As implied by organizers, this talk is not a conference summary but rather an outline of progress/challenges/``frontiers'' of the theory. Some fundamental questions addressed are:
Why is sQGP such a good liquid? Do we understand (de)confinement and what do we know about ``magnetic'' objects creating it? Can we understand the AdS/CFT predictions, from the gauge theory side? Can they be tested experimentally? Can AdS/CFT duality help us understand rapid equilibration/entropy production? Can we work out a complete dynamical ``gravity dual'' to heavy ion collisions?
The historical context of the recent results from high energy heavy ion reactions devoted to the search of quark-gluon plasma (QGP) is reviewed, with emphasis on the surprises encountered. The evidence for QGP from heavy ion reactions is compared with that available from particle reactions.
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.]
Based on simple physics arguments it is shown that the concept of quark-gluon plasma, a state of matter consisting of uncorrelated quarks, antiquarks, and gluons, has a fundamental problem.
We analyze the known moving boundary effects in plasma and briefly review a mechanism for particle acceleration through a plasma front. We then show how this mechanism may affect particles crossing the boundary of an expanding quark gluon plasma.
A quasiclassical theory of the synchrotron-like gluon emission is discussed. We show that the synchrotron emission may be important in the jet quenching if the plasma instabilities generate a chromomagnetic field about $m^{2}_{D}/g$. Our gluon spectrum disagrees with that obtained by Shuryak and Zahed within Schwinger's proper time method.
An alternate picture of the deconfined phase of gauge theories is described. Instead of a plasma, the theory is viewed as a condensate of Polyakov lines. The pressure is determined by an elementary mean field theory.
I consider the dissociation of a boosted quarkonium in a quark-gluon plasma. This dissociation is due to absorption of a thermal gluon. I discuss the dissociation in terms of the velocity of the quarkonium and the temperature of the quark-gluon plasma. I compare this dissociation rate to the one calculated without including the velocity of the quarkonium.
I consider the behavior of the quark-antiquark potential, called the Cornell Potential, in a quark-gluon plasma. Since mesons are no longer bound in the quark-gluon plasma, there might be a relationship between the string tension of the quark-antiquark potential, the mass of the quark, and the coupling constant.
Signatures of dominant and central production of glueballs (binary gluonic mesons) in heavy ion and hadromic collisions are discussed. Search strategies are proposed.
The gluon polarization tensor for the quark-gluon plasma with shear viscosity is derived with the viscous chromohydrodynamics. The longitudinal and transverse dielectric functions are evaluated from the gluon polarization tensor, through which the polarization energy loss suffered by a fast quark traveling through the viscous quark-gluon plasma is investigated. The numerical analysis indicates that shear viscosity significantly reduces the polarization energy loss.
We study the quark energy loss in an expanding quark-gluon plasma. The expanding plasma produced in high energy AA-collision is described by Bjorken's model. The dependence of the energy loss on the infrared cutoff for the radiated gluons, on the quark mass, and on the initial conditions of QCD plasma is investigated.
Here we present a self-consistent quasi-particle model for quark-gluon plasma and apply it to explain the non-ideal behaviour seen in lattice simulations. The basic idea, borrowed from electrodynamic plasma, is that the gluons acquire mass as it propagates through plasma due to collective effects and is approximately equal to the plasma frequency. The statistical mechanics and thermodynamics of such a system is studied by treating it as an ideal gas of massive gluons. Since mass or plasma frequency depends on density, which itself is a thermodynamic quantity, the whole problem need to be solve…
We present new, non-abelian, solutions to the equations of motion which describe the collective excitations of a quark-gluon plasma at high temperature. These solutions correspond to longitudinal and transverse plane-waves propagating through the plasma.
We review both lattice evidences and theoretical arguments supporting the existence of electric flux tubes in quark-gluon plasma, above the deconfinement transition temperature $T>T_c$. At the end of this comment, we also point out certain questions which still needs to be answered.
Within the closed-time-path formalism of nonequilibrium QCD, we derive a Slavnov-Taylor (ST) identity for the gluon polarization tensor. The ST identity takes the same form both in Coulomb and covariant gauges. Application to quasi-uniform quark-gluon plasma (QGP) near equilibrium or nonequilibrium quasistationary QGP is made.
I consider the dissociation of the upsilon meson due to absorption of a thermal gluon. I discuss the dissociation rate in terms of the energy density, the number density, and the temperature of the quark-gluon plasma. I compare this to the effect due to screening.
The entropy of the quark-gluon plasma can be calculated from QCD using (approximately) self-consistent approximations. Lattice results for pure gauge theories are accurately reproduced down to temperatures of the order of 2.5$T_c$. Comparisons with other approaches to the thermodynamics of the quark-gluon plasma are briefly discussed.
Strangeness, charmonium and open charm yields in relativistic nucleus-nucleus collisions are considered within statistical model approach as potential signals of the quark-gluon plasma.
The small surface tension of the interface between hadronic and quark-gluon-plasma domains, along with a negative curvature tension, implies that the uniform plasma is unstable against spontaneous formation of hadronic bubbles. We furthermore show that spherical bubbles are not stable against small perturbations.
The transverse and longitudinal transport coefficients for jets in a quark-gluon plasma, $\hat{q}$ and $\hat{e}$, are extracted from simulations of the VNI/BMS parton cascade model. We study their variation under the strong coupling and the parton mass in the medium. We show that their ratio is sensitive to the mass of the plasma constituents. Experimental measurements of both quantities could provide new insights into the nature of the quark-gluon plasma as seen by hard probes.
We calculate photon production from a quark-gluon plasma which is anisotropic in momentum space including the Compton scattering and quark/anti-quark annihilation processes. We show that for a quark-gluon plasma which has an oblate momentum-space anisotropy the photon production rate has an angular dependence which is peaked transverse to the beam line. We propose to use the angular dependence of high-energy medium photon production to experimentally determine the degree of momentum-space isotropy of a quark-gluon plasma produced in relativistic heavy-ion collisions.
We derive hydrodynamic-like equations that are applicable to short-time scale color phenomena in the quark-gluon plasma. The equations are solved in the linear response approximation, and the gluon polarization tensor is derived. As an application, we study the collective modes in a two-stream system and find plasma instabilities when the fluid velocity is larger than the speed of sound in the plasma. The chromo-hydrodynamic approach, discussed here in detail, should be considered as simpler over other approaches and well-designed for numerical studies of the dynamics of an unstable quark-gluo…
We calculate the order α_s finite temperature correction to dilepton production in quark-gluon plasma arising from the two-loop photon self-energy diagrams for high invariant mass M >> T.
It is shown that due to contribution of the hadrons, emitted directly from the inner hot region of central heavy ion collision, radial flow of the final state hadrons is rather sensitive to the creation of quark-gluon plasma with mixed phase.
A calculation of thermal gluon decay shows that this process contributes significantly to strangeness production in a quark-gluon plasma. Our analysis does not support recent claims that this is the dominant process. In our calculations we take into account the resummed form of the transverse and longitudinal parts of the gluon propagator following the Braaten-Pisarski method. Our results are subject to the uncertainty concerning the estimate of the damping rate entering the effective gluon propagator.
In this work, we calculate the binding energies of the $J/ψ$, the $Υ$, and the Toponium in quark-gluon plasma. We also calculate the temperature of the quark-gluon plasma at which these quarkonia dissociate. We approach the problem from a quantum mechanical point of view. We use the variational method and the screening Debye potential in order to obtain these binding energies.
We consider the quark antiquark potential of a quarkonium moving with velocity $v$ through a quark-gluon plasma at temperature T. An explicit, configuration-space expression is found for the screened interaction between the quarks constituting the meson. This potential is non-spherical, but axially symmetric about the direction of $v$.
We present new, non-abelian, solutions to the equations of motion which describe the collective excitations of a quark-gluon plasma at high temperature. These solutions correspond to spatially uniform color oscillations.
A model of cut-off momentum distribution functions in a Quark Gluon Plasma with finite baryon chemical potential is discussed. This produces a quark gluon plasma signature in Ultra Relativistic Nuclear Collisions with a specific structure of the dilepton spectrum in the transverse momentum region of $(1-4)~GeV$ and the dilepton production rate is found to be a strong decreasing function of the chemical potential.
In this talk I briefly discuss the thermodynamics of the quark-gluon plasma The calculation of the free energy of a hot gluon plasma to leading order in hard-thermal-loop perturbation theory is outlined. The HTL free energy is compared with the weak-coupling expansion and lattice results.
The quark and gluon viscosities are calculated in quark-gluon plasmas to leading orders in the coupling constant by including screening. For weakly interaction QCD and QED plasmas dynamical screening of transverse interactions and Debye screening of longitudinal interactions controls the infrared divergences. For strongly interacting plasmas other screening mechanisms taken from lattice calculations are employed. By solving the Boltzmann equation for quarks and gluons including screening the viscosity is calculated to leading orders in the coupling constant. The leading logarithmic order is ca…
We present an effective relaxation-time theory to study the collisionless quark-gluon plasma. Applying this method we calculate the damping rate to be of order $g^2T$ and find plasmon scattering is the damping mechanism. The damping for the transverse mode is stronger than the longitudinal one.
The effects of a thermalized gas of gluons in a q,q bar plasma is investigated. Then the interplay between Debye screening and confinement is analyzed in a simplified model. While the one-gluon exchange gives results very similar, but not equal, to the electric case, the phenomenological introduction of confinement leads to very different results.
By considering the non-perturbative effects associated with the fundamental modular region, a new phase of a Gluon Plasma at finite density is proposed. It corresponds to the transition from glueballs to non-perturbative gluons which condense at a non vanishing momentum. In this respect the proposed phase is analogous to the color superconducting LOFF phase for fermionic systems.
Some aspects of heavy flavor probes of quark-gluon plasma (QGP) including quarkonia and open heavy flavor D- and B-mesons, aimed to study the properties of QGP, are discussed in this lecture note.
We study radiative parton energy loss in an expanding quark-gluon plasma with magnetic monopoles. We find that for realistic number density of thermal monopoles obtained in lattice simulations parton rescatterings on monopoles can considerably enhance energy loss for plasma produced in $AA$ collisions at RHIC and LHC energies. However, contrary to previous expectations, monopoles do not lead to the surface dominance of energy loss.
The dissipative corrections to the hydrodynamic equations describing the evolution of energy-momentum tensor and parton densities are derived in a simple way using the scaling approximation for the expanding quark gluon plasma at finite baryon density. This procedure has been extended to study the process of chemical equilibration using a set of rate equations appropriate for a viscous quark gluon plasma. It is found that in the presence of dissipation, the temperature of the plasma evolves slower, whereas the quark and gluon fugacities evolve faster than their counterparts in the ideal case w…
In weakly interacting quark-gluon plasmas diffusion of color is found to be much slower than the diffusion of spin and flavor because color is easily exchanged by the gluons in the very singular forward scattering processes. If the infrared divergence is cut off by a magnetic mass, $m_{mag}\sim α_sT$, the color diffusion is $D_{color}\sim (α_s\ln(1/α_s)T)^{-1}$, a factor $α_s$ smaller than spin and flavor diffusion. A similar effect is expected in electroweak plasmas above $M_W$ due to $W^\pm$ exchanges. The color conductivity in quark-gluon plasmas and the electrical conductivity in electrowe…
A few topics of the transport theory of quark-gluon plasma are reviewed. A derivation of the transport equations form the underlaying dynamical theory is discussed within the $ϕ^4$ model. Peculiarities of the kinetic equations of quarks and gluons are considered and the plasma (linear) response to the color field is studied. The chromoelectric tensor permeability is found and the plasma oscillations are discussed. Finally, the filamentation instability in the strongly anisotropic parton system from ultrarelativistic heavy-ion collisions is discussed in detail.
We calculate the two-body interaction of spherical hadronic bubbles immersed in a gluon plasma at temperatures above the phase transition. Modeling the bubbles with the MIT bag we find that the two body potential is repulsive for all bubble-bubble distances considered. This implies that a static configuration of spherical hadronic bubbles in a gluon background is consistent with the bag model of QCD.
We demonstrate that for a finite-size quark-gluon plasma the induced gluon radiation from heavy quarks is stronger than that for light quarks when the gluon formation length becomes comparable with (or exceeds) the size of the plasma. The effect is due to oscillations of the light-cone wave function for the in-medium $q\to gq$ transition. The dead cone model by Dokshitzer and Kharzeev neglecting quantum finite-size effects is not valid in this regime. The finite-size effects also enhance the photon emission from heavy quarks.
Nonperturbative picture of strong interacting quark-gluon plasma is given based on the systematic Field Correlator Method. Equation of state, phase transition in density-temperature plane is derived and compared to lattice data as well as subsequent thermodynamical quantities of QGP.
We show that partons traversing a quark-gluon plasma can lose substantial amounts of energy also by scatterings, and not only through medium-induced radiation as mainly considered previously. Results from Monte Carlo simulations of soft interactions of partons, emerging from a hard scattering, through multiple elastic scatterings on gluons in an expanding relativistic plasma show a sizeable jet quenching which can account for a substantial part of the effect observed in RHIC data.
By decomposing the distribution functions and color field to regular and fluctuation parts, the solution of the semi-classical kinetic equations of quark-gluon plasma is analyzed. Through expanding the kinetic equations of the fluctuation parts to third order, the nonlinear permittivity including the self-interaction of gauge field is obtained and a rough numerical estimate is given out for the important $\vk =0$ modes of the pure gluon plasma.
We study the influence of finite kinematic boundaries on the induced gluon radiation from a fast quark in a finite size quark-gluon plasma. The calculations are carried out for fixed and running coupling constant. We find that for running coupling constant the kinematic correction to the radiative energy loss is small for quark energy larger than about 5 GeV. Our results differ both analytically and numerically from that obtained by the GLV group [6]. The effect of the kinematic cut-offs is considerably smaller than reported in [6].
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.
A quark propagating through the quark gluon plasma and scattering off the thermal gluons can radiate photons in states with definite angular momentum and magnetic helicity. These states, known as the Chandrasekhar-Kendall states, are eigenstates of the curl operator and have a non-trivial topology. I compute spectrum of these states in the ultrarelativistic limit and study its properties.
We report on the effect of the quantum statistics on the two-proton spin correlation (SC) in cold and thermal nuclear matter. We have found that two nucleons SC function can be well approximated by a guassian with correlations length $σ\sim1.2$ fm. We have proposed SC measurement on low protons energy as test of the quark-gluon plasma formation in relativistic heavy ions collisions.
Transition from the quark-gluon (QG) plasma to a hadronic gas is studied in the framework of the relativistic combustion theory. The calculations reveal that the QG phase must be in a strongly supercooled state. The stability of this solution with respect to minor modifications is investigated. In particular the effect of an admixture of hadronic matter in the QG phase is considered in detail.
The kinetic properties of relativistic quark-gluon and electron-photon plasmas are described in the weak coupling limit. The troublesome Rutherford divergence at small scattering angles is screened by Debye screening for the longitudinal or electric part of the interactions. The transverse or magnetic part of the interactions is effectively screened by Landau damping of the virtual photons and gluons transferred in the QED and QCD interactions respectively. Including screening a number of transport coefficients for QCD and QED plasmas can be calculated to leading order in the interaction stren…
We discuss the energy loss of energetic parton jets in quark-gluon plasma above the deconfinement temperature $T_c$ by the interaction with scalar and pseudoscalar glueballs. It is shown that the loss by this mechanism is quite important and may play the important role of the observed jet-quenching.
Two signatures of the quark-gluon plasma -- strangeness `enhancement' and $J/ψ$ `suppression' -- in nucleus--nucleus collisions at the SPS energies are critically discussed.
We present a model of charmonium as two heavy quarks propagating classically in a weakly coupled quark-gluon plasma. The quarks interact via a static, color-dependent potential and also suffer collisions with the plasma particles. We calculate the radiation width of the color octet state (for fixed, classical $q\bar q$ separation) and find that it is long-lived provided a finite gluon mass is used to provide a threshold energy.
The role of color-magnetic monopoles in a pure gauge plasma at high temperature $T>2T_c$ is considered. In this temperature regime, monopoles can be considered heavy, rare objects embedded into matter consisting mostly of the usual "electric" quasiparticles, quarks and gluons. The gluon-monopole scattering is found to hardly influence thermodynamic quantities, yet it produces a large transport cross section, significantly exceeding that for pQCD gluon-gluon scattering up to quite high $T$. This mechanism keeps viscosity small enough for hydrodynamics to work at LHC.
We apply continuum percolation to proton-proton collisions and look for the possible threshold to phase transition from confined nuclear matter to quark gluon plasma. Making the assumption that J/Psi suppression is a good signal to the transition, we discuss this phenomenon for pp collisions, in the framework of a dual model with strings.
The Debye screening mass for a quark-gluon plasma at high temperature is calculated to next-to-leading order in the QCD coupling constant from the correlator of two Polyakov loops. The result agrees with the screening mass defined by the location of the pole in the gluon propagator as calculated by Rebhan. It is logarithmically sensitive to nonperturbative effects associated with the screening of static chromomagnetic fields.
We explore the thermodynamics of the gluon plasma in SU(3) Yang-Mills theory emerging from the non-trivial spatial dynamics of valence gluons. The lattice data suggest that these gluons interact with each other linearly at large spatial separations. At high temperatures, valence gluons should reproduce the pressure of the non-interacting Stefan-Boltzmann plasma along with the leading perturbative correction. These properties of valence gluons can be modeled in terms of the integral over their trajectories. We calculate such a world-line integral analytically and obtain the pressure and the int…
In this talk, I review the status of the calculation of the photon production rate in a hot quark-gluon plasma. Particular emphasis is given to the discussion of the various length scales of the problem.
