Thermal Dimuon Yields at NA60

Dilepton emission rates from a hadronic gas at finite temperature and baryon density are completely constrained by broken chiral symmetry in a density expansion. The rates can be expressed in terms of vacuum correlations which are measured in $e^+e^-$ annihilation, $\tau$ decays and photo-reactions on nucleons and nuclei. In this paper, the theoretical results are summarized and the total dimuon yield is calculated by integrating the dimuon rates over the space-time history of a fireball based on hydrodynamic calculations with CERN SPS conditions. The resulting dimuon yield is in good agreement with the recent measurements reported by NA60.Comment: 9 pages, 8 figure

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

Simulating elliptic flow with viscous hydrodynamics

In this work we simulate a viscous hydrodynamical model of non-central Au-Au collisions in 2+1 dimensions, assuming longitudinal boost invariance. The model fluid equations were proposed by \"{O}ttinger and Grmela \cite{OG}. Freezeout is signaled when the viscous corrections become large relative to the ideal terms. Then viscous corrections to the transverse momentum and differential elliptic flow spectra are calculated. When viscous corrections to the thermal distribution function are not included, the effects of viscosity on elliptic flow are modest. However, when these corrections are included, the elliptic flow is strongly modified at large $p_T$. We also investigate the stability of the viscous results by comparing the non-ideal components of the stress tensor ($\pi^{ij}$) and their influence on the $v_2$ spectrum to the expectation of the Navier-Stokes equations (\pi^{ij} = -\eta \llangle \partial_i u_j \rrangle). We argue that when the stress tensor deviates from the Navier-Stokes form the dissipative corrections to spectra are too large for a hydrodynamic description to be reliable. For typical RHIC initial conditions this happens for \eta/s \gsim 0.3.Comment: 34 pages, 40 figures added references, updated figure 1

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

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

Thermal photons in QGP and non-ideal effects

We investigate the thermal photon production-rates using one dimensional boost-invariant second order relativistic hydrodynamics to find proper time evolution of the energy density and the temperature. The effect of bulk-viscosity and non-ideal equation of state are taken into account in a manner consistent with recent lattice QCD estimates. It is shown that the \textit{non-ideal} gas equation of state i.e $\epsilon-3\,P\,\neq 0$ behaviour of the expanding plasma, which is important near the phase-transition point, can significantly slow down the hydrodynamic expansion and thereby increase the photon production-rates. Inclusion of the bulk viscosity may also have similar effect on the hydrodynamic evolution. However the effect of bulk viscosity is shown to be significantly lower than the \textit{non-ideal} gas equation of state. We also analyze the interesting phenomenon of bulk viscosity induced cavitation making the hydrodynamical description invalid. We include the viscous corrections to the distribution functions while calculating the photon spectra. It is shown that ignoring the cavitation phenomenon can lead to erroneous estimation of the photon flux.Comment: 11 pages, 13 figures; accepted for publication in JHE

The Bulk Channel in Thermal Gauge Theories

We investigate the thermal correlator of the trace of the energy-momentum tensor in the SU(3) Yang-Mills theory. Our goal is to constrain the spectral function in that channel, whose low-frequency part determines the bulk viscosity. We focus on the thermal modification of the spectral function, $\rho(\omega,T)-\rho(\omega,0)$. Using the operator-product expansion we give the high-frequency behavior of this difference in terms of thermodynamic potentials. We take into account the presence of an exact delta function located at the origin, which had been missed in previous analyses. We then combine the bulk sum rule and a Monte-Carlo evaluation of the Euclidean correlator to determine the intervals of frequency where the spectral density is enhanced or depleted by thermal effects. We find evidence that the thermal spectral density is non-zero for frequencies below the scalar glueball mass $m$ and is significantly depleted for $m\lesssim\omega\lesssim 3m$.Comment: (1+25) pages, 6 figure

Bjorken Flow, Plasma Instabilities, and Thermalization

At asymptotically high energies, thermalization in heavy ion collisions can be described via weak-coupling QCD. We present a complete treatment of how thermalization proceeds, at the parametric weak-coupling level. We show that plasma instabilities dominate the dynamics, from immediately after the collision until well after the plasma becomes nearly in equilibrium. Initially they drive the system close to isotropy, but Bjorken expansion and increasing diluteness makes the system again become more anisotropic. At time \tau ~ \alpha^(-12/5) Q^(-1) the dynamics become dominated by a nearly-thermal bath; and at time \tau ~ \alpha^(-5/2) Q^(-1)$ the bath comes to dominate the energy density, completing thermalization. After this time there is a nearly isotropic and thermal Quark-Gluon Plasma.Comment: 22 pages, 5 figure

Long-Range Rapidity Correlations in Heavy Ion Collisions at Strong Coupling from AdS/CFT

We use AdS/CFT correspondence to study two-particle correlations in heavy ion collisions at strong coupling. Modeling the colliding heavy ions by shock waves on the gravity side, we observe that at early times after the collision there are long-range rapidity correlations present in the two-point functions for the glueball and the energy-momentum tensor operators. We estimate rapidity correlations at later times by assuming that the evolution of the system is governed by ideal Bjorken hydrodynamics, and find that glueball correlations in this state are suppressed at large rapidity intervals, suggesting that late-time medium dynamics can not "wash out" the long-range rapidity correlations that were formed at early times. These results may provide an insight on the nature of the "ridge" correlations observed in heavy ion collision experiments at RHIC and LHC, and in proton-proton collisions at LHC.Comment: 32 pages, 2 figures; v2: typos corrected, references adde

Transport coefficients and resonances for a meson gas in Chiral Perturbation Theory

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 (ChPT). Our method is based on the study of Feynman diagrams taking into account collisions in the plasma by means of the non-zero particle width. This implies a modification of the standard ChPT power counting scheme. We discuss the importance of unitarity, which allows for an accurate high energy description of scattering amplitudes, generating dynamically the $\rho (770)$ and $f_0(600)$ mesons. Our results are compatible with analyses of kinetic theory, both in the non-relativistic very low-$T$ regime and near the transition. We show the behavior with temperature of the electrical and thermal conductivities as well as of the shear and bulk viscosities. We obtain that bulk viscosity is negligible against shear viscosity, except near the chiral phase transition where the conformal anomaly might induce larger bulk effects. Different asymptotic limits for transport coefficients, large-$N_c$ scaling and some applications to heavy-ion collisions are studied.Comment: Invited talk given at the international workshop Hot Quarks 2008, Estes Park, Colorado, USA, August 18-23 2008. Accepted as a regular article in Eur.Phys.J.C. 18 pages EPJC style, 23 figure