and p-p collisions at LHC energies will be presented.

### Primary author

Prof.
Rolf Scharenberg
(Purdue University)

### Co-authors

Prof.
Andrew Hirsch
(Purdue University)
Brijesh Kumar Srivastava
(Purdue University (US))