Thermalization of gluons in ultrarelativistic heavy ion collisions by including three-body interactions in a parton cascade

We develop a new 3 + 1 dimensional Monte Carlo cascade solving the kinetic on-shell Boltzmann equations for partons including the inelastic $gg\ensuremath{\leftrightarrow}ggg$ pQCD processes. The back reaction channel is treated---for the first time---fully consistently within this scheme. An extended stochastic method is used to solve the collision integral. The frame dependence and convergency are studied for a fixed tube with thermal initial conditions. The detailed numerical analysis shows that the stochastic method is fully covariant and that convergency is achieved more efficiently than within a standard geometrical formulation of the collision term, especially for high gluon interaction rates. The cascade is then applied to simulate parton evolution and to investigate thermalization of gluons for a central Au+Au collision at RHIC energy. For this study the initial conditions are assumed to be generated by independent minijets with ${p}_{T}>{p}_{0}=2$ GeV. With that choice it is demonstrated that overall kinetic equilibration is driven mainly by the inelastic processes and is achieved on a scale of 1 fm/c. The further evolution of the expanding gluonic matter in the central region then shows almost an ideal hydrodynamical behavior. In addition, full chemical equilibration of the gluons follows on a longer time scale of about 3 fm/c.