Thermalization In Heavy-ion Collisions Research Articles

Hard gluon evolution in the last stage of the bottom-up thermalization

The study of how fast thermalization in heavy ion collisions occurs has been one of the central topics in the heavy ion community. In the weak coupling picture this thermalization occurs from ‘the bottom up’: high energy partons, formed early in the collision, radiate low energy gluons which then proceed to equilibrate among themselves, forming a thermal bath that brings the high energy sector to equilibrium. In this scheme we apply a model on parton energy loss to discuss the effects of medium expansion on the thermalization problem and estimate the average transverse momentum diffusivity for thermalization in a Bjorken expanding medium.

Approach to thermalization and hydrodynamics

I review recent progress in thermalization in heavy-ion collisions, with particular emphasis on hydrodynamic attractor, and also report recent progress in hydrodynamic fluctuations.

Correlations far from equilibrium in charged strongly coupled fluids subjected to a strong magnetic field

Within a holographic model, we calculate the time evolution of 2-point and 1-point correlation functions (of selected operators) within a charged strongly coupled system of many particles. That system is thermalizing from an anisotropic initial charged state far from equilibrium towards equilibrium while subjected to a constant external magnetic field. One main result is that thermalization times for 2-point functions are significantly (approximately three times) larger than those of 1-point functions. Magnetic field and charge amplify this difference, generally increasing thermalization times. However, there is also a competition of scales between charge density, magnetic field, and initial anisotropy, which leads to an array of qualitative changes on the 2- and 1-point functions. There appears to be a strong effect of the medium on 2-point functions at early times, but approximately none at later times. At strong magnetic fields, an apparently universal thermalization time emerges, at which all 2-point functions appear to thermalize regardless of any other scale in the system. Hence, this time scale is referred to as saturation time scale. As extremality is approached in the purely charged case, 2- and 1-point functions appear to equilibrate at infinitely late time. We also compute 2-point functions of charged operators. Our results can be taken to model thermalization in heavy ion collisions, or thermalization in selected condensed matter systems.

Time-dependent observables in heavy ion collisions. Part II. In search of pressure isotropization in the \u03c64 theory

To understand the dynamics of thermalization in heavy ion collisions in the perturbative framework it is essential to first find corrections to the free-streaming classical gluon fields of the McLerran-Venugopalan model. The corrections that lead to deviations from free streaming (and that dominate at late proper time) would provide evidence for the onset of isotropization (and, possibly, thermalization) of the produced medium. To find such corrections we calculate the late-time two-point Green function and the energy-momentum tensor due to a single 2 → 2 scattering process involving two classical fields. To make the calculation tractable we employ the scalar φ4 theory instead of QCD. We compare our exact diagrammatic results for these quantities to those in kinetic theory and find disagreement between the two. The disagreement is in the dependence on the proper time τ and, for the case of the two-point function, is also in the dependence on the space-time rapidity η: the exact diagrammatic calculation is, in fact, consistent with the free streaming scenario. Kinetic theory predicts a build-up of longitudinal pressure, which, however, is not observed in the exact calculation. We conclude that we find no evidence for the beginning of the transition from the free-streaming classical fields to the kinetic theory description of the produced matter after a single 2 → 2 rescattering.

Initial conditions in AA and pA collisions

A full understanding of the spacetime evolution of the QCD matter created in a heavy ion collision requires understanding the properties of the initial stages. In the weak coupling picture these are dominated by classical gluon fields, whose properties can also be studied via the scattering of dilute probes off a high energy hadron or nucleus. A particular challenge is understanding small systems, where LHC data is also showing signs of collective behavior. We discuss some recent results of on the initial matter production and thermalization in heavy ion collisions, in particular in the gluon saturation framework.

Parametric instability of classical Yang-Mills fields in an expanding geometry

We investigate the instability of classical Yang-Mills field in an expanding geometry under a color magnetic background field within the linear regime. We consider homogeneous, boost-invariant and time-dependent color magnetic fields simulating the glasma configuration. We introduce the conformal coordinates which enable us to map an expanding problem approximately into a nonexpanding problem. We find that the fluctuations with finite longitudinal momenta can grow exponentially due to parametric instability. Fluctuations with finite transverse momenta can also show parametric instability, but their momenta are restricted to be small. The most unstable modes start to grow exponentially in the early stage of the dynamics and they may affect the thermalization in heavy-ion collisions.

Entanglement and fast quantum thermalization in heavy ion collisions

Let [Formula: see text] be subsystem of a larger system [Formula: see text] and [Formula: see text] be a typical state from the subspace of the Hilbert space [Formula: see text] satisfying an energy constraint. Then [Formula: see text] is nearly thermal. We discuss how this observation is related to fast thermalization of the central region ([Formula: see text]) in heavy ion collisions (HIC), where [Formula: see text] represents other degrees of freedom (soft modes, hard jets, collinear particles) outside of [Formula: see text]. Entanglement between the modes in [Formula: see text] and [Formula: see text] play a central role: the entanglement entropy [Formula: see text] increases rapidly in the collision. In gauge–gravity duality, [Formula: see text] is related to the area of extremal surfaces in the bulk, which can be studied using gravitational duals.

Kinetic evolution of the glasma and thermalization in heavy-ion collisions

In relativistic heavy-ion collisions, a highly occupied gluonic matter is created shortly after initial impact, which is in a nonthermal state and often referred to as the Glasma. Successful phenomenology suggests that the glasma evolves rather quickly toward the thermal quark–gluon plasma (QGP) and a hydrodynamic behavior emerges at a very early time ~ô(1) fm/c. Exactly how such "apparent thermalization" occurs and connects the initial conditions to the hydrodynamic onset, remains a significant challenge for theory as well as phenomenology. We briefly review various ideas and recent progress in understanding the approach of the glasma to the thermalized QGP, with an emphasis on the kinetic theory description for the evolution of such far-from-equilibrium and highly overpopulated, thus weakly-coupled yet strongly interacting glasma.

Anisotropy of Photon Production: Initial Eccentricity or Magnetic Field

Recent measurements of the azimuthal anisotropy of direct photons in heavy-ion collisions at the energies of Relativistic Heavy Ion Collider show that it is of the same order as the hadronic one. This finding appears to contradict the expected dominance of photon production from a quark-gluon plasma at an early stage of a heavy-ion collision. A possible explanation of the strong azimuthal anisotropy of the photons, given recently, is based on the presence of a large magnetic field in the early phase of a collision. In this Letter, we propose a method to experimentally measure the degree to which a magnetic field in heavy-ion collisions is responsible for the observed anisotropy of photon production. The experimental test proposed in this Letter may potentially change our understanding of the nonequilibrium stage and possible thermalization in heavy-ion collisions.

Nonequilibrium two-particle irreducible evolution of theO(N)model with longitudinal expansion

Motivated by the problem of thermalization in heavy-ion collisions, we present numerical simulations of the nonequilibrium evolution of the O(N) model in 1+2 dimensions with longitudinal expansion and in the presence of a background field. We work in the NLO approximation of the 1/N expansion and consider both the strong and weak coupling cases. Special emphasis is put on the difference between the 2PI formalism and the classical statistical approach. In the 2PI case at strong coupling, we find some evidence of the Bose-Einstein (exponential) distribution in the expanding system.

Characteristics of Thermalization of Boost-Invariant Plasma from Holography

We report on the approach toward the hydrodynamic regime of boost-invariant N=4 super Yang-Mills plasma at strong coupling starting from various far-from-equilibrium states at τ=0. The results are obtained through a numerical solution of Einstein's equations for the dual geometries, as described in detail in the companion article [M. P. Heller, R. A. Janik, and P. Witaszczyk, arXiv:1203.0755]. Despite the very rich far-from-equilibrium evolution, we find surprising regularities in the form of clear correlations between initial entropy and total produced entropy, as well as between initial entropy and the temperature at thermalization, understood as the transition to a hydrodynamic description. For 29 different initial conditions that we consider, hydrodynamics turns out to be definitely applicable for proper times larger than 0.7 in units of inverse temperature at thermalization. We observe a sizable anisotropy in the energy-momentum tensor at thermalization, which is nevertheless entirely due to hydrodynamic effects. This suggests that effective thermalization in heavy-ion collisions may occur significantly earlier than true thermalization.

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 \sim {\alpha^{{\frac{{ - 12}}{5}}}}Q_s^{{ - 1}} $ the dynamics become dominated by a nearly-thermal bath; and at time $ \tau \sim {\alpha^{{\frac{{ - 5}}{2}}}}Q_s^{{ - 1}} $ the bath comes to dominate the energy density, completing thermalization. After this time there is a nearly isotropic and thermal Quark-Gluon Plasma.

Towards thermalization in heavy-ion collisions: CGC meets the 2PI formalism

We propose to apply the two-particle irreducible (2PI) formalism to the problem of thermalization in heavy-ion collisions in the Color Glass Condensate (CGC) picture. We consider the 2PI effective action to three loops and derive a set of coupled equations for the classical Yang-Mills field and the quantum fluctuations in the boost invariant coordinate system. The initial condition and the relation to previous works are also discussed.

Heavy ion collisions in AdS 5

We study heavy ion collisions at strong ʼt Hooft coupling using AdS/CFT correspondence. Heavy ion collisions correspond to gravitational shock wave collisions in AdS 5. We construct the metric in the forward light cone after the collision perturbatively through expansion of Einstein equations in graviton exchanges. We obtain an analytic expression for the metric including all-order graviton exchanges with one shock wave, while keeping the exchanges with another shock wave at the lowest order. We read off the corresponding energy-momentum tensor of the produced medium. Unfortunately this energy-momentum tensor does not correspond to ideal hydrodynamics, indicating that higher order graviton exchanges are needed to construct the full solution of the problem. We also show that shock waves must completely stop almost immediately after the collision in AdS 5, which, on the field theory side, corresponds to complete nuclear stopping due to strong coupling effects, likely leading to Landau hydrodynamics. Finally, we perform trapped surface analysis of the shock wave collisions demonstrating that a bulk black hole, corresponding to ideal hydrodynamics on the boundary, has to be created in such collisions, thus constructing a proof of thermalization in heavy ion collisions at strong coupling.

Shock Wave Collisions and Thermalization in AdS5

We study heavy ion collisions at strong 't Hooft coupling using AdS/CFT correspondence. According to the AdS/CFT dictionary heavy ion collisions correspond to gravitational shock wave collisions in AdS_5. We construct the metric in the forward light cone after the collision perturbatively through expansion of Einstein equations in graviton exchanges. We obtain an analytic expression for the metric including all-order graviton exchanges with one shock wave, while keeping the exchanges with another shock wave at the lowest order. We read off the corresponding energy-momentum tensor of the produced medium. Unfortunately this energy-momentum tensor does not correspond to ideal hydrodynamics, indicating that higher order graviton exchanges are needed to construct the full solution of the problem. We also show that shock waves must completely stop almost immediately after the collision in AdS_5, which, on the field theory side, corresponds to complete nuclear stopping due to strong coupling effects, likely leading to Landau hydrodynamics. Finally, we perform trapped surface analysis of the shock wave collisions demonstrating that a bulk black hole, corresponding to ideal hydrodynamics on the boundary, has to be created in such collisions, thus constructing a proof of thermalization in heavy ion collisions at strong coupling.

Parton rearrangement and fast thermalization in heavyion collisions at RHIC and LHC energies

The implications of parton rearrangement processes on the dynamics of ultra-relativistic heavy-ion collisions have been investigated. A microscopic transport approach, namely the quark gluon string model (QGSM) which has been extended for a locally density-dependent partonic rearrangement and fusion procedure served as the tool for this investigations. The model emulates effectively the dynamics of a strongly coupled quark plasma and final hadronic interactions. Main QGSM results on anisotropic flow components v1 and v2 at top RHIC energy are compiled. Predictions for the pseudorapidity dependence of directed and elliptic flow in Pb+Pb collisions under LHC conditions are presented.

Toward thermalization in heavy ion collisions at strong coupling

We find the trapped surface for a collision of two sourceless shock waves in AdS5 and conclude that such collisions always lead to a creation of a black hole in the bulk. Due to holographic correspondence, in the boundary gauge theory this result proves that a thermalized medium (quark-gluon plasma) is produced in heavy ion collisions at strong coupling (albeit in $$\mathcal{N} $$ = 4 super-Yang-Mills theory). We present new evidence supporting the analytic estimate for the time of thermalization that exists in the literature and find that thermalization time is parametrically much shorter than the time of shock wave stopping, indicating that our result may be relevant for description of heavy ion collision experiments.

Early times and thermalization in heavy ion collisions: a summary of experimental results for photons, light vector mesons, open and hidden heavy flavors

This contribution summarizes the main experimental results presented at the 2009 Quark Matter conference concerning single and dilepton production in proton and heavy ion collisions at high energy. The dilepton invariant mass spectrum has been measured over a range that extends from the π 0 mass to the ϒ mass, and for various collision energies at SPS, Fermilab, Hera and RHIC. This paper focuses on the various contributions (photons, low mass vector mesons, open and hidden heavy flavors) to this spectrum and discuss their implications on our understanding of the matter formed in heavy ion collisions.

What the inflaton might tell us about RHIC/LHC

Topical phenomena in high-energy physics related to collision experiments of heavy nuclei (“Little Bang”) and early universe cosmology (“Big Bang”) involve far-from-equilibrium dynamics described by quantum field theory. One example concerns the role of plasma instabilities for the process of thermalization in heavy-ion collisions. The reheating of the early universe after inflation may exhibit rather similar phenomena following a tachyonic or parametric resonance instability. Certain universal aspects associated to nonthermal fixed points even quantitatively agree, and considering these phenomena from a common perspective can be fruitful.

The unstable glasma

We discuss results from 3+1-D numerical simulations of SU(2) Yang--Mills equations for an unstable Glasma expanding into the vacuum after a high energy heavy ion collision. We expand on our earlier work on a non-Abelian Weibel instability in such a system and study the behavior of the instability in greater detail on significantly larger lattices than previously. We establish the time scale for the onset of the instability and demonstrate that the growth rate is robust as one approaches the continuum limit. For large violations of boost invariance, non-Abelian effects cause the growth of soft modes to saturate. At late times, we observe significant creation of longitudinal pressure and a systematic trend towards isotropy. These time scales however are significantly larger than those required for early thermalization in heavy ion collisions. We discuss additional effects in the produced Glasma that may speed up thermalization.