We compute and study the drag force acting on a heavy quark propagating through the matter produced in the collision of two sheets of energy in a strongly coupled gauge theory that can be analyzed holographically. Although this matter is initially far from equilibrium, we find that the equilibrium expression for heavy quark energy loss in a homogeneous strongly coupled plasma with the same instantaneous energy density or pressure as that at the location of the quark describes many qualitative features of our results. One interesting exception is that there is a time delay after the initial collision before the heavy quark energy loss becomes significant. At later times, once a liquid plasma described by viscous hydrodynamics has formed, expressions based upon assuming instantaneous homogeneity and equilibrium provide a semi-quantitative description of our results - as long as the rapidity of the heavy quark is not too large. For a heavy quark with large rapidity, the gradients in the velocity of the hydrodynamic fluid result in qualitative consequences for the 'drag' force acting on the quark. In certain circumstances, the force required to drag the quark through the plasma can point opposite to the velocity of the quark, meaning that the force that the plasma exerts on a quark moving through it acts in the same direction as its velocity. And, generically, the force includes a component perpendicular to the direction of motion of the quark. Our results support a straightforward approach to modeling the drag on, and energy loss of, heavy quarks with modest rapidity in heavy ion collisions, both before and after the quark-gluon plasma hydrodynamizes, and provide cautionary lessons at higher rapidity.
We study the energy loss of a heavy quark propagating through the matter produced in the collision of two sheets of energy [1]. Even though this matter is initially far-from-equilibrium we find that, when written in terms of the energy density, the equilibrium expression for heavy quark energy loss describes most qualitative features of our results well. At later times, once a plasma described by viscous hydrodynamics has formed, the equilibrium expression describes the heavy quark energy loss quantitatively. In addition to the drag force that makes it lose energy, a quark moving through the o…
In heavy-ion collisions, the quark-gluon plasma is produced far from equilibrium. This regime is currently inaccessible by quantum chromodynamics (QCD) computations. We calculate shear transport and entropy far from equilibrium in a holographic model, defining a time-dependent ratio of shear viscosity to entropy density, $η/s$. Large deviations of up to 60% from its near-equilibrium value, $1/4π$, are found for realistic situations at the Large Hadron Collider. We predict the far-from-equilibrium time-dependence of $η/s$ to substantially affect the evolution of the QCD plasma and to impact the…
Recently we have proved the NRQCD factorization in heavy quarkonium production at high energy colliders at all orders in coupling constant. In this paper we extend this to non-equilibrium QCD and prove the NRQCD factorization in heavy quarkonium production at all orders in coupling constant in non-equilibrium QCD. This proof is necessary to study heavy quarkonium production from quark gluon plasma at RHIC and LHC.
Using gauge/gravity duality, we study emission and absorption rates of scalar quanta from far-from-equilibrium N = 4 supersymmetric Yang-Mills plasma. By comparing the emission and absorption rates to expectations from the Fluctuation-Dissipation Theorem, we study how the spectrum thermalizes and how the thermalization time depends on the four momentum of the emitted quanta.
Heavy quark $R_{AA}$ and $v_2$ have been calculated at RHIC energy considering initial conditions with and without pre-equilibrium phase to highlight the effect of the latter on heavy quark observables. The momentum evolution of the heavy quark has been studied by means of the Boltzmann transport equation. To model the pre-equilibrium phase we have used the KLN initial condition. We have found that the pre-equilibrium phase impacts the $R_{AA}$ of about 20-25 $\%$ whereas the impact on $v_2$ is very negligible. We have also calculated heavy quark $R_{AA}$ and $v_2$ in the case of initializatio…
Heavy ion collisions at ultrarelativistic energies offer the opportunity to study the irreversibility of multiparticle processes. Together with the many-body decays of resonances, the multiparticle processes cause the system to evolve according to Prigogine's steady states rather than towards statistical equilibrium. These results are general and can be easily checked by any microscopic string-, transport-, or cascade model for heavy ion collisions. The absence of pure equilibrium states sheds light on the difficulties of thermal models in describing the yields and spectra of hadrons, especial…
The drag and diffusion coefficients of heavy quarks (HQs) have been evaluated in the pre-equilibrium phase of the evolving fireball produced in heavy ion collisions at RHIC and LHC energies. The KLN and classical Yang-Mills spectra have been used for describing the momentum distributions of the gluons produced just after the collisions but before they thermalize. The interaction of the HQs with these gluons has been treated within the framework of perturbative QCD. We have observed that the HQs are dragged almost equally by the kinetically equilibrated and out-of-equilibrium gluonic systems. W…
The yields of heavy flavored hadrons emitted from strangeness-rich QGP are evaluated within chemical non-equilibrium statistical hadronization model, conserving strangeness, charm, and entropy yields at hadronization.
Recently we have proved NRQCD color octet factorization of S-wave and P-wave heavy quarkonia production at all orders in coupling constant in QCD in vacuum at high energy colliders in Eur. Phys. J. C76 (2016) 448 and in arXiv:1807.04722 [hep-ph] respectively. In this paper we extend this to prove NRQCD color octet factorization of P-wave heavy quarkonium production in non-equilibrium QCD at RHIC and LHC at all orders in coupling constant. This proof is necessary to study the quark-gluon plasma at RHIC and LHC.
Isolated quantum systems in extreme conditions can exhibit unusually large occupancies per mode. This over-population gives rise to new universality classes of many-body systems far from equilibrium. We present theoretical evidence that important aspects of non-Abelian plasmas in the ultra-relativistic limit admit a dual description in terms of a Bose condensed scalar field theory.
Recent work on chemical equilibrium in heavy ion collisions is reviewed. The energy dependence of thermal parameters is discussed. The centrality dependence of thermal parameters at SPS energies is presented.
The effects of gluon radiation by charm quarks on the transport coefficients {\it e.g.} drag, longitudinal and transverse diffusion and shear viscosity have been studied within the ambit of perturbative quantum chromodynamics (pQCD) and kinetic theory. We found that while the soft gluon radiation has substantial effects on the transport coefficients of the charm quarks in the quark gluon plasma its effects on the equilibrium distribution function is insignificant.
Shear viscosity is a crucial property of QCD matter which determines the collective behavior of the the quark-gluon plasma (QGP) in ultrarelativistic heavy-ion collisions. Extending the near-equilibrium, high-precision investigations in theory and experiment, we take into account the fact that, in a collision, the QGP is generated far from equilibrium. We use the AdS/CFT correspondence to study a strongly coupled plasma and find a significant impact on the ratio of shear viscosity to entropy density, $η/s$. In particular, we investigate the initial heating phase and find a decrease reaching do…
We show that the inclusion of a recently found additional term of the spin polarization vector at local equilibrium which is linear in the symmetrized gradients of the velocity field, and the assumption of hadron production at constant temperature restore the quantitative agreement between hydrodynamic model predictions and local polarization measurements in relativistic heavy ion collisions at $\sqrt{s_{\rm NN}} = 200$ GeV. The longitudinal component of the spin polarization vector turns out to be very sensitive to the temperature value, with a good fit around 155 MeV. The implications of thi…
There is experimental and theoretical evidence that the broad rapidity distribution of net proton yield in central heavy-ion collisions at SPS energies could be a signal of non-equilibrium properties of the system. We show that the broad rapidity shape can be well reproduced in the framework of a non-linear relativistic Fokker-Planck dynamics which incorporates non-extensive statistics and anomalous diffusion.
The real-time dissociation of the heavy quarkonium in a strongly coupled boost-invariant non-Abelian plasma relaxing towards equilibrium is analyzed in a holographic framework. The effects driving the plasma out of equilibrium are described by boundary quenching, impulsive variations of the boundary metric. Quarkonium is represented by a classical string with endpoints kept close to the boundary. The evolution of the string profile is computed in the time-dependent geometry, and the dissociation time is evaluated for different configurations with respect to the direction of the plasma expansio…
Within an advanced Langevin-hydrodynamics framework coupled to a hybrid fragmentation-coalescence hadronization model, we study heavy flavor quenching and flow in relativistic heavy-ion collisions. We investigate how the initial heavy quark spectrum, the energy loss and hadronization mechanisms of heavy quarks in medium, the evolution profile of pre-equilibrium stage, the flow of medium and the temperature dependence of heavy quark diffusion coefficient influence the suppression and elliptic flow of heavy mesons at RHIC and the LHC. Our result shows that different modeling of initial condition…
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…
In this work, we assess the importance of non-equilibrium dynamics in the production of photons from the late stages of relativistic heavy-ion collisions. The p$_\mathrm{T}$-differential spectra and $v_2$ of photons from the late hadronic stage are computed within a non-equilibrium hadron transport approach, and compared to the results of a local equilibrium evolution using ideal relativistic hydrodynamics. It is found that non-equilibrium dynamics enhance the late-stage photon production at low p$_\mathrm{T}$ and decreases it at higher p$_\mathrm{T}$ compared to the estimate from hydrodynamic…
The hypothesis of local equilibrium (LE) in relativistic heavy ion collisions at energies from AGS to RHIC is checked in the microscopic transport model. We find that kinetic, thermal, and chemical equilibration of the expanding hadronic matter is nearly reached in central collisions at AGS energy for $t \geq 10$ fm/$c$ in a central cell. At these times the equation of state may be approximated by a simple dependence $P \cong (0.12-0.15) ε$. Increasing deviations of the yields and the energy spectra of hadrons from statistical model values are observed for increasing bombarding energies. The o…
We have proposed a novel way to specify the initial conditions of a dissipative fluid dynamical model for a given energy density $\varepsilon=u_μT^{μν}u_ν$ and baryon number density $n=N^μu_μ$, which does not impose the so-called Landau matching condition for an off-equilibrium state. In addition to usual two parameters for equilibrium part, i.e., $α\equiv μ/T$, $β\equiv1/T$ (where $T$ is separation temperature and $μ$ is separation chemical potential introduced to separate equilibrium part from the off-equilibrium state), a dissipative strength $γ$ is newly introduced to specify the off-equil…
Particle yields in heavy ion collisions show an overwhelming evidence for chemical or relative chemical equilibrium at all beam energies. The rapidity dependence of the thermal parameters $T$ and $μ_B$ can now be determined over a wide range of rapidities and show a systematic behavior towards an increase in $μ_B$ away from mid-rapidity.
Chemical non-equilibrium version of the statistical hadronization model combined with a single-freeze-out scenario is used to analyze the transverse-momentum spectra of pions, kaons and protons produced in heavy-ion collisions at sqrt(sNN) = 2.76 TeV. With the statistical parameters found in earlier studies of hadronic ratios and two new geometric parameters determined by the absolute normalization and slopes of the spectra, we obtain a very good agreement between the data and the model predictions. In particular, the enhancement of pions observed at the very low transverse-momenta is very wel…
(3+1)D event-by-event pre-equilibrium dynamics in heavy-ion collisions
Wilczek Quantum Center, 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）；Department of Physics, University of Jyväskylä（约恩苏大学物理系）；Helsinki Institute of Physics（赫尔辛基物理研究所）；Fakultät für Physik, Universität Bielefeld（比勒费尔德大学物理学院）；Institute of Particle Physics and Key Laboratory of Quark and Lepton Physics (MOE), Central China Normal University（华中师范大学粒子物理与夸克轻子物理教育部重点实验室）
Strongly correlated systems far from equilibrium can exhibit scaling solutions with a dynamically generated weak coupling. We show this by investigating isolated systems described by relativistic quantum field theories for initial conditions leading to nonequilibrium instabilities, such as parametric resonance or spinodal decomposition. The non-thermal fixed points prevent fast thermalization if classical-statistical fluctuations dominate over quantum fluctuations. We comment on the possible significance of these results for the heating of the early universe after inflation and the question of…
Relativistic collisions of light on heavy ions (p+Au at sqrt(s)=7.7 GeV, p+Au, d+Au,3He+Au at sqrt(s)=62.4 GeV and 200 GeV and p+Pb, 3He+Pb at sqrt(s)=5.02 TeV) are simulated using "superSONIC", a model that includes pre-equilibrium flow, viscous hydrodynamics and a hadronic cascade afterburner. Even though these systems have strong gradients and only consist of at most a few tens of charged particles per unit rapidity, one finds evidence that a hydrodynamic description applies to these systems. Based on these simulations, the presence of a triangular flow component in d+Au collisions at sqrt(…
Prescaling is a far-from-equilibrium phenomenon which describes the rapid establishment of a universal scaling form of distributions much before the universal values of their scaling exponents are realized. We consider the example of the spatio-temporal evolution of the quark-gluon plasma explored in heavy-ion collisions at sufficiently high energies. Solving QCD kinetic theory with elastic and inelastic processes, we demonstrate that the gluon and quark distributions very quickly adapt a self-similar scaling form, which is independent of initial condition details and system parameters. The dy…
We develop a macroscopic description of the space-time evolution of the energy-momentum tensor during the pre-equilibrium stage of a high-energy heavy-ion collision. Based on a weak coupling effective kinetic description of the microscopic equilibration process (à la "bottom-up"), we calculate the non-equilibrium evolution of the local background energy-momentum tensor as well as the non-equilibrium linear response to transverse energy and momentum perturbations for realistic boost-invariant initial conditions for heavy ion collisions. We demonstrate how this framework can be used on an event-…
Dissipative processes in relativistic fluids are known to be important in the analyses of the hot QCD matter created in high-energy heavy-ion collisions. In this work, I consider dissipative corrections to energy and conserved charge densities, which are conventionally assumed to be vanishing but could be finite. Causal dissipative hydrodynamics is formulated in the presence of those dissipative currents. The relation between hydrodynamic stability and transport coefficients is discussed. I then study their phenomenological consequences on the observables of heavy-ion collisions in numerical s…
We examine the thermalization of an ensemble of the octet of pseudoscalar mesons, in the isospin symmetric limit, whose interactions are constrained through chiral symmetry, unitarity, and measurements. The reaction amplitudes generate all resonances up to masses of about 2 GeV, with twelve input parameters, namely f_pi, three masses, and eight low energy constants (LECs) of chiral perturbation theory. In linear response theory, we find that matter takes an extremely long time to thermalize. These long relaxation times are directly related to the fact that these mesons are pseudo-Goldstone bos…
We present a first principles approach to study the Chiral Magnetic Effect during the pre-equilibrium stage of a heavy-ion collision. We discuss the dynamics of the Chiral Magnetic Effect and Chiral Magnetic Wave based on real-time lattice simulations with dynamical (Wilson and Overlap) fermions simultaneously coupled to color and electromagnetic fields. While for light quarks we observe a dissipation-less transport of charges as in anomalous hydrodynamics, we demonstrate that for heavier quarks the effects of explicit chiral symmetry breaking lead to a significant reduction of the associated …
Experimental measurement of the elliptic flow parameter $v_2$ and hydrodynamic model together showed that thermalization in the central region at the Relativistic Heavy Ion Collider to be perplexingly fast. This is a mystery in itself since none of the numerical perturbative QCD models are able to achieve such a feat. By exploiting a theoretical oversight on collinear processes in an out-of-equilibrium system it is argued that, in the bottom-up thermalization scenario, equilibration can proceed at a higher rate than what is expected in the conventional perturbative QCD picture.
The assumption of local equilibrium in relativistic heavy ion collisions at energies from 10.7 AGeV (AGS) up to 160 AGeV (SPS) is checked in the microscopic transport model. Dynamical calculations performed for a central cell in the reaction are compared to the predictions of the thermal statistical model. We find that kinetic, thermal and chemical equilibration of the expanding hadronic matter are nearly approached late in central collisions at AGS energy for $t \geq 10$ fm/$c$ in a central cell. At these times the equation of state may be approximated by a simple dependence $P \cong (0.12-0.…
We derive relativistic viscous hydrodynamic equations invoking the generalized second law of thermodynamics for two different forms of the non-equilibrium single-particle distribution function. We find that the relaxation times in these two derivations are identical for shear viscosity but different for bulk viscosity. These equations are used to study thermal dilepton and hadron spectra within longitudinal scaling expansion of the matter formed in relativistic heavy-ion collisions. For consistency, the same non-equilibrium distribution function is used in the particle production prescription …
We compute analytically the anisotropic flow in an expanding mixture of several species of relativistic massive particles. We find that a single collision per particle in average already leads to sizable elliptic flow, with mass ordering between the species.
The microscopic description of heavy-ion reactions at low beam energies is achieved within hadronic transport approaches. In this article a new approach SMASH (Simulating Many Accelerated Strongly-interacting Hadrons) is introduced and applied to study the production of non-strange particles in heavy-ion reactions at $E_{\rm kin}=0.4-2A$ GeV. First, the model is described including details about the collision criterion, the initial conditions and the resonance formation and decays. To validate the approach, equilibrium properties such as detailed balance are presented and the results are compa…
We obtain within Fokker-Planck dynamics an explicit generalization of Einstein's relation between drag, diffusion and equilibrium distribution for a spatially homogeneous system, considering both the transverse and longitudinal diffusion for dimension n>1. We then provide a complete characterization of when the equilibrium distribution becomes a Boltzmann/J"uttner distribution, and when it satisfies the more general Tsallis distribution. We apply this analysis to recent calculations of drag and diffusion of a charm quark in a thermal plasma, and show that only a Tsallis distribution describes …
A standard calculation of the energy density of heavy stable particles that may pair-annihilate into light particles making up thermal medium is performed to second order of coupling, using the technique of thermal field theory. At very low temperatures a power law of temperature is derived for the energy density of the heavy particle. This is in sharp contrast to the exponentially suppressed contribution estimated from the ideal gas distribution function. The result supports a previous dynamical calculation based on the Hartree approximation, and implies that the relic abundance of dark matte…
A model with non-uniform flow in the longitudinal direction is proposed for the relativistic heavy-ion collisions and compared with the 14.6 A GeV/c Si-Al and 10.8 A GeV/c Au-Au collision data. The stronger influence of transparency on the distribution of heavier produced particles and the larger stopping in the heavier collision system are accounted for by using a new geometrical parameterization picture. The central dips in the proton and deuteron rapidity distributions for Si-Al collision are reproduced.
Using gauge/gravity duality, we study the creation and evolution of anisotropic, homogeneous strongly coupled $\mathcal N=4$ supersymmetric Yang-Mills plasma. In the dual gravitational description, this corresponds to horizon formation in a geometry driven to be anisotropic by a time-dependent change in boundary conditions.
Using gauge/gravity duality, we study the creation and evolution of boost invariant anisotropic, strongly coupled N = 4 supersymmetric Yang-Mills plasma. In the dual gravitational description, this corresponds to horizon formation in a geometry driven to be anisotropic by a time-dependent change in boundary conditions.
Dynamic equations for quantum fields far from equilibrium are derived by use of functional renormalisation group techniques. The obtained equations are non-perturbative and lead substantially beyond mean-field and quantum Boltzmann type approximations. The approach is based on a regularised version of the generating functional for correlation functions where times greater than a chosen cutoff time are suppressed. As a central result, a time evolution equation for the non-equilibrium effective action is derived, and the time-evolution of the Green functions is computed within a vertex expansion…
Hadron yields in high energy heavy ion collisions have been fitted and reproduced by thermal models using standard statistical distributions. These models give insight into the freeze-out conditions at varying beam energies. In this paper we investigate changes to this analysis when the statistical distributions are replaced by Tsallis distributions for hadrons. We investigate the appearance of near-thermal equilibrium state at SPS and RHIC energies. We obtain better fits with smaller chi^2 for the same hadron data, as applied earlier in the thermal fits for SPS energies but not for RHIC energ…
Heavy Quark Momentum Broadening in a Non-Abelian Plasma away from Thermal Equilibrium
The Institute of Mathematical Sciences, a CI of Homi Bhabha National Institute（印度马哈拉施特拉邦数学科学研究所）；Fakultät für Physik, Universität Bielefeld（比勒费尔德大学物理学院）
The phenomenon of prethermalization and the subsequent steps of thermalization are analyzed in the framework of the chiral quark model. We solve the quantum equations of motion of the field theory derived from the 2PI effective action and study the time scales of equilibration. We find that already after a 0.6 fm/c long period of time some equilibrium features appear, even though the system is still far from equilibrium. This might be an ingredient for understanding the success of ideal hydrodynamic description.
We study the local equilibrium in the central $V = 125$ fm$^3$ cell in heavy-ion collisions at energies from 10.7 AGeV (AGS) to 160 AGeV (SPS) calculated in the microscopic transport model. In the present paper the hadron yields and energy spectra in the cell are compared with those of infinite nuclear matter, as calculated within the same model. The agreement between the spectra in the two systems is established for times $t \geq 10$ fm/$c$ in the central cell. The cell results do not deviate noticeably from the infinite matter calculations with rising incident energy, in contrast to the appa…
The time evolution of the energy transport triggered in a strongly coupled system by a temperature gradient is holographically related to the evolution of an asymptotically AdS black brane. We study the far-from-equilibrium properties of such a system by using the AdS/CFT correspondence. In particular, we describe the appearance of a steady state, and study the information flow by computing the time evolution of the holographic entanglement entropy. Some universal properties of the quenching process are presented.
We analyze the connection between $p_T$ and multiplicity distributions in a statistical framework. We connect the Tsallis parameters, $T$ and $q$, to physical properties like average energy per particle and the second scaled factorial moment, $F_2=\langle n(n-1) \rangle / {\langle n \rangle}^2$, measured in multiplicity distributions. Near and far from equilibrium scenarios with master equations for the probability of having $n$ particles, $P_n$, are reviewed based on hadronization transition rates, $μ_n$, from $n$ to $n+1$ particles.
The production of dileptons with an invariant mass in the range 1 GeV < M < 5 GeV provides unique insight into the approach to thermal equilibrium in ultrarelativistic nucleus-nucleus collisions. In this mass range, they are produced through the annihilation of quark-antiquark pairs in the early stages of the collision. They are sensitive to the anisotropy of the quark momentum distribution, and also to the quark abundance, which is expected to be underpopulated relative to thermal equilibrium. We take into account both effects based on recent theoretical developments in QCD kinetic theory, an…
Possible universal dynamics of a many-body system far from thermal equilibrium are explored. A focus is set on meta-stable non-thermal states exhibiting critical properties such as self-similarity and independence of the details of how the respective state has been reached. It is proposed that universal dynamics far from equilibrium can be tuned to exhibit a dynamical phase transition where these critical properties change qualitatively. This is demonstrated for the case of a superfluid two-component Bose gas exhibiting different types of long-lived but non-thermal critical order. Scaling expo…
