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From the colour glass condensate to filamentation: systematics of classical Yang–Mills theory
(2019)
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() and SU(), 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.
Lattice QCD with heavy quarks reduces to a three-dimensional effective theory of Polyakov loops, which is amenable to series expansion methods. We analyse the effective theory in the cold and dense regime for a general number of colours, Nc. In particular, we investigate the transition from a hadron gas to baryon condensation. For any finite lattice spacing, we find the transition to become stronger, i.e. ultimately first-order, as Nc is made large. Moreover, in the baryon condensed regime, we find the pressure to scale as p ∼ Nc through three orders in the hopping expansion. Such a phase differs from a hadron gas with p ∼ N0c, or a quark gluon plasma, p ∼ N2c, and was termed quarkyonic in the literature, since it shows both baryon-like and quark-like aspects. A lattice filling with baryon number shows a rapid and smooth transition from condensing baryons to a crystal of saturated quark matter, due to the Pauli principle, and is consistent with this picture. For continuum physics, the continuum limit needs to be taken before the large Nc limit, which is not yet possible in practice. However, in the controlled range of lattice spacings and Nc-values, our results are stable when the limits are approached in this order. We discuss possible implications for physical QCD.
The QCD equation of state at finite baryon density is studied in the framework of a Cluster Expansion Model (CEM), which is based on the fugacity expansion of the net baryon density. The CEM uses the two leading Fourier coefficients, obtained from lattice simulations at imaginary μB, as the only model input and permits a closed analytic form. Excellent description of the available lattice data at both μB = 0 and at imaginary μB is obtained. We also demonstrate how the Fourier coefficients can be reconstructed from baryon number susceptibilities.