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 logarithmic corrections, ∼α_sln²L/τ₀, that were recently identified in the study of p_⊥-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+γ, with γ=2√(α_sN_c/π), as compared to the standard scaling in L²