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On the Chiral imbalance and Weibel Instabilities

We study the chiral-imbalance and the Weibel instabilities in presence of the quantum anomaly using the Berry-curvature modified kinetic equation. We argue that in many realistic situations, e.g. relativistic heavy-ion collisions, both the instabilities can occur simultaneously. The Weibel instability depends on the momentum anisotropy parameter $ξ$ and the angle ($θ_n$) between the propagation vector and the anisotropy direction. It has maximum growth rate at $θ_n=0$ while $θ_n=π/2$ corresponds to a damping. On the other hand the pure chiral-imbalance instability occurs in an isotropic plasma and depends on difference between the chiral chemical potentials of right and left-handed particles. It is shown that when $θ_n=0$, only for a very small values of the anisotropic parameter $ξ\sim ξ_c$, growth rates of the both instabilities are comparable. For the cases $ξ_c<ξ\ll1$, $ξ\approx 1$ or $ξ\geq 1$ at $θ_n=0$, the Weibel modes dominate over the chiral-imbalance instability if $μ_5/T\leq1$. However, when $μ_5/T\geq1$, it is possible to have dominance of the chiral-imbalance modes at certain values of $θ_n$ for an arbitrary $ξ$.