Anisotropies in momentum space at finite Shear Viscosity in ultrarelativistic heavy-ion collisions

Abstract

Within a parton cascade we investigate the dependence of anisotropies in momentum space, namely the elliptic flow $v_2=<cos(2\varphi )>$ and the $v_4=<cos(4\varphi )>$, on both the finite shear viscosity $\eta$ and the freeze-out (f.o.) dynamics at the RHIC energy of 200 AGeV. In particular it is discussed the impact of the f.o. dynamics looking at two different procedures: switching-off the collisions when the energy density goes below a fixed value or reducing the cross section according to the increase in $\eta /s$ from a QGP phase to a hadronic one. We address the relation between the scaling of $v_2(p_T)$ with the eccentricity ${ϵ}_x$ and with the integrated elliptic flow. We show that the breaking of the $v_2(p_T)/{ϵ}_x$ scaling is not coming mainly from the finite $\eta /s$ but from the f.o. dynamics and that the $v_2(p_T)$ is weakly dependent on the f.o. scheme. On the other hand the $v_4(p_T)$ is found to be much more dependent on both the $\eta /s$ and the f.o. dynamics and hence is indicated to put better constraints on the properties of the QGP. A first semi-quantitative analysis show that both $v_2$ and $v_4$ (with the smooth f.o.) consistently indicate a plasma with $4\pi \eta /s\sim 1-2$.

Comments: 7 pages. Proceedings of the International School of Nuclear Physics in Erice, Sicily, to appear in Progress in Particle and Nuclear Physics