Collective non-Abelian instabilities in a melting Color Glass Condensate

TL;DR

First results for (3 + 1)D simulations of SU(2) Yang-Mills equations for matter expanding into the vacuum after a heavy ion collision are presented and the numerical ratio gamma/kappa0 is compared to the corresponding value predicted by the hard thermal loop formalism for anisotropic plasmas.

Abstract

We present first results for 3+1-D simulations of SU(2) Yang-Mills equations for matter expanding into the vacuum after a heavy ion collision. Violations of boost invariance cause a Weibel instability leading soft modes to grow with proper time $τ$ as $\exp(Γ\sqrt{g^2μτ})$, where $g^2μ$ is a scale arising from the saturation of gluons in the nuclear wavefunction. The scale for the growth rate $Γ$ is set by a plasmon mass, defined as $ω_{\rm pl}= κ_0 \sqrt{\frac{g^2μ}τ}$, generated dynamically in the collision. We compare the numerical ratio $Γ/κ_0$ to the corresponding value predicted by the Hard Thermal Loop formalism for anisotropic plasmas.

Figures (4)

• Figure 1: The maximum Fourier mode amplitudes of $\tau^2 T^{\eta\eta}$ for $g^2\mu L=67.9$, $N_\perp=N_\eta=64$, $N_\eta a_\eta=1.6$. Also shown are best fits with $\exp{\tau}$ and $\exp{\sqrt{\tau}}$ behavior. The former is clearly ruled out by the data.
• Figure 2: The mode number $k_\eta$ for which the maximum amplitude of $\tau^2 T^{\eta\eta}$ occurs (see Fig.\ref{['fig:maxFM']}); again for $g^2\mu L=67.9$, $N_\perp=N_\eta=64$, $N_\eta a_\eta=1.6$. $k_{\rm min}$ denotes the smallest $k_\eta$ mode that could be excited in the lattice simulation.
• Figure 3: Time evolution of $\omega_{\rm pl.}$, for fixed $g^2 \mu L=22.6$ and lattice spacings $g^2 \mu a_\perp=0.707,0.354,0.177$ ($N_\perp=32,64,128$), respectively.
• Figure 4: Dependence of $\omega_{\rm pl.}$ with respect to $g^2 \mu L$; $g^2 \mu a_\perp=0.707$ for all $g^2 \mu L$ except $g^2 \mu L=67.9$, for which it is $g^2 \mu a_\perp=1.06$.