Mean Field Dynamics in Non-Abelian Plasmas from Classical Transport Theory

Based on classical transport theory, we present a general set of covariant equations describing the dynamics of mean fields and their statistical fluctuations in a non-Abelian plasma in or out-of-equilibrium. A procedure to obtain the collision integrals for the Boltzmann equation from the microscopic theory is described. As an application, we study a hot non-Abelian plasma close to equilibrium, where the fluctuations are integrated out explicitly. For soft fields, and at logarithmic accuracy, we obtain B\"odeker's effective theory.Comment: 4 pages, revtex, no figures. Typo removed, a reference updated, version as to appear in Phys. Rev. Let

Heavy Quark Radiative Energy Loss - Applications to RHIC

Heavy quark energy loss in a hot QCD plasma is computed taking into account the competing effects due to suppression of zeroth order gluon radiation bellow the plasma frequency and the enhancement of gluon radiation due to transition energy loss and medium induced Bremsstrahlung. Heavy quark medium induced radiative energy loss is derived to all orders in opacity, $(L/\lambda_g)^n$. Numerical evaluation of the energy loss suggest small suppression of high $p_\perp$ charm quarks, and therefore provide a possible explanation for the null effects observed by PHENIX in the prompt electron spectrum in $Au+Au$ as $\sqrt{s}=130$ and 200 AGeV.Comment: 4 pages, 4 figures, Contributed to 17th International Conference on Ultra Relativistic Nucleus-Nucleus Collisions (Quark Matter 2004), Oakland, California, 11-17 Jan 200

Transport Theory of Massless Fields

Using the Schwinger-Keldysh technique we discuss how to derive the transport equations for the system of massless quantum fields. We analyse the scalar field models with quartic and cubic interaction terms. In the $\phi^4$ model the massive quasiparticles appear due to the self-interaction of massless bare fields. Therefore, the derivation of the transport equations strongly resembles that one of the massive fields, but the subset of diagrams which provide the quasiparticle mass has to be resummed. The kinetic equation for the finite width quasiparticles is found, where, except the mean-field and collision terms, there are terms which are absent in the standard Boltzmann equation. The structure of these terms is discussed. In the massless $\phi^3$ model the massive quasiparticles do not emerge and presumably there is no transport theory corresponding to this model. It is not surprising since the $\phi^3$ model is anyhow ill defined.Comment: 32 pages, no macro

Non-Abelian Excitations of the Quark-Gluon Plasma

We present new, non-abelian, solutions to the equations of motion which describe the collective excitations of a quark-gluon plasma at high temperature. These solutions correspond to spatially uniform color oscillations.Comment: 8 pages LaTex, 1 figure (not included; available upon request), Saclay preprint T94/0

Decoherence and energy loss in QCD cascades in nuclear collisions

The medium modifications in the properties of QCD cascades are considered. In particular, the changes in the intrajet rapidity distributions due to medium-induced decoherence, collisional losses of cascade gluons and those of final prehadrons are analyzed

Color plasma oscillation in strangelets

The dispersion relation and damping rate of longitudinal color plasmons in finite strange quark matter (strangelets) are evaluated in the limits of weak coupling, low temperature, and long wavelength. The property of the QCD vacuum surrounding a strangelet makes the frequency of the plasmons nearly the same as the color plasma frequency of bulk matter. The plasmons are damped by their coupling with individual excitations of particle-hole pairs of quarks, of which the energy levels are discretized by the boundary. For strangelets of macroscopic size, the lifetime of the plasmons is found to be proportional to the size, as in the case of the usual plasma oscillations in metal nanoparticles.Comment: 9 pages (REVTeX), 2 Postscript figures, to be published in Phys. Rev.

Color conductivity and ladder summation in hot QCD

The color conductivity is computed at leading logarithmic order using a Kubo formula. We show how to sum an infinite series of planar ladder diagrams, assuming some approximations based on the dominance of soft scattering processes between hard particles in the plasma. The result agrees with the one obtained previously from a kinetical approach.Comment: 15 pages, 4 figures. Explanations enlarged, two figures and some refs added, typos corrected. Final version to be published in Phys.Rev.

Classical Gluon Radiation in Ultrarelativistic Nuclear Collisions: Space-Time Structure, Instabilities, and Thermalization

We investigate the space-time structure of the classical gluon field produced in an ultrarelativistic collision between color charges. The classical solution which was computed previously in a perturbative approach is shown to become unstable on account of the non-Abelian self-interaction neglected in the perturbative solution scheme. The time scale for growth of the instabilities is found to be of the order of the distance between the colliding color charges. We argue that these instabilities will eventually lead to thermalization of gluons produced in an ultrarelativistic collision between heavy nuclei. The rate of thermalization is estimated to be of order $g^2 \mu$, where $g$ is the strong coupling constant and $\mu^2$ the transverse color charge density of an ultrarelativistic nucleus.Comment: 11 pages, REVTeX, eps-, aps-, and psfig-style files, 7 figs., figs. 2-5 in gif-format, a uucompressed version of this paper including all figures (ca. 2.2 Mb) is available at ftp://nt1.phys.columbia.edu/pub/stabil/stab.u

Longitudinal subtleties in diffusive Langevin equations for non-Abelian plasmas

Boedeker has recently argued that non-perturbative processes in very high temperature non-Abelian plasmas (such as electroweak baryon number violation in the very hot early Universe) can be quantitatively described, to leading logarithmic accuracy, by a simple diffusive effective theory. Boedeker's effective theory is intended to describe the long-distance transverse electric and magnetic fields which are responsible for non-perturbative dynamics. His effective theory, however, also contains long-wavelength longitudinal electric fields. We discuss several subtleties in the treatment of longitudinal dynamics which were not closely examined in Boedeker's original treatment. Somewhat to our surprise, we find that within its domain of validity Boedeker's effective theory does correctly describe both longitudinal and transverse fluctuations. We also show that, as far as the transverse dynamics of interest is concerned, Boedeker's effective theory could be replaced by a transverse-only theory that removes the longitudinal dynamics altogether. In the process, we discuss several interesting aspects of stochastic field theories.Comment: 29 pages, Section III rewritten, other minor change

From colored glass condensate to gluon plasma: equilibration in high energy heavy ion collisions

The initial distribution of gluons at the very early times after a high energy heavy ion collision is described by the bulk scale $Q_s$ of gluon saturation in the nuclear wavefunction. The subsequent evolution of the system towards kinetic equilibrium is described by a non-linear Landau equation for the single particle distributions \cite{Mueller1,Mueller2}. In this paper, we solve this equation numerically for the idealized initial conditions proposed by Mueller, and study the evolution of the system to equilibrium. We discuss the sensitivity of our results on the dynamical screening of collinear divergences. In a particular model of dynamical screening, the convergence to the hydrodynamic limit is seen to be rapid relative to hydrodynamic time scales. The equilibration time, the initial temperature, and the chemical potential are shown to have a strong functional dependence on the initial gluon saturation scale $Q_s$.Comment: 34 pages, 10 figure