Collective modes of a collisional anisotropic quark-gluon plasma

In this paper we consider the collective modes of a momentum-space anisotropic quark-gluon plasma taking into account the effect of collisions between the plasma constituents. Our analysis is carried out using a collisional kernel of Bhatnagar-Gross-Krook form and extends prior analyses in the literature by considering all possible angles of propagation of the gluonic modes relative to the momentum-anisotropy axis. We extract both the stable and unstable modes as a function of the collision rate and confirm prior findings that gluonic unstable modes can be eliminated from the spectrum if the collision rate is sufficiently large. In addition, we discuss the conditions necessary for the existence of unstable modes and present evidence that unstable mode growth rates are maximal for modes with momentum along the anisotropy direction. Finally, we demonstrate that when there is a finite collisional rate, gluonic unstable modes are absent from the spectrum at both small and large momentum anisotropy. These results pave the way for understanding the impact of collisions on a variety of non-equilibrium quark-gluon plasma observables.