Transport properties of a meson gas

We present recent results on a systematic method to calculate transport coefficients for a meson gas (in particular, we analyze a pion gas) at low temperatures in the context of Chiral Perturbation Theory. Our method is based on the study of Feynman diagrams with a power counting which takes into account collisions in the plasma by means of a non-zero particle width. In this way, we obtain results compatible with analysis of Kinetic Theory with just the leading order diagram. We show the behavior with temperature of electrical and thermal conductivities and shear and bulk viscosities, and we discuss the fundamental role played by unitarity. We obtain that bulk viscosity is negligible against shear viscosity near the chiral phase transition. Relations between the different transport coefficients and bounds on them based on different theoretical approximations are also discussed. We also comment on some applications to heavy-ion collisions.Comment: 4 pages, 4 figures, IJMPE style. Contribution to the International Workshop X Hadron Physics (2007), Florianopolis, Brazil. Accepted for publication in IJMPE; 1 typo correcte

Spectral densities for hot QCD plasmas in a leading log approximation

We compute the spectral densities of $T^{\mu\nu}$ and $J^{\mu}$ in high temperature QCD plasmas at small frequency and momentum,\, $\omega,k \sim g^4 T$. The leading log Boltzmann equation is reformulated as a Fokker Planck equation with non-trivial boundary conditions, and the resulting partial differential equation is solved numerically in momentum space. The spectral densities of the current, shear, sound, and bulk channels exhibit a smooth transition from free streaming quasi-particles to ideal hydrodynamics. This transition is analyzed with conformal and non-conformal second order hydrodynamics, and a second order diffusion equation. We determine all of the second order transport coefficients which characterize the linear response in the hydrodynamic regime.Comment: 39 pages, 6 figures. v3 contains an analysis of the bulk channel with non-conformal hydrodynamics. Otherwise no significant change

The ratio of viscosity to entropy density in a pion gas satisfies the KSS holographic bound

We evaluate the ratio of shear viscosity to entropy density in a pion gas employing the Uehling-Uehlenbeck equation and experimental phase-shifts parameterized by means of the SU(2) Inverse Amplitude Method. We find that the ratio for this monocomponent gas stays well above the KSS 1/(4 pi) bound. We find similar results with other sets of phase shifts and conclude the bound is nowhere violated.Comment: 2 page text, three figures. V2: short comment and graph added to assert that a minimum of eta/s is not discarded from the hadron, low T side in a heavy-ion collisio

Femtoscopy of the system shape fluctuations in heavy ion collisions

Dipole, triangular, and higher harmonic flow that have an origin in the initial density fluctuations has gained a lot of attention as they can provide additional important information about the dynamical properties (e.g. viscosity) of the system. The fluctuations in the initial geometry should be also reflected in the detail shape and velocity field of the system at freeze-out. In this talk I discuss the possibility to measure such fluctuations by means of identical and non-identical particle interferometry.Comment: 4 pages, Proceedings of Quark Matter 2011 Conference, May 23 - May 28, Annecy, Franc

Azimuthal distributions of radial momentum and velocity in relativistic heavy ion collisions

Azimuthal distributions of radial (transverse) momentum, mean radial momentum, and mean radial velocity of final state particles are suggested for relativistic heavy ion collisions. Using transport model AMPT with string melting, these distributions for Au + Au collisions at 200 GeV are presented and studied. It is demonstrated that the distribution of total radial momentum is more sensitive to the anisotropic expansion, as the anisotropies of final state particles and their associated transverse momentums are both counted in the measure. The mean radial velocity distribution is compared with the radial {\deg}ow velocity. The thermal motion contributes an isotropic constant to mean radial velocity

Quark-Gluon Plasma - New Frontiers

As implied by organizers, this talk is not a conference summary but rather an outline of progress/challenges/``frontiers'' of the theory. Some fundamental questions addressed are: Why is sQGP such a good liquid? Do we understand (de)confinement and what do we know about ``magnetic'' objects creating it? Can we understand the AdS/CFT predictions, from the gauge theory side? Can they be tested experimentally? Can AdS/CFT duality help us understand rapid equilibration/entropy production? Can we work out a complete dynamical ``gravity dual'' to heavy ion collisions?Comment: final talk at Quark Matter 2008, Jaipur, India, Feb.200

Azimuthal anisotropy: transition from hydrodynamic flow to jet suppression

Measured 2nd and 4th azimuthal anisotropy coefficients v_{2,4}(N_{part}), p_T) are scaled with the initial eccentricity \varepsilon_{2,4}(N_{part}) of the collision zone and studied as a function of the number of participants N_{part} and the transverse momenta p_T. Scaling violations are observed for p_T \alt 3 GeV/c, consistent with a $p_T^2$ dependence of viscous corrections and a linear increase of the relaxation time with $p_T$. These empirical viscous corrections to flow and the thermal distribution function at freeze-out constrain estimates of the specific viscosity and the freeze-out temperature for two different models for the initial collision geometry. The apparent viscous corrections exhibit a sharp maximum for p_T \agt 3 GeV/c, suggesting a breakdown of the hydrodynamic ansatz and the onset of a change from flow-driven to suppression-driven anisotropy.Comment: 5 pages, 4 figs; submitted for publicatio

Transport coefficients, spectral functions and the lattice

Transport coefficients are determined by the slope of spectral functions of composite operators at zero frequency. We study the spectral function relevant for the shear viscosity for arbitrary frequencies in weakly-coupled scalar and nonabelian gauge theories at high temperature and compute the corresponding correlator in euclidean time. We discuss whether nonperturbative values of transport coefficients can be extracted from euclidean lattice simulations.Comment: 25 pages with 7 eps figures, discussion improved, acknowledgement added; to appear in JHE

Dissipative corrections to particle spectra and anisotropic flow from a saddle-point approximation to kinetic freeze out

Lang C, Borghini N. Dissipative corrections to particle spectra and anisotropic flow from a saddle-point approximation to kinetic freeze out. The European Physical Journal C. 2014;74(7): 2955.A significant fraction of the changes in momentum distributions induced bydissipative phenomena in the description of the fluid fireball created inultrarelativistic heavy ion collisions are actually taking place when the fluidturns into individual particles. We study these corrections in the limit of alow freeze-out temperature of the flowing medium, and show that they mostlyaffect particles with a higher velocity than the fluid. For these, we deriverelations between different flow harmonics, from which the functional form ofthe dissipative corrections could ultimately be reconstructed from experimentaldata

Thermalization vs. Isotropization & Azimuthal Fluctuations

Hydrodynamic description requires a local thermodynamic equilibrium of the system under study but an approximate hydrodynamic behaviour is already manifested when a momentum distribution of liquid components is not of equilibrium form but merely isotropic. While the process of equilibration is relatively slow, the parton system becomes isotropic rather fast due to the plasma instabilities. Azimuthal fluctuations observed in relativistic heavy-ion collisions are argued to distinguish between a fully equilibrated and only isotropic parton system produced in the collision early stage.Comment: 12 pages, presented at `Correlations and Fluctuations in Relativistic Nuclear Collisions', MIT, April 05, minor correction