Jet-induced collective modes in an anisotropic quark-gluon plasma

We discuss the characteristics of collective modes induced by relativistic jets in a collisionless anisotropic quark-gluon plasma (AQGP) assuming a colorless Tsunami-like momentum distribution of the jet partons. Within the framework of the transport equation, we derive and discuss the dispersion relations for both the stable and unstable modes of the composite system in the Vlasov approximation. We consider the case when the wave vector is parallel to the anisotropy direction as the growth rate of the unstable mode is maximum in this scenario. When the wave vector ($\mathbf{k}$) is perpendicular to the jet velocity (${\mathbf{v}}_{\text{jet}}$), two stable modes are found (referred to as mode I and mode II hereafter) of which one is independent of the jet velocity. In case of $\mathbf{k}\parallel {\mathbf{v}}_{\text{jet}}$, we obtain two identical modes (mode I) and one distinct mode (referred to as mode III hereafter). In all of the cases it is found that stable modes shift toward the light cone for nonzero values of the anisotropy parameter ($\xi$) and the jet strength ($\eta$). In case of unstable mode I, the growth rate increases with $\xi$ for fixed $\eta$. The growth rate in case of modes II and III increases with $\xi$ and $\eta$, and the nature of the increase depends on the jet velocity.

Figure 1

Dispersion relation for the stable mode I for an anisotropy parameter $\xi =\{0,1,5\}$ and fixed $\eta =0.1$.

Figure 2

Dispersion relation for the stable mode II for an anisotropy parameter $\xi =\{0,1,5\}$ and different $\eta =\{0.05,0.1\}$ at two jet velocities $v_{\text{jet}}=\{0.55,0.99\}$.

Figure 3

Imaginary part of the dispersion relation of the unstable mode I at $\xi =1$ (left) and at $\xi =5$ (right) for different values of $\eta =\{0,0.05,0.1\}$.

Figure 4

Imaginary part of the dispersion relation of the unstable mode II as a function of $k$ for two different values of the velocity of the jet with the variation of $\xi$ and $\eta$. The left (right) panel corresponds to $v=0.55(0.99)$.

Figure 5

Dispersion relation for the stable mode III for an anisotropy parameter $\xi =\{0,1,5\}$ and different $\eta =\{0.05,0.1\}$ at two jet velocities $v_{\text{jet}}=\{0.55,0.99\}$.

Figure 6

Imaginary part of the dispersion relation of the unstable mode III as a function of $k$ for two different values of the velocity of the jet with the variation of $\xi$ and $\eta$. The left (right) panel corresponds to $v=0.55(0.99)$.