Transport Coefficient to Trace Anomaly in the Clustering of Color Sources Approach

From our previously obtained shear viscosity to entropy density ratio ($η/s$) in the framework of clustering of color sources (Color String Percolation Model: CSPM), we calculate the jet quenching parameter $\hat {q}$ and trace anomaly $Δ= (\varepsilon -3\it p)/T^{4}$ as a function of temperature. It is shown that the scaled $\hat {q}/T^{3}$ is in agreement with the recent JET Collaboration estimates. The inverse of $η/s$ is found to represent $Δ$. The results for $Δ$ are in excellent agreement with Lattice Quantum Chromo Dynamics (LQCD) simulations. From the trace anomaly and energy density $ε$, the equation of state is obtained as a function of temperature and compared with LQCD simulations. It is possible that there is a direct connection between the $η/s$ and $Δ$. Thus the estimate of transport coefficient $η/s$ provides $\hat {q}$ and $Δ$ as a function of temperature. Both $Δ$ and $η/s$ describe the transition from a strongly coupled QGP to a weakly coupled QGP.

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