Renormalization of the jet-quenching parameter

We study the radiative processes that affect the propagation of a high energy gluon in a dense medium, such as a quark-gluon plasma. In particular, we investigate the role of the large double logarithms corrections, $\sim\alpha_s \ln^2 L/\tau_0$,thatwererecentlyidentifiedinthestudyof$p_\perp$-broadening by Liou, Mueller and Wu. We show that these large corrections can be reabsorbed in a renormalization of the jet quenching parameter controlling both momentum broadening and energy loss. We argue that the probabilistic description of these phenomena remains valid, in spite of the large non-locality in time of the radiative corrections. The renormalized jet-quenching parameter is enhanced compared to its standard perturbative estimate. As a particular consequence, the radiative energy loss scales with medium size $L$ as $L^{2+\gamma }$, with $\gamma =2\sqrt{{\alpha }_s{N}_c\mathrm{/}\pi }$, as compared to the standard scaling in $L^2$.