From the colour glass condensate to filamentation: Systematics of classical Yang-Mills theory

The non-equilibrium early time evolution of an ultra-relativistic heavy ion collision is often described by classical lattice Yang-Mills theory, starting from the colour glass condensate (CGC) effective theory with an anisotropic energy momentum tensor as initial condition. In this work we investigate the systematics associated with such studies and their dependence on various model parameters (IR, UV cutoffs and the amplitude of quantum fluctuations) which are not yet fixed by experiment. We perform calculations for SU(2) and SU(3), both in a static box and in an expanding geometry. Generally, the dependence on model parameters is found to be much larger than that on technical parameters like the number of colours, boundary conditions or the lattice spacing. In a static box, all setups lead to isotropisation through chromo-Weibel instabilities, which is illustrated by the accompanying filamentation of the energy density. However, the associated time scale depends strongly on the model parameters and in all cases is longer than the phenomenologically expected one. In the expanding system, no isotropisation is observed for any parameter choice. We show how investigations at fixed initial energy density can be used to better constrain some of the model parameters.