From a colored glass condensate to the gluon plasma: Equilibration in high energy heavy ion collisions

The initial distribution of gluons at the very early times after a high-energy heavy ion collision is described by the bulk scale $Q_s$ of gluon saturation in the nuclear wave function. The subsequent evolution of the system towards kinetic equilibrium is described by a nonlinear Landau equation for the single particle distributions [A. H. Mueller, Nucl. Phys. B572, 227 (2000); Phys. Lett. B 475, 220 (2000)]. In this paper, we solve this equation numerically for the idealized initial conditions proposed by Mueller, and study the evolution of the system to equilibrium. We discuss the sensitivity of our results on the dynamical screening of collinear divergences. In a particular model of dynamical screening, the convergence to the hydrodynamic limit is seen to be rapid relative to hydrodynamic time scales. The equilibration time, the initial temperature, and the chemical potential are shown to have a strong functional dependence on the initial gluon saturation scale $Q_s.$