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.
Pressure isotropization of an equilibrating quark-gluon plasma produced in relativistic heavy ion collisions is studied within the framework of a multi-phase transport model (AMPT). The time evolution of the bulk properties of the quark-gluon plasma is found to depend on its expansion dynamics and hadronization scheme as well as the scattering cross sections among quarks and gluons. It is further found that the pressure isotropy of the produced quark-gluon plasma can only be achieved temporarily, indicating that there is only partial thermalization during the time evolution of the quark-gluon …
Numerical solutions of the Wong-Yang-Mills equations with anisotropic particle momentum distributions are presented. Their isotropization by collective effects due to the classical Yang-Mills field is shown.
To describe momentum isotropization of gluon matter produced in ultrarelativistic heavy-ion collisions, the transport rate of gluon drift and the transport collision rates of elastic ($gg \leftrightarrow gg$) as well as inelastic ($gg \leftrightarrow ggg$) perturbative quantum chromodynamics- (pQCD) scattering processes are introduced and calculated within the kinetic parton cascade Boltzmann approach of multiparton scatterings (BAMPS), which simulates the space-time evolution of partons. We define isotropization as the development of an anisotropic system as it reaches isotropy. The inverse o…
The expanding fireball shortly after a heavy ion collision may be qualitatively described by a condensate of color fields or gluons which is analogous to Bose-Einstein-condensation for massive bosonic particles. This condensate is a transient non-equilibrium phenomenon and breaks Lorentz-boost symmetry. The dynamics of color field condensates involves collective excitations and is rather different from the perturbative scattering of gluons. In particular, it provides for an efficient mechanism to render the local pressure approximately isotropic after a short time of 0.2 fm/c. We suggest that …
We study the isotropization of a homogeneous, strongly coupled, non-Abelian plasma by means of its gravity dual. We compare the time evolution of a large number of initially anisotropic states as determined, on the one hand, by the full non-linear Einstein's equations and, on the other, by the Einstein's equations linearized around the final equilibrium state. The linear approximation works remarkably well even for states that exhibit large anisotropies. For example, it predicts with a 20% accuracy the isotropization time, which is of the order of t_iso \lesssim 1/T, with T the final equilibri…
We study the coupled Wong Yang-Mills equations for both U(1) and SU(2) gauge groups and anisotropic particle momentum distributions numerically on a lattice. For weak fields with initial energy density much smaller than that of the particles we confirm the existence of plasma instabilities and exponential growth of the fields which has been discussed previously. Also, the SU(2) case is qualitatively similar to U(1), and we do find strong ``abelianization'' of the non-Abelian fields during the period of exponential growth. However, the effect nearly disappears when the fields are strong. This i…
I review our current understanding of the processes driving the thermalization and isotropization of the quark gluon plasma (QGP) created in ultrarelativistic heavy ion collisions (URHICs). I begin by discussing the phenomenological evidence in favor of the creation of a thermal but momentum-space anisotropic QGP in URHICs. I then discuss the degree of isotropization using viscous (dissipative) hydrodynamics, weak-coupling approaches to QGP dynamics, and strong-coupling approaches to QGP dynamics. Finally, I report on recent progress in the area of real-time non-abelian gauge field simulations…
We propose that rapidity dependent momentum correlations can be used to extract the shear relaxation time $τ_π$ of the medium formed in high energy nuclear collisions. The stress-energy tensor in an equilibrium quark-gluon plasma is isotropic, but in nuclear collisions it is likely very far from this state. The relaxation time $τ_π$ characterizes the rate of isotropization and is a transport coefficient as fundamental as the shear viscosity. We show that fluctuations emerging from the initial anisotropy survive to freeze-out, in excess of thermal fluctuations, influencing rapidity correlation …
Azimuthal momentum isotropization in the Quark-Gluon Plasma thermalization
University of Heidelberg（海德堡大学）；Shanghai Institute for Advanced Studies, University of Science and Technology of China（上海高等研究院，中国科学技术大学）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）；Hefei National Laboratory（合肥国家实验室）；Universidade de Santiago de Compostela（圣地亚哥德孔波斯特拉大学）；Axencia Galega de Innovación (GAIN), Xunta de Galicia（加利西亚自治区创新署（GAIN））
Hydrodynamical modeling of heavy ion collisions at RHIC suggests that the quark-gluon plasma (QGP) "thermalizes" in a remarkably short time scale, about 0.6 fm/c. We argue that this should be viewed as indicating fast isotropization, but not necessarily complete thermalization, of the non-equilibrium QGP. Non-Abelian plasma instabilities can drive local isotropization of an anisotropic QGP on a time scale which is faster than ordinary perturbative scattering processes. As a result, we argue that theoretical expectations based on weak coupling analysis are not necessarily in conflict with hydro…
We calculate leading-order dilepton yields from a quark-gluon plasma which has a time-dependent anisotropy in momentum space. Such anisotropies can arise during the earliest stages of quark-gluon plasma evolution due to the rapid longitudinal expansion of the created matter. Two phenomenological models for the proper time dependence of the parton hard momentum scale, p_hard, and the plasma anisotropy parameter, xi, are constructed which describe the transition of the plasma from its initial non-equilibrium state to an isotropic thermalized state. The first model constructed interpolates betwee…
Hydrodynamic description requires a local thermodynamic equilibrium of the system under study but an approximate hydrodynamic behaviour is already manifested when a momentum distribution of liquid components is not of equilibrium form but merely isotropic. While the process of equilibration is relatively slow, the parton system becomes isotropic rather fast due to the plasma instabilities. Azimuthal fluctuations observed in relativistic heavy-ion collisions are argued to distinguish between a fully equilibrated and only isotropic parton system produced in the collision early stage.
In this article we report on our results about the computation of the elliptic flow of the quark-gluon-plasma produced in relativistic heavy ion collisions, simulating the expansion of the fireball by solving the relativistic Boltzmann equation for the parton distribution function tuned at a fixed shear viscosity to entropy density ratio $η/s$. Our main goal is to put emphasis on the role of a saturation scale in the initial gluon spectrum, which makes the initial distribution far from a thermalized one. We find that the presence of the saturation scale reduces the efficiency in building-up th…
The impact of radiative processes on kinetic equilibration is studied via a radiative transport model. The 2 <-> 3 processes can significantly increase the level of thermalization. These processes lead to an approximate coupling constant scaling of the evolution of the pressure anisotropy qualitatively different from the case with only 2 -> 2 partonic processes. Furthermore, thermal and Color Glass Condensate motivated initial conditions are shown to share the same asymptotic evolution when 2 <-> 3 processes are included. This emphasizes the unique role of radiative processes in Quark-Gluon Pl…
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.
Theoretical studies on the early-time dynamics in the ultra-relativistic heavy-ion collisions are reviewed including pedagogical introductions on the initial condition with small-x gluons treated as a color glass condensate, the bottom-up thermalization scenario, plasma/glasma instabilities, basics of some formulations such as the kinetic equations and the classical statistical simulation. More detailed discussions follow to make an overview of recent developments on the fast isotropization, the onset of hydrodynamics, and the transient behavior of momentum spectral cascades.
We describe some of the recent progress in the calculation of thermodynamic quantities in QCD at high temperatures and densities by weak-coupling techniques and extrapolation to realistic coupling strength. We argue that a (mostly) weakly coupled quark-gluon plasma at temperatures only a few times the transition temperature is not yet ruled out by the observed fast apparent thermalization at RHIC, as nonabelian plasma instabilities might provide an efficient mechanism for fast isotropization even in a collisionless plasma.
Expansion dynamics at the yoctosecond timescale affect the evolution of the quark gluon plasma (QGP) created in heavy ion collisions. We show how these dynamics are accessible through Hanbury Brown and Twiss (HBT) intensity interferometry of direct photons emitted from the interior of the QGP. A detector placed close to the beam axis is particularly sensitive to early polar momentum anisotropies of the QGP. Observing a modification of the HBT signal at the proposed FoCal detector of the LHC ALICE experiment would allow to measure the isotropization time of the plasma and could provide first ex…
A hot and dense partonic system can be produced in the early stage of a relativistic heavy ion collision. How it equilibrates is important for the extraction of Quark-Gluon Plasma properties. We study the chemical and kinetic equilibrations of the Quark-Gluon Plasma using a radiative transport model. Thermal and Color-Glass-Condensate motivated initial conditions are used. We observe that screened parton interactions always lead to partial pressure isotropization. Different initial pressure anisotropies result in the same asymptotic evolution. Comparison of evolutions with and without radiativ…
We calculate the nuclear modification factor ($R_{AA}$) of light hadrons by taking into account the initial state momentum anisotropy of the quark gluon plasma (QGP) expected to be formed in relativistic heavy ion collisions. Such an anisotropy can result from the initial rapid longitudinal expansion of the matter. A phenomenological model for the space time evolution of the anisotropic QGP is used to obtain the time dependence of the anisotropy parameter $ξ$ and the hard momentum scale, $p_{\rm hard}$. The result is then compared with the PHENIX experimental data to constrain the isotropizati…
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.
We calculate the medium dilepton yield from a quark-gluon plasma which has a time-dependent local momentum-space anisotropy. A phenomenological model for the hard momentum scale, p_hard(tau), and plasma anisotropy parameter, xi(tau), is constructed which interpolates between free streaming behavior at early times (tau << tau_iso) and ideal hydrodynamic behavior at late times (tau >> tau_iso). We show that high-energy dilepton production is sensitive to the assumed plasma isotropization time, tau_iso, and can therefore be used to experimentally determine the time of onset for hydrodynamic expan…
The quark-gluon plasma, possibly created in ultrarelativistic heavy-ion collisions, is a strongly interacting many-body parton system. By comparison with strongly coupled electromagnetic plasmas (classical and non-relativistic) it is concluded that the quark-gluon plasma could be in the liquid phase. As an example for a strongly coupled plasma, complex plasmas, which show liquid and even solid phases, are discussed briefly. Furthermore, methods based on correlation functions for confirming and investigating the quark-gluon-plasma liquid are presented. Finally, consequences of the strong coupli…
We describe some of the recent progress in our understanding of the dynamics of strongly correlated gluons at high parton densities. Computations in the Color Glass Condensate effective field theory provide a good description of inclusive and semi-inclusive final states in DIS, p+p and p+A collisions at small x. In nucleus-nucleus collisions, they provide an ab initio description of entropy generation, decoherence, isotropization and the onset of hydrodynamic flow. The successful description of a wide range of phenomena from RHIC to LHC is outlined and possibilities for more stringent tests no…
We review the Color Glass Condensate effective theory, that describes the gluon content of a high energy hadron or nucleus, in the saturation regime. The emphasis is put on applications to high energy heavy ion collisions. After describing initial state factorization, we discuss the Glasma phase, that precedes the formation of an equilibrated quark-gluon plasma. We end this review with a presentation of recent developments in the study of the isotropization and thermalization of the quark-gluon plasma.
In this work we study the non-equilibrium dynamics of a quark-gluon plasma, as created in heavy-ion collisions. We investigate how big of a role plasma instabilities can play in the isotropization and equilibration of a quark-gluon plasma. In particular, we determine, among other things, how much collisions between the particles can reduce the growth rate of unstable modes. This is done both in a model calculation using the hard-loop approximation, as well as in a real-time lattice simulation combining both classical Yang-Mills-fields as well as inter-particle collisions. The new extended vers…
The quark-gluon plasma close to the critical temperature is a strongly interacting system. Using strongly coupled, classical, non-relativistic plasmas as an analogy, we argue that the quark-gluon plasma is in the liquid phase. This allows to understand experimental observations in ultrarelativistic heavy-ion collisions and to interpret lattice QCD results. It also supports the indications of the presence of a strongly coupled QGP in ultrarelativistic heavy-ion collisions.
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 $2 \to 2$ scattering process involving two c…
Ultra-relativistic electromagnetic plasmas can be used for improving our understanding of the quark-gluon plasma. In the weakly coupled regime both plasmas can be described by transport theoretical and quantum field theoretical methods leading to similar results for the plasma properties (dielectric tensor, dispersion relations, plasma frequency, Debye screening, transport coefficients, damping and particle production rates). In particular, future experiments with ultra-relativistic electron-positron plasmas in ultra-strong laser fields might open the possibility to test these predictions, e.g…
We discuss the characteristics of collective modes induced by relativistic jets in an anisotropic quark-gluon plasma(AQGP). Assuming a tsunami-like initial jet distribution, it is found that the dispersion relations for both the stable and unstable modes are modified substantially due to the passage of jet compared to the case when there is no jet. It has also been shown that the growth rate of instability first increases compared to the no jet case and then completely turned into damping except the case when the jet velocity is perpendicular to the wave vector in which case the instability al…
We compute by numerical integration of the Dirac equation the number of quark-antiquark pairs initially produced in the classical color fields of colliding ultrarelativistic nuclei. While the number of qqbar pairs is parametrically suppressed in the coupling constant, we find that in this classical field model their production rate is comparable to the thermal ratio of gluons/pairs = 9 N_f/32. After isotropization one thus would have quark-gluon plasma in chemical equilibrium.
We show that the extensively studied equation of state (EOS) of strongly coupled QED plasma fits the recent lattice EOS data of gluon plasma remarkably well, with appropriate modifications to take account of color degrees of freedom and running coupling constant. Hence we conclude that the quark gluon plasma near the critical temperature is a strongly coupled color-Coulombic plasma.
By considering the Debye screening and damping rate of gluons, the viscosity coefficient of the quark-gluon plasma was evaluated via real-time finite temperature QCD in the relaxation time approximation at finite temperature and chemical potential . The results show that both the damping rate and the chemical potential cause considerable enhancements to the viscosity coefficient of hot dense quark-gluon plasma.
We study the radiative correction to $p_T$-broadening of a fast quark in a quark-gluon plasma beyond the soft gluon approximation. We find that the radiative processes can suppress considerably $p_T$-broadening. This differs dramatically from previous calculations to logarithmic accuracy in the soft gluon approximation, predicting a considerable enhancement of $p_T$-broadening.
Since the quark-gluon plasma (QGP) reveals some obvious similarities to the well-known electromagnetic plasma (EMP), an accumulated knowledge on EMP can be used in the QGP studies. After discussing similarities and differences of the two systems, we present theoretical tools which are used to describe the plasmas. The tools include: kinetic theory, hydrodynamic approach and diagrammatic perturbative methods. We consider collective phenomena in the plasma with a particular emphasis on instabilities which crucially influence temporal evolution of the system. Finally, properties of strongly coupl…
Chromodynamic fluctuations in the collisionless quark-gluon plasma are found as a solution of the initial value linearized problem. The stable and unstable plasmas are discussed.
Brief review of the hadronic probes that are used to diagnose the quark-gluon plasma produced in relativistic heavy ion collisions and interrogate its properties. Emphasis is placed on probes that have significantly impacted our understanding of the nature of the quark-gluon plasma and confirmed its formation.
Non-Abelian plasma instabilities play an important role in the non-equilibrium dynamics of a weakly coupled quark-gluon plasma. Using the discretized hard loop framework we calculate the time evolution of soft gluonic fields in a longitudinally free streaming background. Extrapolating our results to energies probed in relativistic heavy-ion collisions we find a pressure anisotropy that persists for a few fm/c. However, the chromofields quickly develop a Boltzmann longitudi- nal energy spectrum, suggesting fast longitudinal thermalization of the quark gluon plasma even though it remains momentu…
We study a smooth crossover transition in the gas of quark-gluon bags. The equation of state at high temperature is that of the quark-gluon plasma. However, the system consists of the bags with finite volumes which are defined by the model parameters of the mass-volume bag spectrum. Possible structures in this {\it cluster} quark-gluon plasma are classified.
A calculation of the thermal quark propagator is presented taking the gluon condensate above the critical temperature into account. The quark dispersion relation following from this propagator is derived.
We present a calculation of the thermal quark propagator taking the gluon condensate above the critical temperature into account. The quark dispersion relation following from this propagator, describing two massive modes, is discussed.
We study the color randomization of two-gluon states produced after splitting of a primary fast gluon in the quark-gluon plasma. We find that for the LHC conditions the color randomization of the $gg$ pairs is rather slow. At jet energies $E=100$ and $500$ GeV, for typical jet path length in the plasma in central Pb+Pb collisions, the $SU(3)$-multiplet averaged color Casimir of the $gg$ pair differs considerably from its value $2N_c$ for a fully randomized $gg$ state. Our calculations of the energy dependence for generation of the nearly collinear decuplet $gg$ states, that can lead to the bar…
The implications of a numerical error in the photon production rate on the direct photon spectrum of a chemically non-equilibrated quark-gluon plasma are discussed.
We calculate the $p_T$ distributions of jet conversion photons from {\em Quark Gluon Plasma} with pre-equilibrium momentum-space anisotropy. A phenomenological model has been used for the time evolution of hard momentum scale $p_{\rm hard}(τ)$ and anisotropy parameter $ξ(τ)$. As a result of pre-equilibrium momentum-space anisotropy, we find significant modification of the jet conversion photon $p_T$ distribution. For example, with {\em fixed initial condition} (FIC) pre-equilibrium anisotropy, we predict significant enhancement of the jet-photon $p_T$ distribution in the entire region, whereas…
We study the radiative correction to $p_\perp$-broadening of a fast quark in a quark-gluon plasma beyond the soft gluon approximation. We find that the radiative contribution to quark $\langle p_\perp^2\rangle$ for RHIC and LHC conditions is negative.
The observational consequences of certain broken symmetries in a thermalised quark gluon plasma are elucidated. The signature under study is the spectrum of dileptons radiating from the plasma, through gluon fusion. Being a pure medium effect, this channel is non-vanishing only in plasmas with explicitly broken charge conjugation invariance. The emission rates are also sensitive to rotational invariance through the constraints imposed by Yang's theorem. This theorem is interpreted in the medium via the destructive interference between various multiple scattering diagrams obtained in the specta…
A calculation of the thermal quark propagator is presented taking the gluon condensate above the critical temperature into account. The quark dispersion relation and the dilepton production following from this propagator are derived.
We study the influence of the magnetic field on the photon emission from the quark-gluon plasma created in $AA$ collisions. We find that even for very optimistic assumption on the magnitude of the magnetic field for noncentral $AA$ collisions the effect of magnetic field is very small.
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.
Recent experiments at RHIC and theoretical considerations indicate that the quark-gluon plasma, present in the fireball of relativistic heavy-ion collisions, might be in a liquid phase. The liquid state can be identified by characteristic correlation and structure functions. Here definitions of the structure functions and pair correlations of the quark-gluon plasma are presented as well as perturbative results. These definitions might be useful for verifying the quark-gluon-plasma liquid in QCD lattice calculations.
We study dimuonium $(μ^+μ^-)$ production in the quark-gluon plasma created in relativistic heavy ion collisions. The production is controlled by the process $q\bar q\rightarrow (μ^+μ^-)g$, and the dimuonium motion in the plasma is described by a transport equation. While the electrodynamics dominated dimuonium yield is not high enough, the transverse energy distribution carries the information of the plasma at RHIC and LHC energies.
