Jet Quenching versus Jet Enhancement: a Quantitative Study of the BDMPS-Z Gluon Radiation Spectrum

We study the gluon radiation spectrum off a hard in-medium produced quark in the multiple soft rescattering formalism of Baier-Dokshitzer-Mueller-Peigne-Schiff, and of Zakharov (BDMPS-Z). Its dependence on the quark and gluon energy, on the gluon transverse momentum, on the in-medium pathlength and on the rescattering properties of the nuclear medium is analyzed quantitatively. The two components of gluon radiation, the hard vacuum radiation associated to the quark production vertex, and the medium-induced rescattering contribution interfer destructively. For small spatial extensions of the medium, this destructive interference overcompensates the hard vacuum radiation, and the total medium-induced radiative energy loss decreases proportional to L^3. Medium-induced gluon production dominates only above a finite critical length which varies between 3 and more than 6 fm depending on the rescattering properties of the medium. Deviations from the BDMPS-L^2-behaviour persist above the critical length. The medium dependence of the angular gluon distribution is dominated by Brownian transverse momentum broadening. This results in a depletion of the low transverse momentum part of both the hard and the medium-induced contribution. As a consequence, the medium-induced energy loss outside a finite angular cone size can be more than a factor two larger than the total medium-induced radiative energy loss. We discuss implications of these results for the jet quenching signal in relativistic heavy ion collisions at RHIC and LHC.