The study of how fast thermalization in heavy ion collisions occurs has been one of the central topics in the heavy ion community. In the weak coupling picture this thermalization occurs from "the bottom up": high energy partons, formed early in the collision, radiate low energy gluons which then proceed to equilibrate among themselves, forming a thermal bath that brings the high energy sector to equilibrium. In this scheme we apply a model on parton energy loss to discuss the effects of medium expansion on the thermalization problem and estimate the average transverse momentum diffusivity for thermalization in a Bjorken expanding medium.
In the initial stage of the bottom-up picture of thermalization in heavy ion collisions, the gluon distribution is highly anisotropic which can give rise to plasma instability. This has not been taken account in the original paper. It is shown that in the presence of instability there are scaling solutions, which depend on one parameter, that match smoothly onto the late stage of bottom-up when thermalization takes place.
In this talk, I review the important role played by plasma instabilities in the thermalization of quark-gluon plasmas at very high energy. [Conference talk presented at Strong and Electroweak Mattter 2004, Helsinki, Finland, June 16--19.]
The early thermalization is crucial to the quark-gluon plasma as a perfect liquid and results from many-body scattering. We calculate squared amplitudes for elastic parton-parton-parton scattering in perturbative QCD. Transport equations with the squared amplitudes are established and solved to obtain the thermalization time of initially produced quark-gluon matter and the initial temperature of quark-gluon plasma. We find that the thermalization times of quark matter and gluon matter are different.
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 thermalization time for a Quark-Gluon-Plasma is estimated from a quantum transport model beyond the quasi-particle approach (or kinetic gas theory). While our ansatz is crude concerning the properties of ''real'' quarks and gluons, it nevertheless takes very serious the basic principles of quantum field theory for non-equilibrium states. It is found, that the thermalization time obtained from quantum transport theory is substantially longer than from kinetic theory. In our view this casts some doubts on scenarios which a priori assume a thermalized quark gluon plasma.
The elastic scattering of gqq, gqqbar and gqbarqbar and the thermalization of quark-gluon matter are studied. According to Feynman diagrams at the tree level, squared amplitudes for the elastic gqq scattering and the elastic gqqbar scattering are derived in perturbative QCD. Transport equations including the squared amplitudes for the elastic gqq, gqqbar and gqbarqbar scattering are established. Corresponding to anisotropic gluon and quark distributions created in central Au-Au collisions at RHIC, solutions of the transport equations show that thermalization time of quark matter can be shorten…
We present a possible scaling solution to pre-equilibrium evolution which interpolates between the instability present in the dense gluon system produced immediately after a heavy ion collision and the final equilibration which occurs later. Our solution depends on a single parameter $δ$. Depending on the value of $δ$, our proposed solution matches onto the bottom-up picture either at an intermediate stage or toward the end of the evolution given by bottom-up. We discuss in detail the reasons why we believe our solution is self-consistent, and we also point out why it is difficult to actually …
Within a pQCD inspired kinetic parton cascade we simulate the space time evolution of gluons which are produced initially in a heavy ion collision at RHIC energy. The inelastic gluonic interactions $gg \leftrightarrow ggg$ do play an important role: For various initial conditions it is found that thermalization and the close to ideal fluid dynamical behaviour sets in at very early times. Special emphasis is put on color glass condensate initial conditions and the `bottom up thermalization' scenario. Off-equilibrium $3\to 2$ processes make up the very beginning of the evolution leading to an in…
Employing a newly developed pQCD inspired parton cascade we simulate the space time evolution of gluons which are produced initially in a heavy ion collision at RHIC energy. The inelastic $gg \leftrightarrow ggg$ interactions are for the first time implemented obeying full detailed balance. The numerical results show that thermalization of gluons is mainly driven by the inelastic gluonic interactions and reaches equilibrium at $1\sim 2$ fm/c. In simulations for noncentral collisions considerable partonic elliptic flow $v_2$ is generated being comparable with the experimental data.
We describe how thermalization occurs in heavy ion collisions in the framework of perturbative QCD. When the saturation scale $Q_s$ is large compared to $Λ_{QCD}$, thermalization takes place during a time of order $α^{-13/5}Q_s^{-1}$ and the maximal temperature achieved is $α^{2/5}Q_s$.
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…
A number of promising results of a new 3+1 dimensional Monte Carlo parton cascade including inelastic multiplication processes (gg <--> ggg) are elaborated: (1) thermalization and chemical saturation; (2) the onset of longitudinal hydrodynamical expansion; (3) the build up of elliptic flow. We first briefly outline the basic idea of the algorithm. Full simulations are done with initial conditions for the kinetic partons via minijets or with ones stemming from a color glass condensate. The inclusion of the inelastic channels leads to a very fast kinetic equilibration and also to an early creati…
Elastic gluon-gluon-quark (gluon-gluon-antiquark) scattering is studied in perturbative QCD with 123 Feynman diagrams at the tree level. Individually squared amplitudes and interference terms of the Feynman diagrams are derived. With the elastic gluon-gluon-quark scattering and the elastic gluon-gluon-antiquark scattering transport equations are established. In the thermalization process of initially created quark-gluon matter, this matter is governed by elastic 2-to-2 scattering and elastic 3-to-3 scattering. Solutions of the transport equations show that initially created quark-gluon matter …
We investigate thermalization of gluons in spatially homogeneous systems using the Boltzmann equation in diffusion approximation. A complete picture on thermalization is obtained for both initially under- and over-populated systems. In an initially under-populated system, we find that its soft sector undergoes three stages: overheating, cooling/overcooling and reheating before full thermalization is achieved. In an initially over-populated system, we find that its soft sector only undergoes two stages towards full thermalization: overheating and cooling. The cooling stage is consistently drive…
Elastic parton-parton-parton scattering is briefly reviewed and is included in transport equations of quark-gluon matter. We solve the transport equations and get thermal states from initially produced quark-gluon matter. Both gluon matter and quark matter take early thermalization, but gloun matter has a shorter thermalization time than quark matter.
We ``quantify'' the role of elastic as well as inelastic gg<->ggg pQCD processes in kinetic equilibration within a pQCD inspired parton cascade. The contributions of different processes to kinetic equilibration are manifested by the transport collision rates. We find that in a central Au+Au collision at RHIC energy pQCD Bremstrahlung processes are much more efficient for momentum isotropization compared to elastic scatterings. For the parameters chosen the ratio of their transport collision rates amounts to 5:1.
We investigate modification of Kolmogorov wave turbulence in QCD calculating gluon spectra as functions of time in the presence of a low energy source which feeds in energy density in the infrared region at a time-dependent rate. Then considering the picture of saturation constraints as has been constructed in the "bottom-up" thermalization approach we revisit that picture for RHIC center-mass energy, $W = 130 {GeV}$, and also extend it to LHC center-mass energy, $W = 5500 {GeV}$, thus for two cases having an opportunity to calculate the equilibration time, $tau_{eq|therm}$, of the gluon syste…
We study the thermalization of gluons far from thermal equilibrium in relativistic kinetic theory. The initial distribution of gluons is assumed to resemble that in the early stage of ultrarelativistic heavy ion collisions. Only elastic scatterings in static, nonexpanding gluonic matter are considered. At first we show that the occurrence of condensation in the limit of vanishing particle mass requires a general constraint for the scattering matrix element. Then the thermalization of gluons with Bose-Einstein condensation is demonstrated in a transport calculation. We see a continuously increa…
Kinetic equations are used to study thermalization of the anisotropic quark-gluon plasma produced by decays of color flux tubes possibly created at the very early stages of relativistic heavy-ion collisions. The decay rates of the initial color tubes are given by the Schwinger formula, while the collision terms are taken in the relaxation-time approximation. By connecting the relaxation time with viscosity we analyze production and thermalization processes in the plasma characterized by different values of the ratio of the shear viscosity to entropy density.
The deconfinement transition and the hadronization mechanism at high energy are related to the quark-antiquark string breaking and the corresponding temperature depends on the string tension $σ$. In the Unruh scheme of hadron production it turns out $T = \sqrt{σ/2π}$, with $σ\simeq \E$, the vacuum energy density. In heavy ion collisions at lower energy, i.e. large baryonchemical potential, $μ_B$, the dynamics is dominated by Fermi statistics and baryon repulsion. However one can still consider $\E$ as the relevant physical scale and its evaluation as a function of the baryon density, in a nucl…
We study thermalization of strongly coupled gauge theory plasma in the presence of magnetic field using the AdS/CFT correspondence. We utilize the falling energy-shell model as a holographic description of gauge theory plasma undergoing thermalization, and find the effect of magnetic field on thermalization time in various space-time dimensions. Our results demonstrate that magnetic field universally hastens thermalization of strongly coupled gauge theory plasma.
We discuss the role of elastic and inelastic collisions and their interplay in the thermalization of the quark-gluon plasma. We consider a simplified situation of a static plasma, spatially uniform and isotropic in momentum space. We focus on the small momentum region, which equilibrates first, and on a short time scale. We obtain a simple kinetic equation that allows for an analytic description of the most important regimes. The present analysis suggests that the formation of a Bose condensate, expected when only elastic collisions are present, is strongly hindered by the inelastic, radiative…
We investigate how thermalization of gluons depends on the initial conditions assumed in ultrarelativistic heavy ion collisions at RHIC. The study is based on simulations employing the pQCD inspired parton cascade solving the Boltzmann equation for gluons. We consider independently produced minijets with $p_T > p_0=1.3 \sim 2.0$ GeV and a color glass condensate as possible initial conditions for the freed gluons. It turns out that full kinetic equilibrium is achieved slightly sooner in denser system and its timescale tends to saturate. Compared with the kinetic equilibration we find a stronger…
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 estimate the ratio of the thermalization time over the freeze-out time using a holographic AdS-Vaidya model for quark-gluon plasma formed in the heavy ion collisions. In the model the process of thermalization is described as formation of the black hole in AdS space while dethermalization process, related with the freeze-out, as the black hole evaporation due to the Hawking radiation that is modeled by the Vaidya metric with a negative mass. In this model the thermalization takes place only at small scales and absent in the infrared region. At small scales the system tends towards a state o…
In this paper, we study the thermalization of gluons and N_f flavors of massless quarks and antiquarks in a spatially homogeneous system. First, two coupled transport equations for gluons and quarks (and antiquarks) are derived within the diffusion approximation of the Boltzmann equation, with only 2<-> 2 processes included in the collision term. Then, these transport equations are solved numerically in order to study the thermalization of the quark-gluon plasma. At initial time, we assume that no quarks or antiquarks are present and we choose the gluon distribution in the form f = f_0 theta (…
We argue that multi-particle production in high energy hadron and nuclear collisions can be considered as proceeding through the production of gluons in the background classical field. In this approach we derive the gluon spectrum immediately after the collision and find that at high energies it is parametrically enhanced by ln(1/x) with respect to the quasi-classical result (x is the Bjorken variable). We show that the produced gluon spectrum becomes thermal (in three dimensions) with an effective temperature determined by the saturation momentum Qs, T= c Qs/2pi during the time ~1/T; we estim…
We present recent developments concerning Higgs production in bottom quark annihilation and gluon fusion. For bottom quark annihilation, we show the transverse momentum distribution of the associated jets. Furthermore, we discuss the distribution of events into n-jet bins for n=0 and n>0 at NNLO and NLO, respectively. For gluon fusion, the quality of the heavy-top limit for differential quantities at O(α_s^4) is studied by taking into account higher order terms in the 1/m_{top} expansion.
We compute the complete next-to-leading order SUSY-QCD corrections for the associated production of a charged Higgs boson with a top quark via bottom-gluon fusion. We investigate the applicability of the bottom parton description in detail. The higher order corrections can be split into real and virtual corrections for a general two Higgs doublet model and into additional massive supersymmetric loop contributions. We find that the perturbative behavior is well under control. The supersymmetric contributions consist of the universal bottom Yukawa coupling corrections and non-factorizable diagra…
Thermalization of a longitudinally expanding color glass condensate with Bjorken boost invariant geometry is investigated within microscopical parton cascade BAMPS. Our main focus lies on the detailed comparison of thermalization, observed in BAMPS with that suggested in the \BUp scenario. We demonstrate that the tremendous production of soft gluons via $gg \to ggg$, which is shown in the \BUp picture as the dominant process during the early preequilibration, will not occur in heavy ion collisions at RHIC and LHC energies, because the back reaction $ggg\to gg$ hinders the absolute particle mul…
The measurement of hadronic Higgs Boson branching ratios H -> bb, H -> gg for a light Standard Model-like Higgs boson produced at 250 GeV centre of mass energy at the International Linear Collider (ILC) is presented. The tools and techniques used for the analysis are briefly discussed.
In these lectures, I will attempt a pedagogical and qualitative introduction to the theory of equilibrium and thermalization of quark-gluon plasmas. I assume only that the reader is familiar with quantum field theory at zero temperature and with QCD as the theory of the strong interactions. I focus on the limit of small alpha_s, which in principle should be relevant at extremely high temperature because of asymptotic freedom, and in any case provides a clean theoretical context in which to discuss a variety of phenomena. Topics discussed include the basic equilibrium formalism for finite-tempe…
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…
In this work, I calculate the $p_\perp$ resolved spectra for the three stages of the \textit{bottom-up} scenario, which are comparable to the thermal contribution, particularly at higher values of the saturation scale $Q_S^2$. Analytical solutions are obtained by including a parametrization of scaling solutions from far-from-equilibrium classical statistical lattice simulations into a small angle kinetic rate. Furthermore, a theoretically motivated ansatz is used to account for near-collinear enhancement of the low-$p_\perp$ radiation. The system is phenomenologically constrained using the cha…
For an energetic jet propagating through a weakly-coupled quark-gluon plasma, we present the physical picture of jet quenching in longitudinal phase-space, as emerging from the interplay between the medium-induced, quasi-democratic, branchings and the elastic collisions responsible for the thermalization of the soft branching products.
Thermalization of a longitudinally expanding color glass condensate with Bjorken boost invariant geometry is investigated within parton cascade BAMPS. Our main focus lies on the detailed comparison of thermalization, observed in BAMPS with that suggested in the Bottom-Up scenario. We demonstrate that the tremendous production of soft gluons via $gg \to ggg$, which is shown in the Bottom-Up picture as the dominant process during the early preequilibration, will not occur in heavy ion collisions at RHIC and LHC energies, because the back reaction $ggg\to gg$ hinders the absolute particle multipl…
To achieve an understanding of the thermalization of a quark-gluon plasma, starting from QCD without using model assumptions, is a formidable task. We study the early stage dynamics of a relativistic heavy ion collision in the framework of real time simulations of classical Yang-Mills theory in a static box with the color glass condensate as initial condition. Our study generalizes a previous one by Fukushima and Gelis from SU(2) to the realistic case of SU(3). We calculate the chromo-electric and chromo-magnetic energy densities as well as the ratio of longitudinal and transverse pressure as …
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 argue that isotropization and, consequently, thermalization of the system of gluons and quarks produced in an ultrarelativistic heavy ion collision does not follow from Feynman diagram analysis to any order in the coupling constant. We conclude that the apparent thermalization of quarks and gluons, leading to success of perfect fluid hydrodynamics in describing heavy ion collisions at RHIC, can only be attributed to the non-perturbative QCD effects not captured by Feynman diagrams. We proceed by modeling these non-pertrubative thermalization effects using viscous hydrodynamics. We point out…
We study soft-gluon radiation in top quark decay within the framework of perturbative fragmentation functions. We present results for the b-quark energy distribution, accounting for soft-gluon resummation in both the MSbar coefficient function and in the initial condition of the perturbative fragmentation function. The results show remarkable improvement and the b-quark energy spectrum in top quark decay exhibits very little dependence on factorization and renormalization scales. We present some hadron-level results in both x_B and moment space by including non-perturbative information determi…
We complete the physical picture for the evolution of a high-energy jet propagating through a weakly-coupled quark-gluon plasma by investigating the thermalization of the soft components of the jet. We argue that the following scenario should hold: the leading particle emits a significant number of mini-jets which promptly evolve via quasi-democratic branchings and thus degrade into a myriad of soft gluons, with energies of the order of the medium temperature T. Via elastic collisions with the medium constituents, these soft gluons relax to local thermal equilibrium with the plasma over a time…
We report recent progress on understanding the thermalization of the quark-gluon plasma during the early stage in a heavy ion collision. The initially high overpopulation in the pre-equilibrium gluonic matter (``glasma'') is shown to play a crucial role. The strongly interacting nature (and thus fast evolution) naturally arises as an {\em emergent property} of this pre-equilibrium matter where the intrinsic coupling is weak but the highly occupied gluon states coherently amplify the scattering. A possible transient Bose-Einstein Condensate is argued to form dynamically on a rather general grou…
Elastic scattering of charm (c) and bottom (b) quarks via D- and B-meson resonance states in an expanding, strongly interacting quark-gluon plasma is investigated. Drag and diffusion coefficients are calculated from an effective model based on chiral symmetry and heavy-quark effective theory, and utilized in a relativistic Langevin simulation to obtain transverse-momentum spectra and elliptic flow (v_2) of c- and b-quarks. The hadronization to D- and B-mesons is described by coalescence and fragmentation, and the resulting decay-electron spectra are compared to recent RHIC data.
We present the complete physical picture for the evolution of a high-energy jet propagating through a weakly-coupled quark-gluon plasma (QGP) by analytical and numerical investigation of thermalization of the soft components of the jet. Our results support the following physical picture: the leading particle emits a significant number of mini-jets which promptly evolve via multiple branching and thus degrade into a myriad of soft gluons, with energies of the order of the medium temperature $T$. Via elastic collisions with the medium constituents, these soft gluons relax to local thermal equili…
Early local equilibration of a hot medium created in high-energy heavy ion collisions has been one of the long standing issues in hadron physics. The glasma model predicts that the medium initially has a large amount of high-momentum gluons but few quarks. We develop a phenomenological model based on collinear splitting and recombination of quarks and gluons for a simplified description of thermalization and chemical equilibration. We find that both could be achieved in a short time but chemical equilibration is slower than thermalization.
This article describes the code SusHi (for "Supersymmetric Higgs") which calculates the cross sections $pp/p\bar{p}\rightarrowϕ+X$ in gluon fusion and bottom-quark annihilation in the SM and the MSSM, where $ϕ$ is any of the neutral Higgs bosons within these models. Apart from inclusive cross sections up to NNLO QCD, differential cross sections with respect to the Higgs' transverse momentum $p_T$ and (pseudo-)rapidity $y(η)$ can be calculated through NLO QCD. In case of gluon fusion, SusHi contains NLO QCD contributions from the third family of quarks and squarks, NNLO corrections due to top-q…
One possible evolutionary scenario of the dense gluon system produced in an ultrarelativistic heavy ion collision is the bottom-up thermalization scenario, which describes the dynamics of the system shortly after the collision via the decay of originally produced hard gluons to soft ones through QCD branching processes. The soft gluons form a thermal bath that subsequently reaches thermalization and/or equilibration. There is a scaling solution to the bottom-up problem that interpolates between its early stage, which has a highly anisotropic gluon distribution, and its final stage of equilibra…
We estimate the thermalization time in two colliding shock waves holographic model of heavy-ion collisions. For this purpose we model the process by the Vaidya metric with a horizon defined by the trapped surface location. We consider two bottom-up AdS/QCD models that give, within the colliding shock waves approach, the dependence of multiplicity on the energy compatible with RHIC and LHC results. One model is a bottom-up AdS/QCD confining model and the other is related to an anisotropic thermalization. We estimate the thermalization time and show that increasing the confining potential decrea…
Charm- and bottom-quark rescattering in a Quark-Gluon Plasma (QGP) is investigated with the objective of assessing the approach towards thermalization. Employing a Fokker-Planck equation to approximate the collision integral of the Boltzmann equation we augment earlier studies based on perturbative parton cross sections by introducing resonant heavy-light quark interactions. The latter are motivated by recent QCD lattice calculations which indicate the presence of "hadronic" states in the QGP. We model these states by colorless (pseudo-) scalar and (axial-) vector D- and B-mesons within a heav…
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 the prospects to get information about the early and hot stages of deconfined matter produced in relativistic heavy-ion collisions by analyzing dilepton and single-lepton spectra. Energy losses of heavy quarks in deconfined matter and thermalization effects in hadron matter and their influence on lepton spectra are considered.
In ultra-relativistic heavy ion collisions, the matter formed shortly after the collision is a dense, out of equilibrium, system of gluons characterized by a semi-hard momentum scale $Q_{\rm s}$. Simple power counting arguments indicate that this system is over-occupied: the gluon occupation number is parametrically large when compared to a system in thermal equilibrium with the same energy density. On short time scales, soft elastic scatterings tend to drive the system towards the formation of a Bose--Einstein condensate that contains a large fraction of the gluons while contributing little t…
A Higgs boson produced in association with one or more bottom quarks is of great theoretical and experimental interest to the high-energy community. A precise prediction of its total and differential cross-section can have a great impact on the discovery of a Higgs boson with large bottom-quark Yukawa coupling, like the scalar (h^0 and H^0) and pseudoscalar (A^0) Higgs bosons of the Minimal Supersymmetric Standard Model (MSSM) in the region of large \tanβ. In this paper we apply the threshold resummation formalism to determine both differential and total cross-sections for b g \to bΦ(where Φ= …
Magnetized bottom-up thermalization in heavy-ion collisions
Institute of Physics, Academia Sinica（中央研究院物理研究所）；College of Integrative Sciences and Arts, Arizona State University（亚利桑那州立大学整合科学与艺术学院）；Department of Physics, Arizona State University（亚利桑那州立大学物理系）
