Abstract
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.
Highlights
From a theoretical point of view, a heavy-ion collision has different stages
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
We focus on the early time dynamics of the gauge fields out of equilibrium, where we pursue a purely classical treatment of Yang–Mills theory
Summary
From a theoretical point of view, a heavy-ion collision has different stages. As an initial condition, one assumes the colour glass condensate (CGC), i.e. an effective field theory description of boosted, saturated gluons [4]. We focus on the early time dynamics of the gauge fields out of equilibrium, where we pursue a purely classical treatment of Yang–Mills theory. We attempt to quantify the dependence of our results on various model parameters introduced in the literature, like the amplitude of initial boost non-invariant fluctuations, an IR cutoff to emulate colour neutrality on the scale of nucleons as well as a UV cutoff on the initial momentum distribution Many of these issues have already been addressed one by one when they were introduced, as indicated but not in their interplay, as we attempt to do here. In order to choose canonical field variables and construct a Hamiltonian, we set
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