Renormalization of the jet-quenching parameter

Abstract

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, $\sim {\alpha }_s{\ln }^{2}L/{\tau }_0$, that were recently identified in the study of $p_{\perp }$-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 $\gamma =2\sqrt{{\alpha }_s{N}_c/\pi }$, as compared to the standard scaling in $L^2$.

Comments: 27 pages, 14 figures. Some rewriting to improve the clarity of the presentation. New figures added. A short discussion of the large N_c limit included. Typos corrected