Can Thermalization in Heavy Ion Collisions be Described by QCD Diagrams?

The onset of thermalization in heavy ion collisions in the weak coupling framework can be viewed as a transition from the initial state Color Glass Condensate dynamics, characterized by the energy density scaling like $\epsilon \sim 1/\tau$ with $\tau$ the proper time, to the hydrodynamics-driven expansion of the quark-gluon plasma with $\epsilon \sim 1/\tau^{4/3}$ (or higher power of $1/\tau$ for the boost non-invariant case). We argue that, at any order of the perturbative expansion in the QCD coupling constant, the gluon field generated in an ultrarelativistic heavy ion collision leads to energy density scaling as $\epsilon \sim 1/\tau$ for late times $\tau \gg 1/Q_s$. Therefore it is likely that thermalization and hydrodynamic description of the gluon system produced in heavy ion collisions can not result from perturbative QCD diagrams at these late times. At earlier times with $\tau \sim 1/Q_s$ the subleading corrections to $\epsilon$ in $1/\tau$ expansion (terms scaling like $\sim 1/\tau^{1+\Delta}$ with $\Delta >0$) may become important possibly leading to hydrodynamic-like behavior of the gluon system. Still, we show that such corrections do not contribute to the particle production cross section, and are likely to be irrelevant for physical observables. We generalize our results by including massless quarks into the system. Thus, it appears that the apparent thermalization of quarks and gluons, leading to success of Bjorken hydrodynamics in describing heavy ion collisions at RHIC, can only be attributed to the non-perturbative QCD effects.