It has recently been realized that the Balitsky-JIMWLK equations have serious shortcomings as equations to be used in small-x evolution near the unitarity limit. A recent generalization of the Balitsky equations has been given which corrects these shortcomings. In this paper we present an equivalent discussion, but in terms of the JIMWLK equation where we show that a new (fourth order functional derivative) term should be included. We also present a stochastic version of the new equation which, however, has some unusual mathematical aspects which are not as yet well understood.
We investigate the thermalization and the chemical equilibration of a parton plasma created from Au+Au collision at LHC and RHIC energies starting from the early moment when the particle momentum distributions in the central region become for the first time isotropic due to longitudinal cooling. Using the relaxation time approximation for the collision terms in the Boltzmann equations for gluons and for quarks and the real collision terms constructed from the simplest QCD interactions, we show that the collision times have the right behaviour for equilibration. The magnitude of the quark (antiquark) collision time remains bigger than the gluon collision time throughout the lifetime of the plasma so that gluons are equilibrating faster than quarks both chemically and kinetically. That is we have a two-stage equilibration scenario as has been pointed out already by Shuryak sometimes ago. Full kinetic equilibration is however slow and chemical equilibration cannot be completed before the onset of the deconfinement phase transition assumed to be at Tc = 200 MeV. By comparing the collision entropy density rates of the different processes, we show explicitly that inelastic processes, and not elastic processes as is commonly assumed, are dominant in the equilibration of the plasma and that gluon branching leads the other processes in entropy generation. We also show that, within perturbative QCD, processes with higher power in αs need not be less important for the purpose of equilibration than those with lower power. The state of equilibration of the system has also a role to play. We compare our results with those of the parton cascade model.
LPTHE-Orsay 96/26, BI-TP 96/18
We investigate Kolmogorov wave turbulence in QCD or, in other words, we calculate the spectrum of gluons as a function of time, f k (t), in the presence of a source which feeds in energy density in the infrared region at a constant rate. We find an early, an intermediate and a late time form for the gluon spectrum. Wave turbulence in QCD turns out to be somewhat different than the turbulence in the case of φ 4 -type theories studied by Zakharov, L'vov and Falkovich. The hope is that a good understanding of QCD wave turbulence might lead to a better understanding of the instability problem in the early stages of the evolution after a heavy ion collision.
We show the evolution of a gluon plasma towards equilibrium starting at some
early moment when the momentum distribution in the central region is
momentaneously isotropic. Using HIJING results for Au+Au collision as initial
input, we consider thermalization and chemical equilibration simultaneously at
both LHC and RHIC energies. Thermalization is shown to be driven chiefly by
inelastic process in our scenario contradicting common assumption that this is
the role of elastic process. We argue that only the inelastic dominancy depends
on the initial conditions but not the dominance itself.Comment: 14 pages + 4 postscript figures, latex2e file, final version to
appear in Nucl. Phys.
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