We establish the existence of a far-from-equilibrium attractor in weakly-coupled gauge theory undergoing one-dimensional Bjorken expansion. We demonstrate that the resulting far-from-equilibrium evolution is insensitive to certain features of the initial condition, including both the initial momentum-space anisotropy and initial occupancy. We find that this insensitivity extends beyond the energy-momentum tensor to the detailed form of the one-particle distribution function. Based on our results, we assess different procedures for reconstructing the full one-particle distribution function from the energy-momentum tensor along the attractor and discuss implications for the freeze-out procedure used in the phenomenological analysis of ultra-relativistic nuclear collisions.
We provide a generalized formulation of fluctuating hydrodynamics for the far-from-equilibrium noisy medium. As an example, we consider a noisy plasma experiencing Bjorken expansion, for which the leading order evolution is captured by hydrodynamic attractor of classical hydrodynamics, while the quadratic couplings of fluctuations are solved effectively via a generalized version of the hydrodynamic kinetic equation. In the far-from-equilibrium plasma, backreaction of hydrodynamic fluctuations results in renormalization of transport properties, as well as long time tails, of high orders. In par…
We study the far-off-equilibrium dynamics of a Bjorken expanding non-conformal system within kinetic theory and hydrodynamics. We show that, in contrast to the conformal case, neither shear nor bulk viscous pressure relax quickly to a non-equilibrium attractor. In kinetic theory an early-time, far-from-equilibrium attractor exists for the scaled longitudinal pressure, driven by the rapid longitudinal expansion of the medium. Second-order dissipative hydrodynamics fails to accurately describe this attractor, but a modified anisotropic hydrodynamic formulation reproduces it and provides excellen…
There is mounting evidence suggesting that relativistic hydrodynamics becomes relevant for the physics of quark-gluon plasma as the result of nonhydrodynamic modes decaying to an attractor apparent even when the system is far from local equilibrium. Here we determine this attractor for Bjorken flow in N=4 supersymmetric Yang-Mills theory using Borel summation of the gradient expansion of the expectation value of the energy momentum tensor. By comparing the result to numerical simulations of the flow based on the AdS/CFT correspondence we show that it provides an accurate and unambiguous approx…
We establish the existence of a far-from-equilibrium attractor in weakly-coupled gauge theory undergoing 0+1d Bjorken expansion which goes beyond the energy-momentum tensor to the detailed form of the one-particle distribution function. We then demonstrate that the dynamics can be re-scaled at intermediate times and represented by universal exponents. Finally, we assess different procedures for reconstructing the full one-particle distribution function from the energy-momentum tensor along the attractor and discuss implications for the freeze-out procedure used in the phenomenological analysis…
We study the thermalization process in highly occupied non-Abelian plasmas at weak coupling. The non-equilibrium dynamics of such systems is classical in nature and can be simulated with real-time lattice gauge theory techniques. We provide a detailed discussion of this framework and elaborate on the results reported in~\cite{Berges:2013eia} along with novel findings. We demonstrate the emergence of universal attractor solutions, which govern the non-equilibrium evolution on large time scales both for non-expanding and expanding non-Abelian plasmas. The turbulent attractor for a non-expanding …
Numerical simulations of expanding plasma based on the AdS/CFT correspondence as well as kinetic theory and hydrodynamic models strongly suggest that some observables exhibit universal behaviour even when the system is not close to local equilibrium. This leading behaviour is expected to be corrected by transient, exponentially decaying contributions which carry information about the initial state. Focusing on late times, when the system is already in the hydrodynamic regime, we analyse numerical solutions describing expanding plasma of strongly coupled N=4 supersymmetric Yang-Mills theory and…
In this proceedings contribution I review recent work in kinetic theory which demonstrates that, for system undergoing Bjorken expansion, there exists an attractor in all moments of the one-particle distribution function. I discuss how this attractor emerges in both exact solutions obtained in relaxation time approximation (RTA) and the effective kinetic theory approach to high-temperature quantum chromodynamics (QCD). The QCD effective kinetic theory collisional kernel used includes both elastic (2 <-> 2) and LPM-resummed inelastic (2 <-> 1) contributions. The results obtained indicate that a…
We study the dissipative evolution of (0+1)-dimensionally expanding media with Bjorken symmetry using the Boltzmann equation for massive particles in relaxation-time approximation. Breaking conformal symmetry by a mass induces a non-zero bulk viscous pressure in the medium. It is shown that even a small mass (in units of the local temperature) drastically modifies the well-known attractor for the shear Reynolds number previously observed in massless systems. For generic nonzero particle mass, neither the shear nor the bulk viscous pressure relax quickly to a non-equilibrium attractor; they app…
We establish a set of equations for moments of the distribution function. In the relaxation time approximations, these moments obey a coupled set of equations that can be truncated order-by-order. Solving the equations of moments, we are able to identify an attractor solution that controls a transition from a free streaming fixed point to a hydrodynamic fixed point. In particular, this attractor solution provides a renormalization of the effective value of the shear viscosity to entropy density ratio, $η/s$, taking into account off-equilibrium effects.
Jet energy loss in anisotropic plasmas meets limiting attractors
SUBATECH UMR 6457 (IMT Atlantique, Université de Nantes, IN2P3/CNRS)（SUBATECH联合研究单位6457（大西洋理工大学，南特大学，法国国家科学研究中心/法国原子能和替代能源委员会））；Institute for Theoretical Physics, TU Wien（维也纳工业大学理论物理研究所）；Department of Physics, ETH Zürich（苏黎世联邦理工学院物理系）；MIT Center for Theoretical Physics – a Leinweber Institute, Massachusetts Institute of Technology（麻省理工学院理论物理中心——莱因韦伯研究所）
Recently we have reported the correct formulation of the lattice QCD method at the zero temperature to study the hadron formation from the quarks and gluons by incorporating the non-zero boundary surface term in QCD which arises due to the confinement of quarks and gluons inside the finite size hadron. In this paper we extend this to the finite temperature QCD and present the correct formulation of the lattice QCD method at the finite temperature to study the hadron formation from the quark-gluon plasma.
We derive an expression for the heavy quark damping rate in hot quark gluon plasma in presence of flow. Here all the bath particles here are out of equilibrium due to the existence of non-zero velocity gradient. The magnetic sector shows similar infrared divergences even after hard thermal loop corrections as one encounters in case of non-viscous plasma. We estimate the first order correction in ($η/s$) for heavy quark damping rate due to the non-zero viscosity of the QCD plasma.
QCD plasma instabilities appear to play an important role in the equilibration of quark-gluon plasmas in heavy-ion collisions in the theoretical limit of weak coupling (i.e. asymptotically high energy). It is important to understand what non-linear physics eventually stops the exponential growth of unstable modes. It is already known that the initial growth of plasma instabilities in QCD closely parallels that in QED. However, once the unstable modes of the gauge-fields grow large enough for non-Abelian interactions between them to become important, one might guess that the dynamics of QCD pla…
QCD plasma instabilities, caused by an anisotropic momentum distributions of the particles in the plasma, are likely to play an important role in thermalization in heavy ion collisions. We consider plasmas with two different components of particles, one strongly anisotropic and one isotropic or nearly isotropic. The isotropic component does not eliminate instabilities but it decreases their growth rates. We investigate the impact of plasma instabilities on the first stage of the ``bottom-up'' thermalization scenario in which such a two-component plasma emerges, and find that even in the case o…
It is pointed out that the size of the interaction region, as determined from HBT analyses, is increased due to the transition time necessary the convert the quarks and gluons into hadrons. A rough estimate yields an increase of R_HBT by about 15%.
A Lagrangian density for viscous quark-gluon plasma has been constructed within the fluid-like QCD framework. Gauge symmetry is preserved for all terms inside the Lagrangian, except for the viscous term. The transition mechanism from point particle field to fluid field, and vice versa, is discussed. The energy momentum tensor that is relevant for the gluonic plasma having the nature of fluid bulk of gluon sea is derived within the model. By imposing conservation law in the energy momentum tensor, shear viscosity appears as extractable from the equation.
We study the role of QCD plasma instabilities in non-equilibrium quark-gluon plasmas. First, we argue that such instabilities must drastically modify the "bottom-up" thermalization scenario for heavy-ion collisions. Second, we discuss conditions for the existence of instabilities in a more general context than previously treated in the QCD literature. We also give a thorough qualitative review of the origin of instabilities. We discuss some mechanisms whereby the growth of plasma instabilities saturates. Finally, we solve explicitly for instabilities and their growth rates for two extreme case…
We determine viscosity corrections to the retarded, advanced and symmetric gluon self energies and to the static propagator in the weak-coupling "hard loop" approximation to high-temperature QCD. We apply these results to calculate the imaginary part of the heavy-quark potential which is found to be smaller (in magnitude) than at vanishing viscosity. This implies a smaller decay width of quarkonium bound states in an anisotropic plasma.
The quark-gluon plasma created in heavy-ion collisions is not in local thermal equilibrium at early times. Despite this, dissipative hydrodynamics describes the evolution of the energy-momentum tensor quite well after only roughly 0.5 - 1 fm/c. This can be understood using the concept of a non-equilibrium dynamical attractor. The attractor is a uniquely identifiable solution to the dynamical equations to which all solutions are drawn as the system evolves. Once solutions collapse onto the non-equilibrium attractor they are ``pseudo-thermalized'' in the sense that they have lost information abo…
We present real-time lattice simulation results for nonequilibrium quark production from an over-occupied gluon plasma in longitudinally expanding geometry. The quark number density per unit transverse area and rapidity shows almost linear growth in time, and its growth rate appears to be consistent with a simple kinetic theory estimate involving only two-to-two scattering processes in small-angle approximation. We also find that quarks produced at early times satisfy a nonequilibrium scaling law.
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 coll…
We present the derivation of heavy quark energy loss in a viscous QCD plasma using kinetic theory. Shear flow changes both boson and fermion distribution functions which eventually modify heavy quark energy loss. Due to presence of non-zero flow gradient in the medium all the bath particles here are out of equilibrium. In these types of plasmas we show that without plasma screening effects heavy quark energy loss suffers similar type of infrared divergence as one encounters in non-viscous plasma. The screening effects are incorporated consistently through Hard Thermal Loop resummation perturba…
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 consider quarkonium in a hot QCD plasma which, due to expansion and non-zero viscosity, exhibits a local anisotropy in momentum space. At short distances the heavy-quark potential is known at tree level from the hard-thermal loop resummed gluon propagator in anisotropic perturbative QCD. The potential at long distances is modeled as a QCD string which is screened at the same scale as the Coulomb field. At asymptotic separation the potential energy is non-zero and inversely proportional to the temperature. We obtain numerical solutions of the three-dimensional Schroedinger equation for this …
A mass scale $μ_c$ representing the boundary between effective theories of strong interactions and perturbative QCD (infrared and ultraviolet regimes) exists when the $β$-function is characterized by a simple pole. This behaviour, which is known to occur in N=1 supersymmetric Yang-Mills theories, leads to an infrared attractor in the evolution of the coupling constant, with the mass scale $μ_c$ of the attractor providing a natural boundary between the infrared and ultraviolet regimes. It is demonstrated that [2|2], [3|1] and [1|3] Pade-approximant versions of the three-flavour QCD $β$-function…
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 exploit a recent non-perturbative determination of the momentum broadening kernel $C(b_{\bot})$ in impact parameter space \cite{Moore:2021jwe}, to determine the momentum space broadening kernel $C(q_{\bot})$ in high-temperature QCD plasmas. We show how to use the non-pertubatively determined kernel $C(q_{\bot})$ to compute the medium-induced splitting rates in a QCD plasma of finite size. We compare the resulting in-medium splitting rates to the results obtained with leading-order and next-to-leading order perturbative determinations of $C(q_{\bot})$, as well as with various approximations …
We compute the shear viscosity of two-flavor QCD plasma in an external magnetic field in perturbative QCD at leading log order, assuming that the magnetic field is weak or soft: $eB\sim g^4\log(1/g)T^2$. We show that the shear viscosity takes a form $η=\barη(\bar B)T^3/(g^4\log(1/g))$ with a dimensionless function $\barη(\bar B)$ in terms of a dimensionless variable $\bar B=(eB)/(g^4\log(1/g)T^2)$. The variable $\bar B$ corresponds to the relative strength of the effect of cyclotron motions compared to the QCD collisions: $\bar B\sim l_{mfp}/l_{cyclo}$. We provide a full numerical result for t…
The quark-gluon plasma, which is produced at an early stage of ultrarelativistic heavy-ion collisions, is expected to be initially strongly populated with chromodynamic fields. We address the question how heavy quarks interact with such a turbulent plasma in comparison with an equilibrated one of the same energy density. For this purpose we derive a Fokker-Planck transport equation of heavy quarks embedded in a plasma of light quarks and gluons. We first discuss the equilibrium plasma and then the turbulent one applying the same approach, where the heavy quarks interact not with the plasma con…
We compute the energy loss of heavy quarkonia in high temperature QCD plasmas and investigate the energy loss effects on quarkonium suppression. Based on the effective vertex derived from the Bethe-Salpeter amplitude for quarkonium, the collisional and radiative energy loss are determined by quarkonium-gluon elastic scattering and the associated gluon-bremsstrahlung, respectively. In the energy regime $E<m_Υ^2/T$ the collisional energy loss is dominant over the radiative one, and the total energy loss increases with the plasma temperature and the initial energy of quarkonium. Our numerical ana…
Non-conformal attractor behavior is studied by solving non-conformal second order viscous hydrodynamics with respect to boost-invariant plasmas. Numerical solutions of the relative decay rate of the enthalpy density, the inverse shear and bulk Reynolds numbers, all exhibit universal patterns towards an ideal fluid description at late stages, demonstrating the existence of non-conformal hydrodynamic attractor. However, as a generic feature, the non-conformal hydrodynamic attractor emerges only at late times, which differs drastically from the behavior observed in conformal systems. The absence …
The non-abelian analog of the Landau-Pomeranchuk-Migdal effect is investigated in perturbative QCD. Extending our previous studies, the suppression of induced soft bremsstrahlung due to multiple scatterings of quarks in the spinor representation is considered. The effective formation time of gluon radiation due to the color interference is shown to depend on the color representation of the emitting parton, and an improved formula for the radiative energy loss is derived that interpolates between the factorization and Bethe-Heitler limits.
We investigate possible mass shift and width broadening of J/psi in hot gluonic matter using QCD sum rule. Input values of gluon condensates at finite temperature are extracted from lattice QCD data for the energy density and pressure. Although stability of the moment ratio is achieved only up to T/Tc ~ 1.05, the gluon condensates cause a decrease of the moment ratio, which results in change of spectral properties. Using the Breit-Wigner form for the phenomenological side, we find that mass shift of J/psi just above Tc can reach maximally 200 MeV and width can broaden to dozens of MeV.
We compute the spectral densities of $T^{μν}$ and $J^μ$ in high temperature QCD plasmas at small frequency and momentum,\, $ω,k \sim g^4 T$. The leading log Boltzmann equation is reformulated as a Fokker Planck equation with non-trivial boundary conditions, and the resulting partial differential equation is solved numerically in momentum space. The spectral densities of the current, shear, sound, and bulk channels exhibit a smooth transition from free streaming quasi-particles to ideal hydrodynamics. This transition is analyzed with conformal and non-conformal second order hydrodynamics, and a…
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…
After the discovery of the Quantum Chromodynamics (QCD), many experimental and theoretical efforts have been made to investigate physics issues involved in ultra relativistic heavy-ion collisions. The fundamental goal of this work is to present a short guide of the underlying theory of strong interactions with emphasis on the light vector mesons based on the exceptional work of R.Rapp and J.Wambach. Today widely believed that deconfinement and chiral symmetry restoration probably takes place in a hot and dense hadronic medium as this produced at these collisions. We focus at the place where th…
Thermal (Th-)QCD properties appear to disagree with lattice (L-)QCD results, which suggests that Th-QCD does not have a valid perturbative expansion. However, we reproduce L-QCD using the first order $α_s$ corrections in Th-QCD.
The electrical conductivity in the hot phase of the QCD plasma is extracted from a quenched lattice measurement of the Euclidean time vector correlator for 1.5 < T/T_c < 3. The spectral density in the vicinity of the origin is examined using a method specially adapted to this region, and a peak at small energies is seen. The continuum limit of the electrical conductivity, and the closely related soft photon emissivity of the QCD plasma, are then extracted from a fit to the Fourier transform of the temporal vector correlator.
We calculate the bound state properties of $J/ψ$ in a hot and dense QCD plasma using phenomenological potentials augmented by inputs from perturbative QCD. The temperature and density region of study will be relevant in future heavy ion collision experiments at FAIR. We find that the effect of baryon density on the dissociation of $J/ψ$ is small in this regime. However we indicate that if there is a critical end point in the QCD phase diagram then strong density fluctuation will dissociate charmonia near hadronization. The measurement of $J/ψ$ suppression can therefore signify the existence of…
The quark-gluon plasma in stellar structure is investigated using the fluid-like QCD approach. The classical energy momentum tensor relevant for high energy and hot plasma having the nature of fluid bulk of gluon sea is calculated within the model. The transition of gluon field from point particle field inside stable hadrons to relativistic fluid field in hot plasma and vice versa is briefly discussed. The results are applied to construct the equation of state using the Tolman--Oppenheimer--Volkoff equation to describe the hot plasma dominated stellar structure.
We derive the expression for the collisional energy loss in two stream plasma induced by the fluctuating chromoelectric field. It is revealed that the main contribution here comes from the unstable modes which grow exponentially with time. A strong direction dependence of the energy loss has also been demonstrated.
The static forces between electric charges and currents are modified at the loop level by the presence of a plasma. While electric charges are screened, currents are not. The effective coupling constant at long distances is enhanced in both cases as compared to the vacuum, and by different amounts, a clear sign that Lorentz symmetry is broken. We investigate these effects quantitatively, first in a QED plasma and secondly using non-perturbative simulations of QCD with two light degenerate flavors of quarks.
The bulk viscosity, $ζ$ and its ratio with the shear viscosity, $ζ/η$ have been studied in an anisotropically expanding pure glue plasma in the presence of turbulent color fields. It has been shown that the anisotropy in the momentum distribution function of gluons, which has been determined from a linearized transport equation eventually leads to the bulk viscosity. For the isotropic (equilibrium) state, a recently proposed quasi-particle model of pure SU(3) lattice QCD equation of state has been employed where the interactions are encoded in the effective fugacity. It has been argued that th…
The partonic energy loss has been calculated taking both the hard and soft contributions for all the $2 \to 2$ processes, revealing the importance of the individual channels. Cancellation of the intermediate separation scale has been exhibited. Subtleties related to the identical final state partons have properly been taken into account. The estimated collisional loss is compared with its radiative counter part. We show that there exists a critical energy ($E_c$) below which the collisional loss is more than its radiative counterpart. In addition, we present closed form formulas for both the c…
We study the response functions (chromo-electric susceptibilities) of quark-gluon plasma as a function of temperature in the presence of interactions. We consider two equations of state for hot QCD. The first one is fully perturbative, of $O(g^5)$ EOS and, and the second one which is $O[g^6\ln(1/g)+δ]$, incorporates some non-perturbative effects. Following a recent work (Physical Review {\bf C 76}, 054909(2007)), the interaction effects contained in the EOS are encapsulated in terms of effective chemical potentials($\tildeμ$) in the equilibrium distribution functions for the partons.By using t…
We present the first lattice QCD study of up to $3S$ and $2P$ bottomonia at non-zero temperatures. Correlation functions of bottomonia were computed using novel bottomonium operators and a variational technique, within the lattice non-relativistic QCD framework. We analyzed the bottomonium correlation functions based on simple physically-motivated spectral functions. We found evidence of sequential in-medium modifications, in accordance with the sizes of the bottomonium states.
We determine the hard-loop resummed propagator in an anisotropic QCD plasma in general covariant gauges and define a potential between heavy quarks from the Fourier transform of its static limit. We find that the potential exhibits angular dependence and that binding of very small quarkonium states is stronger than in an isotropic plasma.
Comparison of two appropriately chosen screening masses of colour singlet operators in the pure glue QCD plasma indicates that at sufficiently high temperature it contains a weakly-interacting massive quasi-particle with the quantum numbers of the electric gluon. Still in the deconfined phase, but closer to T_c, the same mass ratio is similar to that at zero temperature, indicating that the propagating modes are more glueball-like, albeit with a lower scale for the masses. We observe a continuity between these two regimes.
The structure of compact star core filled by gluon matter plasma is investigated within the fluid-like QCD framework. The energy momentum tensor, density and pressure relevant for gluonic plasma having the nature of fluid bulk of gluon sea are derived within the model. It is shown that the model provides a new equation of state for perfect fluid with only a single parameter of fluid distribution ϕ(x). The results are applied to construct the equation of state describing the gluonic plasma dominated compact star core. The equations of pressure and density distribution are solved analytically fo…
Numerical simulations of quantum chromodynamics at nonzero temperature provide information from first principles about the physical properties of the quark gluon plasma. Because the lattice approximation can be refined indefinitely, results of lattice simulations now provide the most reliable basis for our understanding of the nonperturbative characteristics of the plasma and of the high temperature phase transition. Following a brief overview of the methodology of lattice gauge theory at nonzero temperature, recent results and insights from lattice simulations are discussed. These include our…
We present an overview of a perturbative-kinetic approach to jet propagation, energy loss, and momentum broadening in a high temperature quark-gluon plasma. The leading-order kinetic equations describe the interactions between energetic jet-particles and a non-abelian plasma, consisting of on-shell thermal excitations and soft gluonic fields. These interactions include 2<->2 scatterings, collinear bremsstrahlung, and drag and momentum diffusion. We show how the contribution from the soft gluonic fields can be factorized into a set of Wilson line correlators on the light cone. We review recent …
