Scalings of Elliptic Flow for a Fluid at Finite Shear Viscosity

Within a parton cascade approach we investigate the scaling of the differential elliptic flow $v_2(p_T)$ with eccentricity $\epsilon_x$ and system size and its sensitivity to finite shear viscosity. We present calculations for shear viscosity to entropy density ratio $\eta/s$ in the range from $1/4\pi$ up to $1/\pi$, finding that the $v_2$ saturation value varies by about a factor 2. Scaling of $v_2(p_T)/\epsilon_x$ is seen also for finite $\eta/s$ which indicates that it does not prove a perfect hydrodynamical behavior, but is compatible with a plasma at finite $\eta/s$. Introducing a suitable freeze-out condition, we see a significant reduction of $v_2(p_T)$ especially at intermediate $p_T$ and for more peripheral collisions. This causes a breaking of the scaling for both $v_2(p_T)$ and the $p_T-$averaged $v_2$, while keeping the scaling of v_2(p_T)/\la v_2\ra. This is in better agreement with the experimental observations and shows as a first indication that the $\eta/s$ should be significantly lower than the pQCD estimates. We finally point out the necessity to include the hadronization via coalescence for a definite evaluation of $\eta/s$ from intermediate $p_T$ data.Comment: 5 pages, 5 figures. Two points in fig.4 has been change

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

Within a parton cascade we investigate the dependence of anisotropies in momentum space, namely the elliptic flow $v_2=$ and the $v_4=$, 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 $\epsilon_x$ and with the integrated elliptic flow. We show that the breaking of the $v_2(p_T)/\epsilon_x$ 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 $4\pi \eta/s \sim 1-2$.Comment: 7 pages. Proceedings of the International School of Nuclear Physics in Erice, Sicily, to appear in Progress in Particle and Nuclear Physic

Does the NJL chiral phase transition affect the elliptic flow of a fluid at fixed η/s\eta/s?

We have derived and solved numerically the Boltzmann-Vlasov transport equations that includes both two-body collisions and the chiral phase transition by mean of NJL-field dynamics. The scope is to understand if the field dynamics supply new genuine effects on the build-up of the elliptic flow $v_2$, a measure of the asymmetry in the momentum space, and in particular if it can affect the relation between $v_2$ and the shear viscosity to entropy ratio $\eta/s$. Solving the transport equation with a constant cross section for the condition of $Au+Au$ collisions at $\sqrt{s_{NN}}=200$ AGeV it is shown a sizable suppression of $v_2$ due to the attractive nature of the field dynamics that generates the constituent mass. However the key result is that if $\eta/s$ of the system is kept fixed by an appropriate local renormalization of the cross section the $v_2$ does not depend on the details of the collisional and/or field dynamics and in particular it is not affected significantly by the chiral phase transition.Comment: 5 pages, 5 figure

Isospin Effects on Strangeness in Heavy-Ion Collisions

Kaon properties are studied within the framework of a fully covariant transport approach. The kaon-nucleon potential is evaluated in two schemes, a chiral perturbative approach and an effective One-Boson-Exchange model. Isospin effects are explicitly accounted for in both models. The transport calculations indicate a significant sensitivity of momentum distributions and total yields of $K^{0,+}$ isospin states on the choice of the kaon-nucleon interaction. Furthermore, isospin effects are rather moderate on absolute kaon yields, but appear on strangeness ratios. This is an important issue in determining the high density symmetry energy from studies of strangeness production in heavy-ion collisions.Comment: 15 papes, 5 figures. Accepted for publication in Nuclear Physic

Isospin effects on sub-threshold kaon production at intermediate energies

We show that in collisions with neutron rich heavy ions at energies around the production threshold K^0 and K^+ yields might probe the isospin dependent part of the nuclearEquation of State (EoS) at high baryon densities. In particular we suggest the K^0/K^+ ratio as a promising observable. Results obtained in a fully covariant relativistic transport approach are presented for central Au+Au collisions in the beam energy range 0.8-1.8~AGeV. The focus is put on the EoS influence which goes beyond the "collision-cascade" picture. The isovector part of the in-medium interaction affects the kaon multiplicities via two mechanisms: i) a "symmetry potential" effect, i.e. a larger neutron repulsion in n-rich systems (isospin fractionation); ii) a "threshold" effect, due to the change in the self-energies of the particles involved in inelastic processes. Genuine relativistic contributions are revealed, that could allow to directly ``measure'' the Lorentz structure of the effective isovector interaction.Comment: 5 pages, 2 figures, revtex