Isotropization and Hydrodynamization in Weakly Coupled Heavy-Ion Collisions

Abstract

We numerically solve the (2+1)-dimensional effective kinetic theory of weak coupling QCD under longitudinal expansion, relevant for early stages of heavy-ion collisions. We find agreement with viscous hydrodynamics and classical Yang-Mills simulations in the regimes where they are applicable. By choosing initial conditions that are motivated by a color-glass-condensate framework, we find that for Q_{s}=2 GeV and α_{s}=0.3 the system is approximately described by viscous hydrodynamics well before τ≲1.0 fm/c.

Initial conditions for hydrodynamics from weakly coupled pre-equilibrium evolution

“…In ref. [16] (which includes one of the authors), it was shown that the EKT, starting with initial conditions motivated by the Color-Glass Condensate (CGC) saturation framework [17][18][19][20][21], reaches hydrodynamics in a phenomenologically reasonable time scale of ∼ 10/Q s , where Q s is the (adjoint representation) saturation scale, which is estimated to be of order of few GeV for central heavy-ion collisions at the LHC. This first calculation used the EKT to monitor the equilibration of a uniform plasma of infinite transverse extent during a Bjorken expansion.…”

Kinetic theory of a longitudinally expanding system

“…This has been seen in numerical studies of the Boltzmann equation for a longitudinally expanding system [19,20]. Firstly, one can check that the Boltzmann equation with only the classical terms 04003-p.4 Figure 4.…”

“…The curve labeled λ = 0 is a classical approximation, while the curves for λ = 0.5, 1, 5, 10 are obtained with the full Boltzmann equation. Plot taken from [20], with time labels added by us for clarity.…”

Thermalization in the initial stage of heavy ion collisions

“…. Thermalization routes of overoccupied system with different anisotropy parameter ξ and coupling λ in the EKT (figure taken from [10]). The black line corresponds to the calculation in classical limit.…”