Collective non-Abelian instabilities in a melting Color Glass Condensate

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 $\tau$ as $\exp (\Gamma \sqrt{g^2\mu \tau })$, where $g^2\mu$ is a scale arising from the saturation of gluons in the nuclear wavefunction. The scale for the growth rate $\Gamma$ is set by a plasmon mass, defined as ${\omega }_{\mathrm{pl}}={\kappa }_0\sqrt{\frac{g^2\mu }{\tau }}$, generated dynamically in the collision. We compare the numerical ratio $\Gamma /{\kappa }_0$ to the corresponding value predicted by the Hard Thermal Loop formalism for anisotropic plasmas.

Comments: 4 pages, 4 figures, revtex4; v2: typos corrected, discussion on growth rate in expanding system added, accepted for publication in PRL