Heavy quark collisional energy loss in the quark-gluon plasma including finite relaxation time

In this paper, we calculate the soft-collisional energy loss of heavy quarks traversing the viscous quark-gluon plasma including the effects of a finite relaxation time ${\tau }_{\pi }$ on the energy loss. We find that the collisional energy loss depends appreciably on ${\tau }_{\pi }$ . In particular, for typical values of the viscosity-to-entropy ratio, we show that the energy loss obtained using ${\tau }_{\pi }$ = 0 can be $\sim$ 10$\mathrm{\%}$ larger than the one obtained using ${\tau }_{\pi }$ = 0. Moreover, we find that the energy loss obtained using the kinetic theory expression for ${\tau }_{\pi }$ is much larger that the one obtained with the ${\tau }_{\pi }$ derived from the Anti de Sitter/Conformal Field Theory correspondence. Our results may be relevant in the modeling of heavy quark evolution through the quark-gluon plasma.