We employ a non-equilibrium Quantum Chromodynamics (QCD) kinetic description to study the kinetic and chemical equilibration of the Quark-Gluon Plasma (QGP) at weak coupling. Based on our numerical framework, which explicitly includes all leading order processes involving light flavor degrees of freedom, we investigate the thermalization process of homogeneous and isotropic plasmas far-from equilibrium and determine the relevant time scales for kinetic and chemical equilibration. We further simulate the longitudinally expanding pre-equilibrium plasma created in ultrarelativistic heavy-ion collisions at zero and non-zero density of the conserved charges and study its microscopic and macroscopic evolution towards equilibrium.
We report on a new equilibration scenario in relativistic heavy ion collisions, the scenario of the Increasingly Strongly Interacting Parton Plasma, and the effects of this scenario on equilibration and open charm, photon and dilepton production. The parton plasma is shown to be a very special kind of many-body system, which contains new physics concerning the approach towards equilibrium. This is likely to be unique to the parton plasma.
We derive the transport equations of quark-gluon plasma in the quasi-linear approximation. The equations are either of the Balescu-Lenard or Fokker-Planck form. The plasma's dynamics is assumed to be governed by longitudinal chromoelectric fields. The isotropic plasma, which is stable, and the two-stream system, which is unstable, are considered in detail. A process of equilibration is briefly discussed in both cases. The peaks of the two-stream distribution are shown to rapidly dissolve in time.
We investigate the medium induced fragmentation of jets in a high-temperature QCD plasma. Based on an effective kinetic theory of QCD, we study the non-equilibrium evolution of the jet shower and the chemical equilibration of jet fragments in the medium. By including radiative emissions as well as elastic interactions, our approach extends all the way from the jet energy scale to the temperature of the medium and includes important effects such as the recoil of the medium. We present results for the in-medium fragmentation, including chemical and kinetic equilibration of the soft fragments and…
We show the evolution of a gluon plasma towards equilibrium starting at some early moment when the momentum distribution in the central region is momentaneously isotropic. Using HIJING results for Au+Au collision as initial input, we consider thermalization and chemical equilibration simultaneously at both LHC and RHIC energies. Thermalization is shown to be driven chiefly by inelastic process in our scenario contradicting common assumption that this is the role of elastic process. We argue that only the inelastic dominancy depends on the initial conditions but not the dominance itself.
We solve a leading-order QCD kinetic theory with light quarks and gluon degrees of freedom to study the non-equilibrium dynamics of the quark-gluon plasma (QGP). By including both elastic and inelastic scatterings for quarks and gluon, the model is proficient to describe kinetic and chemical equilibration of the QGP, and thus connects the initial (semi-) hard production of partons at early times with the hydrodynamic description of a near-thermalized quark-gluon plasma after the first fm/c of the collision. Within this approach, we investigate the time scales and mechanisms for kinetic and che…
We study thermalization, hydrodynamization, and chemical equilibration in out-of-equilibrium Quark-Gluon Plasma starting from various initial conditions using QCD effective kinetic theory, valid at weak coupling. In non-expanding systems gauge bosons rapidly lose information of the initial state and achieve kinetic equilibrium among themselves, while fermions approach the equilibrium distribution only at later time. In systems undergoing rapid longitudinal expansion, both gluons and quarks are kept away from equilibrium by the expansion, but the evolution is well described by fluid dynamics ev…
Due to anisotropic momentum distributions the parton system produced at the early stage of relativistic heavy-ion collisions is unstable with respect to the magnetic plasma modes. The instabilities isotropize the system and thus speed up the process of its equilibration. The whole scenario of the instabilities driven isotropization is reviewed.
We explore the out-of-equilibrium dynamics of the Quark-Gluon Plasma at zero and finite net-baryon density based on an effective kinetic theory of Quantum Chromo Dynamics (QCD). By investigating the isotropization of the longitudinal pressure, we determine the relevant time and temperature scales for the onset of viscous hydrodynamics, and quantify the dependence on the chemical composition of the QGP. By extrapolating our results to realistic coupling strength, we discuss phenomenological consequences regarding the role of the pre-equilibrium phase at different collision energies.
The chemical equilibration of the parton distribution in collisions of two heavy nuclei at the CERN Large Hadron Collider is investigated. Initial conditions are obtained from a self-screened parton cascade calculation. The onset of transverse expansion of the system is found to impede the chemical equilibration. The system initially approaches chemical equilibrium, but then is driven away from it, when the transverse velocity becomes large.
The chemical equilibration of a highly unsaturated quark-gluon plasma has been studied at finite baryon density. It is found that in the presence of small amount of baryon density, the chemical equilibration for gluon becomes slower and the temperature decreases less steeply as compared to the baryon free plasma. As a result, the space time integrated yield of dilepton is enhanced if the initial temperature of the plasma is held fixed. Even at a fixed initial energy density, the suppression of the dilepton yields at higher baryo-chemical potential is compensated, to a large extent, by the slow…
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 colli…
A set of kinetic equations is used to study equilibration of the anisotropic quark-gluon plasma produced by decays of color flux tubes possibly created at the very early stages of ultra-relativistic heavy-ion collisions. The decay rates of the initial color fields are given by the Schwinger formula, and the collision terms are treated in the relaxation-time approximation. By connecting the relaxation time with viscosity we are able to study production and thermalization processes in the plasma characterized by different values of the ratio of the shear viscosity to entropy density, eta/s. For …
We initiate the study of equilibration rates of strongly coupled quark-gluon plasmas in the absence of conformal symmetry. We primarily consider a supersymmetric mass deformation within ${\cal N}=2^{*}$ gauge theory and use holography to compute quasinormal modes of a variety of scalar operators, as well as the energy-momentum tensor. In each case, the lowest quasinormal frequency, which provides an approximate upper bound on the thermalization time, is proportional to temperature, up to a pre-factor with only a mild temperature dependence. We find similar behaviour in other holographic plasma…
Thermalization in an expanding parton plasma is studied within the framework of Boltzmann equation in the absence of any mean fields. In particular, we study the time-dependence of the relaxation time to the lowest order in finite temperature QCD and how such time-dependence affects the thermalization of an expanding parton plasma. Because of Debye screening and Landau damping at finite temperature, the relaxation time (or transport rates) is free of infrared divergencies in both longitudinal and transverse interactions. The resultant relaxation time decreases with time in an expanding plasma …
Within the framework of a dynamical and physically transparent model developed earlier, we study the time evolution of various quark flavours in the baryon-free region in ultrarelativistic heavy ion collisions. We show that even under optimistic conditions, the quark-gluon system fails to achieve chemical equilibrium.
We investigate the thermalization and the chemical equilibration of a parton plasma created from Au+Au collision at LHC and RHIC energies starting from the early moment when the particle momentum distributions in the central region become for the first time isotropic due to longitudinal cooling. Using the relaxation time approximation for the collision terms in the Boltzmann equations for gluons and for quarks and the real collision terms constructed from the simplest QCD interactions, we show that the collision times have the right behaviour for equilibration. The magnitude of the quark (anti…
We study the production and equilibration of the gluon-minijet plasma expected to be formed in the central region of ultrarelativistic heavy-ion collisions at the BNL-RHIC and the CERN-LHC by solving a self-consistent relativistic transport equation. We compute the minijet production within perturbative QCD. Subsequent collisions among the semi-hard partons are treated by considering the elastic gg -> gg processes with screening of the long wavelength modes taken into account. We determine the time $τ_{eq}$ where close to ideal hydrodynamic flow sets in, and find rather similar numbers for cen…
We study far-from-equilibrium physics of strongly interacting plasmas at criticality and zero charge density for a wide range of dynamical scaling exponents z in d dimensions using holographic methods. In particular, we consider homogeneous isotropization of asymptotically Lifshitz black branes with full backreaction. We find stable evolution and equilibration times that exhibit small dependence of z and are of the order of the inverse temperature. Performing a quasinormal mode analysis we find a corresponding narrow range of relaxation times, fully characterized by the fraction z/(d-1). For z…
Production and equilibration of quark-gluon plasma are studied within the color flux-tube model, at the RHIC and LHC energies. Non-Abelian relativistic transport equations for quarks, antiquarks and gluons, are solved in the extended phase space which includes coordinates, momenta and color. Before the chromoelectric field is formed, hard and semihard partons are produced via minijets which provide the initial conditions necessary to solve the transport equations. The model predicts that in spite of the vast difference between the RHIC and LHC incident energies, once the local equilibrium is r…
The dependence of the equilibration of the parton plasma on the value of the strong coupling is studied in Au+Au collisions at LHC and at RHIC energies. With increasing coupling, the following are found to happen: 1) both thermal and chemical equilibration speed up, 2) in the final degree of equilibration, only quarks and antiquarks show obvious improvements but not gluons and 3) the plasma cools much more rapidly. The deconfinement phase transition will therefore takes place sooner and it naturally results in the shortening of the parton phase of the plasma. The exact duration of this phase i…
We study chemical equilibration in out-of-equilibrium Quark-Gluon Plasma using the first principles method of QCD effective kinetic theory, accurate at weak coupling. In longitudinally expanding systems--relevant for relativistic nuclear collisions--we find that for realistic couplings chemical equilibration takes place after hydrodynamization, but well before local thermalization. We estimate that hadronic collisions with final state multiplicities ${dN_\text{ch}}/{dη}\gtrsim 10^2$ live long enough to reach approximate chemical equilibrium, which is consistent with the saturation of strangene…
Fast thermalization, a subsequent strong buildup of elliptic flow of QCD matter and jet-quenching as found at the Relativistic Heavy Ion Collider (RHIC) are understood as the consequence of perturbative QCD (pQCD) interactions within the 3+1 dimensional parton cascade BAMPS. The main contributions stem from pQCD inspired bremsstrahlung. Comparisons to Au+Au data of the flow parameter v_2 as a function of participation number as well as the gluonic contribution to the nuclear modification factor R_AA for most central collisions are given. Also the shear viscosity to entropy ratio is dynamically…
The effect of baryon density on parton production processes of $gg\rightleftharpoons ggg$ and $gg\rightleftharpoons q{\bar q}$ is studied using full phase space distribution function and also with inclusion of quantum statistics i.e. Pauli blocking and Bose enhancement factors, in the case of both saturated and unsaturated quark gluon plasma. The rate for the process $gg \rightleftharpoons q{\bar q}$ is found to be much less as compared to the most commonly used factorized result obtained on the basis of classical approximation. This discrepancy, which is found both at zero as well as at finit…
The relaxation of a strongly coupled plasma towards the hydrodynamic regime is studied by analyzing the evolution of local and nonlocal observables in the holographic approach. The system is driven in an initial anisotropic and far-from equilibrium state through an impulsive time-dependent deformation (quench) of the boundary spacetime geometry. Effective temperature and entropy density are related to the position and area of a black hole horizon, which has formed as a consequence of the distortion. The behavior of stress-energy tensor, equal-time correlation functions and Wilson loops of diff…
Hot gluons are the dominant components of the QCD plasma to be formed in future high energy heavy ion experiments. In this paper we study the elementary processes in the plasma medium for gluon multiplication based on all orders of the tree-diagrams in perturbative QCD. When applying to the chemical equilibration in the expanding system, we found that the gluons reaches chemical equilibrium well within its plasma phase. The inclusion of all the next-to-leading order processes makes the equilibration considerably faster than the simple $gg\leftrightarrow ggg$ one considered previously.
Due to long chemical equilibration times within standard hadronic reactions during the hadron gas phase in relativistic heavy ion collisions it has been suggested that the hadrons are "born" into equilibrium after the quark gluon plasma phase. Here we develop a dynamical scheme in which possible Hagedorn states contribute to fast chemical equilibration times of baryon anti-baryon pairs (as well as kaon anti-kaon pairs) inside a hadron gas and just below the critical temperature. Within this scheme, we use master equations and derive various analytical estimates for the chemical equilibration t…
Lattice data for the QCD equation of state and the baryon susceptibility near the crossover phase transition (at zero baryon density) are used to determine the input parameters of a 5-dimensional Einstein-Maxwell-Dilaton holographic model that provides a consistent holographic framework to study both equilibrium and out-of-equilibrium properties of a hot and {\it baryon rich} strongly coupled quark-gluon plasma (QGP). We compare our holographic equation of state computed at nonzero baryon chemical potential, $μ_B$, with recent lattice calculations and find quantitative agreement for the pressu…
The uncertainty in the equilibration in heavy ion collisions due to the choice of the value of the coupling is examined. The results of the equilibration are indeed affected by this choice. In particular, a variation of $\a_s$ from 0.3 to 0.5 reduces the parton phase of the plasma by as much as 4.0 fm/c and increasing coupling causes a reduction in the generated entropy. As far as equilibration is concerned, larger coupling results in faster equilibration both chemically and kinetically but improvements only happen to the fermions. These are accompanied by more rapid cooling and therefore shor…
In these remarks I explain the motivation which leads us to consider chemical nonequilibrium processes in flavor equilibration and in statistical hadroniziation of quark--gluon plasma (QGP). Statistical hadronization allowing for chemical non-equilibrium is introduced. The reesults of fits to RHIC-130 results, including multistrange hadrons, are shown to agree only with the model of an exploding QGP fireball.
Strangeness production was investigated during the equilibration of a gluon dominated parton plasma produced at RHIC and LHC energies. The time evolution of parton densities are followed by a set of rate equations in a 1-dimensional expanding system. The strangeness production will depend on the initial chemical equilibration level and in our case the parton densities will remain far from the full equilibrium. We investigate the influence of gluon fragmentation on final strangeness content.
We study thermalization by applying gradient expansion to the Kadanoff-Baym equations of the 2PI effective action to two-loop in a theory with Dirac fermions coupled to scalars. In addition to those chemical potentials which equilibrate in the on-shell limit, we identify modes which are conserved in this approximation, but which relax when off-shell effects are taken into account. This implies that chemical equilibration does not require higher loop contributions to the effective action and is compatible with the gradient expansion. We explicitly calculate the damping time-scales of both, on- …
We calculate the rate of collisional decay of the axial charge in an ultrarelativistic electron-positron plasma, also known as the chirality flipping rate. We find that contrary to the existing estimates, the chirality flipping rate appears already in the first order in the fine-structure constant $α$ and is therefore orders of magnitude greater than previously believed. The main channels for the rapid relaxation of the axial charge are the collinear emission of a weakly damped photon and the Compton scattering. The latter contributes to the $\mathcal{O}(α)$ result because of the infrared dive…
Plasma instabilities can play a fundamental role in quark-gluon plasma equilibration in the high energy (weak coupling) limit. Early simulations of the evolution of plasma instabilities in non-abelian gauge theory, performed in one spatial dimension, found behavior qualitatively similar to traditional QED plasmas. Later simulations of the fully three-dimensional theory found different behavior, unlike traditional QED plasmas. To shed light on the origin of this difference, we study the intermediate case of two spatial dimensions. Depending on how the "two-dimensional'' theory is formulated, we…
The discontinuity, or imaginary part of a self-energy at finite temperature is proportional to the rate at which the corresponding particles are produced when very few of them are present, and also to the rate at which their phase space density approaches the thermal one. These relations were suggested by Weldon [1], who demonstrated them for low orders in perturbation theory. Here we show that they are valid at leading order in a linear coupling of the produced particles, and to all orders in all other interactions of the hot plasma, if there is a separation of the time scales for the product…
We calculate the probability distribution P(k_\perp) for the momentum perpendicular to its original direction of motion that an energetic quark or gluon picks up as it propagates through weakly coupled quark-gluon plasma in thermal equilibrium.
We study the nonequilibrium growth of a weakly interacting homogeneous Bose gas after a quench from a high-temperature state to a temperature below the Bose-Einstein critical condensation temperature. We quantitatively characterize the departure from thermal equilibrium and observe the presence of two equilibration time scales. The equilibration times are shown to be inversely proportional to the density.
$\hat q$ is the average squared transverse momentum transfer per unit length to a high-energy particle traversing a QCD medium such as a quark-gluon plasma. We find the (UV-regulated) value of $\hat q$ to leading order in the weak coupling limit, $\alphas(T) \ll 1$. We then use this value to generalize previous analytic results on the gluon bremsstrahlung and pair production rates for massless high-energy particles in a weakly-coupled quark-gluon plasma, at next-to-leading logarithmic order.
We investigate how relativistic, nonabelian plasmas approach equilibrium in a general context. Our treatment is entirely parametric and for small Yang-Mills coupling $α$. First we study isotropic systems with an initially nonequilibrium momentum distribution. We consider both the case of initially very high occupancy and initially very low occupancy. Then we consider systems which are anisotropic. We consider both weak anisotropy and large anisotropy, and allow the occupancy to be parametrically large or small. Writing the typical momentum of an initial excitation as Q and the final temperatur…
We calculate P(k_\perp), the probability distribution for an energetic parton that propagates for a distance L through a medium without radiating to pick up transverse momentum k_\perp, for a medium consisting of weakly coupled quark-gluon plasma. We use full or HTL self-energies in appropriate regimes, resumming each in order to find the leading large-L behavior. The jet quenching parameter \hat q is the second moment of P(k_\perp), and we compare our results to other determinations of this quantity in the literature, although we emphasize the importance of looking at P(k_\perp) in its entire…
The chemical equilibration of heavy quarks in a quark-gluon plasma proceeds via annihilation or pair creation. For temperatures T much below the heavy quark mass M, when kinetically equilibrated heavy quarks move very slowly, the annihilation in the colour singlet channel is enhanced because the quark and antiquark attract each other which increases their probability to meet, whereas the octet contribution is suppressed. This is the so-called Sommerfeld effect. It has not been taken into account in previous calculations of the chemical equilibration rate, which are therefore incomplete for T <…
The definition of thermal relaxation time is extended to chemically non-equilibrated quark-gluon plasma and the chemical non-equilibrated thermal relaxation times for partons are calculated using the non-equilibrium Debye mass as the infrared regulator. The dependence of the thermal relaxation time on the fugacity is given and the influence of the chemical non-equilibration is discussed. We find that there are threshold fugacities $λ_g^*$ and $λ_q^*$ for gluons and quarks. For λ_g < λ_g^* (λ_q < λ_q^*), τ_g^{NEQ}/τ_g^{EQ} (τ_q^{NEQ}/τ_q^{EQ}) decreases strongly with increasing fugacity, while …
We compute by numerical integration of the Dirac equation the number of quark-antiquark pairs produced in the classical color fields of colliding ultrarelativistic nuclei. The backreaction of the created pairs on the color fields is not taken into account. While the number of qqbar pairs is parametrically suppressed in the coupling constant, we find that in this classical field model it could even be compatible with the thermal ratio to the number of gluons. After isotropization one could thus have quark-gluon plasma in chemical equilibrium.
We derive a simple formula for the stopping distance for a high-energy quark traveling through a weakly-coupled quark gluon plasma. The result is given to next-to-leading-order in an expansion in inverse logarithms ln(E/T), where T is the temperature of the plasma. We also define a stopping distance for gluons and give a leading-log result. Discussion of stopping distance has a theoretical advantage over discussion of energy loss rates in that stopping distances can be generalized to the case of strong coupling, where one may not speak of individual partons.
We report about a recent calculation of the heavy quarkonium mass and decay width in a quark-gluon plasma, whose temperature T and screening mass m_D satisfy the hierarchy m alpha_s >> pi T >> m alpha_s^2 >> m_D, m being the heavy-quark mass, up to order m alpha_s^5. The calculation may be relevant to understand the behavior of the Y(1S) in a quark-gluon plasma at present-day colliders.
We report a recent calculation of the heavy quarkonium energy levels and decay widths in a quark- gluon plasma whose temperature is much smaller than the inverse radius of the bound state, based on a Non-Relativistic Effective Field theory framework for heavy quarkonium at finite temperature. Relevance for the phenomenology of the Y(1S) in heavy ion collisions is also discussed.
We study the dynamics of weakly coupled non-abelian plasmas within the frameworks of classical-statistical lattice gauge-theory and kinetic theory. We focus on a class of systems which are highly occupied, isotropic at all times and initially characterized by a single momentum scale. These represent an idealized version of the situation in relativistic heavy ion-collisions in the color-glass condensate picture, where on a time scale $1/Q_s$ after the collision of heavy nuclei a longitudinally expanding plasma characterized by the saturation scale $Q_s$ is formed. Our results indicate that the …
We study the production and the evolution of quark-gluon plasma expected to be formed in ultra relativistic heavy-ion collisions, within the color flux-tube model. We introduce the gluonic component in the Boltzmann equation, which we solve in the phase space which is extended to include the SU(3) color degree of freedom. The color degree of freedom is shown to play a decisive role in equilibration, and in fixing the temperature of the plasma. We further find that the soft partons that we study here contribute substantially to the bulk properties. Finally, the model is shown to provide a detai…
We compute the next-to-leading order O(g) correction to the thermal photon production rate in a QCD plasma. The NLO contributions can be expressed in terms of gauge invariant condensates on the light cone, which are amenable to novel sum rules and Euclidean techniques. We expect these technologies to be generalizable to other NLO calculations. For the phenomenologically interesting value of alpha_s=0.3, the NLO correction represents a 20% increase and has a functional form similar to the LO result.
Magnetic plasma instabilities appear to play an important role in the early stages of quark-gluon plasma equilibration in the high energy (weak coupling) limit. Numerical studies of the growth of such instabilities from small seed fluctuations have found initial exponential growth in their energy, followed by linear growth once the associated color magnetic fields become so large that their non-abelian interaction are non-perturbative. In this paper, we use simulations to determine the nature of this linear energy growth. We find that the long-wavelength modes associated with the instability h…
We compute the homogeneous limit of non-hydrodynamic quasinormal modes (QNM's) of a phenomenologically realistic Einstein-Maxwell-Dilaton (EMD) holographic model for the Quark-Gluon Plasma (QGP) that is able to: i) {\it quantitatively} describe state-of-the-art lattice results for the QCD equation of state and higher order baryon susceptibilities with $2+1$ flavors and physical quark masses up to highest values of the baryon chemical potential currently reached in lattice simulations; ii) describe the nearly perfect fluidity of the strongly coupled QGP produced in ultrarelativistic heavy ion c…
Plasma instabilities can play a fundamental role in plasma equilibration. There are similarities and differences between plasma instabilities in abelian and non-abelian gauge theories. In particular, it has been an open question whether non-abelian self-interactions are the limiting factor in the growth of non-abelian plasma instabilities. We study this problem with 3+1 dimensional numerical simulations. We find that non-abelian plasma instabilities behave very differently from abelian ones once they grow to be non-perturbatively large, in contrast with earlier results of 1+1 dimensional simul…
We study production and equilibration of pions and muons in relativistic electron-positron-photon plasma at a temperature $T\ll m_μ, m_π$. We argue that the observation of pions and muons can be a diagnostic tool in the study of the initial properties of such a plasma formed by means of strong laser fields. Conversely, properties of muons and pions in thermal environment become accessible to precise experimental study.
