EMMI Rapid Reaction Task Force on "Thermalization in Non-abelian Plasmas"

Recently, different proposals have been put forward on how thermalization proceeds in heavy-ion collisions in the idealized limit of very large nuclei at sufficiently high energy. Important aspects of the parametric estimates at weak coupling may be tested using well-established classical-statistical lattice simulations of the far-from-equilibrium gluon dynamics. This has to be confronted with strong coupling scenarios in related theories based on gauge-string dualities. Furthermore, closely related questions about far-from-equilibrium dynamics arise in early-universe cosmology and in non-relativistic systems of ultracold atoms. These were central topics of the EMMI Rapid Reaction Task Force meeting held on December 12-14, 2011, at the University of Heidelberg, which we report on.Comment: 13 pages, summary of the EMMI Rapid Reaction Task Force on "Thermalization in Non-abelian Plasmas", December 12-14, 2011, University of Heidelberg, German

Early anisotropic hydrodynamics and the RHIC early-thermalization and HBT puzzles

We address the problem if the early thermalization and HBT puzzles in relativistic heavy-ion collisions may be solved by the assumption that the early dynamics of the produced matter is locally anisotropic. The hybrid model describing the purely transverse hydrodynamic evolution followed by the perfect-fluid hydrodynamic stage is constructed. The transition from the transverse to perfect-fluid hydrodynamics is described by the Landau matching conditions applied at a fixed proper time. The global fit to the RHIC data reproduces the soft hadronic observables (the pion, kaon, and the proton spectra, the pion and kaon elliptic flow, and the pion HBT radii) with the accuracy of about 20%. These results indicate that the assumption of the very fast thermalization may be relaxed. In addition, the presented model suggests that a large part of the inconsistencies between the theoretical and experimental HBT results may be removed.Comment: replaced with the version published in Phys.Rev.C 8

Free-streaming approximation in early dynamics of relativistic heavy-ion collisions

We investigate an approximation to early dynamics in relativistic heavy-ion collisions, where after formation the partons are free streaming and around the proper time of 1 fm/c undergo a sudden equilibration described in terms of the Landau matching condition. We discuss physical and formal aspects of this approach. In particular, we show that initial azimuthally asymmetric transverse flow develops for non-central collisions as a consequence of the sudden equilibration. Moreover, the energy-momentum tensor from the free-streaming stage matches very smoothly to the form used in the transverse hydrodynamics, whereas matching to isotropic hydrodynamics requires a more pronounced change in the energy-momentum tensor. After the hydrodynamic phase statistical hadronization is carried out with the help of THERMINATOR. The physical results for the transverse-momentum spectra, the elliptic-flow, and the Hanbury-Brown--Twiss correlation radii, including the ratio R_out/R_side as well as the dependence of the radii on the azimuthal angle (azHBT), are properly described within our approach. The agreement is equally good for a purely hydrodynamic evolution started at an early proper time of 0.25 fm/c, or for the free streaming started at that time, followed by the sudden equilibration at tau ~1 fm/c and then by perfect hydrodynamics. Thus, the inclusion of free streaming allows us to delay the start of hydrodynamics to more realistic times of the order of 1 fm/c.Comment: 10 pages, 12 figure

Space-time evolution of bulk QCD matter

We introduce a combined fully three-dimensional macroscopic/microscopic transport approach employing relativistic 3D-hydrodynamics for the early, dense, deconfined stage of the reaction and a microscopic non-equilibrium model for the later hadronic stage where the equilibrium assumptions are not valid anymore. Within this approach we study the dynamics of hot, bulk QCD matter, which is being created in ultra-relativistic heavy ion collisions at RHIC. Our approach is capable of self-consistently calculating the freezeout of the hadronic system, while accounting for the collective flow on the hadronization hypersurface generated by the QGP expansion. In particular, we perform a detailed analysis of the reaction dynamics, hadronic freezeout, and transverse flow.Comment: 24 pages, 27 figure

Phasespace Correlations of Antideuterons in Heavy Ion Collisions

In the framework of the relativistic quantum molecular dynamics approach ({\small RQMD}) we investigate antideuteron ($\overline{d}$) observables in Au+Au collisions at 10.7~AGeV. The impact parameter dependence of the formation ratios $\overline{d}/\overline{p}^2$ and ${d}/{p}^2$ is calculated. In central collisions, the antideuteron formation ratio is predicted to be two orders of magnitude lower than the deuteron formation ratio. The $\overline{d}$ yield in central Au+Au collisions is one order of magnitude lower than in Si+Al collisions. In semicentral collisions different configuration space distributions of $\overline{p}$'s and $\overline{d}$'s lead to a large ``squeeze--out'' effect for antideuterons, which is not predicted for the $\overline{p}$'s

Hydrodynamic transport functions from quantum kinetic theory

Starting from the quantum kinetic field theory [E. Calzetta and B. L. Hu, Phys. Rev. D37, 2878 (1988)] constructed from the closed-time-path (CTP), two-particle-irreducible (2PI) effective action we show how to compute from first principles the shear and bulk viscosity functions in the hydrodynamic-thermodynamic regime. For a real scalar field with $\lambda \Phi ^{4}$ self-interaction we need to include 4 loop graphs in the equation of motion. This work provides a microscopic field-theoretical basis to the ``effective kinetic theory'' proposed by Jeon and Yaffe [S. Jeon and L. G. Yaffe, Phys. Rev. D53, 5799 (1996)], while our result for the bulk viscosity reproduces their expression derived from linear response theory and the imaginary-time formalism of thermal field theory. Though unavoidably involved in calculations of this sort, we feel that the approach using fundamental quantum kinetic field theory is conceptually clearer and methodically simpler than the effective kinetic theory approach, as the success of the latter requires clever rendition of diagrammatic resummations which is neither straightforward nor failsafe. Moreover, the method based on the CTP-2PI effective action illustrated here for a scalar field can be formulated entirely in terms of functional integral quantization, which makes it an appealing method for a first-principles calculation of transport functions of a thermal non-abelian gauge theory, e.g., QCD quark-gluon plasma produced from heavy ion collisions.Comment: 25 pages revtex, 11 postscript figures. Final version accepted for publicatio

In-medium relativistic kinetic theory and nucleon-meson systems

Within the $\sigma-\omega$ model of coupled nucleon-meson systems, a generalized relativistic Lenard--Balescu--equation is presented resulting from a relativistic random phase approximation (RRPA). This provides a systematic derivation of relativistic transport equations in the frame of nonequilibrium Green's function technique including medium effects as well as flucuation effects. It contains all possible processes due to one meson exchange and special attention is kept to the off--shell character of the particles. As a new feature of many particle effects, processes are possible which can be interpreted as particle creation and annihilation due to in-medium one meson exchange. In-medium cross sections are obtained from the generalized derivation of collision integrals, which possess complete crossing symmetries.Comment: See nucl-th/9310032 for revised version which the authors incompetently resubmitted rather than correctly replacing thi

Fluctuation of Gaps in Hadronization at Phase Transition

Event-by-event fluctuations of hadronic patterns in heavy-ion collisions are studied in search for signatures of quark-hadron phase transition. Attention is focused on a narrow strip in the azimuthal angle with small $\Delta y$. The fluctuations in the gaps between particles are quantified by simple measures. A scaling exponent $\alpha$ is shown to exist around $T_c$. An index $\xi$ is shown to characterize the critical fluctuation; it is a numerical constant $\xi=0.05\pm0.01$. All the measures considered in this gap analysis are experimentally observable. Whether or not the theoretical predictions, based on simulations using 2-dimensional Ising model, are realistic for heavy-ion collisions, analysis of the experimental data suggested here should be carried out, since the existence of a scaling behavior is of interest in its own right.Comment: 10 pages LaTex + 8 eps figure

Fluctuations driven isotropization of the quark-gluon plasma in heavy ion collisions

Averaged over ensemble of initial conditions kinetic transport equations of weakly coupled systems of quarks and gluons are derived. These equations account for the correlators of fluctuations of particles and classical gluon fields. The isotropization of particle momenta by field fluctuations at the early prethermal stage of matter evolution in ultrarelativistic heavy ion collisions is discussed. Our results can be useful for understanding under what conditions isotropization of the quark-gluon plasma in ultrarelativistic heavy ion collisions can be reached within phenomenologically observed time scales.Comment: 16 pages, misprints corrected, to be published in Phys. Rev.

Time evolution in linear response: Boltzmann equations and beyond

In this work a perturbative linear response analysis is performed for the time evolution of the quasi-conserved charge of a scalar field. One can find two regimes, one follows exponential damping, where the damping rate is shown to come from quantum Boltzmann equations. The other regime (coming from multiparticle cuts and products of them) decays as power law. The most important, non-oscillating contribution in our model comes from a 4-particle intermediate state and decays as 1/t^3. These results may have relevance for instance in the context of lepton number violation in the Early Universe.Comment: 19 page