# Quark Matter 2012

12-18 August 2012
US/Eastern timezone

## Relation Between the Trace Anomaly and Shear Viscosity in Clustering of Color Sources and the Equation of State of the QGP

16 Aug 2012, 16:00
2h

Poster QCD at finite temperature and density

### 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))

### Presentation Materials

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