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 $gg\leftrightarrow ggg$ 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.