Medium-Induced QCD Cascade: Democratic Branching and Wave Turbulence

We study the average properties of the gluon cascade generated by an energetic parton propagating through a quark-gluon plasma. We focus on the soft, medium-induced emissions which control the energy transport at large angles with respect to the leading parton. We show that the effect of multiple branchings is important. In contrast with what happens in a usual QCD cascade in vacuum, medium-induced branchings are quasidemocratic, with offspring gluons carrying sizable fractions of the energy of their parent gluon. This results in an efficient mechanism for the transport of energy toward the medium, which is akin to wave turbulence with a scaling spectrum $\sim 1/\sqrt{\omega }$. We argue that the turbulent flow may be responsible for the excess energy carried by very soft quanta, as revealed by the analysis of the dijet asymmetry observed in Pb-Pb collisions at the LHC.

Figure 1

Plot (in log-log scale) of $\sqrt{x}{D}_0(x,\tau )$, with $D_0(x,\tau )$ given by Eq. (6), as a function of $x$ for various values of $\tau$ (full lines from bottom to top, $\tau =0.01$, 0.02, 0.1, 0.2, 0.4; dashed lines from the top down, $\tau =0.6$, 0.9).

Figure 2

The function $\sqrt{x}{D}_{\mathrm{tb}}(x,\tau )$ [Eq. (8) for $A=1$] at various times—from early time, where it resembles Fig. 1, until late time, when it approaches the steady state and saturates at the value $A/2\pi$ at small $x$. The values of $\tau$ are, from bottom to top, 0.01, 0.02, 0.05, 0.1, 0.2, 0.5, and 1.