Session L13: Minisymposium on Flow, Eccentricity and the Equation of State in RHIC

Importance of correlations and fluctuations on the initial eccentricity

One of the early, important discoveries at RHIC was that the magnitude of the elliptic flow component, v$_2$, was not only large, but also for the first time reached the limit predicted by hydrodynamical calculations. In a hydrodynamics picture, elliptic flow is understood to be a consequence of the spatial anisotropy of the initial matter distribution. This anisotropy is usually characterized by the eccentricity of the overlap region of the colliding nuclei. Thus, the interpretation of the anisotropic flow data requires a detailed understanding of the effective initial source eccentricity. In this talk, various ways of defining this effective eccentricity will be addressed. In particular, the focus will be on the participant eccentricity, which defines the initial-state asymmetry wrt the major axes of the overlap ellipse formed by the participants. Reasonable variation of the density parameters in the Glauber simulation, as well as variations in how matter production is modeled, do only moderately affect the eccentricity. However, as will be outlined, participant spatial correlations in the interaction of two nuclei do play an essential role, in particular for the Cu+Cu system. Including these correlations in the calculation of the participant eccentricity results in larger values for the eccentricity. One particularly important consequence is that the fourth order participant eccentricity cumulant does not approach the spatial anisotropy obtained assuming a smooth nuclear matter distribution.   

Elliptic Flow and HBT radii of thermal photons from ideal hydrodynamics

Ideal hydrodynamics has been successful in describing many characteristics of the fireball created in a heavy ion collision. Through studying the elliptic flow ($v_2$) of thermally emitted particles and the corresponding Hanbury-Brown Twiss (HBT) radii, we obtain a picture of both the dynamics and geometry of a collision. Typically $v_2$ and HBT radii are calculated for abundant particles such as charged pions which decouple from the thermal medium at later times. Photons, however, decouple from the medium when they are created, particularly from the early hot QGP stage. We explore the photon elliptic flow and HBT radii for noncentral Au+Au collisions using an ideal hydrodynamical model to describe the collision. We predict a strong change in the pT dependence of the photon elliptical flow as compared to hadronic flow from hydrodynamics. We also present our first results of photon HBT radii from ideal hydrodynamics, in particular the azimuthal oscillations of the HBT radii.   

Causal Viscous Hydrodynamics in 2+1 Dimensions

The viscosity of the QGP is a hotly debated theoretical subject, and first principles calculations are difficult. It is thus important to try to extract the viscosity from experimental data. Viscous hydrodynamics provides a tool that can attack this problem and which may work in regions where ideal hydrodynamics fails. Using the 2nd order Israel-Stewart formulation of (2+1)- dimensional viscous hydrodynamics, we numerically study the effects from shear viscosity on the hydrodynamics evolution of a QGP, the final hadron spectra, and their elliptical flow coefficient $v_2$, for Cu+Cu collisions at RHIC. It turns out that the elliptic flow $v_2$ is very sensitive to the QGP shear viscosity, and that even the lowest bound, derived from AdS/CFT conjecture, $\eta/s=1/4\pi$, leads to a large suppression of $v_2$. We also explore the scaling behavior of $v_2$ with the initial source eccentricity $\varepsilon_x$, by computing $v_2/\varepsilon_x$ as a function of charged hadron multiplicity in both ideal hydrodynamics and viscous hydrodynamics, comparing Cu+Cu and Au+Au collisions at a variety of impact parameters and collision energies.   

High-$p_T$ Measurement of Azimuthal Anisotropy of Electrons from Semi-leptonic Decay of Open Heavy Flavor Mesons in Au+Au Collisions at $\sqrt{s_{NN}}=200 GeV$ by the PHENIX Experiment

The azimuthal anisotropy of open heavy flavor mesons at RHIC provides information about the early stages of heavy ion collisions. PHENIX observed a large azimuthal anisotropy parameter $v_2$ of electrons from heavy flavor decays from RHIC Run4 at low tranverse momentum. Together with the observation of constituent quark scaling of $v_2$ for light hadrons, the electron $v_2$ is consistent in coalescense models with charm quarks flowing as much as light quarks. With the addition of a reaction plane detector in PHENIX and the increased statistics of RHIC Run7, $v_2$ of electrons can be measured with much-improved precision, answering the question of whether heavy flavor continues to flow in the range of $p_T$ in which beauty production is believed to be comparable to that of charm. We present the $p_T$ and collision centrality dependency of the azimuthal anisotropy of single electrons from open heavy flavor decays from RHIC Run7 data in PHENIX.   

Phase Diagram of the Linear Sigma Model wiht Quarks at Finite Temperature and Density

The study of QCD at low energies is relevant in explaining the world around us but is extremely difficult due to the mathematical structure of the theory. The linear sigma model is a well known and simple effective model for low-energy QCD. We couple the $O(4)$ linear sigma model to quark fields in order to study the effects of the quarks and mesons on the chiral phase transition as functions of the temperature $T$ and the quark chemical potential $\mu_q$. As an effective model for QCD, we hope to reproduce some aspects of the QCD phase diagram, namely, the line of first order transitions that has a critical end-point at a second order transiton. We study how this line varies with changing pion mass. We use the self-consistent Cornwall-Jackiw-Tomboulis method in an extended Hartree approximation using a summation over all daisy diagrams. We study the mesonic and quark properties, including mean field, fluctuations and effective masses and how they relate to the transition structure.   

Persistent Quark Confinement in RHIC

The purposes of this paper are: 1) to review the problem of quark confinement and/or the existence of free quarks outside of nucleons during the collision of gold ions in RHIC [1]; and 2) to propose a new approach to the results. The primary theories which guided the RHIC project were the lattice QCD and the theory of asymptotic freedom. The theories predicted the production of a deconfined gaseous plasma. A perfect liquid was obtained instead. It is possible to consider quarks as a material phase in equilibrium with another internal phase (gluons?). Deconfining a quark from its environment would destroy it. Destruction of quarks may take place during the first phase of the relativistic collision of gold ions. For a very short time components of the ions may be broken into tiny fragments, while a huge amount of kinetic energy is converted to matter. The primitive matter and gluons radiate from the fireball. This matter may be more elementary than quarks, and also undetectable, until it hadronizes. The primeval properties of such most elementary particles will be postulated. [1] Nuclear Physics A 757 (2005) 1 - 283   

Quantitative Constraints on the RHIC Medium: Theory and Experiment Limitations

The heavy ion physics program aims to quantitatively describe the medium produced. Experimental data with high statistics and well studied systematic uncertainties are now available. In this talk we describe quantitative constraints on medium properties calculated within various model frameworks. We then describe the theory and experimental limitations, and discuss the path forward.