Transport Properties of the Quark-Gluon Plasma -- A Lattice QCD Perspective

Transport properties of a thermal medium determine how its conserved charge densities (for instance the electric charge, energy or momentum) evolve as a function of time and eventually relax back to their equilibrium values. Here the transport properties of the quark-gluon plasma are reviewed from a theoretical perspective. The latter play a key role in the description of heavy-ion collisions, and are an important ingredient in constraining particle production processes in the early universe. We place particular emphasis on lattice QCD calculations of conserved current correlators. These Euclidean correlators are related by an integral transform to spectral functions, whose small-frequency form determines the transport properties via Kubo formulae. The universal hydrodynamic predictions for the small-frequency pole structure of spectral functions are summarized. The viability of a quasiparticle description implies the presence of additional characteristic features in the spectral functions. These features are in stark contrast with the functional form that is found in strongly coupled plasmas via the gauge/gravity duality. A central goal is therefore to determine which of these dynamical regimes the quark-gluon plasma is qualitatively closer to as a function of temperature. We review the analysis of lattice correlators in relation to transport properties, and tentatively estimate what computational effort is required to make decisive progress in this field.Comment: 54 pages, 37 figures, review written for EPJA and APPN; one parag. added end of section 3.4, and one at the end of section 3.2.2; some Refs. added, and some other minor change

Glueballs, gluon condensate, and pure glue QCD below T_c

A quasiparticle description of pure glue QCD thermodynamics at T<T_c is proposed and compared to recent lattice data. Given that a gas of glueballs with constant mass cannot quantitatively reproduce the early stages of the deconfinement phase transition, the problem is to identify a relevant mechanism leading to the observed sudden increase of the pressure, trace anomaly, etc. It is shown that the strong decrease of the gluon condensate near T_c combined with the increasing thermal width of the lightest glueballs might be the trigger of the phase transition.Comment: 5 pages, 5 figures; analysis refined in v2, explanations added; v3 to appear in EPJ

Second Harmonic Generation for a Dilute Suspension of Coated Particles

We derive an expression for the effective second-harmonic coefficient of a dilute suspension of coated spherical particles. It is assumed that the coating material, but not the core or the host, has a nonlinear susceptibility for second-harmonic generation (SHG). The resulting compact expression shows the various factors affecting the effective SHG coefficient. The effective SHG per unit volume of nonlinear coating material is found to be greatly enhanced at certain frequencies, corresponding to the surface plasmon resonance of the coated particles. Similar expression is also derived for a dilute suspension of coated discs. For coating materials with third-harmonic (THG) coefficient, results for the effective THG coefficients are given for the cases of coated particles and coated discs.Comment: 11 pages, 3 figures; accepted for publication in Phys. Rev.

Quasi-particle model for lattice QCD: quark-gluon plasma in heavy ion collisions

We propose a quasi-particle model to describe the lattice QCD equation of state for pure SU(3) gauge theory in its deconfined state, for $T \ge 1.5T_c$. The method involves mapping the interaction part of the equation of state to an effective fugacity of otherwise non-interacting quasi-gluons. We find that this mapping is exact. Using the quasi-gluon distribution function, we determine the energy density and the modified dispersion relation for the single particle energy, in which the trace anomaly is manifest. As an application, we first determine the Debye mass, and then the important transport parameters, {\it viz}, the shear viscosity, $\eta$ and the shear viscosity to entropy density ratio, $\eta/{\mathcal S}$. We find that both $\eta$ and $\eta/{\mathcal S}$ are sensitive to the interactions, and that the interactions significantly lower both $\eta$ and $\eta/\mathcal S$.Comment: 10 pages, 8 figures, epj class file, version accepted for publication in Euro. Phys.J

Improved Holographic QCD

We provide a review to holographic models based on Einstein-dilaton gravity with a potential in 5 dimensions. Such theories, for a judicious choice of potential are very close to the physics of large-N YM theory both at zero and finite temperature. The zero temperature glueball spectra as well as their finite temperature thermodynamic functions compare well with lattice data. The model can be used to calculate transport coefficients, like bulk viscosity, the drag force and jet quenching parameters, relevant for the physics of the Quark-Gluon Plasma.Comment: LatEX, 65 pages, 28 figures, 9 Tables. Based on lectures given at several Schools. To appear in the proceedinds of the 5th Aegean School (Milos, Greece

Fluctuations, dissipation and the dynamical Casimir effect

Vacuum fluctuations provide a fundamental source of dissipation for systems coupled to quantum fields by radiation pressure. In the dynamical Casimir effect, accelerating neutral bodies in free space give rise to the emission of real photons while experiencing a damping force which plays the role of a radiation reaction force. Analog models where non-stationary conditions for the electromagnetic field simulate the presence of moving plates are currently under experimental investigation. A dissipative force might also appear in the case of uniform relative motion between two bodies, thus leading to a new kind of friction mechanism without mechanical contact. In this paper, we review recent advances on the dynamical Casimir and non-contact friction effects, highlighting their common physical origin.Comment: 39 pages, 4 figures. Review paper to appear in Lecture Notes in Physics, Volume on Casimir Physics, edited by Diego Dalvit, Peter Milonni, David Roberts, and Felipe da Rosa. Minor changes, a reference adde

Measurement of the B0-anti-B0-Oscillation Frequency with Inclusive Dilepton Events

The $B^0$-$\bar B^0$ oscillation frequency has been measured with a sample of 23 million \B\bar B pairs collected with the BABAR detector at the PEP-II asymmetric B Factory at SLAC. In this sample, we select events in which both B mesons decay semileptonically and use the charge of the leptons to identify the flavor of each B meson. A simultaneous fit to the decay time difference distributions for opposite- and same-sign dilepton events gives $\Delta m_d = 0.493 \pm 0.012{(stat)}\pm 0.009{(syst)}$ ps$^{-1}$.Comment: 7 pages, 1 figure, submitted to Physical Review Letter

Fat and carbohydrate metabolism during and following hemorrhagic shock in puppies: A comparison of different resuscitation protocols

Shock states continue to carry a high mortality rate in the pediatric age group. Using a puppy model, we measured the initial metabolic response to hemorrhagic shock and to 3 resuscitation regimens: whole blood 1∶1 (replacement∶shed), lactated Ringer's 3∶1, and 5% albumin in lactated Ringer's 1∶1. Despite the immature nature of the puppy's enzyme, cardiovascular, and nervous systems, responses very similar to those in adult animals were seen. Serum glucose and free fatty acids rose during shock and declined with resuscitation as cardiac output returned toward normal. Serum lactate levels rose similarly but continued to rise for a short period after resuscitation and were associated with a further fall in pH consistent with “hidden acidosis.” Only small changes were noted in triglyceride and cholesterol levels. The metabolic responses noted following each of the 3 resuscitation protocols were similar. This study suggests that the immature animal responds to hemorrhagic shock in ways similar to the adult. The better initial hemodynamic response to resuscitation with high-volume lactated Ringer's or lactated Ringer's with 5% albumin was offset by the better buffering capacity of blood resuscitation. All 3 regimens were equally efficacious in providing initial metabolic recovery in this experimental hemorrhagic shock model. Les états de choc s'accompagnent d'une mortalité élevée chez les enfants. En ayant recours à l'expérimentation chez le chiot, les auteurs ont mesuré les modifications métaboliques initiales en réponse au choc hémoragique et à sa correction par 3 agents différents: sang complet (1∶1), solution de Ringer (3∶1) et solution de Ringer enrichie de 5% d'albumine. Malgré la nature immature des enzymes du chiot, du système cardio-vasculaire et du système nerveux, les réponses furent identiques à celles observées chez le chien adulte. Le glucose et les acides gras libres s'élevèrent au cours du choc et s'abaissèrent lors de la réanimation dès que le débit cardiaque revint à la normale. Les niveaux du lactate sanguin s'élevèrent de la même manière mais l'élévation continua pendant une courte période après la réanimation, cependant que le pH s'abaissait, démasquant une “acidose cachée”. Les taux des triglycérides et du cholestérol furent seulement discrètement altérés. Les réponses métaboliques étudiées en fonction des 3 méthodes de réanimation furent identiques. Cette étude suggère que le chiot répond de la même façon que le chien adulte au choc hémorragique et que les 3 méthodes de réanimation employant chacune des agents différents ont une efficacité identique. Los estados shock mantienen una elevada mortalidad en los grupos de edad pediátrica. Utilizando un modelo de shock en cachorros, se determinó la respuesta metabólica inicial al shock hemorrágico y a tres diferentes regimenes de resucitación: sangre total 1∶1 (reemplazo: pérdida), lactato de Ringer 3∶1, y albúmina al 5% en lactato de Ringer 1∶1. A pesar de la naturaleza inmadura de los sistemas enzimático, cardiovascular y nervioso del cachorro, las respuestas fueron muy similares a las observadas en animales adultos. La glucosa sérica y los ácidos grasos libres ascendieron durante el shock y declinarion en la medida que el débito cardiaco retornaba a lo normal. Los niveles de lactato sérico ascendieron en forma similar, pero continuaron su ascenso por un corto periodo de tiempo después de la resucitación, encontrándose asociados con una caida adicional del pH consistente con “acidosis oculta”. Sólo se presentaron cambios leves en los niveles de triglicéridos y colesterol. Las respuestas metabólicas observadas en cada uno de los tres protocolos de resucitación fueron similares. Este estudio sugiere que el animal inmaduro responde al shock hemorrágico de manera similar al adulto. La mejor respuesta hemodinámica inicial a la resucitación con altos volúmenes de lactato de Ringer o con lactato de Ringer con albúmina al 5%, fue compensada con una mejor capacidad de amortiguación observada en la resucitación con sangre. Los tres regimenes fueron igualmente eficaces en lograr la recuperación metabólica inicial en este modelo experimental de shock hemorrágico.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41311/1/268_2005_Article_BF01655348.pd

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