Thermalization, Isotropization and Elliptic Flow from Nonequilibrium Initial Conditions with a Saturation Scale

In this article we report on our results about the computation of the elliptic flow of the quark-gluon-plasma produced in relativistic heavy ion collisions, simulating the expansion of the fireball by solving the relativistic Boltzmann equation for the parton distribution function tuned at a fixed shear viscosity to entropy density ratio $\eta/s$. Our main goal is to put emphasis on the role of a saturation scale in the initial gluon spectrum, which makes the initial distribution far from a thermalized one. We find that the presence of the saturation scale reduces the efficiency in building-up the elliptic flow, even if the thermalization process is quite fast $\tau_{therm} \approx 0.8 \,\rm fm/c$ and the pressure isotropization even faster $\tau_{isotr} \approx 0.3 \,\rm fm/c$. The impact of the non-equilibrium implied by the saturation scale manifests for non-central collisions and can modify the estimate of the viscosity respect to the assumption of full thermalization in $p_T$-space. We find that the estimate of $\eta/s$ is modified from $\eta/s \approx 2/4\pi$ to $\eta/s \approx 1/4\pi$ at RHIC and from $\eta/s \approx 3/4\pi$ to $\eta/s \approx 2/4\pi$ at LHC. We complete our investigation by a study of the thermalization and isotropization times of the fireball for different initial conditions and values of $\eta/s$ showing how the latter affects both isotropization and thermalization. Lastly, we have seen that the range of values explored by the phase-space distribution function $f$ is such that at $p_T<0.5\, \rm GeV$ the inner part of the fireball stays with occupation number significantly larger than unity despite the fast longitudinal expansion, which might suggest the possibility of the formation of a transient Bose-Einstein Condensate.